COLLOID 
CHEMISTRY 
Wisconsin Lectures 
BY 
THE SVEDBERG 
American Chemical Society 
Monograph Series 
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1924 Copyright, 1924, By 
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19 EAST 24th STREET, NEW YORK, U. S. A. Preface 
The text of this monograph is based upon a series of lectures given 
at the University of Wisconsin during the spring and summer of 
1923. The manner of exposition has not been greatly changed from 
the stenographic report of the lectures. Most of the illustrations of 
the text were projected as lantern slides. More emphasis was placed 
on a graphical representation of the experimental data than on pre- 
senting the material in the form of tables. This same method of 
presentation of data has been adopted in the text. 
The author has attempted to give a general survey of colloid 
chemistry. Special attention has been accorded to recent develop- 
ment of colloid chemistry technique. Emphasis has been placed on 
quantitative investigations rather than on qualitative experiments. 
It is the author's belief that a real advance in colloid chemistry is 
possible only by developing methods of accurate measurements for 
the study of colloids. By purely qualitative experiments more con- 
fusion than progress has been obtained. What we need is good quan- 
titative investigations of systems as well denned as possible. 
The author is conscious of having, perhaps, given undue space to 
description of research done in his laboratory at Upsala, but perhaps, 
in a science like colloid chemistry which is still in an undeveloped 
state, it is advisable to present as much as possible such phenomena 
as the author has really experienced. 
But for the kind invitation to give lectures and organize research 
in colloid chemistry extended by Professor J. H. Mathews, Director 
of the Course of Chemistry at the University of Wisconsin, this 
attempt to review colloid chemistry would not have been ventured 
and deep appreciation is expressed to him for the sustained support 
and encouragement which he has rendered the author. 
The author desires to acknowledge the privilege of having this 
book published as a Scientific Monograph of the American Chemical 
Society. 
The manuscript was read by Professor E. D. Fahlberg before it 
was submitted to the Board of Editors and the author wishes to 
express his sincere thanks for the valuable and indefatigable help 
rendered in straightening out the lingual irregularities. 
Madison, Wis., July, 1923. 
The Author. ILLUSTRATIONS 
All illustrations appearing in this book have been made from original drawings 
and photographs except those below, which have been taken from the following 
publications: 
Fig. 2, 47, 75, 94 from Freundlich's "Kapillarchemie" 
Fig. 3, from Chem. and Met. Eng. 
Fig. 4, 6, 7, 15, 20 from the writer's "Formation of Colloids" 
Fig. 5 from Zeitschr. fur Elektrochem. 
Fig. 8 from Meddel. Nobelinst., Stockholm 
Fig. 32 from Nova Acta, Upsala 
Fig. 25, 26 from Arkiv. for Kemi, Stockholm 
Fig. 27 from Meddel. Carlsberg Lab., Kjobenhavn. 
Fig. 29, 34, 37, 38 from Zeitschr. phys. Chem. 
Fig. 30, 84, 87 from Koll.-Zeitschr. 
Fig. 40, 43, 44 from Carl Zeiss' Catalogues 
Fig. 42 from Zeitschr. wiss. Mikroskop. 
Fig. 45 from Verhandl. Deutsch, phys. Ges. 
Fig. 46, 48 from the writer's "Die Existenz der Molekule" 
Fig. 56, 60 from Journ. Amer. Chem. Soc. 
Fig. 59 from Zeitschr. anorg. Chem. CONTENTS 
PAGE 
Introduction and History 11 
Part I. Formation of the Colloid Particle 21 
Dispersion 22 
Dispersion in gases 22 
Dispersion in liquids 24 
Condensation 27 
Condensation in vacuo and in gases .... 28 
Condensation in liquids 49 
Reduction 55 
Oxidation 63 
Dissociation 66 
Double decomposition 78 
Purification 82 
Part II. The Colloid Particle as a Molecular Kinetic 
Unit 91 
The Brownian movements 91 
Osmotic pressure 92 
Diffusion 93 
Sedimentation equilibrium 96 
The translatory and rotatory Brownian move- 
ments 102 
The fluctuations 118 
The size, shape and structure of the particle . . 127 
The ultramicroscope 127 
Sedimentation 136 
Methods based upon osmotic pressure, diffusion, 
sedimentation equilibrium and Brownian 
movements 149 
Ultrafiltration 153 
X-ray analysis 154 
Light absorption and Tyndall effect .... 156 
Double refraction 163 
9 10 
CONTENTS 
PAGE 
Part III. The Colloid Particle as a Micell 167 
Adsorption 167 
The clectrokinetic phenomena . .... 179 
Endosmosis, endosmotic currents and catapho- 
resis 179 
Potential and charge of the particle .... 192 
The isoelectric point 198 
Osmosis, membrane-equilibrium 201 
Viscosity 206 
Coagulation 209 
Hydrophobe sols 209 
Hydrophile sols 223 
Gels 232 
Gelatination 233 
Swelling and imbibition 236 
Elasticity 241 
Diffusion and chemical reactions in gels . . . 245 
Part IV. The Destruction of the Particle 249 COLLOID CHEMISTRY 
Introduction and History 
The science of colloids is, as a rule, dealt with as a part of physical 
chemistry. This assumption may be all right and to a considerable 
extent founded in the nature of the colloid phenomena but, admitting 
this, we should bear in mind that the principle used in collecting the 
colloid phenomena and arranging them to a science is not the same 
as the principle used in putting together or discerning the ordinary 
branches of physics and chemistry. Colloid chemistry, for instance, 
is not like electro-chemistry, photo-chemistry, thermo-chemistry, 
optics, electricity, etc., the science of a certain group of phenomena, 
it is the science of a certain group of material systems, the science of 
systems of a certain structure. In this respect, colloid chemistry 
resembles to a certain extent, bio-chemistry. Bio-chemistry is the 
science of certain systems-not so much certain phenomena. 
Colloid chemical treatment of certain phenomena is often regarded 
as contradictory to, e.g. the pure chemical or the electro-chemical 
treatment. We often hear people speak of the colloid chemical theory 
of adsorption in contradistinction to the purely chemical theory; and 
of the colloid chemical theory of proteins in contradistinction to the 
chemical or the electrochemical theory of proteins. To a certain 
extent this is only a quibble about words and terms. Traced to their 
very sources, all forces chemical, colloid-chemical and physical are 
electrical in nature and therefore both physics and chemistry deal 
with the same forces-the attractions and repulsions between electrons 
and positive nuclei. This does not hinder us from dividing the vast 
field into practical domains of cultivation according to methods used 
for the work. Colloid chemistry is such a domain. The colloid 
chemist must not forget however that his science does not operate 
with any specific forces or substances and that the colloid phenomena 
traced back to their sources are built up of ordinary physical and 
chemical phenomena. So for instance, it is not admissible to regard 
11 12 
COLLOID CHEMISTRY 
the degree of dispersion in a colloid system as an arbitrary property 
determining the system, but it is of importance because it forces 
certain conditions upon the system. 
Almost every kind of material can be used for the building up of 
a colloid'; the great difficulty is to find out general laws governing 
the behaviour of colloids; hence the study of the different colloid 
systems must precede the formulation of general laws. The chief 
difficulty for the colloid chemist is that the systems he has to deal 
with are very complicated and very difficult to define; and, very 
difficult to reproduce exactly. It is often difficult to repeat a colloid 
chemical experiment. Another difficulty is that the colloid chemist 
must master almost the whole domain of chemistry and physics in 
order to be able to pay due attention to all the various phenomena 
occurring in colloid systems. On the other hand certain groups of 
phenomena are, of course, of a higher importance than others; and 
in the following I will on the whole consider only these groups. 
Research in colloid chemistry is at present working along two 
different lines: (1) the study of artificial systems of greatest possible 
simplicity with the object to find out general laws; (2) the study of 
natural systems which appear in the organisms or as technical products 
of high importance, with the object to learn their properties and the 
way to their synthesis. These two branches of research ought to 
support one another; the former can give directive rules for the latter; 
the latter offers suggestions and occasionally pure-cultivated systems 
to the former branch. The systems which the latter branch is treat- 
ing are as a rule rather complicated; and, frequently rather ill-defined. 
We may ask if it would not be more rational to confine research to an 
intense study of the former class of systems-the more simple col- 
loids,-and leave the second class for the present. The answer is, 
that the systems of the second class are of such overwhelming im- 
portance that every little progress today is of the greatest value-we 
cannot afford to wait for the general results which no doubt the 
former branch will give us, we must see what can be gained now. 
On the other hand I think it might be worth while to bear in mind 
that in the long run the study of the simpler systems will be of con- 
siderable importance for the study of the systems of the latter class; 
nay-it might be the only way to get results of a more permanent 
value. 
The chief problem of Colloid Chemistry is the investigation of 
the structure of colloid systems. The astonishingly rapid growth of INTRODUCTION AND HISTORY 
13 
this science may be attributed to the fact that both Chemistry and 
Physics have for a long time been developed without regarding the 
influence of ultramicroscopic structure on a great many phenomena. 
Now we know that the main part of all living beings is built up of 
colloids, of systems possessing a specific structure; and, that a number 
of very important technical products derived from organisms are col- 
loids-hence the great interest which the bio-sciences or the medical 
sciences and industry take in colloid chemistry. So, for instance, to 
name some technical applications, colloid chemistry is of importance 
in the industries of tanning, dyeing, fermentation, cellulose products, 
starch, gelatine, glues, soaps, rubber, nitrocellulose, celluloid, textile 
products, dairy, agriculture, bread-making, asphalt, petroleum, photog- 
raphy, clay products, cements, in the purification of water, etc. 
The important thing in colloid chemistry is not to measure all 
possible properties of the colloid system; it is to find out its structure 
in a wider sense of the word-for this knowledge will enable us to 
arrange the colloid systems within the general frame of chemistry and 
physics. It is because we do not know the structure of the colloid 
systems that we are forced to make a special science of them. 
The central point in colloids is the particle-like the molecule in 
chemistry and the cell in biology. The colloid particle, the "micell," 
is indeed a sort of intermediate between those two. In certain respects 
the colloid particle possesses the properties of the molecule (e.g. as a 
molecular kinetic unit), in certain other respects it has the compli- 
cated, partly autoregulative, properties of the cell. The latter prop- 
erties are to a great extent due to the surface field around the particle. 
Dividing the material with regard to the particle we have first 
(1) The formation of the particle; 
then 
(2) The particle as a molecular kinetic unit. Under this heading 
comes the Brownian movements and the discussion of the size and 
form of the particle. 
We have further 
(3) The particle regarded as a micell-that is, the particle taken 
with its surrounding surface field, its adsorbed ions, molecules, etc. 
The last step in our study would be to consider 
(4) The destruction of the particle, regarded as part of the colloid 
system. So far we do not however know very much about the latter 
process; only a few investigations have been carried out along this line. 
Before we enter into more detailed discussion of colloid chemistry, 14 
COLLOID CHEMISTRY 
I will try to outline the history of the development of the leading 
ideas. It is well known, I think, that colloid chemistry is regarded 
as being founded by Graham. Graham was the first to give general 
methods for preparing colloid systems and he introduced the names 
"sol" for a colloid solution and the name "gel" for the product formed 
by setting of the solution (1). Already before Graham, we meet with 
indications of observations on colloids. In many papers, we find 
such references about colloid properties of matter. For instance, 
Macquer in his "Dictionnaire de Chymie," Paris, 1774, states that "all 
these gold tinctures (aurum potabile) are nothing but gold which is 
made extremely finely divided and floating in an oily fluid. They 
are therefore, properly speaking, no tinctures and they may be called 
drinkable gold only so far as we connect with this name no other idea 
than the one that the gold is swimming in a fluid and is made into 
particles so fine that it may itself be regarded as potable in the form 
of a fluid" (2). 
At the beginning of the nineteenth century, wTe find many observa- 
tions about colloids. So, for instance, Berzelius says about the yellow 
solution of As2S3 obtained by treating As2O3 with hydrogen sulphide 
that "this solution probably ought to be regarded more as a suspension 
of transparent particles" (3). 
The Italian chemist, Selmi, in 1843, studied series of different solu- 
tions of e.g. sulphur, Prussian blue, casein, albumin and other colloids. 
He experimented with them and expressed the opinion that they 
were not ordinary solutions but are built up of small particles sus- 
pended in the liquid (4). 
These colloid solutions were known when Graham's work, in 1861, 
appeared. Graham divided all substances known into two classes: 
crystalloids and colloids with regard to their diffusion properties. He 
studied both free diffusion and diffusion through membranes and 
found that the substances of the first class: the crystalloids, diffuse 
readily through a membrane and move rapidly in free diffusion while 
the substances of the second class, the colloids, do not penetrate a 
membrane such as parchment paper but move extremely slowly in 
free diffusion. 
Graham used for his investigations a method of separating crys- 
talloids and colloids by means of membranes that were impermeable 
to colloids but permeable to crystalloids and he called this method of 
separation dialysis. Graham's original dialyzer consisted of two rings 
of hard rubber, between which was fixed a piece of parchment paper. INTRODUCTION AND HISTORY 
15 
Fig. 1 shows Graham's original dialyzer now preserved in the Science 
Museum in London, together with some bottles containing colloids 
prepared by Graham. 
Graham's principle of dividing all the different kinds of material 
into these two divisions-the crystalloid and the colloid-depends on 
the property of diffusion. From the modern point of view, crystal- 
loids and colloids differ in structure, the mass unit in a colloid-the 
particle-consisting of a great number of molecules. That is, we look 
upon crystalloids and colloids not as different kinds of substances but 
merely as different kinds of structural systems. 
Graham's sols and gels may be looked upon as systems built up 
of the same kind of units. In the sols-at least in the dilute ones- 
the arrangement of the units is governed by the same forces which 
determine the arrangement of the molecules in a solution; the number 
Fig. 1.-Graham's original dialyzer. 
of particles per unit volume determines the structure of a sol. In a 
gel a certain number of particles can be arranged in different ways, 
forming different kinds of aggregates, different kinds of network of 
cells-therefore the study of the structure of the gel is much more 
complicated than the study of the structure of the sol. 
Almost at the same time that Graham made his classical investi- 
gations with diffusion and dialysis, Faraday carried out a series of 
optical experiments with colloids, especially with gold colloids, and he 
expressed the opinion that these gold sols are not solutions in the 
ordinary meaning of the word, but contain gold particles suspended 
in the liquid. For instance: The red gold fluids "when in their finest 
state, often remain unchanged for many months and have all the 
appearance of solutions. But they never are such, containing in fact 
no dissolved but only diffused gold. The particles are easily rendered 
evident by gathering the rays of the sun (or a lamp) into a cone by 
a lens, and sending the part of the cone near the focus into the fluid. 16 
COLLOID CHEMISTRY 
The cone becomes visible, and though the illuminated particles can- 
not be distinguished because of their minuteness, yet the light they 
reflect is golden in character" (5). 
Tyndall found that the scattered light from the particles is polar- 
ized and the light cone in a sol is therefore often called the Faraday- 
Tyndall light cone (6). 
Besides this experiment with liquid sols Faraday made other ex- 
periments with solid gold sols, i.e. ruby glass. He put a drop of gold 
salt solution on a piece of glass and heated it. Part of the gold was 
dissolved in the glass and reduced, giving it the ruby color of col- 
loid gold. 
If we now proceed to the end of the nineteenth century, about 
1892, we meet with the very important investigations by Linder and 
Picton with arsenious sulphide sols. The study of the properties of 
those arsenious sulphide sols were made by different methods. The 
different kinds of sols were called alpha, beta, gamma and delta sols. 
The alpha solution was the most turbid, the most strongly opalescent, 
and the delta solution the clearest. The authors found that they got 
the clearest sols when treating very dilute solutions of arsenious oxide 
with hydrogen sulphide. Linder and Picton expressed the opinion 
that these sols are built up of particles, and that the size of the 
particles differs for different sols, being largest in the alpha sols and 
smallest in the delta sols (7). 
We see that, little by little, the opinion is expressed that colloids 
are not solutions in the true sense of the word, but that they are built 
up of particles. It was not before the first decade of the twentieth 
century however that it was fully proved that colloids consist of 
particles. This conclusive proof was rendered by Siedentopf and 
Zsigmondy's ultramicroscope (1903) (8). Faraday had actually been 
of the opinion that there must be particles in the light beam which 
shows up in a gold sol but he could not make the individual particles 
visible. Now, the method of Siedentopf and Zsigmondy was simply 
to observe the Faraday-Tyndall cone of light by means of a micro- 
scope. When we look at that light cone directly, the particles are 
so near to one another and the amount of light from the single particle 
is so small that it is impossible for the eye to distinguish it. Sieden- 
topf and Zsigmondy used a strong source of light such as an arc, 
collecting the light by means of a lens, throwing an image of the crater 
on a fine slit; then by means of another lens throwing a reduced image 
of this slit through a new condensing system. This last condensing INTRODUCTION AND HISTORY 
17 
system consists of a microscopic lens and the beam therefore becomes 
a very fine and intense one. This very fine, well defined beam of light 
was thrown into a cell containing the colloid. If we observe the light 
beam in the sol at right angles with an ordinary microscope of suffi- 
ciently high resolving power, we are able to see the individual particles. 
Of course we cannot get a true picture of the particles. They are 
too small to give a real image, but we get the diffraction image or the 
light scattered by the particle. 
By means of this and other kinds of ultra-microscopes which have 
been constructed, we have been able to study the movements of the 
particles. Early in the nineteenth century, about 1827, the English 
botanist, Robert Brown, found that particles large enough to be visible 
in the microscope showed a kind of rather slow irregular oscillatory 
movements (9). Using the ultramicroscope which enables us to ob- 
serve much smaller particles than those studied by Brown we find 
an exceedingly lively kind of Brownian movement (10). The theory 
of the Brownian movements was worked out by Einstein in 1905 upon 
the assumption that it is due to the impacts of the surrounding mole- 
cules and that the translatory kinetic energy of a suspended particle 
is equal to the energy of a molecule (11). We have been able to check 
up this theory and we have found that the particles behave indeed as 
if they were heavy molecules-the molecular weight corresponding to 
the apparent weight of the particle. 
Another phenomenon important in colloid chemistry is the cata- 
phoresis or the migration of particles in an electric field. In the 
middle of the nineteenth century Quincke found that particles ob- 
served under the microscope and exposed to the influence of an electric 
field, moved toward one of the poles-different poles for different 
kinds of material (12). The same has been found to be the case with 
the particles in ordinary colloids and the study of cataphoresis is 
now one of the most important branches of colloid chemistry. 
A phenomenon which is quite characteristic of the colloid systems 
is that of coagulation. Many colloids are very sensitive to impurities 
and it is often found to be very difficult to prepare them, because the 
particles are aggregated by minute traces of impurities, especially 
electrolytes (13). Already Faraday, in his early investigations, rec- 
ognized the importance of cleanliness in colloid chemistry. "All the 
vessels used in these operations must be very clean; though of glass 
they should not be supposed in proper condition after wiping, but 
should be soaked in water, and after that rinsed with distilled water. 18 
COLLOID CHEMISTRY 
A glass supposed to be clean, and even a new bottle, is quite able to 
change the character of a given gold fluid" (5). 
The investigations that have been made during the last two 
decades have given us much new material about coagulation and the 
precipitation of the particles. We have found that, in many cases, 
the coagulation can be brought back again-that is the coagulation 
is reversible. Probably the coagulation is always reversible in prin- 
ciple, and only consists in aggregation of the particles. At least in 
many cases the particles preserve their individuality in the aggregates 
and we can dissolve the aggregates again and get the sol back. By 
such experiments we have been able to prove that the number of 
particles we get back when reversing the coagulation is exactly the 
same as we had in the sol. Even after repeating the coagulation and 
dissolving several times the number of the particles remains the 
same (14). 
Another very remarkable feature of the coagulation is that the 
different ions act in very different ways (15). The valency of the 
ions is of great importance. The ions of high valency have a much 
higher coagulating power than the ions of low valency-much higher 
than in proportion to their electrical charge. If we compare such salts 
as KC1, BaCl2 and A1C13, the coagulating power rises very rapidly 
when we go from the mono-valent K ■ to the tri-valent Al • • • (16). 
These are the principal properties of colloid solutions. The prop- 
erties of the products produced by coagulation and by gelatination 
are much more complicated and difficult to study. The gels are of 
great importance, but we do not yet know very much about their 
structure. 
With regard to the terminology of colloid chemistry it may be 
pointed out that according to Wolfgang Ostwald's suggestion both 
sols and gels are included in the term disperse system. The medium 
corresponding to the solvent in an ordinary solution is the dispersion 
medium and the particles corresponding to the solute form the disperse 
phase (17). Graham's terms hydrosol and hydrogel for aqueous dis- 
perse systems and alcosol and alcogel for alcoholic disperse systems 
are still in use. 
The discontinuities of the systems which we deal with in colloid 
chemistry range from say 200 pp which is about the limit of micro- 
scopic vision down to say 1 pp, or molecular dimensions (1 pp - 
1 millionth mm.). Sometimes, however, it is instructive to study 
coarser disperse systems, systems of clearly visible microscopic dis- INTRODUCTION AND HISTORY 
19 
persity; and sometimes, comparisons between systems of molecular 
dispersity and colloids are desirable. Solutions of very large mole- 
cules probably show to some extent the same properties as ordinary 
colloids and such solutions may therefore be included in colloid 
chemistry. PART I 
FORMATION OF THE COLLOID PARTICLE (18) 
Colloids, or disperse systems, can be formed in two different ways: 
(1) by subdividing coarse material into fine particles or (2) by gath- 
ering smaller particles or molecules or atoms together to a particle 
of the size of a colloid particle. The first class we call dispersion 
methods and the second class condensation methods. In the con- 
densation method the relative surface is decreased, the material is 
brought together within a smaller boundary than before. In the dis- 
persion method, the relative surface of the system is increased (19). 
What at first observation might be regarded as a dispersion process 
has often, on closer investigation, been found to be really a conden- 
sation process, e.g., the formation of colloids by means of the electric 
arc. If we strike an arc between two metal electrodes immersed in a 
liquid we get particles in colloid solution. We transfer the solid metal 
over in the form of colloid particles and from that point, we may 
regard it as a dispersion process, but on closer inspection, we find that 
metal gas is formed by the arc after which follows condensation of 
the gas, so that the process is a condensation process, if we regard 
it just before the formation of the particle. The condensation proc- 
esses are, by far, more numerous than the dispersion processes. There 
is always in matter a tendency to decrease the boundary surface. 
The surface tension, according to the second law of thermodynamics 
tends to reduce the surface-that is, the free energy will decrease. 
There is always a tendency toward aggregation and condensation, so 
that condensation processes are more common than dispersion 
processes. 
The conditions under which the particles are produced are very 
important in the formation of colloids. Often we bring the particles 
we produce under such conditions that they cannot exist as single 
particles. We call the particles formed directly by the dispersion or 
condensation process the primary particles. They may at once aggre- 
gate or coalesce to more coarse particles. These processes go along 
21 22 
COLLOID CHEMISTRY 
for some time and stop so that we get a new equilibrium; we call 
these new particles formed the secondary particles or the secondary 
degree of dispersion and the first kind the primary degree of dis- 
persion. 
One of the most important things in investigating the formation 
of disperse systems is the relation between the experimental conditions 
and the size of the particles formed-not only the average size but the 
distribution of the sizes. We very seldom-almost never-get parti- 
cles of equal size. We get various sizes when we try to produce a 
colloid. To be able to account for the properties of the system we 
must find the distribution curve-that is the relation between a cer- 
tain distribution function and the size, i.e. the radius; or the relation 
between the percentage number of particles or the percentage mass, 
or volume of particles and the different sizes. This problem will be 
discussed in detail later. 
Dispersion 
Dispersion in Gases.-The dispersion processes in gases have not 
been studied very much from the standpoint of colloid chemistry. As 
a rule dispersion processes in gases give rather coarse systems. Re- 
cently, there has been an advance in the study of the dispersion 
processes in gases. The German physicist Regener has introduced a 
sort of atomizer giving particles of uniform size (20). If we carry 
out the disintegration of the liquid in such an apparatus as shown in 
Fig. 2, we can separate the coarser particles from the smaller. The 
spray goes up through the spiral shown in the figure and the coarse 
particles are thrown against the wall and stick there while the fine 
spray can be drawn off with the gas jet. If this spiral has a radius 
of only 1 cm. and if the velocity of the gas is only 10 m. per second 
(that is not a very high velocity for a gas) we find that the force is 
more than 1000 times the acceleration in the field of gravity. Thus 
the separation is very efficient. 
The method of disintegrating a liquid by means of a gas jet is used 
very often for producing colored flames-e.g. for spectroscopic pur- 
poses. If the suction tube of an atomizer is dipped into a beaker con- 
taining e.g. a sodium salt, and oxygen is pressed through the air tube 
of the atomizer into a colorless Bunsen flame, a very intense colored 
flame is produced. 
Another application of the formation of dispersed systems in gases 
by disintegration of a liquid is the method of sputtering molten metal FORMATION OF THE COLLOID PARTICLE 
23 
onto a surface to be plated or of applying paint by means of an 
atomizer and compressed air (21). In the purification of air we 
have another example of the application of the spray process. A 
spray of pure water is introduced into the air to be purified. The 
dust particles are coagulated by the minute water drops and the spray 
gradually settles, leaving very pure air. This system is actually used 
in many industrial plants-for instance, in the plants for manufactur- 
ing celluloid film for photographic purposes, where the air must be 
absolutely free from dust. 
Fig. 2.-Regener's atomizer. 
As to the mechanism of the formation of spray, we do not know 
very much, but it does seem that it would not be a simple disintegra- 
tion of the liquid by the gas jet but must rather be due to the forma- 
tion of bubbles or thin lamellae of the liquid. These lamellae then 
explode when we have the air bubble rising through the liquid to the 
surface. A very thin liquid film is formed. That means an immense 
increase of the surface and this film breaks up in pieces of liquid 
lamellae and these pieces of the liquid will, according to the surface 
tension, contract to minute drops. 
Disperse systems in gases can also be produced by producing a 
gas inside a solid body. The volcanic ashes are formed in that way. 
The gases and water are dissolved in the magma under high pressure 24 
COLLOID CHEMISTRY 
and when the pressure is taken off, the gas explodes causing the dis- 
ruption of the solid (22). We can get that on a small scale by heat- 
ing potassium permanganate in a test tube. The oxygen produced 
causes the particles to explode and a black ash is formed (23). 
Dispersion in Liquids.-Dispersion processes in liquids are by far 
more important and much more numerous than those in gases. Many 
of the processes that have been regarded as dispersion processes have 
been found, upon closer investigation, to be condensation processes, 
and there now remain three classes of dispersion processes in liquids: 
partial dissolution, grinding, and emulsification. 
The first type of process has not been studied very much (24). 
Von Weimarn has made an interesting experiment with sulphur. An 
alcoholic solution is cooled by immersing it in liquid air which gives 
a very fine-grained clear solid sulphur alcosol. If this system is 
slowly warmed, we get, at first, a decrease in the degree of dispersity, 
the particles agglomerate, and probably some of the smaller particles 
are dissolved and deposited on the bigger particles. If the warming 
is carried on to the point where the particles dissolve rather rapidly 
we get an increase in the degree of dispersity, that is we get finer 
particles again. The dispersion process does not stop before the 
particles are all dissolved in molecular solution, but on the way to 
complete dissolution we actually get a higher degree of dispersion 
because of that partial dissolution of the colloid sulphur particles (24). 
Another interesting process is the formation of tellurium sols on 
passing oxygen through a solution of K2Te. This is an old experiment 
performed by Berzelius (25). The first stage of the reaction gives 
coarse particles and potassium hydroxide: 
K2Te + 0 + H2O = Te + 2K0H 
and in the second stage those particles are partly dissolved again, 
potassium tellurate being formed: 
Te + 2K0H + O2 = K2TeO3 + H2O. 
We thus get an increase in the degree of dispersity (24). 
Many of the phenomena that have been regarded as processes of 
dispersion are peptization processes, that is only reversed coagulations. 
In some of the peptization processes, there may be partial dissolution 
of the grain but most of the peptizations are only disaggregation 
processes. Some years ago, much commercial interest was displayed 
in a dispersion process invented by the Austrian engineer Kuzel. He FORMATION OF THE COLLOID PARTICLE 
25 
powdered metals very finely and treated them alternately with acid 
and alkaline solutions and with pure water. In this way he was able 
to produce sols of various metals. He coagulated these sols and used 
the coagulum for making filaments for electric lamps. The process is 
of no commercial importance now, for they have learned to draw fila- 
ments of pure tungsten. The mechanism of that process has never 
been cleared up very well. In the grinding process, very fine particles 
are probably formed and aggregated and the treatment with alkalies 
and acids may then simply represent a loosening of the bonds between 
the primary particles (26). 
Von Weimarn, the Russian colloid chemist, suggested preparing 
dispersion systems by a special grinding method. His suggestion was 
to mix the substance to be dispersed with some neutral solid substance 
which would dissolve as a molecular solution in the dispersion medium 
and grind them together (27). He did not make any tests, but in my 
laboratory, Pihlblad used his method with rather good success. If 
we take sulphur and grind it with urea, 1 gram of sulphur -J- 1 gram 
urea, then take 1 gram of the mixture and mix it with 1 gram of pure 
urea, etc., making up a series of mixtures, and then dissolve a portion 
of those ground substances, we get a series of sulphur sols with in- 
creased degree of dispersion. The sols were examined under the ultra- 
microscope and the change of light absorption with change in degree 
of dispersion was studied. Pihlblad also used this method to prepare 
colloid solutions of a dye stuff aniline blue and got a series of varying 
degree of dispersion (28). Quite recently Von Weimarn and his 
co-workers have used the procedure to prepare sols of various material 
taking sugar as the neutral diluting agent (29). 
In the last 2 or 3 years, there has been invented a new process of 
making dispersed systems by mechanical grinding by the Russian 
engineer, Plauson. The principle of his machine, the so-called "Col- 
loid mill," is the following. The substance to be dispersed is sus- 
pended in the dispersion medium in the form of coarse particles, and 
those particles are crushed or torn to pieces by giving part of the 
suspension a very high velocity and allowing it to strike another part 
of the suspension having no velocity or a velocity of opposite direction. 
This can be arranged in different ways, e.g. by passing the liquid 
through a channel in the shaft that holds a metallic disc rotating 
with high speed close to another similar disc rotating in the opposite 
direction (Fig. 3). The suspension has to pass between the two rotat- 
ing discs and accordingly there will be a very high shearing force in 26 
COLLOID CHEMISTRY 
the middle layer of the suspension, tearing the suspended particles to 
pieces. High speed is essential. A peripheral speed of less than 
10 m. per sec. only gives coarse particles. Above 30 m. per sec. the 
size is brought down to colloidal dimensions. The colloid mill is one 
of the most important and promising new procedures for preparing 
colloid solutions by dispersion and machines of this type have already 
been tried with success in some plants interested in production of 
colloids (30). 
Fig. 3.-The colloid mill. 
All previous attempts to get colloids or very finely grained systems 
by mechanical means have failed, and for a long time it was thought 
that one could not get a fine-grained system by purely mechanical 
grinding. Those attempts failed because the particles were coagu- 
lated. Plauson actually adds different kinds of substances to his sus- 
pensions to prevent coagulation. 
In the preparation of emulsions, i.e. disperse systems consisting of 
liquid particles suspended in a liquid, the addition of certain ions or 
colloids, the so-called emulsifying agent, is a very important point. 
The action is probably largely due to the lowering of the surface 
tension but part of it is very likely due to an electrical effect. The 
ions are adsorbed, charging the particles and thus preventing coagula- 
tion (31). The following experiment carried out by Nordlund in the 
writer's laboratory illustrates this fact rather strikingly. We take 
two bottles, one containing mercury and pure water and the other 
mercury and water plus a little potassium citrate (2.5 X 10'3 normal). FORMATION OF THE COLLOID PARTICLE 
27 
Now, if we try to emulsify the mercury by shaking, we find that in the 
pure water very little emulsion is formed, the particles coagulating 
and coalescing very rapidly. In the bottle containing the citrate how- 
ever the mercury is emulsified abundantly and by placing it in a shak- 
ing machine and shaking for an hour or so, we are able to get a 
fairly concentrated disperse system of mercury in water. The parti- 
cles are of different sizes and we can centrifuge out the large particles. 
Then there remains a mercury hydrosol with very fine particles. 
Nordlund went a little further and tried to find out the mechanism 
of the formation of those fine particles. He showed that the emulsi- 
fication can take place in two different ways, either by crushing of 
mercury drops or by bursting of mercury lamellae. If we force water 
containing potassium citrate through a layer of mercury, very thin 
mercury films are produced when the water bubbles rise through 
the mercury. On bursting, those mercury lamellae give rise to ex- 
tremely fine drops of mercury. Nordlund could actually, by having 
a fine intense beam of light passing close to the mercury surface, 
observe the process and could see how the lamellae exploded and 
formed clouds of mercury colloid. If, on the other hand, we eject 
mercury through a fine glass tube against a glass wall under the same 
weak citrate solution, we only get a coarse emulsion (32). These con- 
siderations probably apply also in other emulsifying processes, but 
in cases where the interfacial surface tension is very low, the amount 
of energy required to form a fine drop is not very high and accord- 
ingly one would not expect a very striking difference between the two 
kinds of processes outlined above. Some experiments by the writer 
on the emulsification of oil confirm this conclusion. 
Condensation 
As already stated, the condensation processes are much more 
numerous and so far of much more importance than the dispersion 
processes. Perhaps in the future the colloid mill will be so efficient 
that we can use dispersion processes for the production of almost any 
kind of colloid, but so far the condensation processes are much more 
important. Condensation means that the material which is to form 
the disperse phase of the system has a very high degree of dispersity, 
i.e. is dissolved as ordinary molecules or is present as a gas. In some 
condensation the degree of dispersion decreases too rapidly and coagu- 
lation often sets in. In many cases it is very difficult to regulate the 28 
COLLOID CHEMISTRY 
conditions so that we always get the process to proceed in the same 
way, that is, so that we can reoroduce the system. 
Before condensation sets in, a supersaturation must be created. 
In this supersaturated system there must of course be formed or intro- 
duced some starting points for the condensation. The number of 
particles produced and the degree of dispersity depends upon the num- 
ber of those starting points or centers. The distribution of size of the 
particles will depend on the rate of migration of material to the 
centers; that is, if we have a known quantity of substance to start 
with and a known number of centers, the size of the particles that 
we finally get at the end of the process will depend upon the velocity 
with which the material is delivered to the centers. The starting 
points or centers for the condensation are often produced by the con- 
densation process itself. Sometimes we are able to introduce artificial 
centers and have the condensation set in at those points. Of course 
the distribution of the size of particles will also depend on the way 
of introducing the artificial centers, or on the way of formation of 
the spontaneous centers. The centers introduced or formed first are 
supplied with more material for building up their particles than are 
those introduced or formed towards the end of the condensation 
process and will consequently become larger. If we were able to intro- 
duce all the centers at the beginning, before the condensation process 
sets in, and could avoid spontaneous production of centers, we might 
expect to get much more uniform sized particles. In Zsigmondy's 
nuclear method of preparing gold sols we make use of that principle 
and we actually get rather uniformly sized particles. 
Condensation in Vacuo and in Gases.-Condensation processes in 
vacuo do not give us ordinary colloids as there is no dispersion 
medium, but they are of interest because they throw some light on the 
formation of colloids in gases and in liquids. When a metal is evapo- 
rated in a high vacuum and then condensed, the degree of dispersion 
of the metal will depend not only on the nature and temperature of the 
metal gas, but also on the temperature and nature of the surface upon 
which it is condensed. If we have it in a glass vessel, the metal mole- 
cules do not always stick to the wall for a time long enough to permit 
them to form a precipitate. We can evaporate cadmium, for instance, 
in a high vacuum so that we get an enormous supersaturation of the 
cadmium vapor and still have no condensation. If we cool a spot on 
the wall to about - 80° C. it condenses. Even if we remove the cool- 
ing agent immediately after condensation has started we get all the FORMATION OF THE COLLOID PARTICLE 
29 
metal condensed on it. Hamburger has studied such metal films very 
thoroughly and has made ultramicroscopic investigations of them and 
also studied their electric conductivity. He found that the metals 
with very high boiling points give the most fine-grained condensates. 
By evaporating tungsten and condensing it on a glass wall, he obtained 
films so fine-grained that they could not be resolved with the cardioid 
condenser. In time those films disintegrate forming particles-i.e. 
the film breaks up and forms small metal globules. They can be 
counted in the ultra-microscope. It is probably the same process as 
the explosion of the mercury bubbles. With metals of comparatively 
high vapor pressure, silver for instance, the films are rather unstable, 
and for such metals as cadmium and magnesium with high vapor 
pressures, there is no formation of film at all, you only get granular 
coarse condensates (33). These experiments show that the degree of 
dispersity rises with the difference of temperature between the metal 
gas and the wall, i.e. the degree of dispersity rises with supersaturation 
of the gas. 
Among the condensation processes in gases we have a number of 
very important methods for preparing colloid solutions. All the proc- 
esses founded on the use of the electric arc, producing metal gas by 
means of the arc, condensing it in a gaseous medium and introducing 
the particles into a liquid medium, come under this head. Before we 
proceed to the study of metal condensation, I will give a survey of the 
processes of condensation of vapors from ordinary liquids in gases. 
They are perhaps not of very much practical use for the production 
of colloid solutions, but they are of considerable theoretical value and 
the results that have been arrived at in the study of condensation of 
vapors in gases are very reliable. 
In regard to the formation of liquid drops in a gas, we must take 
into consideration the fact that the vapor pressure of the drops varies 
with the radius. The vapor pressure of a small drop is higher than 
that over a plane surface of the liquid. Of course, we could not get 
any considerable formation of drops in the region where the vapor 
pressure of the liquid is much below the vapor pressure of the drops. 
We must raise the concentration of the vapor, i.e. we must have such 
a high vapor pressure that we approach the vapor pressure of the 
small drops. 
The theory of the relation between vapor pressure and the radius 
of the drop has been worked out by W. Thomson (34). 30 
COLLOID CHEMISTRY 
If we take a small amount of the liquid from the plane surface 
and transfer it to a drop, we have to expend a certain amount of 
energy against the surface tension. Call the radius of the drop r, the 
surface tension a, and the density of the liquid pb then this work is 
equal to --. If we bring back the same amount of the liquid from 
the drop where the vapor pressure is pr to the plane surface where the 
R T d 
pressure is p by means of distillation, we gain the work In 
where R is the gas constant and M the molecular weight. 
These two amounts of energy must be equal. As pr and p are not 
very far apart we can write - - 1 for the logarithm. If we do this, 
we will finally arrive at the formula pr = p -|- - -i.e. the vapor 
pressure of the drop is equal to the vapor pressure of the plane sur- 
2(7 0 
face plus the quantity -, where pv is the density of the vapor. 
Pi r 
If we calculate the increase in vapor pressure for different values 
of r, for instance, 1 p, 10 pp, and 1 pp, we find that the percentage 
increase in vapor pressure is for 
Ip 0.1 per cent 
10 pp 10 " " 
1 pp 100 11 11 
that is, a marked increase in vapor pressure is only attained when we 
reach the domain of colloid dimensions. For microscopic drops the 
increase is very small. We do not know much about the surface 
tension when we come down to such small drops as these, consisting 
as they do of only a few molecules. The surface tension probably 
has a lower value than for large microscopic drops and it will there- 
fore be a decrease in the pr value. Thus, on the whole the increase 
in vapor pressure due to the small size of the drops is not very high 
but it prevents condensation at low degrees of supersaturation (35). 
The vapor pressure of the drops formed in the condensation process 
can be lowered in different ways. Condensation takes place, if the 
drop is formed on small solid particles, such as carbon dust or on 
particles soluble in the liquid formed. We get a similar effect if the 
nuclei for the condensation are electrically charged. J. J. Thomson FORMATION OF THE COLLOID PARTICLE 
31 
has worked out the theory for that case (36). Our formula for the 
increase in vapor pressure can be written 
] Pr _ 2orM 
p ~ RTP1r 
where M is the molar weight. 
It is changed into the following if the drop carries the charge e: 
. pr M e2 \ 
np-RTPi\r 8jit4/ 
If we figure out the effect for one single electron or for a mono-valent 
gas ion, we find in the case of water vapor condensation, that the 
theory would require condensation to begin at a supersaturation of 
about 4.2. 
After this introduction, we are prepared to study the phenomena 
which take place when we suddenly cool a volume of air, or some other 
gas, containing water vapor. The condensation process occurring 
upon cooling has been carefully studied by C. T. R. Wilson in Eng- 
land (37). The most convenient way to cool a volume of air with 
water vapor in it is by making an expansion sudden enough to pre- 
vent heat from the surroundings entering the system during the time 
of observation, i.e. an adiabatic expansion. From the change in 
volume, the volume ratio, we can calculate the drop in temperature 
and from that the degree of supersaturation. If condensation takes 
place, it will go on until so much water is condensed that the heat 
set free during this condensation process causes the remaining water 
vapor to be just saturated at the new temperature. 
We will now see what happens when we make such adiabatic ex- 
pansions on a quantity of saturated water vapor (Fig. 4). At super- 
, ,. , . „ vapor pressure under consideration \ 
saturations below S = 4.2 I S =---- 7- --= I 
\ vapor pressure of saturated vapor / 
no condensation takes place unless there are particles or some other 
contamination present in the vapor. As soon as these dust particles 
have been removed by condensing water on them and allowing the 
drops to settle, no condensation takes place below this degree of 
supersaturation. If we increase the supersaturation above this value, 
we will find that we get condensation on the negative gas ions in the 
interval S = 4.2-5.0. 
If we increase the volume ratio still more, we get condensation 
also on the positive ions at the supersaturations 5.8-6.8. Ions are not 
very numerous in ordinary air, so that the number of drops we get 32 
COLLOID CHEMISTRY 
at supersaturations from 4.2 to 6.8 is low. Therefore, the drops are 
rather large and the degree of dispersion is low. The condensate is 
rain-like. When we come to a supersaturation of about 8, the number 
of drops rises suddenly to a very high value, from a few drops per cc. 
to about 100,000, and then it becomes almost constant. 
The appareance of the condensate changes from a rain-like one to 
a dense white fog and the size of the drops from about 20 p to 0.6 p. 
Of course we could get a fine-grained condensate even in the region 
below S = 8 if we introduced a sufficiently high number of gas ions, 
Fig. 4.-Condensation of water vapor by adiabatic expansion. The diagram 
shows the variation of mass of condensate q and number of particles N per 
cc. with supersaturation S. 
for instance, by exposing the system to X-rays or to the radiations 
from radio-active substances. 
Now the question is: What kind of condensation nuclei are acting 
above S = 8? We do not know very much about that, but as it is a 
spontaneous formation of nuclei, the centers probably consist of aggre- 
gates of water molecules. 
Recently, the condensation by adiabatic expansion of vapors has 
been studied by Andren for other substances than water (38). He 
found that the number of drops corresponding to the sharp bend of 
the curve (Fig. 4) seems to be a characteristic for the substance in 
question. The value of supersaturation corresponding to this part 
of the curve has different values for different substances. For methyl 
alcohol it is 4.0, for ethyl alcohol 2.5, and for propyl alcohol 3.5, for FORMATION OF THE COLLOID PARTICLE 
33 
benzene it is 11.0 and for water about 8.0. The number of drops per 
cc. are 160,000, 300,000, 360,000, 190,000, and 100,000, respectively. 
It is obvious that these results are of great importance for the under- 
standing of condensation processes in gases. If we could determine 
these numbers for the metal vapors, we would certainly know much 
more about the formation of metal colloids. 
An understanding how the spontaneous formation of nuclei in 
gases goes on can probably be attained on the basis of Maxwell's dis- 
tribution curve. With molecules of a given mean velocity, i.e. a given 
temperature the part of the curve corresponding to molecules with 
velocities below a certain limit Vi would at a certain degree of super- 
saturation contribute a certain number of aggregates of molecules 
which would act as condensation nuclei (39). 
The formation of fogs, consisting of liquid drops in a gas, is the 
best known of the condensation processes in gases, but there are other 
processes which are of more practical interest to the colloid chemist. 
These are the condensation of metal vapors in gases. One of the 
simplest forms of metal condensation in gases has been studied by 
Kohlschiitter. He heated metals in various gases and collected the 
condensates on glass or silica plates enclosed in a tube (40), and he 
also evaporated metals by exposing them to an intense beam of posi- 
tive rays and collected the condensates (41). This was attained by 
making the specimen the cathode in a vacuum tube. When the 
cathode is struck by a stream of positively charged particles, there 
is a sudden and enormous rise in temperature at the points where the 
positive particles hit the surface of the cathode and consequently we 
get sudden evaporation of the metal. Some of the evaporated metal 
can be collected on a glass plate near the cathode. 
Fig. 5 shows the influence of the gas on the degree of dispersion 
of zinc condensates in nitrogen and hydrogen at different pressures- 
50 mm., 300 mm., and 700 mm. We see that the size of particles 
increases when the pressure goes down and that at equal pressures 
we get coarser condensates in hydrogen than in nitrogen. As a rule, 
the degree of dispersion was always found to be higher in a gas with 
higher molecular weight and at higher pressure. Studying different 
metals, Kohlschiitter found that the degree of dispersion was higher 
with the more refractory metals, i.e. the higher the degree of satura- 
tion the smaller the particles in the condensate. Of course, we get no 
ordinary colloid solutions in this way with the condensate on a glass 34 
COLLOID CHEMISTRY 
plate but it indicates how the various factors influence the degree 
of dispersion. 
In my laboratory, Nordlund found that he could, by introducing 
a supersaturated mercury vapor into water, get mercury sols (42). 
By injecting a jet of mercury vapor into water, condensation probably 
takes place in the gas phase, i.e. in a mixture of mercury and water 
vapor. The smaller particles formed here are taken up by the water. 
Pressure 700 mm. 
Pressure 300 mm. 
Pressure 50 mm. 
Hydrogen 
Nitrogen 
Fig. 5.-Particles obtained by condensing zinc vapors in hydrogen and nitrogen 
at various pressures (after Kohlschiitter). 
The most powerful means of evaporating metals or producing metal 
gases is that of the electric arc. A series of different methods of 
preparing colloids have been built up on the process of producing 
metal gases by means of the arc, condensing them in a gaseous 
medium, and transferring the particles formed into a liquid. 
When we strike a direct current arc between two silver wires with 
say 110 volts, silver gas is produced and then condensed to particles 
when it gets mixed with the cold gases around it (43). If the arc FORMATION OF THE COLLOID PARTICLE 
35 
is burning under the surface of a liquid, e.g. water or ethyl alcohol, 
the condensation takes place more rapidly than in the case of the 
arc burning in air or nitrogen and the particles are taken up by the 
liquid, forming a colloid solution (Fig. 6). 
This method of preparing colloids by means of the arc immersed 
in a liquid was found by Bredig in 1898 (44). If we study the process 
more carefully we will find that the properties of the sol depend to 
a great extent on the electric and thermal conditions of the arc. 
In the case of the original Bredig arc, the free or unprotected D.C. 
arc in a liquid, the concentration of the silver vapor in the arc is not 
very high. On the other hand the decomposing effect of such a free 
continuous current arc on the surrounding dispersion medium, e.g. 
Fig. 6.-Formation of colloids by means of the free direct current arc 
the alcohol, is comparatively great. The result is that the dispersed 
system we get has not very high degree of dispersity and is rather 
unpure. 
If we enclose the arc so as to protect the electrode surface thermally 
from the cooling action of the liquid, we can increase the concentra- 
tion of the metal vapor considerably and at the same time avoid 
decomposition of the dispersion medium. The result is that we get 
a much higher degree of dispersity and a purer and more concentrated 
sol (45). 
Figure 7 represents the diagram of the arrangement. We have 
the two silver wires enclosed in a silica tube with a hole bored just 
in front of the arc. If we strike an arc with this arrangement we 
get a very high concentration of the silver vapor and we can blow 
out the silver vapor through the hole by applying a pressure of 
nitrogen. A magnetic field will also help to blow out the silver gas. 36 
COLLOID CHEMISTRY 
We can collect the condensate on a glass plate and find that the 
degree of dispersion is much higher than if we have a free arc burning 
in the nitrogen gas. If we have the whole arrangement surrounded 
by a liquid, e.g. ethyl alcohol (Fig. 8) condensed silver will be taken 
up by the liquid forming a silver colloid of much higher degree of 
dispersity than the one produced by means of the free arc. It is 
necessary to use a rather high potential for the enclosed arc, say 
500 volts, and a low intensity, say 1 amp., in order to get a sufficiently 
long arc without fusing the electrodes. 
silver 
nitrogen 
glass 
rubbei 
quartz 
nitrogen 
nitrogen 
Fig. 7.-Production of silver vapor by the enclosed arc. 
It is of interest to compare the spectrum of the free and that of 
the protected arc. Figure 9 gives the spectrum of the unprotected free 
silver arc burning in alcohol (a), the spectrum of the silver arc in 
nitrogen (b), and the spectrum of the protected silver arc as we 
get it with the quartz tube (c). In the case of the free arc, we have 
not only the silver lines but also the broad carbon bands showing 
strong decomposition of the dispersion medium. The spectrum (c), 
or that of the protected arc, only shows the silver lines, and a short 
part of a continuous spectrum emitted from glowing silver particles 
and particles from the silica tube, but no trace of the carbon bands. 
As already pointed out there is a considerable difference in the size FOP MAT ION OF THE COLLOID P ARTICLE 
37 
of the particles of sols produced by means of the free and by means 
of the protected arc. Those of the former are about 40 pp while 
Fig. 8.-Formation of colloids by means of the enclosed arc. 
the latter contain particles of say 4 or 5 pp. There is also a very 
marked difference in light absorption and consequently in color be- 
Fig. 9.-Silver arc spectra; a is the spectrum of the free silver arc burning in 
alcohol; b is the spectrum of the silver arc in nitrogen; c is the spectrum of 
the enclosed arc in alcohol. 
tween those two kinds of sols. In Fig. 10 the light absorption of 
some gold sols is recorded. The free arc in alcohol gave the curve 38 
COLLOID CHEMISTRY 
a, a bluish violet colored sol. The enclosed arc gave the curves b 
and c, representing brownish red or yellowish red sols resembling 
very much the fine grained gold sols obtained by reducing gold 
chloride in water, by means of phosphorus, as shown in curve d. 
One of the drawbacks of the method with the enclosed arc is 
that the silica tube gets so hot that it gives off SiO2 vapors which 
are also condensed and form a part of our colloid solution. It is 
hoped that it will become possible to use some other more refractory 
material, e.g. alumina, and thus get rid of the contamination from 
the tube. Another difficulty is that we cannot use the enclosed arc 
Fig. 10.-Light absorption in gold ethyl alcosols prepared: a by means of the 
free D.C. arc; b and c by means of the enclosed D.C. arc; d by means of 
a reduction method. 
for preparing sols of metals with a very low melting point, at least 
not in its present form, because the electrodes fuse together too 
rapidly. 
We now pass over to the alternating current arc. The way in which 
this arc forms colloids depends to a great extent on the frequency or 
the number of cycles. With ordinary low frequency current, say 
15-60, we get almost the same kind of colloids as with the direct 
current arc. There is, however, a certain difference. The disperse 
systems produced by means of the arc consist of two kinds of particles, 
coarse and fine grained ones. If we measure the distribution curve, 
ds 
i.e., if we plot the radii r as abscissae and a function giving the 
weight of the particles lying between certain radii as ordinates, we get FORMATION OF THE COLLOID PARTICLE 
39 
the type of curve shown in Fig. 11 (46). The coarse-grained and the 
fine-grained part of the system are separated by a gap. In the case 
of the D.C. arc the production of the coarse part is very irregular. 
Passing over to the A.C. arc the coarse grained part increases and 
becomes more regular. It is evident that the coarse part which 
is probably built up of molten particles is produced when interruptions 
of the arc occur. 
Now upon increasing the frequency we find that at 50 cycles we 
get a colloid of almost the same properties as with the direct cur- 
Fig. 11.-Distribution of size of particles in a metal sol produced by means of 
the alternating current arc. 
rent arc; at 500 there is an almost imperceptible change in the prop- 
erties; at 1000 we find that the particles are a little smaller than 
with the direct current arc; and that there is a little increase in 
the amount of coarse particles formed (46). When we get over to 
the high frequency currents, say 105-107 cycles, we have a very 
marked change in the properties of the colloid (47). To produce such 
high frequency currents different methods can be used. 
An oscillatory circuit is built up of a condenser C (Fig. 12) of 
suitable capacity, and the spark gap S where the colloid is to be 
produced. The electric energy can be supplied by connecting the 
spark gap to an induction coil (Method 1) (47) (Fig. 12, 1), to 
an ordinary transformer (Method 2) (48) (Fig. 12, 2), or to a suffi- 40 
COLLOID CHEMISTRY 
ciently high D.C. potential (Method 3) (49) (Fig. 12, 3). The 
first of those two arrangements give damped oscillations, the third 
nearly undamped ones. In some cases it is desirable to transfer 
the oscillations to the colloid producing spark over a high frequency 
/eduction cod 
Low frequency 
transformer 
<500 i/o/t 
battery 
Low frequency 
transformer 
frequency 
transformer 
^/r •spark 
Fig. 12.-Formation of colloids by means of the high frequency current arc 
transformer (Method 4) (Fig. 12, 4). Various kinds of spark gaps 
have been used for the colloid producing spark. Figure 13 shows a 
spark micrometer which the writer used in his first investigations of 
the oscillatory arc. 
The sols produced by means of the oscillatory arc are more fine- 
grained and purer than those produced by means of the D.C. or the 
low frequency A.C. arc. A D.C. arc cadmium alcosol for instance is FORMATION OF THE COLLOID PARTICLE 
41 
grayish in reflected light indicating a comparatively low degree of 
dispersity, while a high frequency A.C. arc cadmium sol is black 
in reflected light indicating a high degree of dispersity. 
An indication of the high degree of purity of the sols prepared 
by means of the oscillatory current arc compared with those pre- 
pared by means of the D.C. current arc is given by the following 
experiments. Nordlund, working in the writer's laboratory, found 
Fig. 13.-Sparc micrometer for the preparation of colloids by means of the high 
frequency arc. 
that the electrical conductivity of a mercury hydrosol prepared by 
means of the oscillatory arc is lower than the conductivity of the 
water used as dispersion medium while the conductivity of a D.C. 
arc mercury hydrosol prepared with the same water is higher than 
the water (50), and Pope found that the conductivity of pure ethyl 
alcohol in an indifferent atmosphere decreases when cadmium is dis- 
persed in it by means of the oscillatory arc. The production of 
the metal colloid by means of the oscillatory arc apparently is ac- 
companied by such a slight amount of decomposition of the medium 42 
COLLOID CHEMISTRY 
and chemical action on the metal that the adsorption on the surface 
of the particles of the impurities present in the liquid more than 
counterbalances the increase in the concentration of impurities caused 
by the arc process. In the case of the D.C. arc, however, the amount 
of foreign substances produced is so high that an increase in con- 
ductivity is actually obtained in spite of the adsorption. 
The two products of the arc, the fine and the coarse grained, 
have been studied by Borjeson in the writer's laboratory (51). Using 
the oscillatory arc, he found that with cadmium in ethyl alcohol the 
coarse grained particles have sizes lying between 25 p and 0.5 p, 
while the average size of the particle in the fine grained part is 
about 5 pp. Probably the latter part of the disperse system, the 
real colloid part, is produced by condensation of the metal gas and 
the coarse grained part by the action of the liquid on the molten 
metal. Some experiments by Borjeson on different alloys have given 
strong evidence in favor of that view. Borjeson found that if we 
have an alloy consisting of two metals of different boiling points 
(Table I) e.g. gold and cadmium and strike an arc between them, 
the sediment formed is richer in the metal with the high boiling 
point than the electrodes are and that the sol is richer in the metal 
of low boiling point, showing that the fine grained part or the sol 
must have been formed by condensation of gas from the boiling metal. 
The sediment then must have been formed out of the remaining metal 
-deprived of part of the volatile metal. 
TABLE I 
Oscillatory Arc Pulverization of Alloys 
Alloy and Boiling 
Point of Components 
Ratio of Components 
In Electrodes 
In Dispersion Product 
In 
Condensation 
Product 
Coarse 
Fraction 
Fine 
Grained 
Fraction 
Au(2500°)-Cd(780°) .. 
0.84 
1.7 
3.0 
0.52 
Au(2500°)-Sn(2270°).. 
0.74 
0.75 
0.81 
0.71 
Bi(1420°)-Cd(780°) .. 
1.0 
1.4 
2.0 
0.77 
Table I also shows that if we divide the sediment in two parts, one 
fine grained and one coarse grained part, the fine grained part is 
richer in the less volatile metal than the coarse grained part. Such FORMATION OF THE COLLOID PARTICLE 
43 
would be the case if the melting globules remained for some time 
in the arc before they are thrown out into the liquid. During this 
period metal would evaporate off from the surface of the globules 
and the particles with largest relative surface, i.e. the small particles, 
would lose more metal by evaporation than the larger ones. This 
process would, of course, tend to concentrate the metal with high 
boiling point in the fine grained fraction of the sediment. 
The percentage amount of coarse grained part increases with in- 
creasing capacity. For cadmium in ethyl alcohol it is about 20 per 
cent at a capacity of 0.0004 microfarad, 40 per cent at 0.003 m.f. 
and 55 per cent at 0.09 m.f. It also increases with decreasing melting 
point of the metal as shown by Table II. 
TABLE II 
Dispersion Product in Oscillatory Arc Pulverization . of Metals 
Dispersion Medium: Ethyl Alcohol. 
Capacity: 0.003 M. F. 
Current Int.: 1.5 Amp. 
Metal 
Percentage 
Dispersion Product 
Melting 
Point of Electrodes 
Pt 
20.2 
1700° 
Au 
25.8 
1064° 
Zn 
41.0 
419° 
Cd 
41.6 
320° 
Sn 
56.8 
232° 
Bi 
59.3 
268° 
The loss in weight of the electrodes is roughly proportional to the 
square of the effective current and varies considerably with the nature 
of the metal. Figure 14 gives a graph of the pulverization of various 
metals in the case of the undamped oscillatory arc, method 1. 
In order to find out how the different kinds of arcs work we 
have studied the amount of colloid produced under different electrical 
conditions and we have also measured the amount of decomposition 
of the dispersion medium. Low self-induction, high capacity and 
short length of arc seem to favor the formation of purer sols. 
By means of the Zsigmondy nuclear method, Borjeson succeeded 
in measuring the size of the particles in sols produced by the oscil- 
latory arc. He found that the initial size of the particles formed- 
i.e. the primary degree of dispersion-does not vary much but that 
the secondary degree of dispersion-that is, the degree of aggregation 
of those primary particles-varies very much with the experimental 44 
COLLOID CHEMISTRY 
conditions. Low velocity of production of the colloid and low tempera- 
ture seem to favor a high secondary degree of dispersion. Table III 
gives some values of the primary size of particles. 
If we try to explain why we get more fine grained colloids with 
Loss /r? ure/g/rf of e/ec/ropes //? rr&. per /7?/r> 
Square or effect/ire correct 
Fig. 14.-Pulverization of metals in the high frequency arc. The diagram shows 
the variation of pulverization with square of effective current in the oscil- 
latory circuit. 
the oscillatory arc than with the continuous direct current arc, we 
must remember that if we measure the current with the hot wire 
ammeter, we measure a sort of mean or average value. With the 
oscillating current arc the current is only closed for a very short time. 
It is only a fraction of the time that corresponds to a stable condition 
of the arc. If we calculate the momentary intensity of the oscillating FORMATION OF THE COLLOID PARTICLE 
45 
TABLE III 
Size of Particles in Sols Formed by the Oscillatory Arc 
Ethyl Alcohol. 
Temp. = - 75°. 
Metal 
Radius of Particles in gn 
Au 
2.8 
Zn 
2.9 
Pt 
3.8 
Cd 
5.0 
arc and the D.C. arc we find that for equal average values of the 
current, the oscillating arc corresponds to very much higher momentary 
values. It is difficult to find exact values of this momentary in- 
tensity, but we are surely not overestimating if we assume the momen- 
tary intensity to be, say 100 amp., when the average current is 2 amp. 
This must give rise to an enormous evaporation of metal in a shcrt 
time, i.e. a very high supersaturation followed by a sudden con- 
densation when the arc goes out. 
The method 2 using a low frequency transformer to supply the 
energy for the oscillatory circuit has been studied by Bodforss and 
Frolich. Method 3 which makes use of an observation by the writer 
that under certain conditions we get undamped oscillations simply 
by connecting our oscillatory circuit to a D.C. potential of 400-500 
volts has been studied by Borjeson in the writer's laboratory. Using 
500 volts the resistance R (Fig. 12) should be about 300 ohms giving 
a current of about 0.1 amp. in the D.C. circuit when the arc is oscil- 
lating and about 2 amp. effective current in the oscillatory circuit with 
a capacity of 4 X 10 3 m.f. 
This arc produces more metal colloid per unit virtual current 
and less decomposition products of the dispersion medium per unit 
metal colloid than does the damped oscillatory arc. The order of 
the metals with regard to the amount pulverized by the arc is not 
quite the same as in the case of the damped oscillatory arc. This 
order seems to be easily influenced by slight variations in the electrical 
conditions of the arc. 
Table IV gives a comparison between the pulverization for the 
methods 1, 2, and 3, as measured by the writer, Borjeson, and Bod- 
forss and Frolich. The figures are not quite comparable because of 
the differences in the electrical conditions and the dispersion media 
used. 46 
COLLOID CHEMISTRY 
TABLE IV 
Pulverization with Different Kinds of Oscillatory Arcs 
Metal 
Pulverization 
Damped Oscillatory Arc 
Undamped 
Oscillatory Arc 
Pb 
Induction Coil 
45 
Low Frequency 
A. C. Transformer 
28 
64 
Bi 
33 
21 
75 
Sb 
25 
18 
130 
Cd 
21 
13 
48 
Zn 
8 
4.8 
25 
The method 3, i.e. the undamped oscillatory current method, 
gives purer sols than method 1. The difficulty is, however, that ac- 
cording to the high concentration in which the sol is produced coagula- 
tion seems to take place more easily than in the case of methods 1 
and 2. 
The method 4 has been studied by Kraemer and the writer in the 
University of Wisconsin Chemical laboratory. It has the great ad- 
vantage of being almost independent of the conductivity of the dis- 
persion medium. When using the methods 1, 2, 3 in dispersion media 
of comparatively high conductivity, e.g. water and aqueous solutions, 
it is necessary to reduce the surface of the electrodes as much as 
possible and arrange the spark so that there are no other metallic 
parts of the circuit in contact with the dispersion medium. No 
such precautions are necessary in the case of method 4. The de- 
composition of the medium is markedly lower than in the other 
methods. In Table V a comparison between the efficiency of methods 
2, 3, 4 is given according to Kraemer's measurements. 
TABLE V 
Comparison between the Efficiency of Different Kinds of Oscillatory Arcs 
Electrodes: Cadmium. 
Dispersion Medium: Ethyl Alcohol. 
Capacity of Osc. Circuit: 0.005 Microfarad. 
Current: 1.35 Amp. 
Method 
m 
Percentage 
Sediment 
v0 
v0/m 
v0/mcoii 
2 
18.8 
38 
30.3 
1.60 
2.62 
3 
32.7 
48.3 
1.44 
4 
15.8 
55 
9.6 
0.61 
1.36 
Here m is the loss in weight of the electrodes in mg. per min.; by 
sediment is understood the coarse grained part of the system formed; FORMATION OF THE COLLOID PARTICLE 
47 
v0 is the number of cc. of gas produced per min. (at 0° and 760 mmm.) 
which serves as a measure of the decomposition of the dispersion 
medium; v0/m is therefore the decomposition per mg. metal and 
vo/meoii. the decomposition per mg. of the fine grained part, i.e. per 
mg. colloid produced. 
By means of the oscillatory arc we have been able to prepare 
colloid solutions of all metal available, even colloid solutions of the 
alcali metals. As dispersion medium for those very active metals, 
we may use ethyl ether. The ether must be very pure-free from 
Fig. 15.-Apparatus for the preparation of organosols of the alkali metals by 
means of the high frequency arc. 
water, of course, and from oxygen. We have to run hydrogen through 
it and have it in contact with sodium wire to keep out moisture. 
Even with these precautions it is difficult to get the ether pure 
enough; therefore we find it advisable to cool the ether to say 
-100° C. to depress the velocity of the chemical reactions. Such 
temperatures can easily be realized by adding liquid air to absolute 
alcohol. Figure 15 shows a suitable kind of pulverization apparatus 
for preparing a sodium sol. The flask F contains a supply of pure 
ether and some sodium wire and the tube T pieces of sodium in a loose 
pile between two platinum wires serving as electrodes. Pure hydrogen 
is passed in at The hydrogen bubbles up through the holes 48 
COLLOID CHEMISTRY 
Px and P2 and drives out the air and passes out at R2. When all the 
air is driven out, we close R2 and apply a slight suction at Rx to 
raise the ether in the tube T. The platinum wires are then connected 
with the oscillating circuit and the apparatus slightly tapped to start 
the sparking. The sodium sol is purple in transmitted light when 
produced and turns blue with time when it gradually coagulates. 
A similar arrangement can be used for the preparation of various 
kinds of metallic sols when high purity is wanted (Fig. 16). The 
metal to be dispersed forms a loose layer between the two sealed in 
Fig. 16.-Apparatus for the preparation of pure sols of various metals by means 
of the high frequency arc. 
platinum wires Pi and P2. Pure dispersion medium can be distilled 
down into the flask through A and the air can be replaced by any 
suitable indifferent gas by means of the tubes A and B. The sol 
can be drawn off through the tube C. The sparking between the 
platinum wires and the next piece of the metal to be studied can be 
neglected if the metal in question is much more easily dispersed than 
platinum. If that is not the case sealed in electrodes of the same 
metal have to be used. 
There is still very much work to be done on the investigations 
of the properties of the metallic organosols. Some recent work done 
by Pope in the writer's laboratory on cadmium sols has emphasized FORMATION OF THE COLLOID PARTICLE 
49 
the role played by small impurities. In the case of cadmium, carbon 
dioxide is especially important. 
A few other kinds of condensation processes in gases have been 
studied, but they are not so very important for the colloid chemist 
at the present time. The supersaturation necessary for the forma- 
tion of disperse systems may be produced by ordinary chemical re- 
action or by a photochemical reaction. Tyndall, for instance, made 
experiments with mixtures of amyl nitrite gas and hydrochloric acid 
'fete/fy m/c/e/ 
Temperatare 
Fig. 17.-Variation in the formation of crystallization nuclei with temperature 
in the case of piperine. 
and got fogs of different degrees of dispersity, but those processes 
have not been studied very carefully so far. 
Condensation in liquids.-As I have already mentioned, the two 
most important things in all condensation processes are: (1) The 
number of the condensation nuclei present and the way in which these 
nuclei are produced, and (2) the velocity of the growth of the 
particles. As most of the particles in colloid solutions are crystals, 
we can call this the velocity of crystallization. 
Before entering into a more detailed discussion of the various 
methods of preparing colloid solutions by condensation processes in 
liquids, I will give a short review of some investigations undertaken 
with the purpose of measuring the velocity of the production of 50 
COLLOID CHEMISTRY 
nuclei and the velocity of crystallization in liquids. These investi- 
gations throw a light on the processes that are now in use for the 
preparation of colloid solutions by means of condensation processes in 
liquids. 
If we consider the velocity of production of nuclei in a molten 
substance, we find that it shows a maximum with regard to tempera- 
ture. For instance, with piperine Tammann (52) found the curve 
given in Fig. 17. The velocity of formation of centers is influenced 
by impurities. In the case'of betol, we find that salicylic acid, and 
■ftementoge of mo/ecu/es of ue/oc/fu u 
Optimum rone for 
formot/on of crustu/- 
/cat/on nuc/e/ 
Decreasing 
temperature 
l/e/oc/fp of mo/ecu/es (r) 
Fig. 18.-Distribution of velocities of molecules and spontaneous formation of 
crystallization nuclei. 
cane sugar lower the velocity of formation of centres while this 
velocity is increased by anisic acid. Of course, we do not know very 
much of the manner in which the substances added influence the 
formation of nuclei. 
The spontaneous formation of nuclei in the molten substance 
might be connected with the distribution curve of the velocities of 
the molecules (Fig. 18). Probably there would be a certain range 
of velocities that favors the production of the nuclei. If the velocity 
is too high, the molecules will not stick together to form an aggre- 
gate; if too slow, the chance of meeting will be very small. If we 
lower the temperature, the distribution curve will move in the direc- FORMATION OF THE COLLOID PARTICLE 
51 
tion indicated in the figure and the velocity of the production 
will increase; when it has passed the maximum, it will decrease 
again (53). 
The velocity of the formation of nuclei in solutions can be treated 
similarly to that of the production of nuclei in supersaturated 
vapors (54). The solubility of the small particles will be higher than 
the solubility of a plane surface of the substance and we find quite the 
same type of equation that we found for the relation between vapor 
g 2a IVI 
pressure and radius of drop, i.e. In = prp , where Sr is the solu- 
o K1 pr 
bility of a drop of radius r. Therefore, the crystallization can only 
proceed when the supersaturation in the solution has reached a certain 
value. 
The velocity of growth of particles also varies with temperature. 
The maximum is often almost constant over a certain range of tem- 
perature. The velocity of formation of nuclei and the velocity of 
crystallization seem to be independent of each other. Freundlich 
mentions two substances having nearly the same melting point, viz., 
piperonal, m.p. 37°, and apiol, m.p. 30°. The velocity of crystal- 
lization is very small in both cases, about 7 mm. per minute at 
0° C. If we measure the velocity of production of nuclei, we find 
that it is much higher for piperonal than for apiol. We can cool 
molten apiol down to 0° for many hours without any formation of 
nuclei. Piperonal, however, can hardly be cooled to 0° without 
solidification. 
The velocity of crystallization is very different in different cases. 
For instance, if we measure the so-called linear velocity of crystal- 
lization, i.e. if we have the substance in a narrow glass tube and start 
crystallization at a certain point and measure the propagation of 
the solidified part we get values differing widely for different sub- 
stances. For phosphorus it is about 60,000 mm. per minute and for 
water about 7000 mm. For salol it is not more than 1 mm. per 
minute (55). 
Additions of impurities have a very strong influence on the velocity 
of crystallization in molten substances. Freundlich has found that the 
depression of the velocity of crystallization by impurities follows the 
adsorption formula, i.e. it depends on the amount of foreign substance 
that has been adsorbed by the small crystals. Benzophenone infected 
by pyrocatechin shows this very clearly (Table VI) (56). 52 
COLLOID CHEMISTRY 
TABLE VI 
Depression of Velocity of Crystallization by Impurities 
Benzophenone -|- pyrocatechin 
Mol Pyrocatechin 
in 100 Mol Benzophenone = c 
Relative Depression of Rate of Crystallization 
Calculated from the Formula 
Observed 
0.2884 c 0 4645 
0.25 
50.0 
50.5 
1 
43.5 
42.3 
2 
36.5 
35.8 
4 
26.1 
26.8 
8 
13.4 
14.3 
Ions of different metals, for instance the ions of the alkali metals, 
have a very striking influence on the velocity of crystallization of 
water as shown by Walton's investigations. It seems that this is 
parallel with the hydration of the ions. We find in the series Li, 
Na, K, that Li has a stronger action than Na and Na stronger 
than K (57). 
The velocity of crystallization in solutions is, of course, the most 
interesting point for the colloid chemist. Here the influence of im- 
purities is quite enormous. A striking example of such an action, 
studied by Marc, is the influence of quinoline yellow upon the velocity 
of crystallization of potassium sulphate (58). Crystallization is 
stopped by the presence of the dye stuff molecules which are adsorbed 
on the crystal surface. The action of the dye stuff depends on its 
concentration. Fig. 19 shows the decrease of supersaturation with 
time caused by crystallization in a K2SO4 solution containing various 
amounts of the dye stuff. 
These phenomena are, of course, of great importance in the forma- 
tion of colloids, for the properties of the colloid solutions formed de- 
pend to a great extent on the rate of growth of their particles. 
It has been known for quite a while that small additions of elec- 
trolytes and other substances have a very great influence on the forma- 
tion of colloids, but this influence has chiefly been attributed to the 
action of the electric charges which the ions give the particles as they 
grow, thus preventing them from coagulating. To some extent, how- 
ever, the action of the additions, e.g. the ions, must be due to the 
influence on the rate of growth of the particles. 
There is another curious action of additions on growing crystals. 
The structure and the form or shape of the crystals produced are often 
changed very much by additions. This has b^en studied by Reinders FORMATION OF THE COLLOID PARTICLE 
53 
in the case of the silver halides. In solutions containing a little 
methylene blue irregular dendritic AgCl crystals were obtained in- 
stead of the ordinary symmetrical ones (59). -This phenomenon is 
of importance for the colloid chemist to note because the properties 
of the colloids depend to a great extent upon the shape of the particles. 
To produce the supersaturation necessary for condensation to begin 
in a solution, different methods can be used. We can raise the super- 
saturation by cooling or by lowering the solubility, e.g. adding sub- 
stances in which the disperse phase is very insoluble or by producing 
the material of the disperse phase either through a chemical reaction 
or a radio active process. 
GMce/rfrtrt/o/? rf //eSQ. 
/.GGg. qu/r/of/ne 
ye//ow per //fer 
O.^g. gu/7?o//ne 
ye//oi4r per //Yer 
77rr?e /r? m/nt/tes 
Fig. 19.-Influence of a foreign ubstance, quinoline yellow, on the velocity of 
crystallization of potassium sulphate. 
In all condensation processes in liquids we have to distinguish 
between volume condensation and surface condensation. If we are 
able to start the condensation process at the same time throughout 
the whole volume, we get what I call volume condensation, and we 
get a comparatively equally grained system. On the other hand, if 
condensation takes place along certain surfaces we have surface con- 
densation and according to the variations in the supply of material 
for the building up of the various particles we get a more unequally 
grained disperse system. For instance, when two solutions react with 
another, we are never able to mix them very well before the con- 
densation process sets in and we, therefore, get surface condensation. 
In such cases, where the condensation process goes on so slowly that 
wTe can mix the reagents before the condensation begins, we are able COLLOID CHEMISTRY 
54 
to approximate volume condensation and accordingly we get a more 
homogeneous system. 
As an example of the production of a sol by cooling, we could 
mention the white fog that appears in a saturated solution of phenol 
in water when it is cooled, or the formation of an ice pentanosol by 
cooling a solution of water in pentane with liquid air (60). 
Another method of getting disperse systems is by lowering the 
solubility. Take for instance a hot saturated solution of palmitic 
acid in alcohol and pour it into boiling water. As the solubility of 
the palmitic acid is lowered very rapidly, the substance is precipi- 
tated in the form of fine particles, giving a milky opalescent liquid. 
We have studied the conditions for the formation of disperse systems 
of palmitic acid and other organic substances such as fats, hydro- 
carbons, resins, etc., in the laboratory of the writer and have found 
that the amount dispersed and the degree of dispersion of the system 
depends to a great extent on the ions present in the solution. If a 
little alkali is added to the water, a more concentrated sol is obtained, 
but upon adding more alkali we come to a maximum-the concentra- 
tion goes down again. To keep such a colloid stable it is neces- 
sary to boil off the solvents, e.g. the alcohol, completely so that 
the solubility of the disperse phase is permanently kept sufficiently 
low (61). 
We can perform the same experiment with a sulphur solution. If 
a sulphur-alcohol solution is poured into water, we get a sulphur 
sol (62). This kind of sol is of great interest because it shows a 
rather different behavior compared with sulphur sols produced by 
chemical reaction, e.g. by mixing hydrogen sulphide with sulphur 
dioxide. The former sol is very sensitive to coagulants, while sulphur 
sols made by chemical reaction are very stable, i.e. very insensitive 
to electrolytes. 
In the few examples mentioned above, the substance of the dis- 
perse phase was formed long before the condensation took place 
and independent of it. Most of the methods of preparing colloids 
by condensation processes in liquids are based on production of 
the disperse phase by chemical reaction just before (he condensation 
takes place or, in some cases, by radioactive processes. 
Suppose we have a solution of radium emanation in water. When 
the emanation breaks down, we get helium and the substances RaA, 
RaB and RaC which are solid substances and form a colloid solu- FORMATION OF THE COLLOID PARTICLE 
55 
tion in the water. These processes have not been as yet studied very 
carefully. 
The most important processes are those based on formation of 
the disperse phase by means of chemical reactions. We can classify 
them with regard to the reaction as follows: (1) reduction, (2) oxida- 
tion, (3) dissociation, (4) double decomposition. 
In order to get stable sols, we must arrange the experiment so 
that the solubility of the disperse phase is very low in the dispersion 
medium, and the concentrations of the ions must be neither too high 
nor too low to give the right electrical charge to the particles. 
Reduction.-The reduction processes are those which have been 
studied most carefully. The best known is the gold reduction, e.g. 
the reduction of chlorauric acid to metallic gold. Almost every 
kind of reducing agent has been studied and it has been found that 
we get different kinds of sols by means of different reducing 
agents (63). One of the most simple reactions and one that can be 
studied quantitatively is the reduction of HAuC14 by means of 
hydrogen peroxide: 
2HAuC14 + 3H2O2 = 2Au + 8HC1 + 3O2, 
that means that every molecule of chlorauric acid will give us 4 
molecules of hydrochloric acid when the reaction is completed. 
We have been able to study this reaction by means of measuring 
the electrical conductivity of the reacting mixture (64). During the 
reaction the conductivity, of course, increases from the value for the 
HAuC14 solution to the value for the HC1 solution-no other electro- 
lytes being involved in the reaction. Now the course of the time- 
conductivity curve is of great interest for our understanding of the 
mechanism of the colloid formation process. If no gold particles (or 
no nuclei) are present in the reduction mixture, there is a sudden 
rise in conductivity of about 30 per cent of the total rise corre- 
sponding to the formation of 4HC1 per Au. This rise is accom- 
panied by a drop in color intensity; the absorption in blue and violet 
goes down. After the sudden rise in conductivity AB (Fig. 20) there 
follows a period of very slow rise BC, and then another period of sud- 
den rise CD up to the final value. The red color characteristic of 
the gold sol appears at C and deepens along the line CD. If we 
examine the sol formation in the ultramicroscope, we find that only 
a negligible number of gold partivies are visible during the period 56 
COLLOID CHEMISTRY 
BC. At C masses of particles suddenly appear and increase in number 
along CD. 
If condensation nuclei, c.g. gold particles, are added to the gold 
salt solution before the reducing agent is added, the reduction proceeds 
along an almost straight line AD' and if such are added during 
the period BC the reaction instantly changes in velocity and is com- 
pleted along the line C"D". 
The explanation may be the following: Upon adding the hydrogen 
peroxide, about 30 per cent of the gold is reduced to gold molecules, 
forming an enormously supersaturated solution of gold in water. 
This balances up the reaction according to the law of mass action. 
The gold molecules slowly condense to colloid gold particles along 
conductivity of 4 H Cl 
conductivity 
conductivity of H Au Cl,, 
Fig. 20.-Formation of a gold sol by reduction of chlorauric acid with hydrogen 
peroxide. 
the line BC and at the point C the size of a great number of particles 
has reached the minimum size of nuclear action, that is,-such a 
size that they are able to act as condensation or crystallization cen- 
ters. According to some experiments by Zsigmondy, this limit is 
supposed to be about 1 or 2 pu in the case of gold (65). The 
reaction follows slowly along the line BC. After the nuclear limit 
is reached at C the reduction process proceeds rapidly, depositing the 
rest of the gold on the gold nuclei formed during the period BC. In 
those cases where nuclei are added, the reduction is accelerated along 
BD' or C"D" in the same way as along CD. 
This process of producing gold colloids by reducing with hydrogen 
peroxide has become very important in recent years, because we can 
prepare colloid solutions of different sized particles by adding dif- 
ferent amounts of nuclei to the reduction mixture. Under certain FORMATION OF THE COLLOID PARTICLE 
57 
conditions the gold is precipitated only on the nuclei added, so that 
we can vary the size of the particles by varying the number of nuclei 
added. Or if we take the same number of nuclei and add them to 
gold chloride solutions of different concentrations, we get different 
amounts of gold deposited on the nuclei. Applying this method, we 
can determine the size of particles in very fine grained solutions,- 
such that contain particles too small to be seen with the ultramicro- 
scope. We simply let the particles grow in a suitable gold reduction 
mixture till they are large enough to be seen in the ultramicroscope 
and to be counted (66). 
In the above case, the reduction process takes place in an acid 
solution. We have, however, quite a number of reduction methods 
for preparing gold colloids working in neutral or in alkaline solution. 
Here probably the first step in the reaction is: 
HAuC14 + 4NaOH = Au(OH)3 + 4NaCl + H2O, 
e.g., insoluble gold hydroxide is formed and this is dissolved in an 
excess of the sodium hydroxide, giving a sodium aurate solution: 
Au (OH) 3 + NaOH = NaAuO2 + 2H2O. 
If a reducing agent such as formaldehyde is added, we have: 
2NaAuO2 + 3HCH0 + NaOH = 2Au + 3HC00Na + 2H2O. 
Naumoff has actually shown that a solution of sodium aurate when 
reduced gives the same kind of gold sol as a mixture of chlorauric 
acid and alkali (67). 
When working in acid solution, there is the possibility that some 
of the gold chloride is hydrolyzed so that we have part of it present 
as Au (OH) 3. This compound is but sparingly soluble, and there- 
fore might form small particles in the water. Probably the amount 
of such particles present is of importance for the properties of the 
colloids which are formed by reduction in acid solution. To get 
reproducible results with hydrogen peroxide methods, it is best to 
use freshly prepared chlorauric acid solutions or dilute the cold con- 
centrated chloride solution immediately before using it. If the con- 
centrated stock solution is kept at low temperature and in darkness, 
there is not much hydrolysis. 
In those cases where we do not add nuclei of gold to the reduction 
mixture, but make use of the spontaneous formation of nuclei in such 
a mixture, we must study the relation between the process of spon- 58 
COLLOID CHEMISTRY 
taneous formation of centers and the velocity of growth of particles, 
and find out whether those two processes are influenced by other 
kinds of centers and by impurities present (68). Zsigmondy and 
his pupils have devoted much time to this study, but it seems that 
small amounts of unknown impurities present complicate the case 
very much. For instance, the kind of water used for the reduction 
is of very great importance. Zsigmondy prepared water with much 
care and found that very pure water could not be used. When work- 
ing with the formaldehyde method, the reduction took place so very 
rapidly that he was unable to mix the reducing agent with the gold 
solution before reduction had already started. He, therefore, got 
very unequal sized particles. It seems that the water contains some 
unknown matter that reduces the velocity of crystallization. 
A systematic study of substances added shows that the velocity 
of crystallization, i.e. the velocity of growth of particles, is reduced 
by the presence of organic colloids, e.g. gelatin, oils and fats. The 
proof that the velocity of crystallization is reduced, we get from the 
fact that the reduction is retarded whether we add gold nuclei or 
not. Thus it is not the spontaneous production of nuclei but the rate 
of crystallization that is changed. 
The spontaneous formation of nuclei is reduced by additions of 
potassium-ferro and ferri-cyanides, and by ammonium salts. Zsig- 
mondy found that in this case the reduction was retarded if no nuclei 
were added. However on adding a quantity of gold sol to such a 
mixture, reduction took place rapidly and therefore the rate of 
crystallization must have been unchanged, but the rate of spontaneous 
production of nuclei depressed. The addition of a small quantity of 
potassium ferrocyanide is therefore sometimes used when we want 
to prevent the spontaneous formation of nuclei, e.g. when determining 
the size of particles by depositing gold upon them (69). The spon- 
taneous formation of nuclei is accelerated by substances like citrates 
and some dye stuffs. 
Already before Zsigmondy carried out these experiments, the writer 
found that in gold colloid reduction processes in alkaline solution, 
the presence of gelatine reduced the velocity of the formation in an 
almost linear manner. The writer further found that if we add an 
electrolyte to such a mixture of HAuC14 and gelatin in alkaline solu- 
tion containing, say hydrazin hydrochloride as a reducing agent, the 
time of formation of the colloid is cut down enormously. If we 
test the action of electrolytes which contain cations of different FORMATION OF THE COLLOID PARTICLE 
59 
valency, we find that the action increases with the valency of the 
cation. Thus BaCL cuts down the time of reduction much more 
than KC1 (70). 
Besides the nuclear method, there is another very curious way of 
varying the degree of dispersity when making a gold colloid, namely, 
by exposing the reduction mixture to ultraviolet light during the 
reduction. Nordenson working in the laboratory of the writer found 
the following phenomenon. If we take a dilute gold chloride solution 
and add hydrogen peroxide, the reduction proceeds very slowly-will 
take perhaps one-half hour and we get a very coarse colloid. Now 
if we expose the reduction mixture to ultraviolet light, the velocity 
of reduction increases very rapidly and we get a fine grained colloid. 
The length of exposure determines the degree of dispersion. An ex- 
posure of 25 sec. to the light of a strong mercury quartz vapor lamp 
reduces the size of the particles from say 100 pp-the size we get with- 
out illumination-to 10 pu (71). 
A satisfactory explanation of this peculiar process has not yet 
been found. It is evident that the number of nuclei is increased by 
the action of the ultra violet light, but the mechanism of this action 
is quite unknown. The light itself has a slight reducing action, i.e. 
if no hydrogen peroxide is added, we will still get a sol,-but a 
very coarse one, and it takes a considerable time to get the gold 
chloride reduced. With reference to the diagram given in Fig. 20 we 
might say that the light causes a rapid condensation of the super- 
saturated molecular gold solution to extremely small gold particles 
which act as nuclei for the rest of the gold. It would probably be of 
considerable interest to study this reaction more in detail. 
The reduction of gold chloride to gold colloid can take place in 
other solvents than water. One of the most interesting cases is the 
formation of gold particles by reduction in glass-the formation of 
gold ruby glass. If we add a small quantity of a gold salt such as 
gold chloride to a suitable glass, e.g. lead or barium glass, and heat 
it, we get an almost colorless glass. If we heat this glass again it 
becomes red. Therefore, probably the first stage consists in a re- 
duction of the gold either to a highly saturated solution of gold in 
glass or to very fine gold particles, probably corresponding to the 
part BC Fig. 20 of the conductivity curve in the water solution. If 
we reheat a strip of colorless glass containing gold, from one end, 
the red color will appear first at the heated end and then proceed 
further along the strip. If we examine it under the ultramicro- 60 
COLLOID CHEMISTRY 
scope, we find that it contains particles and that the number of 
particles is almost constant through the whole length of glass, but 
that their size decreases with the distance from the source of heat. 
The particles are larger in the part of the strip which has been heated 
to a higher temperature. Zsigmondy, who studied the formation of 
the gold ruby glass, assumes that the colorless gold glass contains a 
certain number of gold nuclei ■ or gold particles which can act as 
nuclei, if the supply of gold is high enough. At low temperatures the 
viscosity of the glass is very high, so that the supply of gold to the 
centers is very slow and accordingly the rate of crystallization also 
very slow. When we heat it, the viscosity goes down, the rate of 
diffusion increases and the greater supply of gold to the centers 
raises the velocity of crystallization. The particles in the parts of 
the glass which have been heated to high temperatures have received 
more gold than those in the colder parts. If this explanation is true, 
the formation of the gold ruby glass would be analogous to the 
formation of crystals in a molten substance according to Tammann's 
theory (72). 
Next to gold reduction, the reduction of silver solutions to silver 
sols is one of the reduction processes which has been studied most. 
Silver compounds are very easily reduced to colloid solutions especially 
silver hydroxide. One of the simplest and most interesting processes, 
from a theoretical point of view, is Kohlschiitter's method of pre- 
paring a silver colloid by reducing AgOH with hydrogen (73). A 
saturated solution of silver hydroxide in water is heated on a water 
bath and a current of hydrogen passed through it. The reduction 
takes about an hour. Kohlschiitter studied the process of the forma- 
tion of silver colloids very carefully and found that the reaction is 
probably confined to a thin layer near the walls of the vessel. He 
found that the nature of the material used for a vessel played a very 
important role in the formation. He obtained more fine grained sols 
when the reduction was carried out in a vessel of ordinary glass or 
of quartz than in a vessel of Jena glass. There seems to be no con- 
nection between the solubility of the glass and the properties of the 
colloid obtained. If the reduction is carried out in a platinum vessel, 
the silver is deposited directly on the walls of the vessel in the forni 
of macroscopic crystals. Here the degree of dispersion is very low. 
Kohlschiitter made use of this fact to purify his sols. After passing 
hydrogen through the silver solution for a certain time, we get silver 
particles, but of course there remains a certain amount of silver FORMATION OF THE COLLOID PARTICLE 
61 
hydroxide in solution. If we take the sol containing this mixture of 
silver sol and silver solution and put it in a platinum vessel and 
pass hydrogen through it, the dissolved silver molecules are deposited 
on the walls of the vessel as crystals, and we get a very pure silver 
sol. We can follow the rate of purification by measuring the con- 
ductivity. In the original mixture it is comparatively high but de- 
creases rapidly as the hydrogen is passed through it in a platinum 
vessel. 
Kohlschiitter also studied the formation of silver mirrors. The 
mirrors can be made by depositing silver on glass out of a suitable 
reduction mixture of silver, especially by the use of complex silver 
compounds. He found that all these mirrors are built up of particles 
of silver deposited very close to each other. The degree of dispersion 
is increased when the velocity of the reaction is very low or when 
there is some sort of a suitable protective substance present (74). 
Silver particles are able to act as condensation nuclei in the same 
way as gold particles. Luppo-Cramer has shown that if a solution 
of silver nitrate (4 per cent) is reduced with hydroquinone in the 
presence of gelatine (1 per cent) and a number of silver nuclei, we 
can get the silver deposited upon those nuclei and get a different 
degree of dispersion according to the different number of nuclei 
added. If we increase the number of nuclei, the color of the sols 
obtained goes from gray, blue, and red, over to yellow. Those colors 
correspond to the colors of ordinary silver sols of increasing degree 
of dispersion (75). 
Small quantities of protective substances or impurities have a very 
great influence on the stability of silver sols. The famous silver 
sols prepared by Carey Lea, reducing silver nitrate with ferrous 
citrate contain traces of such protective colloids (76). The silver 
particles formed by reducing silver nitrate with ferrous citrate can 
be precipitated with ammonium nitrate, re-dissolved, and precipi- 
tated again with alcohol. In this way we get a product containing 
about 99 per cent silver. It can be dried and dissolved again, i.e. 
it is a perfectly reversible sol. The silver sols prepared according 
to Carey Lea contain particles of various sizes. Oden working in 
the writer's laboratory showed that these particles of different size 
have a different sensitivity against electrolytes, so that the coarse 
particles are more easily precipitated than the smaller ones, i.e. the 
small particles are most stable. By using ammonium nitrate at very 
low concentration, Oden was able to divide such a Carey Lea sol 62 
COLLOID CHEMISTRY 
containing particles of different sizes into a series of sols of different 
degree of dispersity but with very equal particles in each sol. The 
colors of the series resemble Liippo-Cramer's color scale (77). 
The ordinary electrolysis of silver nitrate must be regarded as 
a colloid process. If we have a solution of silver nitrate, the forma- 
tion of silver on the cathode is somewhat of a coagulation process, as 
shown by the investigations of Kohlschiitter (78). It is evident that 
when the silver atoms or ions are discharged, there is formed a very 
highly supersaturated solution of silver and this molecular solution 
condenses to small particles and these are usually deposited on the 
electrode. By varying the electrical conditions, e.g. the density of 
current, or the nature of the silver salt used, or by putting in a 
protective colloid, we can vary the nature of the silver precipitated 
on the electrode. It is even possible to prepare a colloid silver solu- 
tion by electrolysis using a sufficiently dilute silver solution. Billiter, 
for instance, prepared a silver sol in this way by electrolyzing a 
N/300 silver nitrate solution (79). 
If we make a similar experiment in alcohol, or even if we take 
pure alcohol and two silver electrodes, we find that we get a silver 
colloid. If 500 volts are used the production of silver sol is rather 
abundant (80). Nordenson found that we might exchange the silver 
cathode but not the anode for a platinum one and still get the same 
effect. The explanation of the process, therefore, probably is as 
follows. Some silver is dissolved at the anode by an oxidation 
process and is carried by the current to the cathode where it is either 
electrolyzed or reduced to metallic silver by the hydrogen set free at 
the cathode (81). 
Another process that gives rise to a silver colloid, probably by 
reduction is the following one first observed by the writer. A plate 
of silver is immersed in alcohol or in water and exposed to the 
strong ultra violet illumination from a mercury quartz lamp. We 
get a colloid, not very concentrated, but the yellow color can be 
seen and if we examine it in the ultramicroscope we find plenty of 
particles (82). It is not quite clear how this process goes one. It is 
evident that the silver is dissolved in the alcohol in some way, and 
that the silver solution is reduced to silver particles by the action 
of the light. If we take a solution of silver and expose it to the 
light, we get a reduction. This test is so sensitive that if we take a 
clean silver plate and put it in alcohol for some time without illumi- 
nation and then illuminate the alcohol without the silver plate, we FORMATION OF THE COLLOID PARTICLE 
63 
get some silver particles. A similar phenomenon is observed in water. 
Water which has been in contact with silver always contains some 
kind of silver compound, and this is easily reduced by light (or by 
organic contamination) to a silver colloid. Therefore, we should 
not use silver tubes as stills if we wish to have pure water for colloid 
work (83). 
Many other metals can be prepared in a colloid form by means 
of reduction processes, platinum, mercury, bismuth, copper, tellurium, 
etc., but in those cases the condensation processes have not been 
studied very much from the theoretical point of view. All of the 
work is of a preparatory nature. One of the methods which seems 
to be most promising is that of Paal and his collaborators (84). They 
used alkaline solutions of protalbic and lysalbic acid as a protective 
colloid. These substances are also used as reducing agents in the 
case of gold and silver. For other metals, platinum, copper, tellurium, 
a special reducing agent, e.g. hydrazine hydrochloride must be added. 
These colloids are so stable that they can be dried and redissolved 
again. 
Oxidation.-After this review of the reduction methods, we will 
study the formation of colloids by means of oxidation. There are not 
more than two oxidation processes that are of interest to the colloid 
chemist. The formation of sulphur sols by oxidation of hydrogen 
sulphide and the formation of selenium sols by oxidation of hydrogen 
selenide. Of course, the formation of sulphur sols is the process we 
are most interested in. The action between H2S and O2 is supposed 
to be as follows: 
2H2S + O2 = 2S + 2H2O. 
The oxidation of H2S can also be carried out by means of SO2. 
The simplest way of explaining the reaction is to assume that there 
are formed 3 atoms of sulphur: 
2H2S + SO2 = 3S + 2H2O. 
Most of the sulphur is precipitated in the form of colloid particles. 
This process has been studied very carefully by Oden from the 
point of view of the formation of the colloid particles (85). He has 
found that the amount of colloid sulphur produced and the degree 
of dispersity depend on the concentration of the SO2. It has been 
known for a long time that the reaction between H2S and SO2 does 
not quite proceed according to the above equation. Sulphur and water 64 
COLLOID CHEMISTRY 
are not the only products. There are also formed pentathionic acid 
and other kinds of thio acids. In studying the action of H2S gas 
on a solution of SO2, starting with 1.8 normal solution, Oden found 
that at high concentrations the reaction did not follow the simple 
formula, i.e. the amount of sulphur produced was less than predicted 
by the formula. The other quantities of sulphur must be present as 
acids (pentathionic, etc.). 
TABLE VII 
Formation of Colloid Sulphur by Reaction between ILS and SO2 
''Insoluble" 
(Non- 
Amicro- 
Nearly 
Submi- 
Concentration of 
Colloid 
Colloid) 
scopic 
Visible 
croscopic 
SO2 
Sulphur 
Sulphur 
Particles 
Particles 
Particles 
1.8 normal 
8.333 
0.098 
0.910 
4.218 
3.205 
1.44 " 
9.891 
0.288 
0.160 
2.099 
7.632 
0.9 
13.022 
0.402 
0.052 
0.206 
12.764 
0.45 " 
1.936 
14.908 
Traces 
1.936 
0.225 
Traces 
16.98 
- 
Traces 
Thus starting with 1.8 normal SO2, he got about 8 grams sulphur 
per 100 cc. At a dilution of 0.225 normal, he got almost the quan- 
titative value or 16.98 grams sulphur precipitated. The theoretical 
value should be 17.3. Now if we divide the sulphur produced into 
two parts-the soluble and the insoluble-he found that the insoluble 
part increases with the dilution of SO2 so that we get more colloidal 
sulphur at the high concentrations, and if we compare the amount 
of sulphur as to fine and coarse, we find that there are formed 
more fine grained particles at the high concentrations. This is rather 
interesting. When there is formed much pentathionic acid there is 
also formed much colloidal fine grained sulphur, and at the high 
dilutions where the reaction proceeds according to the simple equa- 
tion, most of the sulphur comes out as insoluble. There is almost 
no stable colloidal sulphur formed under those conditions. According 
to some recent experiments by Freundlich, the stability of the sulphur 
sols produced by such chemical reactions is due to the presence of 
the pentathionic acid and to the adsorption of this acid at the sur- 
face of the particles, and here we find that we actually get the most 
stable colloid sulphur in such concentrations of SO2 where much 
pentathionic acid is also formed (86). 
Oden also studied the similar reactions of the formation of sulphur 
by decomposition of thio salts (87). Sodium thiosulphate is decom- 
posed by means of sulphuric acid: FORMATION OF THE COLLOID PARTICLE 
65 
3Na2S2O3 + 3H2SO4 = 3H2S2O3 + 3Na2S04 
HoSo03 = S + S02 + H20 
2HoS,03 + 2H2O = 2HoS + 2H2SO4 
2H2S + S02 = 3S + 2H2O 
3Na2S2O3 + H2SO4 = 4S + 3Na2S04 + H20 
probably part of the sulphur is formed by the reaction between the 
hydrogen sulphide and the sulphur dioxide produced in this reaction. 
Part of it may be due to a simple decomposition of the thio acid. 
According to the formula given above, % of the sulphur would be 
due to an oxidation process and % to a dissociation process. 
In this case the amount of colloidal sulphur decreases when the 
concentration decreases and also we get more fine grained particles 
at high concentration. When concentrated H2SO4 is slowly added 
to a concentrated cold solution of sodium thiosulphate, we get the 
best results. The colloid formed in this mixture can be freed from 
the impurities by coagulating the particles with sodium chloride, 
centrifuging and dissolving the coagulum again. The sol is reversible 
and can be reprecipitated so that all the H2SO4 can be taken out, but 
according to Freundlich's experiments, the pentathionic acid cannot be 
removed in this way. 
Those sulphur sols which we get either by the reaction of hydrogen 
sulphide on SO2 or the action of H2SO4 on sodium thiosulphate, con- 
tain particles of various sizes. Oden has worked out a method of 
dividing such polydisperse sols in a series of sols of more even sized 
particles by fractional coagulation. As was the case with the silver 
TABLE VIII 
The sulphur 
sol is not coagu- 
Ultra-Microscopic Characteristics 
lated (A), is 
coagulated (B) by 
NaCl of the 
following concen- 
tration 
in normality. 
A 
B 
0.25 
00 
Faint amicroscopic light-cone, no submicrons. 
0.20 
0.25 
Clearly visible amicroscopic light-cone, no sub- 
microns. 
0.16 
0.20 
Strong amicroscopic light-cone, no submicrons. 
0.13 
0.16 
Particles just visible (about 25 pp in diameter). 
0.10 
0.13 
No amicroscopic light-cone, diameter of par- 
ticles 90 pp. 
0.07 
0.10 
No amicroscopic light-cone, diameter of par- 
ticles 140 pp. 
0 
0.07 
No amicroscopic light-cone, diameter of par- 
ticles 210 pp. 
Sulphur Sols of Various Degree of Dispersity 66 
COLLOID CHEMISTRY 
sols, the sulphur particles show different sensitivity to coagulators, the 
fine particles being more stable. They require higher concentration 
of the coagulator to be precipitated. Therefore, upon adding a certain 
electrolyte such as sodium chloride to a sulphur sol, we first get the 
coarse and then the fine particles coagulated. In this way we can 
separate them and prepare a series of sols of different degree of dis- 
persity and of different properties. Those sols have been investigated 
by Oden in the writer's laboratory and have proved of great use for 
the study of various problems. In Table VII the salt sensitivity of 
such a series of sulphur sols together with its ultramicroscopic char- 
acteristics are given. 
Dissociation-The dissociation processes are not of much use for 
the preparation of colloid solutions but they are, nevertheless, very 
important because the formation of a certain kind of solid disperse 
systems is caused by dissociation processes-at least we believe so- 
i.e. the formation of the latent image in the photographic process. 
Very likely the photographic process depends on the formation of a 
highly disperse system, small silver particles in the surface layer of 
the silver halide grains. 
An interesting case of the formation of colloid solutions by means 
of a dissociation process is the preparation of nickel organosols by 
dissociation of Ni(CO)4 (88). If we heat a solution of this compound 
in benzene, it is dissociated: 
Ni(CO)4 = Ni + 4CO. 
The colloid solution of Ni in benzene is of brown or black color, re- 
sembling very much the Ni sols obtained by electric pulverization in 
the arc. 
The dissociation of salts, especially the halides, has been studied 
by R. Lorenz (89). He has found that crystals of PbCl2, T1C1, AgCl, 
or AgBr, prepared in the ordinary way, always contain ultra-micro- 
scopic particles. Those particles are very bright so they are probably 
of metallic nature. To get a crystal of such a substance free from 
particles, it is necessary to pass a mixture of dry CL and hydrochloric 
acid gas through it in a molten state. 
Lorenz was able to get optically empty crystals that showed no 
particles. When exposed to light in the ultramicroscope, particles 
appeared. They are formed by dissociation processes. He found 
that he could get a system of the same kind by melting PbCL and 
introducing a piece of metallic lead into it. If we make such an FOB MATION OF THE COLLOID PABTICLE 
67 
experiment in a test tube of hard glass, melting the PbCL, and 
putting in a piece of lead, brown clouds are formed, and when mixed 
with the molten salt, these give rise to a brown liquid. When we 
cool and examine it in the ultramicroscope, -we find numerous bright 
particles probably of Pb. As yet we have not been able to explain this 
process. It is necessary to heat up to about the boiling point of 
lead, so that lead gas .is given off. We do not know if this is only a 
condensation process in the liquid or if it is some kind of a dissocia- 
tion process. Similar phenomena have been observed in electrolysis. 
When we electrolyze pure PbCl2, we get a dark brown product con- 
taining small metallic particles. 
Another very interesting case of dissociation processes is the forma- 
tion of the blue rock salt. Siedentopf showed that if we expose 
pieces of NaCl (rock salt) to cathode rays, we get a blue or purple 
coloration. When examined in the ultramicroscope, we find that 
there are bright particles present probably consisting of metallic 
Na (90). They seem to be oriented along the lines of cleft of the 
crystals, so probably when in the dissociation process the Cl is set 
free it can only escape leaving free Na at places where there are 
free crystal surfaces but not within the crystal lattice. Blue rock 
salt of exactly the same kind has been found in the salt mines, 
although not very often. This natural product has been studied 
in the ultramicroscope, and shows the same bright particles. Of 
course, it is very improbable that the salt has been exposed to 
cathode rays of an intensity high enough to produce coloration. The 
explanation might be that it has been exposed to the radiations from 
radio-active substances. Most of the natural blue rock salt has been 
found in Austria, a country rich in radium ore. 
Siedentopf found that quite the same kind of blue rock salt could 
be produced by heating crystals of rock salt in a high vacuum and 
exposing to sodium vapors. Fig. 21 shows the arrangement. A 
quantity of pure sodium distilled in high vacuum is at the bottom-B 
of the tube and some rock salt crystals placed higher up at A. If 
we heat this in an electric furnace, the sodium is partly evaporated 
and colors the rock salt blue and red. It is difficult to explain this 
phenomenon. We do not know if it is only a condensation of the 
sodium vapor within the fine clefts of the rock salt crystals or if 
the phenomenon is due to some sort of chemical action of the sodium 
vapors on the NaCl. 
The most important of dissociation processes is, of course, the dis- 68 
COLLOID CHEMISTRY 
sociation of the silver halides. Lorenz found that if we expose an 
optically empty crystal of silver bromide to light, there are produced 
particles that can be seen in the ultramicroscope and they, no doubt, 
consist of metallic silver. If we expose silver halides to a very feeble 
illumination no particles can be seen but upon treating the halide 
with a developer, i.e. a reducing agent of proper reducing potential, 
reduction to metallic silver takes place. Probably there are present 
very small silver particles in such feebly exposed halide crystals- 
particles too small to be seen in the ultramicroscope. 
Fig. 21.-Tube for preparation of blue rock salt. 
The photographic process is very likely based on the formation 
of such very small silver particles in or on the surface of the silver 
halide grains in the film, and the writer, therefore, thinks he is justi- 
fied in giving a short report on the recent advances in the study of 
the photographic processes under the heading of formation of dis- 
perse systems by dissociation. 
The film of an ordinary photographic plate or film consists of a 
layer of gelatine in which are imbedded small crystals of silver 
halides. The gelatin film is supported by a glass plate or by a cel- 
luloid film. Ordinary photographic plates usually contain silver bro- 
mide with about 2 per cent of silver iodide. Such an ordinary 
photographic plate contains a very large number of crystals in a FORMATION OF THE COLLOID PARTICLE 
69 
series of different layers throughout the whole depth of the film. 
It is very difficult to study such a system because if a beam of light 
is sent through the plate, there is scattering, refraction and absorption 
of the light. The illumination along a line orthogonal to the plane of 
the plate is not constant. Some of the light is deviated and different 
crystals are exposed to different intensity of illumination. The investi- 
gations of the photographic process were until quite recently based on 
the study of ordinary plates, and I think that this is the explanation 
to the very slow progress made. 
We have attempted to study the emulsion used for photographic 
plates by coating very thin films on glass plates so that the halide 
grains are practically in a single layer. In such single layer plates 
the action of the light and of the developer is practically uniform. 
An important question to solve before we can start a study of the 
light action on the grains is how the reduction of the grain takes 
place in the developer. Does the development go on until the whole 
grain is reduced to silver, or do only parts of the crystals become 
reduced? Sometimes the halide grains are rather close together. 
Then the question arises whether, when an adjacent grain begins to 
be reduced, this reduction is transferred to the grains near to it or 
not. I have tried to answer this question by taking microphotographs 
of the same grains before developing and after developing. To be 
able to do this without affecting the grain too much by the strong 
illumination in the photomicrographic process, it is necessary to use 
dark red light. Then the reduced silver was dissolved away by means 
of a silver solvent (potassium permanganate or potassium chromate). 
Figure 22 shows a photograph of the single layer plate with a special 
emulsion of small spherical grains (a) before developing, (b) after 
developing, and (c) after dissolving away the metallic silver. 
We can see that all the grains that have been attacked by the 
developer are indeed completely reduced to silver for in such places 
where Fig. b indicates reduction (black irregular grain), Fig. c shows 
complete disappearance of the grain (91). 
A statistical study of the percentage number of grains remaining 
unchanged after development in contact with developed grains has 
given the result that there is no affecting of a grain by the reduc- 
tion process in another grain close to it. According to experiments 
in the Eastman Kodak Laboratory, there is, however, such a transfer 
in cases where the crystals are in actual molecular contact with each 70 
COLLOID CHEMISTRY 
other, i.e. where the grains have actually become part of one and 
the same crystal building (92). If there is a thin layer of gelatin be- 
tween the particles, there is no development of one grain by the other. 
We have also measured the diameter of the grains left after de- 
veloping and dissolving away of silver and compared this value 
with the diameter, of the same grains before development. It was 
found that the diameter of those grains is not changed even if they 
are close to a grain that has been reduced. It, therefore, seems that 
at least in certain cases the halide grain is the unit in the photographic 
process. It is either developed as a whole or not developed at all. 
Fig. 22.-Photomicrograph of the grains of a photographic emulsion: a before 
developing; b after developing; c after developing and dissolving away the 
reduced silver. 
There are, however, cases where a complete reduction of the grains 
does not take place. If we add very much potassium bromide to our 
developers, and study the grains before and after developing and after 
removing the silver, some of the remaining grains have become irregu- 
lar in shape showing that part of them has been developed and then 
dissolved. This is rather important for practical photographic work, 
for the structure of the silver in the negative depends on whether 
the whole halide grain has been reduced or not. If it is reduced 
only partly, we get another kind of graininess in the negative. So 
for certain processes it is better to use a developer that does not FORMATION OF THE COLLOID PARTICLE 
71 
reduce the whole grain but just part of it. From this practical point 
of view, it is important to study the conditions for complete and in- 
complete development. 
After the study of the reducibility of the grain, we will return 
to investigate the mechanism of the light action. Until a few years 
ago such investigations were limited to the study of the so-called 
characteristic curve or blackening curve of the plate under various 
conditions. Diagrams were plotted with the log of exposure as 
abscissae and the so-called density or light absorption coefficient of 
the plate as ordinates. The density, however, is not very char- 
acteristic for the light action; it depends on many other factors and 
does not mean very much from a theoretical standpoint. One of 
the methods of studying the plate that we now use was introduced 
by the writer (93) and by Slade and Higson (94) in England. The 
point in this method is not to study the density but to study the per- 
centage number of developed grains. If we use a developer, that 
either reduces the whole grain or does not reduce it at all, then this 
number is quite definite and independent of the structure of the 
reduced silver. We can plot the exposures as abscissae and the per- 
centage number developable grains as ordinates. In this way we get 
a curve characterizing the light action much better than the old black- 
ening curve. The technique used in my laboratory to find these 
percentage curves consists (1) in coating the emulsion to be studied 
in a thin layer on a glass plate, (2) in making different exposures 
on the plate, (3) in developing with a suitable developer, (4) in dis- 
solving the silver using a silver solvent such as potassium perman- 
ganate, and then (5) in counting the number of grains on the exposed 
and on the unexposed parts of the plate. By subtracting the num- 
ber of grains remaining on the exposed parts from the number on 
the unexposed part, we get the number of grains that have been 
made developable. Usually an emulsion consists of grains of various 
sizes and in such a case we must study the percentage number of 
developable grains for the different sizes of grains within the emulsion. 
If we use this method to study the action of various kinds of radia- 
tion, we find the following. 
Let us first consider the a-rays from a radioactive substance 
The a-rays represent the highest amount of energy that we can 
concentrate in a single ray. We have determined the percentage 
number of developable grains of a certain size after exposing them to 72 
COLLOID CHEMISTRY 
the a-rays and found that this number could be expressed by a formula 
of the type 
P = 100(1-e'kt) 
where t is the time of exposure and k a constant proportional to the 
projective area of the halide grains (Fig. 23). We also measured by 
means of the scintillation method the actual number of a-particles 
striking the plate and calculated the number of a-particles per pro- 
jective area of the halide grains per sec. This value was found equal 
to the constant k. Now if the average number of particles striking 
the grain is kt the percentage probability that no a-particle shall 
strike a grain is 100. e'kt. The probability that a grain shall be struck 
- Number of 
<*part/c/es 
Number of 
Pparf/c/es 
fx/X>SL/re 
Fig. 23.-Variation of percentage number of developable grains with exposure 
in the case of: a a-rays; b p-rays; c light. 
by one or more than one a-particle is therefore 100(1 - e"kt), that 
is equal to our P. Thus to make a grain developable when ex- 
posed to a-rays, it is sufficient that the grain is struck by one single 
a-particle (95). 
If we pass on to rays of less energy, we come to the |3-rays, i.e. 
electrons moving with high velocity. We have studied the |3-rays 
from radium C and tried to determine the percentage curve. It 
seems that at least with the swift |3-rays, we get an exponential curve 
as in the case of a-rays (Fig. 23). We figured out the number of 
P-rays striking the grains and tried the formula P = 100(1- e~kt). 
It was found that though the curve could actually be expressed by 
an equation of the same type, the exponent kt was not equal to 
the number of the |3-rays striking the grain. To make a grain de- 
velopable, it is necessary that a much higher number of |3-rays strike 
the grain (95). 
If we go over to the non-corpuscular radiations and proceed in the FORMATION OF THE COLLOID PARTICLE 
73 
order of decreasing energy, we first arrive at the y-rays and the 
X-rays of high frequency. So far only a few preliminary tests have 
been made with these radiations. It seems that also in this case we 
get an exponential curve expressing the relation between exposure 
and percentage number of developable grains. Passing on down to 
the radiations of low frequency or to ordinary light, we find that we 
get a curve of another type-a curve with an inflection point (Fig. 
23) (96). In the opinion of the writer, one of the chief problems 
in the study of the photographic process is to find out why we get 
Fig. 24.-Photomicrograph of the developable centers, 
a different kind of curve with low frequency. The best way of attacK 
is probably to fill out the gap between the extremely high and ex- 
tremely low frequencies, i.e. to determine the curve for long-waved 
X-rays or short-waved ultraviolet light. Another important way 
of attacking the problem is to study the photographic action of slow 
electrons. 
The second of the new methods for investigating the photographic 
process is to study the so-called developable centers (97). If we 
expose a single-layer plate to a-rays, and develop it with a suitable 
developer, e.g. oxalate developer, for a short time, say 15 sec. and 
take a photomicrograph in red light, the halide grains are apparently 
unchanged (Fig. 24a). Now dissolve away the halide with an ordi- 74 
COLLOID CHEMISTRY 
nary fixing bath and take a picture of the same spot of the specimen. 
It shows small black points (Fig. 24b) and if we print a faint image 
of the halide grains over the picture of those points, we find that they 
are situated on the grains (Fig. 24c). It is hard to get back to 
exactly the same spot in the plate and to the same grains. To make 
this easier, I have used the trick of mixing the emulsion with fine 
ground asbestos. Those fine needles give excellent reference lines. 
These points or centers represent the starting points for the reduc- 
tion of the grains. They of course increase in size during develop- 
ment, but only slightly in number. Various grains contain various 
numbers of centers and for a certain size class of grains, the centers 
are distributed according to the laws of chance, as shown by the 
following Table IX. 
TABLE IX 
Distribution of Developable Centers on the Grains of a Photographic 
Emulsion after Exposure to ci-Rays 
765 grains were studied and divided into two classes, the first containing the 
grains with a diameter less than 1.18 p and the second those with a diameter 
more than 1.18 p. 
Size Class 1. 
Number of grains 263. 
Average radius of grain 0.479 p. 
Average number of centers per grain 
0.461. 
Size Class 2. 
Number of grains 502. 
Average radius of grain 0.727 p. 
Average number of centers per grain 
1.136. 
Number of 
Number 
Number 
Centers pei 
of 
Frequency in Per Cent 
of 
Frequency in 
Per Cent 
Grains 
Grains 
Obs. 
Calc. 
Grains 
Obs. 
Calc. 
0 
168 
64.0 
63.1 
165 
32.9 
32.2 
1 
73 
27.8 
29.0 
178 
35.5 
36.6 
2 
18 
6.8 
6.7 
103 
20.7 
20.8 
3 
4 
1.5 
1.0 
41 
8.0 
7.9 
4 
12 
2.4 
2.2 
5 
3 
0.6 
0.5 
Analogous experiments with grains exposed to the action of X-rays 
or ordinary light gave the result that also in those cases the develop- 
ment only set in at a few points of the halide grain and that those 
points were distributed according to the laws of chance. Experiments 
on photographs of those centers at different stages of development 
show that such a center converts the whole grain into silver. That 
is, the necessary condition for the development of the halide grain is 
that it must contain at least one such developable nucleus. If v is 
the average number of centers per grain, we get the probability of 
the grain containing at least one developable center by subtracting cp FORMATION OF THE COLLOID PARTICLE 
75 
from the total probability or 1. Thus the percentage number of 
developable grains ought to be 
P = 100 (1 - e"). 
We have compared the value for the percentage number that we get 
from the calculation based on the direct determination of the centers 
with that based on the counting of the percentage number of develop- 
able grains according to the procedure as just given. The two curves 
are affine, the values calculated from the number of developable cen- 
ters being slightly lower according to the impossibility of making all 
the centers visible without growing them together to an inextricable 
network of silver. 
By a statistical study of the distribution of the centers within the 
central and the outer part of the grains, as shown in the photomicro- 
graphs, the writer was able to prove that the developable centers, 
or at least the centers that are responsible for the developability of 
a halide grain, are located in the surface layer of the halide grains. 
The number of developable centers per unit area of the halide 
grain should, according to the above experiments, determine the sen- 
sitivity of the silver halide material of the grains. Experiments by 
the writer and Andersson show that this number is indeed fairly con- 
stant for grains of different size within the same (unmixed) emulsion 
(Table X), but varies enormously from one emulsion to another. 
TABLE X 
Percentage Number of Developable Grains and Number of Developable 
Centers in a Photographic Emulsion 
Unit exposure =1=1 sec. at 100 cm. distance from the glowing ball of a 
30 c.p. pointolite lamp. 
Average Area 
of Grain = a 
Exposure 
1 = 1.0 
Exposure 
1 = 1.56 
P 
V 
v/a = c 
P 
V 
v/a = c 
24.2 X 10"'cm2 
38.5 
0.48 
20 X 10" 
61 
0.94 
39 X 10° 
46.5 X 10"' 
56 
0.82 
18 X 10° 
85 
1.90 
41 X 10° 
78.1 X 10"' 
77 
1.47 
19 X 10a 
92 
2.59 
33 X 10a 
Of course there may be cases where all the grains in one and the 
same emulsion are not comparable, i.e. cases where the different grains 
have been formed under different conditions and, therefore, are built 
up of different silver halide material. Such an emulsion actually 
represents a "mixed" emulsion. 
If we sum up the results arrived at by using these new methods 76 
COLLOID CHEMISTRY 
for studying photographic processes, we have the following facts. 
The halide grain is the unit of the photographic process. At least 
under certain conditions, it is made either completely developable or 
not developable-we have simply to measure the percentage number 
of developable grains. For a-rays and ^-rays we probably have the 
same kind of curve-the exponential line. In the case of a-rays, the 
exponent is actually equal to the number of a-rays striking the grain; 
in the case of |3-rays, the number is smaller. It has been possible 
to make the starting points of development visible. Those points 
or developable centers are comparatively few in number and they 
increase with exposure. At least one center is necessary to make a 
grain developable and accordingly the percentage number of develop- 
able grains for a certain exposure is given by the formula 
P = (100 -e"). 
We can calculate the average number of centers from the number of 
developable grains. If we trace the curve showing the relation be- 
tween exposure and number of centers per unit area of grain, we get 
for the a- and |3-rays a straight line, and for light a curve that at 
first is convex and then goes over into a straight line. For a- and 
probably for [3-rays, this number means the number of a- respectively 
|3-particles absorbed per unit area of the surface of the grain and is 
probably the same even for different emulsions. In the case of light, 
however, we get different curves for different emulsions. 
To explain the nature of the developable centers, three different 
hypotheses have been put forward. (1) The centers are a chance 
product of development (98). The reduction must start somewhere 
and it starts at those points. Against this assumption could be said 
that if they are a chance product of development, it is rather surpris- 
ing that they increase but slightly with time of development and 
that their absolute number is so small. (2) The centers are present 
in the grains as especially light sensitive points already before ex- 
posure (99) (100). (3) The number and distribution of the centers 
are entirely due to the action of the radiation striking the halide 
grains (99) (101). 
I think we can discard the first hypothesis as rather unlikely to 
account for the phenomena observed. How about the two others? 
Toy is of the opinion that the centers are present in the grains before 
exposure and constitute the only light sensitive parts of the grain. 
They should be very few in number, of different sensitivities, and have FORMATION OF THE COLLOID PARTICLE 
77 
their sensitivity given by a distribution or frequency curve. Now, 
this extreme form of hypothesis (2) seems to me rather improbable. 
How can we account for the fact that the percentage number of 
developable grains in the case of exposure to a-rays can be calculated 
upon the assumption that each a-particle striking a grain makes it 
developable-that is, that every grain struck by one or more than 
one a-particle is made developable? If the sensitive spots were so 
few as Toy assumes them to be, only very few a-particles would have 
a chance to hit a sensitive spot of the grain. Silberstein favors the 
view that a single light quantum is sufficient to form a developable 
center, but as recent experiments in the Eastman Kodak Laboratory 
seem to indicate that several hundred absorbed quanta are required to 
make a grain developable, he modifies his hypothesis a little, assum- 
ing a limited number of sensitive spots in the grain. Now, as already 
pointed out by the writer and Andersson, the fact that the curves 
giving the relation between exposure and percentage developable 
grains for light have a very pronounced inflexion point, shows that it 
is impossible to account for the formation of the developable centers 
assuming that a single light quantum is able to produce a developable 
center. 
It seems to me that all the facts so far known may be explained 
on the basis of the following hypothesis. The surface of the halide 
grain is capable of supplying the material for the formation of a 
developable center in all its points, but the sensitivity-defined as 
the least amount of energy required to make a certain spot reducible 
by a developer of a certain reduction potential-varies from point to 
point considerably. The variation in sensitivity is probably due to 
the action of the gelatin and other substances added to the emulsion, 
and to the way of making the emulsion. 
The energy of the a-particles is high enough to produce a develop- 
able center-probably an ultramicroscopic silver particle big enough 
to act as a condensation center-wherever it strikes the grain. We 
accordingly get the exponential curve and the number kt in the 
formula 
P = 100(1 -ekt) 
is equal to the number of a-particles striking the grain. The energy 
of a p-particle or of a high frequency quantum (short waved X-rays) 
is still high enough to produce a developable center; but every p-parti- 
cle and every X-ray quantum striking the halide grain does not give 78 
COLLOID CHEMISTRY 
off energy enough in the surface layer of the grain. We therefore 
get an exponential curve obeying the above equation, but kt is less 
than the number of ^-particles or of quanta striking the grain, or 
even absorbed in the grain. It is also possible that not all the spots 
of the halide grain surface are sensitive enough to (3-particles or X-ray 
quanta. The energy of a quantum of ordinary light is too small to 
give a developable center. It is necessary that a certain minimum 
number of light quanta are absorbed within a certain maximum area 
of the grain surface to produce a developable center. Hence we get 
a curve with an inflexion point, and a big number of quanta must be 
absorbed per grain to make a developable center. 
This assumption would involve the hypothesis that those centers 
or starting points would probably consist of a little nucleus of silver, 
a tiny colloid silver particle, and that it is necessary that this silver 
particle reach a certain minimum of size before it can act as a 
condensation nucleus in the process, just as Zsigmondy has found 
that the gold particles must reach a certain size to act as nuclei in 
the gold reduction process. 
Double Decomposition.-The last chapter on the methods of pre- 
paring colloids includes the process of double decomposition. Under 
this head we have the formation of the oxide sols by hydrolysis, the 
formation of sulphide sols by treating soluble salts with hydrogen 
sulphide and different kinds of processes founded on the formation 
of insoluble salts. 
The mechanism of the formation of disperse systems by double 
decomposition has been studied very carefully by Oden in the case 
of formation of BaSO4 from solutions of Ba(SCN)2 and (NH4)2SO4. 
He measured the distribution of size of particles by means of the 
self-recording sedimentation balance constructed by him some years 
ago (1916) and tried to find out the influence of the various experi- 
mental conditions upon the degree of dispersion of the system formed, 
viz., on the form of those distribution curves (102). Oden found 
that the formation of aggregates is one of the principal causes of error 
in such investigations. To prevent the formation of aggregates or 
to peptize the aggregates already formed, he added potassium citrate 
to the sols. As shown by the diagrams, Fig. 25, where the area be- 
tween ordinates drawn from two points on the abscissae axis denotes 
the mass of disperse phase in the radius interval in question, the 
degree of dispersity rises with concentration, i.e. with the degree of FORMATION OF THE COLLOID PARTICLE 
79 
supersaturation. It also increases with decreasing temperature, prob- 
ably due to the decrease in solubility (Fig. 26). 
The formation of colloid solutions by precipitating with hydrogen 
sulphide has played a very prominent part in the history of colloids. 
Fig. 25.-Variation of distribution of size of particles with concentration of 
reacting ions (after Oden). 
Linder and Picton prepared arsenious sulphide sols by treating As2O3 
solutions with hydrogen sulphide and were able to get sols of varying 
opacity by varying the concentration of the As2O3. They assumed 
that these sols are built up of particles of different sizes so that the 
sols prepared from dilute As2O3 solutions contain smaller particles 
than those from concentrated As2O3 solutions (103). Borjeson, work- 80 
COLLOID CHEMISTRY 
ing in the laboratory of the writer, was able to prove that this is 
actually the case (104). 
Table XI gives the size of the particles in As2S3 sols prepared from 
As2O3 solutions of various concentration. 
Now, in the case of the formation of BaSO4 sols, we found that 
Fig. 26.-Variation of distribution of size of particles with temperature 
(after Oden). 
the size of particles decreased with increasing concentration and here 
we find quite the reverse. In the gold reduction processes also, the 
size of particles increased with increasing concentration. The ex- 
planation might be that in such cases where the reaction takes place 
very rapidly, e.g. in the formation of BaS04 sols, the velocity of 
formation of nuclei rises more rapidly with concentration than the 
velocity of crystallization, while in cases where the reaction goes on 
slowly, e.g. in the formation of As2S3 sols or gold sols, the rate of FORMATION OF THE COLLOID PARTICLE 
81 
TABLE XI 
Size of Particles in Arsenious Sulphide Sols 
Concentration of As2O3 
Radius of Particles of As2S3 
1 X 10'2 normal 
39 jxjx 
5 X 1(T4 " 
16 " 
1 X 10'4 " 
11 " 
crystallization rises more rapidly with concentration than the pro- 
duction of nuclei. Another possibility is that in such a case as the 
As2S3 sols, we are dealing with secondary particles consisting of aggre- 
gates of primary particles and that the size of those aggregates are 
determined by coagulating factors. If they are, it would probably 
mean that the size would increase with concentration even if the size 
of the primary particles decreased with increasing concentration. 
Oxide sols can be prepared by hydrolysis of the salts, either by 
diluting the solution, or by dialysis. Many of Graham's sols were 
made by hydrolysis and dialyzing the mixture. A very striking ex- 
periment illustrating the formation of a sol by hydrolysis can be made 
in the following way. A few drops of concentrated ferric chloride is 
mixed with water so as to give an almost colorless solution. If this 
solution is then heated it is hydrolyzed and the oxide particles are 
condensed to colloid particles. Now the light absorbed in the colloid 
is enormous compared with that absorbed in the molecular solution, 
so that the formation of the sol is clearly shown by the darkening 
of the liquid. It is possible to make ferric oxide sols of different 
degrees of dispersity by using different concentrations of the chloride. 
We get just the same relation between the degree of dispersity as in the 
case of the formation of sulphide, i.e. we get smaller particles at the 
low concentrations (105). 
There are, of course, a large number of other double decomposition 
reactions which have been used for the preparation of colloids, but 
they have not been studied very thoroughly from a theoretical point 
of view. Among them are some of Graham's classical methods of 
preparing colloids described in his first paper "Liquid Diffusion Applied 
to Analysis" (1). Silicic acid sols were prepared by decomposing 
sodium silicate by hydrochloric acid and dialyzing. Several oxide 
sols he made by precipitating the oxide from a soluble salt as a 
coagulum and then peptizing and dialyzing. 
Sols of the silver halides have been prepared by reaction between 
silver nitrate and a soluble halide. Lottermoser studied this reaction 82 
COLLOID CHEMISTRY 
and showed that an Agl sol formed in a solution containing an excess 
of KI has its particles negatively charged while a sol formed in 
excess of AgN03 has positive particles (106). 
Some reactions of double decomposition in organic solvents have 
been utilized for the preparation of sols of such substances which are 
too soluble in water to be stable as hydrosols. Thus Paal and his 
co-workers have prepared colloids of NaCl, NaBr, Nai in ben- 
zene (107). 
Purification 
When we speak of the purity of a colloid, we, as a rule, mean 
the relation between the disperse phase and the crystalloids, espe- 
cially the electrolytes present. In order to prepare colloids free from 
electrolytes, we have to use very clean vessels-vessels of hard glass 
and clean them by treating with chromic acid and then with hot water 
or steam for hours. The purity of the water used in preparing 
hydrosols and the organic liquids used for preparing organosols is, 
of course, very important. The properties of water from the stand- 
point of colloid chemistry have been studied, but so far we do not 
know very much about this subject. Impurities often play a promi- 
nent part in the formation of the sols. Organic contamination, for 
instance fats and oils, even if present in very small quantities com- 
pletely. change the properties of a gold sol prepared by the nuclear 
method and this makes it necessary to redistill the water with addition 
of potassium permanganate repeatedly and condense it in a still of 
best material, e.g. quartz. Silver cannot be used because of the solu- 
bility of silver oxide in water. Water condensed in a silver vessel 
contains silver particles formed by reduction of the silver oxide and 
they of course act as nuclei. Silicic acid as an impurity in water 
also must be avoided. Very often we get silicic acid from the glass 
of the vessel. 
If we wish to prepare organosols with a disperse phase that is 
easily oxidized, it is necessary that the liquid should be dry and free 
from oxidizing agents. 
For some purposes, it is necessary to use water that is optically 
empty, i.e. free from suspended particles. It seems that one of the 
best ways to purify water from suspended particles is to filter it, 
using certain precautions, through collodion membranes (108). Cen- 
trifuging may also serve this purpose. If sufficiently pure water is 
allowed to stand for some months in a bottle kept at very constant FORMATION OF THE COLLOID PARTICLE 
83 
temperature, a water comparatively free from particles can be drawn 
off by means of a syphon. Completely particle-free liquids can only 
be gotten by distillation without boiling in vacuum (Martin and 
Kenrick) (109). 
In certain cases, when preparing a colloid, it is necessary that 
there be a certain amount of ions present to prevent coagulation and 
to give stability. These ions must be left, of course. In many cases, 
however, the concentration of the ions in a sol freshly prepared is 
much higher than is necessary or even good for the stability. One 
of the methods of removing such superfluous ions consists in pre- 
cipitating and redissolving the precipitate. 
A sulphur sol prepared with sodium thiosulphate and sulphuric 
acid can be purified by precipitating with NaCl and dissolving the 
coagulum in water and re-precipitating and dissolving again. In this 
way we can remove the sulphuric acid and the sulphate. Silver col- 
loid has been successfully purified by precipitating with ammonium 
nitrate, dissolving, and re-precipitating with alcohol. 
When using centrifuging to separate the coagulum from the liquid, 
it is necessary to choose the centrifugal force not too high so that 
the particles are not pressed together too heavily. If we use very 
high centrifugal force in removing the coagulum from the liquid, 
the coagulum sometimes becomes irreversible-the particles are pressed 
too tightly together so that they coalesce. 
One of the oldest and most generally used methods of purifying 
colloids is dialysis, already used by Graham in 1861. This method 
consists in separating the sol to be purified from the dispersion medium 
by a suitable membrane, permitting the crystalloids to diffuse through 
but holding back the colloid particles. Many different kinds of 
dialyzers have been invented. One of the most recent forms is the 
dialyzing arrangement used by Sorensen for purifying proteins and 
shown in Fig. 27 (110). The pressure outside the collodion bag is kept 
a little lower than the inside to compensate for the osmotic pressure 
and prevent the protein sol from rising too high. A series of dialyzers 
were arranged in parallel and the whole could be kept at low tem- 
perature-at about -f- 5° C. to cut down the hydrolysis as much as 
possible. 
Of importance in dialysis, of course, is the nature of the mem- 
brane. Zsigmondy and his co-workers have studied the properties 
of different membranes from the standpoint of dialysis (111). They 
compared the efficiency of the collodion membrane with the efficiency 84 
COLLOID CHEMISTRY 
of parchment paper. Collodion membrane can be made with pores 
of different size to be used for sols of different degrees of dispersion 
Fig. 27.-Sorensen's dialyzer. 
according to the concentration of the collodion solution used for mak- 
ing the membrane. 
In a certain series of experiments he found the following values. 
TABLE XII 
CoMPA-nxisON BETWEEN DlALYZING POWER OF DIFFERENT MEMBRANES 
Collodion 
Parchment Paper 
Time of 
Relative Amount of 
Time of 
Relative Amount of 
Dialysis 
Electrolytes Present 
Dialysis 
Electrolytes Present 
0 
205 
0 
193.5 
D4 
12.5 
3 
77.2 
2^2 
2.5 
6 
36.8 
3^ . 
1.0 
9 
20.5 
5 
0.5 
21 
3.0 
6 
0.13 
24 
1.5 
7 
0.08 
30 
0.75 
8 
0.04 
45 
0.13 
9 
0.03 
51 
0.05 
20 
0.004 
77 
0.01 FORMATION OF THE COLLOID PARTICLE 
85 
As shown by the table, the efficiency of the collodion is much 
greater than the efficiency of parchment paper but it depends on how 
the collodion membrane is prepared. To get a very effective dialyzer 
with very large pores, we have to use much alcohol and little ether in 
the collodion solution. Of course, the pores must be adjusted so that 
they are not wide enough to let the particles of the colloid through. 
Instead of letting the electrolytes diffuse through the membrane, 
we can apply pressure and filter part of the dispersion medium con- 
taining the electrolytes through it,-this is ultrafiltration (112) (113). 
Fig. 28.-Ultrafiltration apparatus for low pressure. 
The ultrafiltration process has been worked out recently, especially 
by Bechhold (114). Fig. 28 shows a simple kind of ultrafiltration 
arrangement for low pressure. The sol is poured into a collodion 
bag and water pressure applied. 
Fig. 29 shows another type of ultrafiltration apparatus-the Bech- 
hold arrangement-which is used with high pressures. The filter is 
placed on top of a supporting metal gauze and the colloid introduced 
into the vessel. The machine is meant to be used with high pres- 
sure, say 15 atmospheres. The many metallic surfaces involve the 
danger of contamination and therefore the Bechhold apparatus can 86 
COLLOID CHEMISTRY 
hardly be used for filtering sensitive inorganic sols. For purifying 
organic sols such as proteins, it has however proved useful. 
Ultrafiltration and dialysis can also be combined (Wegelin) as 
Fig. 29.-Bechhold's ultrafiltration apparatus for high pressure. 
shown by Fig. 30 (115). The funnel a has the membrane m on top 
pressed against the plate P and is completely filled with liquid when 
the filtration takes place. The pressure is applied at D. Ultra- 
Fig. 30.-Wegelin's apparatus for combined dialysis and ultrafiltration 
filtration takes place and at the same time there is ordinary diffusion 
through the membrane. 
Another method of using a membrane in preventing the colloid 
particles to escape during purification is the so-called electro-dialysis FORMATION OF THE COLLOID PARTICLE 
87 
that has been developed recently. The principle is shown in Fig. 31. 
The vessel is divided into three parts A, B, C by two membranes 
permeable to electrolytes but not to the particles. A and C contain 
Fig. 31.-Arrangement for electro-dialysis. 
the pure dispersion medium. By changing the water in A and C 
from time to time the products of electrolysis are removed and the sol 
contained in B gradually purified. 
Fig. 32.-Oden's apparatus for electro-dialysis. 
Collodion membranes can be used in the electro-dialysis. Fig. 32 
shows such an arrangement used by Oden for the purification of sul- 
phur sols (116). The collodion membrane is fixed to the tube E. 
After the whole apparatus has been filled with water, a sulphur sol 88 
COLLOID CHEMISTRY 
of high concentration is introduced through C and poured down form- 
ing a layer at H. A current is applied and the negatively charged 
particles are carried towards E while the Cl of the electrolyte, HC1, 
gathers around D and is removed from time to time. After a certain 
time the stopcock B is opened so that air can be blown in at A. 
In this way the content is divided into two parts and the purified 
colloid solution of sulphur can be taken out from the knee below E. 
Recently a new membrane material for electro-dialysis experiments 
has been brought on the market by the Electro Filtros Company, 
Rochester, New York. These membranes consist of plates of porous 
SiO2 material and the pores of the plates are filled with a gel of silicic 
acid. These membranes have been used successfully for purifying 
gelatine. 
,g/oss WOo/ 
Fig. 33.-Arrangement for purifying colloids by means of the Hildebrand cell 
Another rather interesting form of electro-dialysis has been used 
for preparing sols of silicic acid (117). It is a modification of the 
Hildebrand cell used in electrochemical work. In Fig. 33 A repre- 
sents a glass vessel and B a layer of mercury. In the center we 
have a glass tube C dipping into the mercury. The sol to be purified, 
sodium silicate for instance, is poured into it. We have water in the 
outer vessel and a connecting wire so that the mercury forms the 
cathode. In the inner vessel we have a rotating anode, say of plati- 
num, such as is used in electro-analysis. If we take a solution of 
sodium silicate and apply a potential, it will be electrolyzed and the 
sodium set free will amalgamate with the mercury. The motion of 
the inner or anode liquid is transferred to the mercury so that the 
amalgam gradually reaches the outer liquid where it is decomposed. FORMATION OF THE COLLOID PARTICLE 
89 
We can facilitate this decomposition by having glass wool in the 
outer vessel in contact with the water. The silica remains in the 
anode chamber and forms a colloid solution. The progress of the 
process can be measured by the drop in the current. If we start with 
a current of 0.55 ampere, in 1 hour we get down to 0.18 amp., and 
in 120 minutes to 0.08 amp.-a rather rapid purification. 
Sedimentation has been used to purify colloids but, of course, that 
method can only be applied in cases where sufficiently rapid sedimen- 
tation can be attained, and there is always the danger of the particles 
gathering on the bottom at such high concentration that they form 
an irreversible coagulum. For the purification of a coarse-grained 
gold sol, this method has been used with success by Westgren (118) 
in the writer's laboratory and it was also applied for purifying gam- 
boge suspensions in Perrin's classical experiments on the Brownian 
movements. PART II 
THE COLLOID PARTICLE AS A MOLECU- 
LAR KINETIC UNIT 
The Brownian Movements 
At the time when Siedentopf and Zsigmondy constructed their 
first ultramicroscope, the ideas concerning the constitution of solu- 
tions were purely thermodynamical among leading physical chem- 
ists (119). Since the studies of Siedentopf and Zsigmondy, we know 
that the colloid solutions are built up of suspended particles. This 
would mean that such solutions would show no osmotic pressure and 
no diffusion. If we have a vessel divided into two parts by means of 
a membrane permeable to the dispersion medium but not to the col- 
loid particles, one would not, from the purely thermodynamical point 
of view, expect any change in the free energy on moving the mem- 
brane, i.e. on changing the volume of the sol. 
From the standpoint of the molecular kinetic theory, however, one 
would expect quite the same change in free energy as in the case of 
an ordinary solution-that is, the kinetic energy of suspended particles 
in a sol should, according to this view, be the same as the kinetic 
energy of a molecule. That is, the mean energy of the particle 
should, be 
3 RT 
2 • N 
where R is the ordinary gas constant, T the temperature, N the 
number of molecules per mol, or the so-called Avogadro constant. 
When it is measured in absolute units 
R = 83.19 X 10° 
and N = 6.06 X 1023 
That is, from the kinetic standpoint, we would expect the colloid 
solution to show osmotic pressure just like an ordinary solution. We 
must, however, bear in mind that the concentration is measured in 
mols per liter. A one molar solution of a colloid from the kinetic 
91 92 
COLLOID CHEMISTRY 
standpoint must contain per liter exactly N number of particles which 
is equal to the number of molecules per mol. This was pointed out 
by Einstein in his first classical paper on the Brownian movements 
in 1905 (120)-a few years after the construction of the ultramicro- 
scope by Siedentopf and Zsigmondy. He showed that according to 
the molecular kinetic theory, the colloidal solutions should give osmotic 
pressure and diffusion just as ordinary solutions, that there is no 
difference between a suspended particle and a molecule. The particles 
in a colloid solution are, according to the kinetic point of view em- 
phasized by Einstein, exposed to an incessant bombardment by the 
surrounding molecules and therefore these particles should move too. 
Single molecules we cannot perceive-provided they are not endowed 
with an abnormal great amount of energy as in the case of the 
a-particles from radioactive substances-but the particles of a colloid 
solution we can see. Thus they give us a direct insight into-or 
rather an image of-the world of the molecules. The microscopical 
phenomena give an image of the molecular ones. 
Hence the great interest connected with the investigations of the 
movements of the particles in colloid solutions. The study of these 
phenomena shows us a world-a microcosmos-with natural laws that 
are in part quite other than those which we are accustomed to from 
the macrocosmos we live in. As a matter of fact the Brownian move- 
ments represent as yet the sole domain of natural science where the 
predictions of the theory of probabilities could be tested to any great 
extent. 
The properties of colloids depend to a great extent on the move- 
ments of the particles and therefore the study of the Brownian move- 
ment is of great importance for the science of colloids in general. 
So, for instance, Smoluchowski on basis of the laws of the Brownian 
movement was able to deduce formulae for the velocity of coagulation. 
Osmotic pressure.-1The first phenomenon we have to expect in .a 
colloid solution from this standpoint is osmotic pressure, and it must 
be equal to 
p RT 
p=TTn 
where n is the number of particles per unit volume, for we get from 
the ordinary law of osmotic pressure 
p^RTc, COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
93 
where c is the number of mols per unit volume 
and c = 
N 
If we try to verify the assumption of the equivalence between a colloid 
particle and a molecule by measuring osmotic pressure, we find it 
to be a very difficult experiment, because of the exceedingly low 
osmotic pressure which we get when the actual number of particles 
is low, as in the case of colloid solutions of known degree of dispersity. 
If we use a gold sol, we can hardly get down to particles smaller 
than 1 pp.. If we calculate from a radius of 1 pp, and take the 
highest concentration we can hope to get, say 0.5 per cent, we get 
values for osmotic pressure expressed in water pressure that only 
amount to about 1 or 2 mm. It is exceedingly difficult to measure 
such small pressures and to be sure that the pressure is not due to 
crystalloid contamination present, e.g. slight amounts of electrolytes. 
The membranes wTe can use are not quite ideal; they always have a 
certain impermeability for electrolytes, and it therefore is difficult to 
be sure that the electrolytes present do not exert any osmotic pres- 
sure. Zsigmondy has made experiments with very fine grained gold 
sols and actually claims that he has been able to measure osmotic 
pressure (121). He also measured the size of the particles by means 
of the ultramicroscope and compared that value with that calculated 
from the formulae for the osmotic pressure. He has actually obtained 
values that check fairly well, but I think his experiments are not 
quite convincing. 
Diffusion.-The second phenomenon that we would expect in a sol 
according to the kinetic point of view is diffusion. For the diffusion 
constant of a colloid solution we get the expression 
N f 
where f is the frictional force acting upon the suspended particle by 
the molecules of the dispersion medium or the solvent. In the case of 
a spherical particle, we have 
f = Gjtqr 
where q is the viscosity of the medium and r the radius of the particle. 
The diffusion constant, D, is defined by the well-known diffusion 
equation 
de _ d2c 
dt - dx2 94 
COLLOID CHEMISTRY 
which expresses that the change of concentration with time is propor- 
tional to the change in the fall of concentration along the x-axis. 
In order to measure the diffusion and check the kinetic formula, 
we must know the solution of the diffusion equation. It can be solved 
in the following way, which has led to the construction of the ordinary 
tables that we use for calculating diffusion experiments (122). If 
we assume that the total height of the liquid = H, height of solution 
= h, the original concentration c0, we get the following rather com- 
plicated formula 
n - oo n2^2Dt 
h , „ c0 _ 1 . mth mix H2 
c - c0 + 2 - 2. - sm . cos -rr . e 
H it n H H 
n = l 
From this we can calculate the amount of the solute in different layers 
of the liquid. To facilitate the calculations, it is advisable to arrange 
the diffusion experiments so that we have the original height of the 
solution equal to of the diffusing column, i.e. H = 4 h. For this 
special case there are tables constructed so that if we know the amount 
of substance in the 4 layers in which the diffusing liquid can be 
divided, we can calculate D (123,124). 
In ordinary diffusion experiments it is, therefore, not necessary 
to use the primary solution of the equation. 
Measurements on gold sols of known radius of particles have 
been carried out by the writer with the object to test the kinetic 
formula (125). Fig. 34 shows the diffusion cylinder used. By means 
of the pipette B the volume of the sol could be run down under the 
dispersion medium. 
The apparatus was mounted in a thermostat in a room of con- 
stant temperature. After the diffusion had gone on for some time 
the diffusing column was divided into four parts. The stopcock 
Mi was turned to position 2 and by means of the side tube a and 
air pressure, the diffusing solution could be run out from the bottom 
of the tube D into small volumetric flasks of volume equal to *4 of 
the diffusion liquid. The concentration of the different layers was 
determined and from these values we can calculate the diffusion con- 
RT 1 
stant. By means of the equation D = . we can, if we 
J N fljtqr ' 
know the diffusion constant and the viscosity, calculate the radius 
of the particle. The diffusion experiments gave r = 1.29 pp. The COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
95 
radius of the particles was also determined by Zsigmondy's nuclear 
method, i.e. by depositing gold on the particles using them as crystal- 
lizing centers. This other method gave for the size of the particles 
Fig. 34.-Diffusion apparatus. 
1.33 p-p,. These two figures check as well as we can expect. In- 
versely, if we take the value 1.33 as the value of r and calculate 
the value of N, the Avogadro constant, we get 5.8 X 1023 for the 
Avogadro constant. The most probable value for N is about 
6.06 X 1023 (Millikan). 96 
COLLOID CHEMISTRY 
Another way of checking the kinetic theory by means of the diffu- 
sion experiments is to measure the concentration at different heights 
in the diffusing colloid. Suppose that we have a very thin layer of 
the diffusing solution under a high column of dispersion medium. 
In this case the diffusion equation can be solved in a much more 
simple way. We find that if Ci and c2 denote the concentrations 
at the heights xx and x2 
4Dt 
Ci = A * e 
x22 
" 4Dt 
c2 = A • e 
_ x22 - x? 
thus - = e ^Dt 
Ci 
That is, if we can determine the concentration at two different heights 
in the solution and if we know the time of diffusion and know the 
heights, we can calculate the diffusion constant D. 
Westgren carried out some series of measurements on selenium 
and gold sols in the writer's laboratory by means of this method (126). 
The concentration was determined by counting the number of par- 
ticles at different heights in the ultramicroscope. A dark field con- 
denser was used and the sol enclosed in a thin cell mounted on a 
microscopic slide. Before starting the diffusion measurements the 
particles were all brought down to the bottom of the cell by centri- 
fuging. The values of r calculated from the D-values agreed very 
well with the r-values of the particles determined by other methods. 
Sedimentation equilibrium.-The third of the fundamental phe- 
nomena that we expect to find in a sol according to the kinetic theory 
is the so-called sedimentation equilibrium. In any colloid solution 
there must exist an equilibrium between osmotic pressure or dif- 
fusion and the force of gravity. The force of gravity tends to draw 
the particles down to the bottom and the diffusion tends to spread 
them out in the liquid. After some time the two forces balance each 
other. 
Einstein (120) was the first to point out that we had to expect 
such a phenomenon, and later Smoluchowski (1906) (127) directed 
attention to the fact that in a colloid solution we have to expect 
exactly the same law as the hypsometric law for the decrease of COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
97 
atmospheric pressure with height. The hypsometric law is of the 
following form 
- ^g(x2 -xj 
p2 = Pi.e 
where M is the molar weight of the gas, g the gravity constant, R the 
gas constant, and T the temperature. 
Quite the same formula must hold for colloid solutions. We have 
only to write it in a form that gives us the molar weight in terms 
of the constants of the sol. The molar weight of a colloid is of 
course equal to the number of particles corresponding to the num- 
ber of particles in 1 gram-molecule multiplied by the apparent mass 
of the particle, or in the case of spherical particles 
4 
M = N. -7tr3(pp- pd) 
o 
where pp is the density of the particle and pd is the density of the 
dispersion medium. That is we get for the osmotic pressure of the 
sol 
N 4 
- g Jtr3(pp- pd) (x2 -xjg 
p2 = pi.e 
Now the osmotic pressure is proportional to the number of particles 
RT 
per unit volume according to equation p = -^-.n so that we can 
substitute for the osmotic pressure p the number of particles n, or 
N 4 
' - ^^(pp-pd) (x2 -xjg 
n2 = nx. e 
That means that if we know the number of particles in a sol in equi- 
librium at a certain height, we can calculate the numbers at any 
height if we know the heights, the radius and the difference in density 
between particles and dispersion medium. 
A very simple way of deducing the above formula has been intro- 
duced by Perrin who was the first to test this law experimentally for 
disperse systems (128). 
If we study a colloid solution in equilibrium in a cylindrical 
vessel and assume that the area of the vessel is 1 sq. cm., we have 
for the osmotic pressures at the heights xx and x2 
RT RT 
Px = ^-.nx ; p2 = -^-.n2. 98 
COLLOID CHEMISTRY 
Now let xx- x2 decrease to dx and we get 
. , , . RT / RT , RT , \ 
Pi - p2 = P - (p + dp) = n - (n + dn L 
or 
, RT j 
dp - ^--dn. 
This change in osmotic pressure when we pass from xx to x2 is bal- 
anced by the gravity force of the particles enclosed between the 
horizontal planes between xx and x2. If n is the number of particles 
per unit volume, this number multiplied by dx gives us the number 
of particles between the planes and the gravity force is 
4 
n.dx. - Jtr3g (pp - pd). 
That is we get 
^-.dn = n.dx. -itr3g(pp - pd) 
dn N 4 , . , 
- = - 3 ™*3g (pp - pd) dx. 
Integrated, this gives us the equation 
N 4 
- 3 ^r3 (pp - pd) (x2 - xx) g 
n2 = nx. e 
The first experimental tests of this equation were made by Perrin 
in 1908 (128). He tried to check the formula by measuring the num- 
ber of particles at different heights in a sol when sedimentation 
equilibrium had been reached and he also measured the radius of 
the particles. His determinations were made by means of a micro- 
scope with dark field condenser, so the distances between the heights 
x were of microscopic dimensions. 
Sedimentation Equilibrium in a Gamboge Suspension 
TABLE XIII 
X 
n 
in p 
Obs. 
Calc. 
a 
100 
a- 25 
116 
iio 
a - 50 
146 
142 
a- 75 
117 
169 
a -100 
200 
201 COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
99 
Table XIII gives an example of Perrin's experiments with gamboge 
suspensions. The number of particles is tabulated starting from 
the height where the number was 100. The agreement between ob- 
served and calculated values of n is fairly good but then the range 
of height is not very wide. 
Westgren made similar measurements in gold sols over a wider 
range of height (129). With a radius of particles of 21 pp, he found 
this law held from the point 0 to 1100 p-that is over a range of 
more than a millimeter. Some of his values are given in Table XIV. 
TABLE XIV 
Sedimentation Equilibrium in a Gold Sol 
Radius of Particles 
Radius of Particles 
= 26 ma 
= 21 p-fj. 
x in jt 
n 
x in p, 
n 
Obs. 
Calc. 
Obs. 
Calc. 
0 
889 
886 
0 
1431 
1176 
100 
692 
712 
50 
1053 
909 
200 
572 
572 
100 
779 
702 
300 
426 
460 
150 
532 
555 
400 
357 
369 
200 
408 
419 
500 
253 
297 
250 
324 
324 
600 
217 
239 
300 
254 
250 
700 
185 
192 
350 
189 
193 
800 
152 
154 
400 
148 
149 
900 
125 
124 
450 
112 
115 
1000 
108 
100 
500 
93 
89 
1100 
78 
80 
Perrin used most of his determinations to calculate the value of 
N or the Avogadro constant (130). He gives as his final figure 
N = 6.8 X 1023. His first determinations gave a higher value, about 
7.1, but in later experiments he obtained lower ones. Probably this 
figure is even now too high because Millikan's most reliable value is 
very close to 6. 
Westgren in his studies of the sedimentation equilibrium of gold 
and selenium sols also determined the Avogadro constant and actually 
obtained lower values than Perrin. He reached the same equilibrium 
from both sides, that is, (1) by allowing the sol to settle and, (2) by 
allowing the particles to diffuse up from a concentrated layer of sol 
at the bottom of the cell. Some of his values of N for the gold 
sols tabulated below (Table XV) give an idea of how much the in- 
dividual determinations fluctuate (131). 100 
COLLOID CHEMISTRY 
TABLE XV 
Westgren's Determinations of the Avogadro Constant 
5.97 X 1023 
6.05 " 
5.97 " 
6.06 " 
6.09 " 
5.98 " 
6.04 " 
6.13 " 
6.08 " 
5.95 " 
6.20 " 
6.04 " 
6.11 " 
5.98 " 
6.08 " 
6.02 " 
6.06 " 
6.05 X 1023 
The mean value of all these determinations is 6.05. It is very close 
to Millikan's value 6.06. 
For the purpose of demonstration, the following arrangement is 
very useful (Westgren). A small cell is prepared by cementing a 
cover glass to a microscopic slide by means of three threads of picein 
(Fig. 35) allowing a space of some hundreds of a mm. between the 
glass surfaces. A gold sol of say 80 pp radius is introduced and the 
cell closed with pure vaseline. The cell is mounted on the stage of the 
Fig. 35.-Cell for sedimentation equilibrium. 
microscope in vertical position with the vaseline edge up. After a 
couple of days the sedimentation equilibrium can be observed. A dark 
field condenser and an arc lamp should be used. 
In some recent experiments the validity of the sedimentation equi- 
librium formula has been doubted. If applied to ordinary colloid 
solutions the formula would require that after sedimentation equi- 
librium is reached, the concentration would decrease ven' rapidly 
with height falling to 1/10 a few mm. from the bottom of the vessel 
holding the sol. Now as a rule we do not find that the particles of COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
101 
our sols go clown to the bottom like this. This fact was pointed out 
by the writer in an article in Stahler's Handbuch 1916 together with 
the suggestion that the discrepancy was probably due to the mixing 
effect of convection currents. For small particles the velocity of fall 
is extremely small and even slight temperature differences within the 
sol would probably disturb the equilibrium considerably. 
Porter, in England, and Burton, in Canada, have made experiments 
that would show that the formula does not hold over a very wide 
range. Porter used a cell of 5 mm. height and studied the dis- 
tribution of the particles in gamboge suspensions (132). He found 
that if he counted the number of particles from the top layer down, 
already at .1 of a mm. from the surface, the sedimentation equilibrium 
did not hold and that further down in the liquid he reached a con- 
stant concentration. At .2 or .3 mm. there was a very distinct devia- 
tion between the curve of the observed sedimentation equilibrium and 
the theoretical curve. He concluded that there are forces acting 
between the particles that prevent the establishment of a simple 
sedimentation equilibrium. 
Burton used a glass tube 94 cm. long provided with a series of 
side tubes (133). The whole thing was filled with a colloid solu- 
tion of copper, made by means of the electric arc. Probably the 
outer layer of the particles is built up of copper oxide. The side 
tubes were sealed off and the apparatus mounted in a room at fairly 
constant temperature and left for 50 days. The side tubes then were 
broken off and the contents drawn off in parts from the different 
openings and analyzed. He found no change in concentration with 
height. 
With regard to Porter's experiments, it is quite likely that the 
sols had not reached equilibrium. He does not state how long he 
waited before making measurements, and in the case of his experi- 
ments it is possible that the temperature was not constant enough 
to allow the particles to reach the sedimentation equilibrium. 
The question whether Einstein's law for the sedimentation equi- 
librium holds over a wide range of height or not is of course of 
considerable importance and it is hoped that further experiments 
will soon allow us to settle the question. In the opinion of the writer, 
Burton's and Porter's experiments do not give conclusive evidence. 
Burton's copper sol was probably built up of partly oxidized particles 
of a loose spongy structure, settling very slowly, and he did not 
keep the temperature constant enough. Porter does not state how 102 
COLLOID CHEMISTRY 
much time he gave the particles to reach the equilibrium. To judge 
from Westgren's experiments in the writer's laboratory, it takes a 
considerable time to reach equilibrium. On the other hand, it is very 
probable that when we get to very high concentrations, the sedi- 
mentation equilibrium formula does not hold. At very high con- 
centrations there are probably repulsive forces acting between the 
particles. Perrin and his co-operators found some such deviations 
in very concentrated gamboge suspensions (134). 
Those phenomena related to the molecular kinetic properties of 
the particles reviewed above, osmotic pressure, diffusion and sedi- 
mentation equilibrium, all deal with a great number of particles, i.e. 
the values that we get are statistical mean values for a large number 
of particles. Osmotic pressure, diffusion and sedimentation equi- 
librium are therefore of quite the same kind as the ordinary physico- 
chemical phenomena we are used to study in crystalloid solutions. 
There is, however, another group of phenomena related to the 
colloid particle as a molecular kinetic unit which deals with a single 
or a few particles and those phenomena are of very great interest 
because they show us a microcosmos with laws of quite another 
kind than what we are accustomed to from the macrocosmos we ordi- 
narily experience. Those phenomena are the Brownian movement- 
the translatory and rotatory movements of the single particle-and 
the fluctuation of the number of particles in a minute volume. 
Translatory and rotatory Brownian movement.-The first phe- 
nomenon, the movement of a single particle, was discovered many 
years ago, in 1826, by the English botanist Brown (9). He examined 
under the microscope a number of pollen grains of Clarckia pulchella 
suspended in water and observed that many of those small particles 
were in constant motion. Their movements, he stated, consisted not 
only in a change of place in the fluid-the translatory Brownian 
movement-but also in a turning around, especially about their longer 
axis-the rotatory Brownian movement. The observations were ex- 
tended to other parts of plants, living and dead, to fossils, coal, 
resins, and finally to inorganic substances such as minerals, earths 
and metals-always with similar results. He only failed to find 
motion in cases where the material was either soluble in water or 
could not be subdivided finely enough. 
As to the cause of this striking phenomenon Brown did not 
suggest any hypothesis at all. He made, however, a series of interest- 
ing negative statements permitting us to exclude a number of assump- COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
103 
tions near at hand. Already in his first paper he expresses the 
opinion that the movements "arose neither from currents in the fluid 
nor from its gradual evaporation, but belonged to the particle itself." 
In his second paper (135) he describes a very ingenious experiment 
which enabled him to prove the insufficiency of such explanations 
as, for instance, mutual attractions or repulsions between the particles, 
action of capillary forces, action of evaporation, of disengagement 
of air bubbles and others. A portion of water containing small 
particles was shaken up with almond oil and a drop of this emulsion 
placed on the stage of the microscope. On examining the preparation 
Brown found that although the small water drops were completely 
immersed in oil, and thus protected from evaporation, the move- 
ments of the small particles suspended in the water was as lively 
as ever. Among the drops there were such which contained only a 
single particle but this isolation did not prevent it from being in 
motion. The above experiment must be regarded as a very con- 
vincing evidence-even to an experimenter of our days-that the 
Brownian movements do not depend upon external forces. 
Naturally Brown's experiments caused much comment and were 
soon repeated by other investigators. They were able to confirm 
Brown's results but did not add much to what Brown had already 
found out. 
Wiener in 1863 made a series of careful experiments and con- 
firmed Brown's opinion that external forces could not be the cause of 
the motion (136). He expressed the view that nothing remains for 
the cause of the motion but an internal movement peculiar to the 
liquid. 
Some years later, two Frenchmen, Carbonelie and Thirion, in 
1874, made some experiments with suspended particles and showed 
that, in fact those movements could be accounted for from the 
kinetic point of view. They pointed out that in the case of such 
small particles the number of impacts of the water molecules or 
the number of shocks is so small that you really get deviations from 
the mean value. Because of the smallness of the particles, the impacts 
of various directions do not cancel out but tend to give a resultant 
force and thus transfer some of their energy of motion upon the 
particle (137). 
All these investigators studied rather large particles. When the 
ultramicroscope was constructed by Siedentopf and Zsigmondy, the 
very intense movements of those small particles made visible in the 104 
COLLOID CHEMISTRY 
ultramicroscope were discovered by them. This aroused new interest 
in the study of the Brownian movements. 
A few years after the construction of the ultramicroscope, the 
theory of the Brownian movements from the kinetic viewpoint was 
published. The scientist who first solved the problem of mathe- 
matically determining the movements which a small particle ought 
to perform under the influence of the heat motion of the surround- 
ing molecules was Einstein (1905) (11)-in later years so famous 
for his theory of relativity. Almost simultaneously an analogous 
theory was arrived at by Smoluchowski (1906) (127), the scientist 
who in the sequel took a most active part in the development of the 
statistics of colloids. Other deductions of the formula for the 
motion have been given by Langevin (1908) (138) and by De Haas- 
Lorentz (139). 
The ideas that were new relative to the vague conceptions of the 
earlier investigators are: (1) the kinetic energy of a particle sus- 
pended in a liquid or a gas is the same as the kinetic energy of a 
molecule, i.e. 3/2.RT/N-as already pointed out in our study of the 
osmotic pressure, the diffusion and the sedimentation equilibrium of 
sols from the kinetic point of view, (2) the experimenter need not 
take into account the real path or the real velocity of the particle 
but may confine himself to the measurement of the average displace- 
ment of the particle in a known time, or to the determining of the 
time required for a known displacement. 
No doubt the Brownian movement is a very complicated one 
with regard to its innermost mechanism and-as pointed out by 
Smoluchowski-we are at the present time probably unable to an- 
alyze it mathematically in its full details (140). The results of 
the motion, however, as predicted by the theory, e.g. the displace- 
ment in a certain time to which the particle is subjected in virtue 
of the motion, seem to be the same whatever assumptions are made- 
within certain limits-with regard to its mechanism. This is borne 
out by the fact that starting from certain general conceptions, we 
arrive at the same final formula by quite independent ways. 
Following Smoluchowski and De Haas-Lorentz we will try to 
outline the deduction of the fundamental formula. Let us assume a 
particle constrained to move quite at random along a straight line 
but always in steps of the constant length 1. The probability of 
motion in positive and in negative direction is equal, i.e. = %. After 
the particle has moved n steps, the probability that among these COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
105 
steps n/2- b are taken in negative direction and n/2 + b in positive 
direction, i.e. that there is an excess of 2b steps in positive direction, is 
n/2 - b n/2 -f- b n j 
(1/2) ' '1/2) • (n/2 -b) ! (n/2-|-b) ! ' 
Upon using Stirling's approximation formula and assuming b small 
compared with n, this probability can be written 
2b2 
/2 n 
</- . e 
I itn 
The displacement of the particle is obviously = 2bl. If the 
initial position be named x0 and the final position x, we have 
2bl = x - x0. Let us assume that dx is small compared with x - x0 
but great compared with 1. Then the probability that the x-coordi- 
nate will fall between x and x -{- dx is equal to the above probability 
expressed in x multiplied with the number of b-values between the 
limits, or 
_ (x - Xp)2 
I 1 2nl2 
V-.dx. 
tit. 2nl- 
Let t denote the time required for each step and introduce t = nt 
I2 
and K = - then we get 
2~ (x- x0)2 
t> / I i 4Kt j 
P(x)dx = Vs^Kt'e -dx' 
This is the probability that we have the particle situated between 
x and x dx after the lapse of the time t. 
With the aid of this probability formula, we can calculate the 
average value of the square of the displacement 
4-00 (x-X0)2 
(x-K^px-x,)*^^. e 4Kt .dx 
- oo 
or 
(x - x0)2 = 2Kt. 
The probability may therefore also be written 
_ (x -Xq)2 
P(x)dx = J-1 e 2(x-x0)\ dx 
1x2 (x- x0)2 106 
COLLOID CHEMISTRY 
Now one might ask if the above reasoning can be brought to 
bear on the Brownian movement. The assumption of the elemen- 
tary steps of constant length 1 in equal times t certainly is some- 
what daring. Furthermore, we have assumed the particle to move 
along a straight line, while in the Brownian movement the particle 
is moving in space. Smoluchowski has shown, however, that we get 
exactly the same expression if we carry out this calculation for a 
similar movement in space, with one exception that the constant K 
has another value. Therefore, there is no objection to applying the 
above formula to a motion in space but we do not know and we 
have no right to assume that in the mechanism of the Brownian 
movement the particle moves in equal steps. Smoluchowski has tried 
to imagine another movement that would come more close to the 
Brownian movement and he has made some calculations, assuming 
that the lengths of the steps were distributed along a distribution 
curve, and got exactly the same expression with a new value for K. 
This shows that whichever mechanism we might assume for the 
motion of the particles we always get the same result: the same 
expression for the probability and the same expression for the average 
square of the displacement. It is difficult to think of any complica- 
tion that would not be included in those assumptions. The particles 
move in space and the steps might be distributed along any distribu- 
tion curve and might therefore be identified with the actual primary 
parts of the path of the particle. 
After this statement we will try to interpret the physical mean- 
ing of the constant K. Let us imagine a number of particles dis- 
tributed within a liquid column in such a way that the number 
of particles per unit volume is n = cp (x), i.e. is a function of the 
height of the column only. In consequence of the Brownian motion- 
or the motion supposed above-this distribution will alter with time 
so that after the lapse of the time t the number per unit volume will 
be nt. The probability that a particle originally situated in £ will 
be in x after the lapse of the time t is 
(x - £)2 
/ 1 4Kt 
I jt4Kt 
hence for q>(£) particles situated in £ 
(x-£)2 
I 1 4Kt J 
dx' COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
107 
After integrating over all the values of £ we have 
+ 00 (x-B) 
nt = I 1 1' z^ 4Kt 
VsKt- P®e 'd? 
00 
but this is the solution of the diffusion equation 
dn _ „ d2n 
dt dx2 
which expresses that the variation of the number of particles-or 
the concentration-with time is proportional to the change in the fall 
of concentration along the x-axis. Thus K denotes the diffusion con- 
stant. It should be borne in mind, however, that this formula is 
deduced from a probability law and that consequently the accordance 
with the thermodynamical diffusion formula is attained first after sum- 
marizing over a great number of particles. 
Using our formula for the diffusion constant of spherical particles 
d = -. 
N fiirqr 
the average square of the displacement can also be written 
(x x p - 2Dt - RT 
(x xo) -2Dt- N . 3^. 
Langevin has adopted a manner of reasoning that permits of a 
deduction of the formula for the translational as well as the rotational 
Brownian motion in a very simple way (138). His deduction how- 
ever does not give us the insight into the mechanism of the Brownian 
motion as that of Smoluchowski. 
The motion of the particle along the x-axis is governed by the 
equation 
d2x . dx . „ 
"ae =~f-dt +x 
where f = the frictional constant, X = the force acting on the particle 
in consequence of the molecular impacts. 
In order to introduce the expression for the kinetic energy, we 
multiply with x and write the equation in the form 
m d2(x2) /dx\2 , 1 d(x2) . v 
2 "dP ra(dt) =-f-2 V +Xx- 108 
COLLOID CHEMISTRY 
If an analogous equation is formed for a great number of particles 
and all those equations summed up, we have 
m d2(x2) RT _ f d(x2) 
2 "Tit2 N~"~2 dt 
/ dx \2 
for the average value of ml I is equal to the double value of 
the kinetic energy for one degree of freedom, viz. RT/N. The 
Xx-expressions vanish in the average value for they are statistically 
as often negative as positive. 
The solution of this equation is 
-X.t 
d 2RT 1 , m 
dt(x) = TT ' f + C ' e 
In the case of times of observation not too short (t > 108 sec.), the 
second term is negligible and we get 
d rr 2RT 1 
dt X - N ' f 
and on integrating from 0 to a certain t-value 
7 u 2RT 1 + 
(x - X0)2 = . j- . t 
or 
(x - x0)2 = 2Dt. 
Now in the above deduction x may be replaced by a general co- 
ordinate a provided a itself is not contained in the expression for 
the kinetic energy and only in terms with constant coefficients. 
Qu 
This is supposed to be the case in the motion in question, and we 
thus get a formula quite analogous to the one deduced above 
7 u o RT 1 + 
(a - a0)2 = 2 . . ^ . t 
Let a denote the angle of rotation and f the frictional constant 
of rotation which in the case of a spherical particle is 
f = 8a:r|r3 
then we have for the average square of the rotatory Brownian move- 
ment 
7 u RT 1 
N 4nqr3 COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
109 
I will now try to show some of the experimental work for the 
movement of the single particle. 
At about the same time when Einstein and Smoluchowski pub- 
lished their theory, the writer made some determinations of the 
Brownian movement by means of the ultramicroscope. The method 
of measurement was rather a crude one compared with the refined 
procedures used in later days, but it showed the general character 
of the phenomenon (141). 
The writer studied the movements of the particles of various 
colloid solutions with the aid of the slit-ultramicroscope and found 
that, when allowing the sol to stream slowly across the field of vision, 
the moving particles are seen as luminous wave-like curves. The 
average double "amplitude" or width and the average "wave-length" 
of these curves could be approximately read on an eye-piece microm- 
eter. Hence, the current velocity of the sol being known, a quantity a 
proportional to the real displacement of the particle (x - x0) and 
the co-ordinated time-interval may be calculated. A series of experi- 
ments with platinum particles of about 25 pit radius at 19° C. in 
various dispersion media gave the following result (Table XVI). 
TABLE XVI 
Brownian Movements of Platinum Particles 
Dispersion Medium 
n-io3 
a in n 
t in sec. 
a/t.10*' 
ai]. 10' 
Acetone 
3.2 
6.2 
0.016 
3.9 
2.0 
Ethyl acetate 
4.6 
3.9 
0.014 
2.8 
1.8 
Amyl acetate 
5.9 
2.9 
0.013 
2.2 
1.7 
Water 
10.2 
2.1 
0.0065 
3.2 
2.1 
Normal propyl alcohol 
22.6 
1.3 
0.0045 
2.9 
2.9 
From these figures the author drew the conclusion that 
a/t = const, 
a q = const. 
Now in the experiments which had led to a/t = const, q was not 
constant but connected to a by the relation a q = const, and vice 
versa. Therefore we have no right to use the two equations inde- 
pendently. This fact may be expressed by uniting them together 
into a/t.aq = const, or 
a2 = const, t/q. 
This is the Einstein formula for the displacement of the particle 
at constant temperature. These early measurements of the author 
have thus led to an empirical formula identical with the theoretical 110 
COLLOID CHEMISTRY 
formula of Einstein and are therefore to be regarded as the first 
quantitative confirmation of the kinetic theory of the Brownian move- 
ments. 
When carrying out these experiments the author was not acquainted 
with Einstein's and Smoluchowski's theoretical work that had just 
been published. Some time after the publication of the investigation 
of the author, there appeared quantitative tests of the kinetic theory 
of the Brownian movements carried out by other scientists with due 
regard taken to the work of Einstein and Smoluchowski. Conse- 
quently in these later experiments the positions of one or several 
particles were recorded at equidistant points of time. 
A report of such observations was published by Seddig 
(1907) (142). He took photographs of the Brownian motion of ver- 
milion particles at the beginning and at the end of a time interval of 
0.1 sec. For the illumination of the particles he used a dark-field 
condenser. According to the kinetic theory we have for the mean 
displacement A of particles of equal size at two different temperatures 
Ti and T2: 
Ai I Fi t]2 
A2 1 T2 TJi 
Seddig compared the values of Ai/A2 calculated in this way with 
those obtained by direct measurement on his photographs. The ex- 
perimental values were constantly greater than the theoretical-the 
average difference being about 6 per cent. 
Seddig thinks the difference is due to the errors in measuring the 
temperature, which procedure is indeed not very easy in such a thin 
preparation as used by him. 
Henri studied (1908) the movements of the particles in rubber 
latex (radius about 1 p) by means of a kinematographic anal- 
ysis (143). The preparation was mounted horizontally and photo- 
graphed with a Zeiss apochromatic lens of 2 mm. focal length and a 
projection ocular n:o 4 in 24 cm. distance. The magnification was 
about 600. He used an electric arc lamp as source of light. The 
records contained 20 pictures per sec. and each exposure had a dura- 
tion of 1/320 sec. 
Henri found, for instance, A = 0.62 p in 1/20 sec. and A = 1.11 p 
in 1/5 sec. while the theoretical law, A = const. Vt, requires 1.24 in 
1/5 sec.-a tolerably good agreement. The absolute values of A cal- 
culated from the Einstein formula are much smaller than the observed COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
111 
ones. Henri further found small additions of acid or alkali to be 
of great influence on the displacements of the particles. As such an 
influence has not been observed in other cases, it is desirable that 
Henri's experiments should be repeated and controlled. 
Perrin and his pupils Chaudesaigues, Dabrowski and Bjerrum 
have carried out a series of very remarkable investigations on the 
translational as well as the rotational Brownian movement (1908- 
1911) (144). They used particles of gamboge and mastic. The 
method of observation was a very simple one; they observed the 
motion of the particles directly in the microscope and noted the posi- 
tion of a particle at equidistant points of time with the aid of a 
camera lucida. Chaudesaigues used (1908) two very equal-sized 
emulsions of gamboge prepared by Perrin. One of the sols contained 
particles of 0.450 p radius, the other one particles of 0.213 p. In two 
of his series of observations he used water as the dispersion medium, 
in two others sugar solutions of high viscosity. 
The observations of Chaudesaigues are in good agreement with 
the theory. 
The mean displacements corresponding to various intervals of 
time should, according to the theory, be proportional to the square 
roots of time, viz. A = const. \/t. 
Chaudesaigues found 
for the times 30 60 90 120 sec. 
the displacements 6.7 9.3 11.8 13.95 p 
while the figures 6.7 9.46 11.6 13.4 
are exactly proportional to the square roots of the time intervals. 
According to the theory, we ought to have 
1 
A = const. . 
V r 
Chaudesaigues found in a certain case when the ratio of the radii 
was 2.1, the reciprocal ratio of the mean squares of the displacements 
to be 2.0. 
According to the theory the relation between viscosity and dis- 
placement should be 
A x 1 
A = const. -= . 
Vn 112 
COLLOID CHEMISTRY 
Chaudesaigues found in case the ratio of the roots of the viscosities 
were 2.0, the ratio of the displacements to be 1.8. 
He further calculated the Avogadro constant N from the Einstein 
formula and found 62 X 1022. 
Perrin himself as well tfs Dabrowski and Bjerrum have carried 
out a great many analogous series of observation in order to settle 
the value of N as accurately as possible. In Table XVII I have put 
together the figures available. It is a pity that all the material of 
observation concerning these interesting measurements has not been 
made public. So, for instance, in some cases we are ignorant of the 
temperature, in others of the viscosity of the dispersion medium, etc. 
Perrin's Determinations of the Avogadro Constant by Measuring the Dis- 
placement of the Particles in the Brownian Movement 
TABLE XVII 
Number of 
Number of 
Displace- 
Nature of 
Particles 
Time 
ments 
Particles 
Observed 
r in p, 
T 
T] in Sec. 
Observed 
Amp, 
N.10~" 
gamboge 
50 
0.212 
290 
0.011 
30 
50 
7.09 
66 
ll 
ll 
CC 
ll 
ll 
60 
ll 
10.65 
59 
n 
u 
CC 
ll 
ll 
90 
ll 
11.31 
78 
u 
u 
CC 
ll 
ll 
120 
ll 
12.00 
89 
gamboge 
50 
0.212 
287 
0.012 
30 
50 
6.71 
68 
n 
u 
ii 
ll 
ll 
60 
ll 
9.30 
70.5 
it 
ll 
cc 
ll 
ll 
90 
ll 
11.83 
71 
u 
u 
ii 
ll 
ll 
120 
ll 
13.96 
62 
By addition 
gamboge 
50 
0.212 
of sugar c:a 
5 times t] of 
30 
50 
56 
water 
gamboge 
0.367 
By addition 
of glycerin 
1500 
68.8 
gamboge 
0.385 
c:a 100 
64 
times t] 
of water 
gamboge 
40 
0.45 
60 
40 
94 
25 
a 
120 
25 
94 
gamboge 
30 
0.50 
66 
mastic 
0.52 
30 
200 
57 
u 
ll 
60 
100 
64 
u 
tt 
120 
50 
67 
u 
It 
240 
25 
70 
mastic 
0.52 
30 
200 
69 
u 
tt 
60 
100 
65 
u 
ll 
120 
50 
64 
u 
ll 
240 
25 
88 
mastic 
200 
0.52 
By addition 
120 
220 
77 
mastic 
2 
5.75 
298 
of urea 1.28 
times r] 
of water 
60 
100 
2.35 
78 COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
113 
Perrin and Chaudesaigues also calculated the distribution of the dis- 
placements observed and found good agreement with the theoretical 
formula as shown by Table XVIII. 
Probability Distribution of Displacements in Brownian Movement 
TABLE XVIII 
Number of 
Displacements 
Displacement between 
Observed 
Calculated 
0 and 
1.7 
86 
92 
1.7 
3.4 
82 
83 
3.4 
5.1 
69 
75 
5.1 
6.8 
62 
58 
6.8 
8.5 
51 
44 
8.5 
10.2 
26 
31 
10.2 
11.9 
22 
21 
11.9 
13.6 
13 
11 
13.6 
15.3 
9 
8 
15.3 
17.0 
6 
6 
The formula for the Brownian motion of rotation was tested by 
Perrin. He prepared mastic globules of 6.5 p radius and suspended 
them in a urea solution having a viscosity 1.28 times that of 
water (145). Some of the globules had small enclosures of impurities 
or defects and by noting the position of such a mark at equidistant 
points of time by means of a camera lucida and squared paper he 
was able to calculate the mean rotation of the particle. He found the 
root of the mean square of rotation per minute to be 14° and the 
Avogadro constant N = 65 X 1022. Consequently the kinetic theory 
of the Brownian movement holds good also for the rotational motion. 
The author worked out a method for measuring the displacements 
of the particles in the slit-ultramicroscope at constant intervals of 
time (146). The arrangement is diagrammatically represented in Fig. 
36. M is the microscope, C the cell for the sol, W a waterbath to 
hold the temperature of the sol constant, A A' the Abbe camera lucida, 
F a little film camera in which a sensitive film is moved with con- 
stant velocity by means of a motor. P is an apparatus throwing a 
little luminous ring into the field of vision of the microscope by means 
of a small electric incandescent lamp and a ring diaphragm. The tube 
containing this lamp has another similar lamp throwing its light 
downwards on the film through a fine hole. This hole is opened and 
shut at constant intervals of time by means of a rotating disk kept 
in motion by a clockwork. The apparatus P rests on the top of 
the camera and can be moved in this plane freely. The experiments 
are carried out in the following way. The observer sees in the 114 
COLLOID CHEMISTRY 
microscope not only the illuminated colloid particles but also a lumi- 
nous ring. He moves the apparatus P, the "pen," so that a particle 
is encircled by the ring and keeps the particle there in following it by 
the ring as it moves. During this process the film receives light im- 
pressions at constant intervals and the Brownian movement of the 
particle is accordingly registered on the film. 
Of course this method is only a substitute for the direct photo- 
graphic registration of the movement of the particle but it is of good 
Fig. 36.-Arrangement for the study of the Brownian movement by means of 
the slit ultramicroscope. 
service in cases when the particles are too small to be photographed. 
By measuring the diagrams we get the projection of the displace- 
ment of the particles on an axis perpendicular to the direction of 
motion of the film. 
In the investigations carried out by the author and by the author 
and Inouye, using this method, the movements of gold particles were 
studied. The following result was obtained (147,148). 
We found the time law of Einstein A = const. Vt confirmed as is 
shown by the Table XIX. COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
115 
TABLE XIX 
The Time Law in Brownian Movement 
Time in Units 
of 1.48 Sec. 
r = 27 p.|x 
A in p 
r - 52 pp 
A in p 
Obs. 
Calc. 
Obs. 
Calc 
1 
3.1 
3.2 
1.4 
1.7 
2 
4.5 
4.4 
2.3 
2.4 
3 
5.3 
5.4 
2.9 
2.9 
4 
6.4 
6.2 
3.6 
3.4 
5 
7.0 
6.9 
4.0 
3.8 
6 
7.8 
7.6 
4.5 
4.2 
With regard to the absolute values of A, we found good agreement 
with Einstein's formula in the case of small gold particles. In Table 
XX some values for particles of radius 22 pu are brought together; 
N is taken as 6 X 1023. 
TABLE XX 
Absolute Measurement of Displacement in Brownian Movement 
Time in Sec. 
Displacement in p, 
Obs. 
Calc. 
1 
4.3 
4.1 
2 
5.8 
5.8 
3 
6.6 
7.6 
4 
8.3 
8.2 
In the case of gold hydrosols with large particles the observed 
displacements were always found to be smaller than the calculated 
values. The author and Inouye studied this circumstance somewhat 
closer and found that the agreement is good only in the case of the 
small gold particles directly reduced. The small particles obtained 
by allowing microscopic gold nuclei to grow in a gold reduction 
mixture are anomalous and so are all the various sorts of larger gold 
particles. Most likely this is due to deviations from the simple 
spherical shape in these particles. The partly coagulated sols contain 
aggregate particles and consequently the resistance factor in the Ein- 
stein formula cannot be represented by 6jtqr. As for the sols pre- 
pared by the nucleus method, the particles might be of needle or leaf 
shape; thus giving rise to a higher resistance. The latter supposition, 
made some years ago by the author, has had a very beautiful con- 
firmation by some recent research by Bjornstahl. He found that a 
sedimenting gold sol shows double refraction and that the gold sols 
of low degree of dispersion show double refraction in magnetic and 116 
COLLOID CHEMISTRY 
electric fields. These observations can only be explained in assum- 
ing the particles to be non-spherical. 
From the determinations of the author and Inouye with regard 
to small particles directly reduced, it follows N = 62 X 1022. 
About the same time when these experiments were carried out, 
there came great progress in the construction of the dark-field con- 
densers and their application to the study of colloid solutions espe- 
cially through the work of Siedentopf. This scientist published a 
photograph of the Brownian movement of the particles in a Carey 
Lea silver sol-the first proof of the possibility of photographing the 
motions of ultramicroscopic particles (149). Siedentopf's cardioid- 
ultramicroscope thus offered a new powerful means in the study of 
the Brownian movements. There is however a serious drawback in 
using such a method as that suggested by Siedentopf's instrument. 
In order to utilize the power of the cardioid-condenser it is necessary 
to enclose the sol under investigation in a very thin layer between 
two quartz plates. Consequently the particles are forced to move in 
a limited volume and their motion will probably be influenced by the 
walls. Anyhow the author deemed it worth while to make an attempt 
to use this photographic method. In 1911 he worked out the main 
parts of the necessary apparatus (150). The arrangements made by 
him were then improved by Nordlund and used for a very cautious 
investigation of the movement of mercury globules suspended in 
water (151). Fig. 37 gives a diagram of the apparatus. 
The light from a 25 amp. arc lamp A is collected by a lens B and 
passes in horizontal direction and slightly converging through an 
absorption cell C 36 cm. in length filled with water in order to remove 
the ultra red. The illuminating beam of light then passes an auto- 
matical central shutter D acted upon by an electric pendulum clock 
giving exposures of a duration of about 1/60 sec. at constant intervals 
of time. The light then reaches the cardioid-condenser F and the 
quartz cell G containing the sol. The cell was thermally protected 
and the temperature measured by means of a good thermometer. On 
the microscope K we used the apochromatic objective 3 mm. espe- 
cially constructed for the cardioid-condenser and the projection ocular 
No. 2 Leitz. The magnification was about 500. The photographic 
registration was made on a plate P moving slowly with constant speed 
in horizontal direction at right angles to the optical axis of the system. 
In order to have reference lines for the measuring of the plates there 
were three fine silver needles R mounted so that they pressed slightly COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
117 
Fig. 37.-Arrangement for photographing the Brownian movement by means of the cardioid-ultramicroscope 118 
COLLOID CHEMISTRY 
on the sensitive film of the plate when the latter was in motion. In 
developing the plate, the traces of the needles became visible as fine 
dark lines. Fig. 38a is the reproduction of the movements of some 
mercury particles when illuminated with continuous light and Fig. 38b 
shows the registration of a single particle in intermittent light as used 
for the measurements. 
The particles under investigation were large enough to move slowly 
downwards under the influence of gravity as shown by the Fig. 38a 
and b. The resistance factor in Einstein's formula could thus be 
determined for each particle by measurements on the plates. 
As hinted above, there is a source of error included in this method 
which is very difficult to correct for, viz., the influence of the walls 
of the cell. Nordlund adopted the correction formula of H. A. Lorentz 
according to which the resistance exerted on a spherical particle mov- 
(9 r \ 
1 + -x- 1 where r 
16a / 
is the radius of the particle and a is the distance between the wall 
and the center of the particle (152). Assuming every position be- 
tween the walls of the cell equally probable, he derived a formula 
with bearing on his observations. In Table XXI the results of 
Nordlund's measurements are summed up. 
TABLE XXI 
Nordlund's Measurements of the Avogadro Constant 
Number of Points 
Thickness 
Registered 
r in g 
A2 in n2 
t in Sec. 
T 
of Cell in p, 
N.IO'23 
78 
0.136 
3.462 
1.481 
291.8 
3.10 
6.72 
68 
0.140 
3.236 
1.481 
291.8 
3.10 
7.00 
75 
0.142 
3.605 
1.481 
292.1 
3.10 
6.23 
68 
0.154 
3.892 
1.481 
292.1 
3.10 
5.26 
56 
0.158 
3.174 
1.481 
291.5 
3.10 
6.10 
35 
0.243 
2.494 
1.481 
291.5 
3.10 
4.62 
53 
0.266 
1.813 
1.481 
292.0 
3.10 
5.96 
100 
0.119 
2.761 
1.000 
292.2 
2.47 
6.64 
83 
0.126 
2.759 
1.000 
293.1 
2.47 
6.18 
116 
0.161 
2.745 
1.000 
291.4 
2.47 
4.57 
79 
0.228 
1.388 
1.000 
291.8 
2.47 
6.05 
53 
0.237 
1.500 
1.000 
292.9 
2.47 
5.53 
The mean value of N is 5.91 X 10 23 
The fluctuations.-Instead of measuring the movement of a single 
particle, we can study the fluctuation in the number of particles 
within a certain small volume, communicating with a large volume 
of a colloid solution. The study of those fluctuations has given us COLLOID PARTICLE A MOLECULAR KINETIC UNIT 
119 
Fig. 38.-Photographic records of the Brownian movement: a with continuous 
illumination; b with intermittent illumination. 120 
COLLOID CHEMISTRY 
the means to calculate the Avogadro constant and make quite a 
series of interesting expirements. 
The theory has been worked out by Smoluchowski. It is of spe- 
cial interest because it throws some light upon the validity of the 
second law of thermodynamics. According to Boltzmann's theoretical 
investigations, the second law of thermodynamics in its usual form 
is only valid for a large number of particles. In a macroscopic sys- 
tem the free energy cannot increase without compensation in some 
other place in the system. Diffusion, for instance, is not reversible. 
Now, when we observe the fluctuations in the number of particles 
within a certain little part of a sol, we actually see diffusion reversed. 
Sometimes we have a large number of particles, i.e. a high concentra- 
tion, sometimes a small number, i.e. a low concentration. It is obvious 
that in microscopic systems fluctuations of entropy occur (153). 
The first thing studied in the fluctuations was the magnitude of the 
average deviation from the average value and the probabilities of a 
certain number. The formula for the probability can be deduced in 
many different ways (154). One of the simplest is the following: 
Let N denote the total number of particles in the sol, p the probability 
that one of the particles shall be situated within the small com- 
municating volume during a certain time interval. Then, according 
to Bernouilli's law, the probability that n particles shall be situated 
within that volume in that time interval is 
N ! 
P (n) = n 1 (N -n) ! • P" • (x -p)N-" • 
Now usually N is very great compared with unity and p very 
small and our formula can therefore be simplified considerably. 
[N-(n-l)] [N-(n -2)] (N-l)N 
n ! (N - n) ! P U -p) 
evidently goes over in 
Nn (NdD 
pn (1 -p)N = . e-Np. 
n ! n ! 
But Np is the average number of particles within the small volume. 
Call this number v and we get 
g-r-wn 
P(n) 
n ! COLLOID PARTICLE A MOLECULAR KINETIC UNIT 
121 
From the probability formula the average fluctuation defined as 
n - v - . n - v 
--- = 8 , i.e. the average value of --- always taken with the 
-f- sign, and the average value of the square of the relative fluctua- 
tions defined as &2, can easily be calculated. 
We get 
_ p-P'vk 
8 - 2 
k ! 
k S v 
when v is a small number, and 
8 = Ji 
T jtv 
when v is a great number; and 
S2 = - 
v 
Those formulae hold good only in cases where there are no forces 
acting between the particles, i.e. in cases where the gas laws hold. 
Let us define compressibility by the expression 
o - dc • 1 
dp c 
where c is the concentration and p the osmotic pressure. Then if 
RT 
P= N-C 
the normal compressibility is 
8 -Al 
" RT' c 
Smoluchowski has shown that in cases where deviations from the gas 
laws occur, we have for small v values 
r ? e-M J(3~ 
k!lpo 
and for large v values 
-8=^ 
i ^Vpo 
The writer tested those formulae (155) and found that for gold 
sols the compressibility is normal, i.e. the gas laws hold, at least up 122 
COLLOID CHEMISTRY 
to a concentration of 10 particles per 1000 p3. Table XXII gives 
such a series of observations: 
TABLE' XXII 
Fluctuations in a Gold Sol 
Number of 
Frequency of n 
8 
n 
Observations 
Obs. 
Calc. 
v Obs. Calc. 
0/00 
0 
112 
0.216 
0.212 
1.545 0.660 0.656 
1.014 
1 
168 
0.324 
0.328 
2 
130 
0.251 
0.253 
volume - 1064 ps 
3 
69 
0.133 
0.130 
4 
32 
0.062 
0.050 
r =19 pp 
5 
5 
0.010 
0.016 
Number of observations 
6 
1 
0.002 
0.004 
per min. = 39 
7 
1 
0.002 
0.001 
For higher concentrations, I found deviations, but according to 
later investigations by Westgren (156), it seems that those deviations 
are due to experimental errors. Westgren actually found no devia- 
tions up to concentrations of about 72 particles per 1000 p3. 
Table XXIII gives some of Westgren's observations. 
TABLE XXIII 
Fluctuations in a Gold Sol 
Number of 
Frequency of n 
8 
n 
Observations 
Obs. 
Calc. 
V 
Obs. Calc. 
p/po 
0 
185 
0.113 
0.114 
2.168 
0.539 0.527 
1.009 
1 
366 
0.236 
0.247 
2 
453 
0.290 
0.269 
72.5 particles per 1000 p,3 
3 
248 
0.160 
0.195 
4 
178 
0.115 
0.106 
5 
87 
0.056 
0.046 
6 
21 
0.013 
0.017 
7 
17 
0.005 
0.005 
8 
2 
0.001 
0.001 
Some observations by Constantin (157) seem to indicate that at 
very much higher concentrations the compressibility actually differs 
from the compressibility of a perfect gas. 
Another important property of the fluctuations is the velocity 
with which the number of particles observed within the small volume 
changes. The writer observed that this velocity varies very much 
with the viscosity of the dispersion medium (158) and Smoluchowski 
has shown that it is possible to work out the theory for the velocity 
of the fluctuation and that we can measure the constant of the Brown- COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
123 
ian movement, and calculate the Avogadro constant from measure- 
ments of the velocity of fluctuation in sols (159). 
The most convenient quantity to calculate is the average square 
of the difference between successive observations. Smoluchowski has 
shown that this average square of the difference An2 is equal to 2vP. 
P depends upon the shape of the volume in which we are counting 
the particles. It also contains the ordinary gas constant, the tem- 
perature, and the size of the particles. Smoluchowski determined the 
actual form of this function P for different kinds of volumes. The 
most important one is the case where we have the colloid enclosed 
in a cell between parallel plates and take into account the number 
of particles within a cylinder of sol between these planes. Here 
the particle can only enter and leave through the cylinder sur- 
face and in such cases Smoluchowski found that the function P only 
a2 
depends upon a quantity a = 4^- where a = radius of the cylinder 
and D the diffusion constant, t the time between observations. It 
TABLE XXIV 
Fluctuations in a Gold Sol 
a = 10.0 ji 
1 = 18.7 n 
t = 1.15 sek 
T = 287.2 
v= 1.873 
r = 63.5 jip. 
544423425346654432232432111212111111111111111111100101100011111121223311211112 
122211132002343443233333433243022343343334523443342333322234221233111221223332 
322222322231221334335563224323323232123443233222223233233212111221011100011111 
111121220000000001000000000000011110111111122211102110111112102110000100000001 
233322212210000000000000000010000110111110100000000221223223234323322223222223 
233443222332443335443344334454453434433334454533443333422343232120012211212122 
1210000000000000002211223211121222333333222211122222222222 22112222222222121101 
101001001000000112112111101111111111010000000000000000110011211101000000011101 
111001120001111210100121110111101011111222100111112232211111111122021200012344 
4343322322322321122212132312322 22322221222311111123212111011032120343344334433 
333223423432344321323423333333223232244431343422121100001110343333212222111112 
312321322000121111111221021101111111111222133211122111231100000002123230111111 
222332211111122112112112112101000000000000101100110001111011010011012221111212 
121231121101101001010010010111121100000002223222223333332344333352231321343322 
221222232322232455445435445314331213132332133211000000021111112222322234346323 
5555654545444322223111222342333422233121233333322323100100111001 2233233332222 
112222222322222223211111112222001100001121001121222222232112 221122222111111111 
201100111110001111111110012223334444443223454443352111111134454443244545444233 
.543133432454332344432552134554343444213 335465674333233245644232122333435334354 
354444476754555333 124 
COLLOID CHEMISTRY 
depends only on the quantity a, but is a rather complicated function 
and can be expressed in different ways but is best expressed by 
P = e-2"[L0(2a) + Lt(2a)], 
where Lo and Lx denote Bessel functions of imaginary argument (160). 
Westgren who has studied the velocity of fluctuations very thoroughly 
calculated numerical tables for the relation between P and a (161). 
Table XXIV gives one of his series of observations. Here 1 means 
the thickness of the cell. 
The calculation of An2, P, a, and N gave the following values 
(Table XXV). 
TABLE XXV 
The Avogadro Constant Determined from the Fluctuations 
Time Interval 
Aln 
P 
a 
N 
1.15 
0.767 
0.205 
7.42 
58 X 10M 
2.31 
1.105 
0.295 
3.52 
55 " 
3.46 
1.267 
0.338 
2.65 
62 " 
4.62 
1.398 
0.374 
2.14 
66 " 
5.77 
1.448 
0.386 
1.99 
78 " 
From the determination of 75,000 differential squares Westgren got 
50 N-values which gave the average values 60.9 X 1022 very close to 
Millikan's value 60.06 X 1022. 
It is interesting to note that it is possible to calculate the Avogadro 
constant or the diffusion constant of the particles without making 
measurements of the displacement of the single particle. The only 
thing you have to do is to make a sufficiently lengthy number of 
observations of the number of particles of known size in a certain 
volume of known size and shape in a liquid of known viscosity at a 
known temperature. 
When we analyze a series of observations like the one above, we 
find some other interesting features that have been brought out by 
Smoluchowski's theory of the phenomenon of fluctuations. There are 
two quantities that are of special interest, namely, the average time 
during which a certain number n of particles can be observed without 
being interrupted by another number, and the average time between 
the appearances of a state characterized by a certain number n. Call 
the first quantity the average duration of n and the second one the 
average time of return of n. Smoluchowski has shown that the aver- 
age duration of n is 
T - - 
1 -F(n,n) COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
125 
and that the average time of return of n is 
1- P(n) _ t l-P(n) 
" n' P(n) "1 -P(n,n) ' P(n) 
where t = the time between observations and P (n,n) is the probability 
that, when going over from one observation to another there is no 
change in the number of particles, i.e. the probability that the number 
n shall be found in the next observation. 
From one of my series of observations Smoluchowski has calculated 
the following values for the average time of duration and the average 
time of return. 
TABLE XXVI 
Fluctuations in a Gold Sol 
v = 1.55 t = 1/39 min. 
T 
Sec. 
0 
Sec. 
n 
Obs. 
Calc. 
Obs. 
Calc. 
0 
2.57 
2.26 
9.35 
8.52 
1 
2.31 
2.38 
4.81 
4.86 
2 
2.11 
2.12 
6.32 
6.23 
3 
1.92 
1.89 
12.1 
12.4 
4 
1.89 
1.72 
28.6 
32.1 
If we ask for the average time between the appearance of a certain 
state with a high number of particles, the above formula can be 
simplified because in such a case both P(n,n) and P(n) are small. 
We get 
„ _ t _ t. e" . n ! 
n" P(n) " "V 
It is interesting to see how long on the average we have to wait 
before a high number once seen appears again. For example, in one 
of my series of observations mentioned above, the average value of n, 
i.e. v, was 1.55 and the time betwcnn observations 1/39 minute. The 
average time for the number 7 to reappear is found to be 28 minutes. 
Now again take a much higher value like 17 for instance. If we ever 
found that number in a colloid solution where the average was 1.55 
there would be a chance to see it again after 50,000 years. That gives 
us an idea of the difference between what we used to call reversible 
and irreversible phenomena. From the standpoint of the probability 
calculation, there are no irreversible phenomena. It depends upon 
the average time for the reappearance if we would call a phenomenon 
reversible or irreversible. If the average time of return is very small, 126 
COLLOID CHEMISTRY 
we call it reversible and if it is very large, so large that we could 
never hope to observe it again we call it irreversible. This, of course, 
throws a very interesting light upon the second law of thermody- 
namics. According to this law we could never expect to see the 
number 7 again in the above series. According to diffusion, the parti- 
cles would spread out and would never be concentrated again in the 
little volume of observation. 
The above reasoning is based upon the assumption that the series 
of observations consists of time points, i.e. that we make the observa- 
tions at successive intervals of time and that each observation is very 
short. Of course, it is possible also to observe the fluctuations con- 
tinuously. Smoluchowski has actually succeeded in working out the 
theory of the phenomenon for continuous observations. It is much 
more complicated than for intermittent observation. Of course, if 
we observe a colloid with an average number of particles, say 1.55, 
continuously, the chance to see the same number, for instance 17, 
again is much greater. If we calculate the time, we have to wait 
before we get the number 17 back again, in the case of continuous 
observation, we find 161 days instead of 50,000 years as in the case 
of intermittent observation. But when we calculate the duration of 
this number 17, that is how long we would have the chance to observe 
this number, we find that it would only appear during 9 X 10"7 seconds 
•-that is, it would be impossible to observe it. That shows that in 
the case where we observe the number of particles continuously, there 
is not only the average time which is of importance, but also the 
average duration of the time during which this number appears. If 
that time is too short we cannot observe it. 
I could mention some other examples to illustrate the length of 
time necessary for a certain state to reappear. Boltzmann has cal- 
culated along similar lines that if we have 1 cc. gas at ordinary pres- 
sure and if we could make a record of all the velocities and the direc- 
tions of the molecules we would, if we waited a sufficiently long time, 
get the same state back again-i.e. the molecules would appear with 
the same velocities and moving in the same direction within certain 
limits. In the case that we would require that those quantities were 
equal within a few cm. we would get the time 101018 years before 
this state was reached again. An analogous calculation shows that 
a pressure difference of 1 per cent between the two halves of 1 cc. 
of a gas at ordinary conditions would on the average just appear COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
127 
each 101010 year. Such a phenomenon seems extremely improbable, 
but it is not impossible. 
Freundlich has pointed out that perhaps the fluctuations in the 
concentration might play a certain role in the life of plants and 
animals. The cell is apparently a very complicated sort of a work- 
shop and it is not impossible that within those small distances in the 
cell the fluctuations of concentrations of colloid particles or molecules 
might be of importance. 
The Size, Shape and Structure of the Particle 
The properties of colloids depend to a great extent upon the size, 
the shape, and the structure of the particles. The determination of 
those quantities is therefore one of the most important things in 
colloid chemistry. The methods used are all more or less physical 
in nature; the particle is considered as a molecular kinetic unit regard- 
less of the field of surface forces surrounding it, i.e. the residual 
valencies of the surface of the particle and the action of the ions and 
molecules adsorbed. Only a few of the methods so far known permit 
a direct measurement of the above properties. Many of the pro- 
cedures we use are based upon the study of the different physical 
properties of the particle and only permit us to draw indirect con- 
clusions-with more or less certainty-on the size, shape and structure 
of the particle. Now we very rarely get a disperse system with 
equally sized or equally shaped particles. As the properties of the 
system depend on the size, shape and structure of the particles, it is 
evident that they also depend on the distribution of those quantities. 
The ultramicroscope.-The most simple and most direct way of 
determining the size of particles is to use the microscope or the ultra- 
microscope. By means of the microscope we can only measure com- 
paratively coarse particles. According to Abbe's diffraction theory 
of the microscope, we can only hope to distinguish points that are 
at a larger distance than 
X 
2 n sin a 
where X is the wave length of the light, n the refractive index of the 
medium between the particle and the lens, and a half the angle at 
which the lens is seen from the particle. The quantity n sin a is 
called the numerical aperture of the lens. Of course the highest value 128 
COLLOID CHEMISTRY 
of the sin of the angle a that we could reach is 1 and in the case that 
n is also 1, i.e. for a dry system, we could never have a numerical 
aperture higher than 1. It is about 0.95 at the best. If we take 
water for an immersion liquid, the refractive index of water being 1.33, 
we can reach a numerical aperture of about 1.25. If we take oil 
immersion-cedar oil that has a refractive index of say 1.515-we 
can get up to 1.4. We could increase the numerical aperture a little 
by using monobrom-naphtalene for immersion liquid but not very 
much. 
If we calculate for those different systems, the dry, the water, and 
the oil systems, the size of the smallest particle that we can see and 
measure in the microscope, taking a wave length of about 500 pp, we 
get for the dry about 260 pipt, for the water 200 pp, and for the oil 
180 pp. Now, of course, it would be possible to use a very short 
Fig. 39.-Diagram of the Siedentopf-Zsigmondy slit-ultramicroscope. 
wave length-to use ultraviolet light for the illumination. Such a 
microscope has actually been built with a lens made of quartz and 
fluorite and corrected for the wave length 275 pp. The limit of 
visibility in this case is about 110 pp, and this represents about the 
best we can hope to reach by means of the ordinary microscope. 
Particles of smaller size, and most particles in sols are smaller, 
cannot be measured in the ordinary microscope. The principle utilized 
for making those particles visible is the following. Any particle that 
can be made to emit light enough can be seen if it is not too close 
to another particle. By diluting the colloid, we are always able to 
fulfill this condition. The problem is to illuminate the particles 
strongly enough and to observe them with an optical system so as 
to get as much light as possible from the particles. That is what we 
do in the ultramicroscope (Fig. 39). The image of a very intense 
source of light, the crater A of a carbon arc for instance is projected 
upon a fine slit B and the image of the slit projected on the particles COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
129 
in the sol to be studied C. At right angles to the illuminating beam 
of light is mounted an ordinary microscope to observe the illuminated 
particles. This simple but very efficient kind of ultramicroscopic 
observation was worked out by Siedentopf and Zsigmondy in 1903 (8). 
Their ultramicroscope is usually called the slit ultramicroscope 
(Fig. 40). 
The efficiency of the ultramicroscope depends on the following 
factors (162): (1) The specific intensity of the source of light, i.e. 
the amount of light given off from the unit surface of the light source, 
should be as high as possible. (2) The aperture of the illuminating 
system and the system used for observing the particles should be as 
high as possible. This includes the condition that the refractive index 
Fig. 40.-The slit-ultramicroscope. 
between the lens and the particles and the angle under which the 
particles are seen should be as high as possible. (3) The third factor 
is the condition of the field of view. We want as high contrasts be- 
tween the particles and the background as possible. (4) The fourth 
factor is the light emitting power of the particles. 
The light source with the highest intensity we can get is the sun, 
but it is very inconvenient to work with, so we usually use the carbon 
arc which gives the next highest specific intensity. The aperture of 
the illuminating system and of the system of observation were com- 
paratively low in the first form of the ultramicroscope. We have a 
very narrow beam of light thrown into the cell containing the sol and 
that of course means that the aperture of the illuminating system is 
not very high. Zsigmondy (163) more recently constructed a new 
ultramicroscope based upon the same principle, i.e. having the illu- 130 
COLLOID CHEMISTRY 
minating beam entering the microscope at right angles, and succeeded 
in increasing the aperture of both the illuminating and the observing 
system considerably. For this purpose the illuminating and the 
observation microscopic lens, both of high aperture, were mounted 
very closely together (Fig. 41). This however caused considerable 
difficulty in the construction of the cell to be used to hold the sol. 
The efficiency of this second kind of ultramicroscope has never 
been very carefully compared with the first type and it seems that 
the size of particles which Zsigmondy has been able to see with the 
new one is not so very much smaller. With an arc lamp and the old 
ultramicroscope the limit for gold particles was about 10 or 15 pp, 
with sunlight it is lower-about 6 pp (164). 
In order to have the field of vision as dark as possible, it is neces- 
sary to use special cells. The windows through which the illuminat- 
Fig. 41.-Diagram of the illumination in Zsigmondy's immersion ultramicroscope. 
ing and observing beams pass should be of quartz to avoid fluorescence. 
The other parts of the cell should be made of black glass. 
The scattering power of the particles we cannot change, but it 
may be possible to utilize the best parts of the spectrum where the 
light given off by the particle is of the highest intensity. In some 
cases the scattering power increases when the wave length decreases. 
It has been suggested that we try to use ultraviolet light to get down 
to small particles. This suggestion has never led to any practical 
results because, in the first place, we cannot get a very strong illu- 
mination with ultraviolet and then it is difficult to observe small 
intensities of ultraviolet light. Ultraviolet cannot be observed directly 
with the eye. We must either photograph it or use a fluorescent screen 
in the eyepiece and those methods of observation are not sensitive 
enough. 
Instead of having the light beams of illumination and observation 
at right angles, we could use different ways of coaxial illumination, 
taking care that the apertures of the two systems are adjusted so that COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
131 
the illuminating rays do not enter the system of observation. One 
of the simplest ways of doing it is to use total reflection (165). Figure 
42 shows the way in which the problem was solved by Cotton and 
Mouton (166). By means of a lens a beam of light is thrown into the 
Fig. 42.-The Cotton and Mouton dark field condenser. 
cell containing a thin layer of colloid solution and is totally reflected 
from the upper surface of the cover glass. 
Fig. 43 gives the Zeiss paraboloid condenser designed by Sieden- 
topf (167). The illuminating beam enters through a ring-shaped 
Fig. 43.-Siedentopf's paraboloid dark field condenser 
diaphragm and is reflected into the cell where it is again totally 
reflected at the upper surface of cover glass. In this way we get 
comparatively good illumination because the aperture is very high. 
Fig. 44 shows the Zeiss cardioid condenser also designed by Sieden- 
topf (168). It gives a considerably higher intensity of illumination. 
By means of the different glass surfaces, the illuminating beam of 
light is reflected into the cell at a very high aperture. 132 
COLLOID CHEMISTRY 
Fig. 45 shows the Jentzsch condenser manufactured by Leitz (169). 
The colloid solution is poured directly into the condenser and the 
Fig. 44.-Siedentopf's cardioid dark field condenser, 
illuminating beam is reflected so that it enters the cell in about the 
same way as in the first ultramicroscope-at right angles, but it enters 
Fig. 45.-Jentzsch's dark field condenser 
symmetrically from all sides, i.e. we have a sort of disc of light con- 
centrated in the sol. 
Of course it is net only the aperture of the illuminating system COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
133 
but also the way in which the rays are concentrated-i.e. the optical 
properties of the system-which is of importance. The picture (Fig. 
44) which gives the diagram of the Zeiss cardioid condenser also shows 
a photograph of the illuminating beam. The beam was made visible 
by placing a piece of fluorescent glass on top of the condenser. It is 
obvious from the figure that the concentration of light in the cardioid 
is almost ideal. A similar photograph of the illuminating beam in the 
paraboloid condenser shows less complete light concentration (170). 
Fig. 46 shows the details of the cell used in the slit ultramicroscope. 
The body of the cell is made of black glass. The windows are of 
quartz and the solution can be passed through the cell orthogonally 
to the section shown in the diagram. We see that the distance from 
the light beams to the walls of the cell is comparatively large and 
Fig. 46.-Diagram of the light beams in the cell of the slit-ultramicroscope. 
this feature is sometimes of importance. In order to determine the 
size of the particles by means of the ultramicroscope, we must be able 
to count the number of particles within a certain volume. We can 
do that by putting a stop with a suitable aperture in the ocular of the 
microscope screening off the main part of the beam so that we only 
see the particles contained in a very small volume. 
A type of cell used by Regener in studying disperse systems in 
gases is shown in Fig. 47 (171). It is built up of a sort of T-tube 
provided with windows. The gas can be passed through the cell. 
Fig. 48 shows the kind of cell used in experiments with the Zeiss 
cardioid condenser. The cell is made out of melted quartz and con- 
sists of two plates. In the lower part there is a ring-shaped groove 134 
COLLOID CHEMISTRY 
and the quartz inside the groove is polished down a few p so that 
by placing a drop of colloid upon the inner platform and covering it 
with the quartz cover glass, we get a thin layer of the colloid enclosed 
Fig. 47.-Regener's cell for the ultramicroscopic study of particles in gases 
between the quartz surfaces. The thickness of the layer is a few p.. 
Quartz is used because we must have a material that does not fluoresce, 
which can be cleaned very carefully, heated and cooled in a dust-free 
atmosphere. 
Fig. 48.-Siedentopf's cell for the cardioid ultramicroscope. 
When we use the slit ultramicroscope to determine the number of 
particles in a certain volume of the sol, we have to place a diaphragm 
in the ocular to be able to observe just a certain part of the light 
beam, and we must also know the depth of the volume. If the volume 
observed is represented by the cylinder C (Fig. 46) the top surface is COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
135 
determined by the diaphragm in the ocular and the height of the 
cylinder by the depth of the illuminating light beam. To measure 
this, the Siedentopf-Zsigmondy ultramicroscope is arranged so that 
the slit which is placed between the light beam and the condensing 
lens can be turned at right angles in order that the depth of the beam 
be transferred to a horizontal plane and thus be made the width 
of the beam. By placing a scale in the ocular, we can measure the 
width of the beam. After turning the slit back 90° again we have 
the measured distance as the depth. During these measurements, the 
cell has to be filled with a dilute solution of eosin or with a fine 
grained sol. 
All we can get from an ultramicroscope measurement is, of course, 
the number of particles in a certain volume, and if we know the total 
mass of the disperse phase contained in it, we can get the average 
mass of the particles. If we know the density p of the particles and 
assume that they are not far from, say spherical, we can, of course, 
determine the linear radius r. We have 
3I~3M 
r = wi- 
1 4jtpn 
where M is the total mass and n the number of particles in the volume 
observed in the ultramicroscope. 
In many cases the particles are too small to be seen in the ultra- 
microscope. A method that can be used in some cases in combination 
with ultramicroscopic determinations is the following. Zsigmondy 
has pointed out that it is possible to deposit gold around small gold 
particles to make them big enough to be seen and counted in the 
ultramicroscope (172). If we know the mass of disperse phase of the 
original sol, we can calculate the size of the original particles. In that 
way we have been able to measure the radius of particles down to 
about r = 1.0 pp. Of course it is very important that all the gold 
be deposited on the particles we are measuring-that there shall be 
no spontaneous formation of particles. According to some investiga- 
tions by Westgren (173), the concentration of the HAuC14 should not 
be less than ICT4 normal and the number of nuclei not less than 5 X 109 
per cc. If we have too few gold nuclei, some of the gold forms new 
particles so that we get too high a number. If we get the same 
number of n per cc. nuclear liquid when we use different amounts of 
our nuclei liquid together with different amounts of HAuC14, i.e. if 
we get a linear relation between the number of particles and the 136 
COLLOID CHEMISTRY 
number of cc. of nuclear liquid that we use, this is a criterion that 
there is no spontaneous formation of particles. In some experiments 
that Westgren made to check up this method, he found that on adding 
a different number cc. of the original colloid or nuclear sol, indicated 
by K in Table XXVII, the number of particles n divided by K was 
fairly constant. 
TABLE XXVII 
Determination of Size of Particles in a Gold Sol by Means of the Nuclear 
Method 
K 
n/K 
8 
15.1 
12 
14.1 
16 
14.4 
20 
14.5 
Borjeson (174) has shown that it is possible to determine the size 
of small particles of other metal colloids by using a suitable gold 
reduction mixture. Not only metals but a few other substances such 
as sulphides can be determined by depositing gold upon the particles. 
The method applies not only to the determination of size of particles 
in hydrosols but also to organosols containing metallic particles. 
TABLE XXVIII 
Determination of Size of Particles in Cadmium Alcosols by Means of the 
Nuclear Method 
Radius of Cd particles as determined 
Volume nuclear liquid-Cd sol-per 
by measurement of degree of disper- 
50 cc. of reduction mixture. 
sion of gold sol formed. 
0.2 
11.4 pji 
0.1 
10.7 
0.05 
11.0 
0.025 
10.9 
If, for instance, we have a colloid solution of platinum in ether, we 
take a certain volume of the ether sol and mix it with alcohol, and 
then a suitable volume of that mixed sol and mix it with water. 
Such a sol can be used as a nuclear liquid and we can count the num- 
ber of particles if they have been made large enough to be seen. 
In this way it is possible to determine by means of the ultramicro- 
scope very small particles in different dispersion media (175). 
Sedimentation.-Another method of equal importance for the de- 
termination of size of particles is the method of measuring the veloc- 
ity of sedimentation. According to investigations by Stokes (176), COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
137 
the constant velocity with which a spherical particle falls in a liquid 
is determined by the following law. The force of friction is 6;tqrv 
and the force of gravity 
4 
-itr3(pp -pd)g 
where q is the viscosity of the liquid, r the radius of the particle, 
v the velocity of fall, pp and pd the densities of the particle and the 
liquid respectively, and g the gravity constant (Fig. 49). The force 
Fig. 49.-Movement of a spherical particle in the field of gravity. 
of gravity and the force of friction are opposed and equal when the 
particle falls with constant velocity, i.e. 
4 
6jtqr.v = g jtr3 (pp - pd) 
or 
- hv 
r- 12 (pP-pd)g 
which is Stokes law for sedimentation of particles. 
If we are able to measure the velocity of fall and if we know 
the viscosity of the liquid, the difference in density between the particle 
and the liquid, and the gravity constant, we can calculate the size. 
A large number of determinations of size of particles have been 
made by using the Stokes' formula. The values obtained by this 
method agree fairly well with those of the ultramicroscope. It is 
often more convenient to measure the rate of fall than to use the 
ultramicroscope (177h 138 
COLLOID CHEMISTRY 
When measuring the rate of fall of particles we often have the 
solution enclosed in a cell between two parallel glass walls so that 
the distance between the wall and the particle is comparatively small. 
In such a case the friction constant is higher than 6;tqr, which 
formula is based on the assumption that the distance from the particle 
to the walls is large. In case the particle is falling contiguous to 
a wall, a correction must be introduced. This problem is so im- 
portant that quite a number of attempts have been made to find 
the correction. According to a formula given by H. A. Lorentz (152), 
the force of friction when a particle with a radius r is falling parallel 
to a wall at the distance 1 is 
(q r \ 
1 + lfrr)* 
According to some recent investigations by Faxen (178), the fric- 
tional force for a spherical particle falling in the middle between 
two parallel walls is 
a 1 
oitnrv. r' 
1-1.004^ + 0.418^- -0.169. 
If we calculate this correction for different values of r and 1, we 
find for r = 1 p, and 1 = 10 p about 10 per cent; for r = 100 pp, 
and 1 = 10 p about 1 per cent. That is for particles of colloidal 
size in a cell not too thin, the correction factor is not so very high. 
The gravity force on this planet is not strong enough to allow 
us to determine the size of very small particles by the method of 
sedimentation. A radius of 50 pp in the case of a heavy metal like 
gold is about the limit. By using a centrifugal force instead of 
the gravity force it is possible to extend the range of the sedimenta- 
tion method considerably. The two opposed and equal forces acting 
dx 
upon the particle (Fig. 50) are the frictional force 6jtqr -t- and the 
Qt 
centrifugal force 
4 
~jtr3(pp - pd)co2x 
where co is the angular velocity, x the distance between the axis of 
revolution and the particle. Hence 
dx _ 2 r2(pp - pd)co2 
dt ~ 9 q COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
139 
If we integrate for the fall between Xi and x2 we have 
x2 t 
| dx _ 2 r-(Pp_ Pd)r 
J x 9 T] J 
Xx o 
lnX2 _ 2_j^(pp-Lp<Jart 
Xi 9 T) 
r=^T3EE 
I 2 (pp - pd)co2t ' 
The experimental details for the application of this procedure 
are now being worked out by Nichols and the writer in the Uni- 
Fig. 50.-Movement of a spherical particle in a field of centrifugal force. 
versity of Wisconsin chemical laboratory and by Rinde and the writer 
in Upsala. The centrifuge is built so that the rate of fall of the 
particle-or the boundary between the clear liquid and the sol-can 
be measured during centrifuging. 
The method of studying the degree of dispersity by means of 
measuring the velocity of fall is important because it has been pos- 
sible to develop methods of measuring the distribution of size of 
particles based on the velocity of fall. As a matter of fact, these 
methods are the only accurate ones of measuring the distribution of 
size of particles so far. 140 
COLLOID CHEMISTRY 
If we use the gravity force, the method of measuring distribution 
of sizes by means of sedimentation can only be applied to compara- 
tively coarse particles, but it will probably be possible to extend this 
method to the use of centrifugal forces, and that would give us- 
as will be shown in the sequel-a means of studying the distribution 
of size of small particles. 
The distribution curve gives the relation between, e.g. the radius 
of particles and a certain function that represents the distribution of 
the sizes. 
A simple way of plotting a distribution curve is to take the 
dn * 
radius of the particle as abscissa and -r- as ordinate where n is 
dr 
the percentage number of particles (Fig. 51). The area between the 
Fig. 51.-Distribution of sizes of particles in a sol as function of the change of 
number of particles with radius. 
radii r and r -|- dr represents the percentage number of particles within 
this interval of radius. We can also choose as our distribution 
ds 
function where s is the percentage mass of particles. It is some- 
times more convenient to plot log r as abscissa instead of r. In order 
to have the area representing the number or mass of particles within 
the interval in question we must in this case multiply the ordinates 
by r. 
The first measurements of distribution curves were carried out 
by the writer and Estrup (179). The rate of fall of a statistically 
sufficient number of particles was measured directly in the ultra- 
microscope. The sol studied was enclosed in a cell between parallel 
walls and illuminated by a dark field condenser. The time required COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
141 
for a particle to move from one mark in the ocular scale to another 
was recorded. In that way we were able to get an idea of the dis- 
tribution of particles in a few disperse systems: viz. a mercury emul- 
sion, a gamboge suspension, the latex of Chelidonium laciniatum Mill, 
and milk. These preliminary experiments showed that the distribu- 
tion curve is very different in different cases. The Chelidonium latex, 
for instance, gave a very steep curve, i.e. it consists of particles of 
nearly the same size, while milk gives a broad curve representing 
particles of different sizes. I think it would be worth while to carry 
Fig. 52.-A sedimenting sol containing particles of different size. 
out some similar investigations for other plants' juices-for instance, 
for the rubber latex. 
To measure the particles directly is, of course, a very tedious 
task. We have made a few experiments to take photographs in the 
ultramicroscope and measure the lines on the plate for a sufficiently 
large number of particles but there are certain difficulties which make 
this method less promising. 
A comparatively simple method of measuring the distribution of 
size of particles by means of the rate of fall is to measure the dis- 
tribution of density in a column of colloid after it has been standing 
a certain time at constant temperature (180). If Fig. 52 represents 
such a column, it is obvious that after a certain time t each height x 142 
COLLOID CHEMISTRY 
corresponds to a certain r value representing a particle which has 
fallen through the distance x. For each x there is a corresponding 
radius. Now let us assume that the column contains particles of 
various sizes. After a certain time particles of a certain size will 
have reached a certain x value, as given by the Stokes formula. The 
particles with a radius greater than r -f- dr will all have passed the 
horizontal plane through x + dx, and all the particles with a radius 
less than r will not have passed the horizontal plane through x. 
If we measure the concentration as a function of height and call 
it c, the above reasoning means that the difference in concentration 
between the heights x + dx and x is due to the amount of disperse 
system that has particles of radius between r and r dr, i.e. the 
change in concentration de corresponds to the change in radius dr. 
If we can measure the change in concentration with height, we can 
get our distribution function dc/dr by taking the difference in the 
reading at successive points and calculate from the Stokes formula 
the values for the radius. We tabulate the values x and c and from 
Stokes formula we calculate the values of r that correspond to x and 
take the difference between successive values of r and c. The ratio 
between the difference will give us our distribution function. Ex- 
pressed mathematically we have 
de 
de _ dx 
dr dr 
dx 
But 
dr A ., „ 
v- = = if r2 = A2x 
dx 2Vx 
thus 
dc'_ de 2^x _ de 2yx 
dr - dx A dr Ig 
12 (pP-pd)gt 
The difficulty is in measuring the variation of concentration with 
height. 
One of the most simple methods of measuring the variation of 
concentration with height, a method that can be applied without dis- 
turbing the equilibrium, is to measure the variation of light absorption 
with height dk/dx. We can, of course, introduce this function instead 
of dc/dx, because the absorption constant k at a certain concentration COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
143 
is equal to kx.c where kx is the light absorption constant at the unit 
concentration. Thus 
dk _ . de 
dx1 dx 
de _ 1 dk 
dx - kx ' dx 
and 
de _ 1 dk 2^5 
dr kx ' dx A 
Now the light absorption often varies with the radius. In such a case 
we have to introduce different values of the light absorption constant 
for the different values of r and that means that the constant kx must 
be taken from a graph giving the relation between the radius of the 
particle and the light absorption constant for a certain wave length. 
Rinde and the writer used this method for determining the dis- 
tribution of size of particles in coarse grained gold sols. 
A very convenient procedure would be to measure the variation of 
concentration with height directly by the absorption of X-rays of 
a suitable wave length. In the case of gold, we could without much 
difficulty find such a wave length but it is not easy to adjust this 
procedure for different suspensions. 
If we want to make measurements of this kind using a centrifugal 
force instead of gravity, the following formula has to be applied 
(Rinde and the writer) 
det 
de _ dx /x + a\2 
dx | 2 (pp - pd)co2t 
where a is the distance between the surface of the sol column-taken 
as the sector of an annulus-and the axis of rotation and ct the con- 
centration after the time t. 
Thus 
do_dc, 2(x+n)^m(^) 
dr dx ' 2 /9 n 
a 12 (pp -pd)(o2t 
Experiments of this kind are now in progress in the University 
of Wisconsin chemical laboratory (Nichols and the writer) and in 144 
COLLOID CHEMISTRY 
Upsala (Rinde and the writer). Photographs of the sol can be taken 
during centrifuging and from measurements on the photographs the 
variation of concentration with distance from the surface of the sol 
can be calculated. 
Instead of measuring distribution of concentration with height in 
a system after a certain time we can measure the amount of sedi- 
mentation on a certain surface-or the increase of weight of the 
sediment with time. A very ingenious method based on that principle 
was worked out by Oden (181). He recorded automatically the 
amount of sediment with time of accumulation on a plate immersed 
in the disperse system and suspended on a balance and he showed 
that the distribution curve can be found from the data given in the 
sedimentation curve. 
The total amount of sediment P on the plate after a certain time 
can be divided into two parts, one part S corresponding to all the 
groups of particles that have completely settled (all groups which 
have particles of such a radius that they have totally reached the 
plate), and another part consisting of those parts of the groups of 
particles of smaller size that have settled on the plate. For each 
of the latter groups the rate of settling is constant and for all groups 
dP 
together equals After the time t the second part therefore 
, , dP , , 
equals t-^r, and we get 
Qb 
dP 
P = S-f-t^-. 
dt 
This equation simply tells us that the sediment is composed of 
two parts-those completely settled and those only partly settled. 
A derivation gives 
dP _ dS d2P dP 
dt " dt + t dt2 + dt 
or 
dS _ d2P 
dt " 1 dt2 ' 
That formula actually gives us the means to calculate the distribution 
curve. Of course we do not want to get the dS/dt but dS/dr. Now 
dS 
dS dt 
dr dr 
dt COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
145 
dr 
and the -v- can be found from the Stokes formula r2 = C2/t. That 
dt 
gives us 
dr r 
dt - 2t 
and 
dS _ 2t2 d2P 
dr- r dt2 
dS 
i.e. the distribution function t- is equal to the second derivative 
dr 
of the weight multiplied by -2t2/r, where r corresponding to dif- 
ferent times can be expressed by the Stokes formula. What we 
actually measure is the relation between P and t. From the 
dP d2P 
P,t-curve the -r-,t-curve can be found and from that one the -,-w L 
dt dt2 ,t 
-curve can be calculated. There is, however, a much simpler way of 
finding the distribution function from the P,t-curve graphically. 
Fig. 53.-Determination of the distribution function from the 
sedimentation curve. 
The ordinate w cut off on the P axis by a tangent (Fig. 53) is 
1 x x dP 
equal to P - t -rr. 
dt 
Thus 
dw , d2P 
dT- 117' 
but we have already found 
dS__. cPP 
dt " dt2 ' 146 
COLLOID CHEMISTRY 
hence dw _ dS 
dt dt 
From this it is obvious that we can determine the dS values by draw- 
ing tangents from successive points on the P,t-curve corresponding 
Fig. 54.-Distribution of sizes of particles in a mercury emulsion as a function 
of mass of particles. 
to equally long time intervals and taking the difference between the 
cuts on the ordinate axis. These differences dS correspond to the dr 
values that can be found by means of Stokes formula. 
Fig. 55.-Distribution of sizes of particles in a mercury emulsion as a function 
of number of particles. 
Oden has with great success used this method for the study of the 
distribution of size of particles of various coarse grained sols such 
as clays, precipitates of barium sulphate, etc. Nordlund has meas- COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
147 
ured the distribution curves of mercury emulsions. Fig. 54 gives 
one of Nordlund's curves plotted with ordinates as a function of 
mass and with log r as abscissae, and Fig. 55 the same scries of 
measurements plotted with ordinates as function of number of particles 
and with r as abscissae. 
Oden's apparatus was originally devised for the study of rather 
coarse systems such as clays and required comparatively large quan- 
tities of particles, viz. about 1 gr. Borjeson using direct weighing 
Fig. 56.-Diagram of arrangement for automatic registration of sedimentation 
of sediment showed that Oden's procedure is capable of being ex- 
tended to small quantities; he used 0.1-0.2 gr. in a sedimentation 
experiment. It is desirable however to be able to use say only 0.02 
gr. and to have the sedimentation of such small quantities recorded 
automatically. 
Rinde and the writer (180) modified Oden's apparatus, adopting 
the principle of compensating automatically the disturbance of equi- 
librium of the balance by means of a coil acting on a tube of iron 
suspended on the arm of the balance and recorded the current in the 
coil by means of a self-registering milliammeter. In this way we 
got a diagram showing the variation of compensating current with 148 
COLLOID CHEMISTRY 
time and this curve can easily be transformed into a curve giving 
the variation of weight of sediment with time. 
Fig. 56 gives a diagram of the apparatus and Fig. 57 a photo- 
graphic view of it. The particles settle on a plate of silica or very 
resistant glass Q, attached to a fine glass or silica rod suspended on 
one arm of the balance and immersed in the sedimentation vessel of 
resistant glass. It is essential to have those parts made of silica or 
insoluble glass in order to prevent coagulation. The sedimentation 
vessel is thermally protected by means of a Dewar vessel. On the 
Fig. 57.-View of apparatus for automatic registration of sedimentation 
other arm of the balance is suspended the iron tube B with its end 
reaching into the coil E. The latter is connected with the regulation 
resistance R, the precision self-registering milliammeter P, an accumu- 
lator battery of 40 volts and the drum resistance T. At the beginning 
of an experiment the resistance R is adjusted so as to give equilibrium. 
When the weight of the plate increases because of the particles settling 
on it, the contact kx consisting of a platinum point and plate is closed 
and by means of a very sensible system of relays the motor M is set 
in motion revolving the drum T. Thereby the sliding contact D is 
carried toward the left and a certain portion of the resistance wire COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
149 
is taken out and thus the equilibrium reestablished. The most diffi- 
cult point in the construction of the apparatus was to get the con- 
tact ki to work satisfactorily. The resistance to direct current of 
such a contact is dependent on the pressure exerted on it. To over- 
come this difficulty we applied a high frequency potential of about 
20 volts between point and plate. This potential was produced by 
means of an audion generator of frequency 600, and the direct cur- 
rent of the contact was cut off from the generator by inserting the 
two condensers Ci and c2. When the contact kx is closed the audion 
relay AKGK sets the electromagnetic relay rx in action and this 
acts on the second electromagnetic relay r2, which closes the cur- 
rent to the motor. In this way it became possible to get the com- 
pensating arrangement to work automatically without affecting the 
sensitivity of the balance. 
Methods based on osmotic pressure, diffusion, sedimentation equi- 
librium and Brownian movements.-Other methods for measuring the 
size of particles, and in some cases the distribution of sizes, are based 
on the Brownian movement and the phenomena connected with the 
Brownian movement. 
From measurements of the osmotic pressure 
n RT 
p = TT-n 
we can find the number of particles n per unit volume, and if we 
know the amount of material per unit volume of the sol and make 
assumptions with regard to the density and the shape of the particles, 
we can calculate the linear dimensions. For ordinary colloid sys- 
tems, the number of particles per unit volume is very small and the 
osmotic pressure therefore exceedingly low. When we try to measure 
the osmotic pressure by means of a membrane, serious errors might 
be caused by the crystalloids present. In some cases the membrane 
used is perhaps slightly semipermeable with regard to the crystal- 
loids present and in other cases there might be established a Donnan 
equilibrium. 
One of the osmometers used for measuring osmotic pressure in 
colloids and constructed by Sorensen is shown in Fig. 58 (182). It 
was built especially for measuring the osmotic pressure in proteins. 
The osmotic pressure is compensated by an equal pressure of air 
regulated by means of a water column. As a membrane, Sorensen 150 
COLLOID CHEMISTRY 
used collodion. Determinations of size of particles with this method 
have not given any appreciable results (183, 184). 
Fig. 58.-Sorensen's osmometer. 
Another phenomenon that can be utilized for the study of size of 
particles is diffusion. The diffusion constant is equal to 
D=^ . JL 
N . 6nqr 
where r is the radius of the spherical particle. In cases where we are COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
151 
unable to count the particles in the ultramicroscope, this method, 
of course, is of considerable value, especially in the case of pro- 
teins (185, 186). A few determinations have been made and it will 
probably be possible to gain considerable information with regard 
to size of particles by means of diffusion experiments (187). Of 
course, if we measure diffusion in the ordinary way, building up a 
column of diffusing liquid out of one layer of solution and three 
layers of solvent on top of it, then calculate the diffusion constant 
from the values of concentration found in those four layers after 
a certain time, we only get an average value of the size. If the 
particles are not equal, the values of the diffusion constant which 
we get from determinations for different layers would, however, be 
slightly different. 
It seems that it might be possible to work out a method for de- 
termining the distribution curve from measurements of diffusion. 
One of the simplest cases that can be treated theoretically is a dif- 
fusion column built up of a very thin layer of solution at the bottom 
and a comparatively high column of solvent on top of it. In this 
case we have for the concentration c1)X of a certain grain class 1 at 
the height x 
x2 
Ci,o.a 4Dxt 
C1" = 2'VSD^6 
If our sol was built up of say only 3 classes of grains with the dif- 
fusion constants Dx D2 D3, we would get for the total concentration 
observed at the height x 
V _ _ 2a 
--- Cobs - , 
X2 X2 X2 
Ci,o 4Dxt c2,0 4D2t c3,0 4D3t 
-4 H C 
VDX VD2 VD3 
This equation contains 6 unknown quantities D1; D2, D3 and c1)0, c2,0, 
c3,0. If measurements were made at different heights and at different 
times, it would be possible to determine the original concentrations 
c0 and the diffusion constants. From these data the amount of particles 
of different size could be calculated. If the sol contained particles 
of all sizes, a similar procedure might be used. We would have to 
decide upon a certain number of size classes and plot the distribu- 
tion curve from the percentage amount of disperse phase correspond- 
ing to the different radius intervals as calculated from the values 
of the diffusion constants found. 152 
COLLOID CHEMISTRY 
Another possibility is to measure the change of concentration with 
height in a diffusion system built up of a relatively high column of 
solvent on top of a relatively high column of solution. In this case 
we have 
y 
_ Ci,o A 2 f - y21 \ 
C"x- 2 (/ yjJe dy) 
o 
y=2W' 
An attempt to determine the distribution of size of particles based 
upon this equation is now in progress in the writer's laboratory. 
The sedimentation equilibrium can, of course, be used for de- 
termination of size of particles. The ratio of the concentration at 
different heights in sedimentation equilibrium is an exponential func- 
tion of the difference in height. As already shown, we have 
N 4 
m - RT ' 3 Pd)g(x2 - xx). 
-2 = e 
Bi 
Westgren (188) has actually made an attempt to determine the dis- 
tribution curve for gold sols by means of the sedimentation equi- 
librium. In the original sol containing particles of different sizes, it 
was found to be very difficult to get accurate values of the distribu- 
tion from measurements of the sedimentation equilibrium. If, how- 
ever, we could by some means make a separation of the particles of 
different sizes and then study sedimentation equilibrium, we could 
get some idea of the distribution of the sizes. 
Westgren enclosed the sol to be studied in a thin cell and centri- 
fuged down the particles to the bottom. It was then turned upside 
down and allowed to stand for some time. If the particles are prac- 
tically in the same layer at the start, the sedimentation will result 
in an almost complete separation of the different sizes, the big 
particles falling rapidly and the small particles more slowly (Fig. 
59A). If we then turn the cell 90°, the particles will settle down 
and after some time we get a sedimentation equilibrium (Fig. 59B). 
If the concentration is then measured as a function of the height at 
different distances from the edge that served as a bottom to the cell 
in the first centrifuging, we get a series of values that enable us 
to calculate the distribution curve. Of course, the values we get in COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
153 
this way are not very accurate because we cannot get a complete 
separation and in the time that is required for the measurements there 
will be a certain diffusion and consequently a certain mixing of the 
particles of different size. 
The measurements of the average displacement of the particles in 
the Brownian movement 
(x2 - Xi)2 = 2Dt 
is also a means for measuring the size. In some studies of the charge 
of particles in gases,-measurements undertaken in order to determine 
the elementary electrical charge,-the size of the particles was actually 
measured by means of the Brownian movements. This formula could 
Fig. 59.-Westgren's measurement of the distribution of sizes of particles in 
a gold sol. 
also be used for measuring distribution curves. Some preliminary 
experiments show that this can be done but because of the rather great 
number of determinations necessary for sufficiently reliable statistics, 
the method has never been worked out in detail (179). 
Ultrafiltration.-The method of ultrafiltration has also been used 
for the study of the size of particles. The values we get by this 
method are, however, very uncertain. 
Bechhold showed that by varying the concentration of the gels 
in the filters used, the size of pores could be varied (189). Ordinary 
filter paper contains pores of about 3 p, hard filter 1.5 p, porcelain 
0.16 p. These filters, of course, will allow ordinary colloids to pass 
through. With filter paper impregnated with collodion or gelatin, 
we can get pores of different size by using solutions of different 
concentration for impregnating them. Bechhold found that the per- 
meability of such filters checked fairly well with the order of size of 154 
COLLOID CHEMISTRY 
particles of the colloids he tested. He also tried to measure the 
absolute size of pores by different methods and at least obtained an 
idea of the order of magnitude of the pores. In one method used, 
air was pressed through the fdter. The critical pressure when air 
bubbles began to appear was measured. If we regard the filter as a 
bundle of capillaries, the diameter of which is d, we get 
, 4 o- 
p X 1-033 X 105 
where o- is the surface tension and p the critical pressure in atmos- 
pheres. If we know the surface tension and measure the pressure, 
we can determine the diameter of the pores. The following figures 
show that rather high pressures have to be applied in such cases where 
the pores are of the same size as the particles in colloid solutions. 
1 atm 300 pp 
10 11 30 pp 
100 " 3 pp 
Bechhold also tried to determine the size by measuring the amount 
of water that filtered through the membrane, calculating the diameter 
from Poiseuille's law of the flow of water through a capillary tube. 
He obtained values that did not check very well with the values 
obtained from the other method, but they were of the same order of 
magnitude. 
If we determine the absolute size of particles by filtering the col- 
loid through filters of different pore widths, we find that on the whole 
we get results that do not check up with the results arrived at by 
more reliable methods. In ultrafiltration there are many factors that 
influence the passage of the particles through the filter. If the 
particles are adsorbed, they will not go through according to the 
size of pores and in some cases the particles might be deformed and 
go through too readily. 
X-ray analysis.-One of the most promising new optical methods 
for studying the structure and size of particles is the X-ray analysis. 
This method has not, as yet, been worked out in detail. In the future 
it will probably prove a very useful instrument for the study of 
colloids (190). 
It is well known that if a narrow beam of homogeneous X-rays 
is thrown against the surface of a crystal reflection will occur if the 
condition 
n A = 2 d sin cp COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
155 
is fulfilled, where X is the wave length, n an integer, d the distance 
between successive planes of highest atom density in the crystal and 
<p the angle between the ray and the planes in the crystal. If the 
crystal is rotated around the axis of the beam, the reflected ray 
forms a cone with the apex in the point where the ray strikes the 
crystal. Then suppose that the crystal is rotated not only around 
the axis of the ray but also around all other possible axes. The 
result will be a series of cones of reflected rays all of which have 
their apex in the same point and with a common axis, derived from 
the different kinds of reflecting planes in the crystal. Debye and 
Hull suggested that instead of rotating the crystal, we should grind 
the crystal to a fine powder. Such a system would contain crystals 
in practically all possible positions with regard to the primary X-ray 
beam. 
The Debye-Hull X-ray analysis in the case of a colloid is carried 
out in the following way. A beam of homogeneous X-rays is passed 
through a thin cylinder of the colloid enclosed in a collodion tube. 
The reflected rays are photographed on a film-usually bent as a 
cylinder around the specimen studied. From measurements on the 
photograph, the angles (p can be found and from those data and the 
wave length of the rays, the distances between the planes in the 
crystal can be calculated. Investigations carried out by Scherrer 
and by Bjbrnstahl have given the result that the particles in most 
sols are crystalline in nature and possess the same crystal lattice as 
the macroscopic crystals. 
Even gold particles of linear dimensions down to 1.9 pp give the 
same kind of an X-ray diagram as a gold wire. When we get down 
to particles of such smallness, there is, however, a certain difference- 
the lines in the X-ray diagram are broader in the case of the fine- 
grained colloid than in the case of a gold wire. Scherrer has shown 
that it is possible to calculate the size of the particles from the 
width B of the lines, taken as the distance between the points on each 
side of the maximum of blackening where the intensity of the radia- 
tion is reduced to half its value. According to Scherrer we have in 
the case of a cubic lattice 
B - 2</- - -- 
1 it a cos <p 
where a is the linear dimension of the particles taken as cubes. 
A very fine-grained gold sol prepared by Zsigmondy and meas- 156 
COLLOID CHEMISTRY 
ured by Scherrer, gave the value 1.86 pp. while the size of the particles 
as determined by means of measuring the osmotic pressure was found 
to be 1.6 pp. When worked out properly this method of determining 
the size of very small particles in colloids will probably prove very 
useful. One of the experimental difficulties is that the colloid to be 
studied by this method must contain the disperse phase in a rather 
high concentration, and that sols coagulate very rapidly under the 
influence of the intense X-ray illumination. To avoid this, Bjorn- 
stahl has used an X-ray camera with the sol streaming in a fine 
cylindrical jet through the center of the camera. 
Light absorption and Tyndall effect.-The size of particles and 
the shape and structure of particles can also be studied by means of 
measuring light absorption and scattering of light by the particles. 
There is no simple relation between the size of particles, and light 
absorption and the scattering respectively, but it is possible to find, 
experimentally, certain empirical relations. Under certain conditions, 
at least, it is possible to find the size of particles from such rela- 
tions (191,192). 
The light absorption can be measured by ordinary methods. If 
a beam of light is passed through a layer of thickness d of a sol, we 
have 
I = Io . e'k • d 
where Io is the intensity of the light that enters the sol, I the intensity 
coming through, and k the absorption constant. Naturally k depends 
on concentration and according to Beer's law that actually holds for 
colloids 
k = kx c 
where kx is the light absorption constant for unit concentration and 
c the concentration. To measure k any suitable spectrophotometer 
may be used, e.g. the Konig-Martens-Grunbaum instrument. The 
intensity of two beams of light, one of them having passed through 
the sol and the other through the dispersion medium, are compared. 
The instrument is constructed so that when the light reaches the 
comparator the two beams are linear polarized in planes orthogonal 
to each other. The comparator is a Nicol prism which can be rotated 
and allows the observer to adjust the two halves of the field of view 
till they become equal. From the angle of rotation, the absorption 
constant can be calculated. 
The method of comparing the intensity of the light absorption in COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
157 
the dispersion medium and in the sol by means of the energy given 
off to a sensitive thermopile has also been used, especially for studies 
in the ultraviolet spectrum (192). The manipulating of a galvanom- 
eter having the high voltage sensitivity required in such measure- 
ments is however rather troublesome. 
A very convenient way of measuring light absorption throughout 
the visible and ultraviolet spectrum was worked out by Rinde in the 
writer's laboratory (193). 
A beam of light from a mercury quartz lamp fed from an accumu- 
lator battery of constant potential was made parallel by means of 
two quartz lenses, passed through the vector wheel S (Fig. 60) rotat- 
ing with constant velocity and then through the photographic shutter 
B which is opened just before the aperture of the wheel passes the 
Fig. 60.-Diagram of arrangement for measuring light absorption. 
beam of light and is shut after the passage. This device enabled us 
to duplicate exactly the times of exposure. The light beam then 
passed the cell A containing the sol and then a system of 3 Nicol 
prisms Nx, N2, N3. These prisms are cut with the end surfaces 
orthogonal to their length direction and are cemented with glycerine. 
Finally, the light beam enters the quartz spectograph Q and its spec- 
trum is photographed on the plate F. 
A series of equal-timed exposures with parallel nicols are taken. 
The sol is then removed and the cell filled with the pure dispersion 
medium. A new series of spectra are taken on the same plate varying 
the intensity of the light by turning the nicol N2 through a certain 
angle cp. If Io denotes the intensity of the light striking the photo- 
graphic plate when the nicols are parallel and the cell is filled with 
the dispersion medium, I = Io cos4 tp is the intensity when the nicol 
N2 is rotated the angle cp. With parallel nicols and the sol in the 158 
COLLOID CHEMISTRY 
cell we have 1' = Io e~kd where I' is the intensity of the light striking 
the plate after having passed through the sol, k the absorption con- 
stant and d the depth of the cell. On comparing the two sets of 
spectra and selecting-for a certain line-the spectrum from one set 
that shows the same intensity on the plate as a spectrum from the 
other we get 
I' = I and e~kd = cos4 (p 
that is 
t 4 . 
k = r • In cos m. 
d 
This method has the advantage of avoiding the error introduced 
when comparing the blackening of the plate for exposures of different 
Fig. 61.-Relation between light absorption and radius of particles in gold sols 
length of time. The values we get are therefore quite independent 
of the different properties of the photographic plate at different ex- 
posures. The lines that we select as being equal actually correspond 
to exposures of equal time and equal intensity. 
By means of one or the other of those methods we have measured 
a series of light absorption curves and the measurements show that 
the light absorption varies with radius of the particles. The diagram 
(Fig. 61) gives the relation between the radius of particle and the 
light absorption constant for a certain wave length, 289 pu. for gold, 
measured by Rinde. The discrepancy between the different experi- 
mental values are not due to errors in the determination of the COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
159 
light absorption constant but to the impossibility of reproducing the 
sols. It shows that at present we could never expect to get the same 
value of light absorption for different samples of the same kind of sol. 
The relation between light absorption and wave length for gold 
sols of varying degree of dispersity as determined experimentally in 
the writer's laboratory by Pihlblad is given in Fig. 62. The maximum 
of light absorption first increases, reaches a maximum and then de- 
creases again with decreasing size of particles. 
Mie (194) has worked out a theory of light absorption in colloid 
Fig. 62.-Light absorption curves for gold sols of different degree of dispersity. 
solutions based upon Lord Rayleigh's theory (195) of the scatter- 
ing of light. For the comparatively coarse grained particles, the 
observed and theoretical values agree fairly well. The difficulty 
comes when we have to study very fine-grained particles. According 
to Mie, there must be a limit value of light absorption corresponding 
to infinitely small particles, i.e. when the size of particles decreases, 
the absorption tends to approach a certain limit. In the case of gold 
sols this limit should already be reached at a size of about 5 pp. In 
some experiments with very fine-grained gold sols, we have found 
light absorptions that are lower than this theoretical limit. It is 
very difficult, however, in the case of these extremely fine-grained 160 
COLLOID CHEMISTRY 
sols, to be sure that the particles are actually made up of metallic 
gold and that there is no oxidation-or that the adsorbed layer on 
the particles might not account for the difference in light absorption. 
There is, however, another theory of light absorption worked out 
by Maxwell Garnett (196) who came to the conclusion that the light 
absorption tends to reach the value for the molecular solution or the 
gas of the same substance as the disperse phase when the size of 
particles decreases. In some series of measurements we have actually 
Fig. 63.-Light absorption curves for sulphur sols of different degree of dispersity 
and for a molecular solution of sulphur. 
found that the light absorption with decrease in size of particles tends 
to go down to the values for the molecular solution. With sulphur 
we get a series of curves of this type. The light absorption of a 
molecular solution of sulphur in absolute alcohol is of a similar type 
and not so very far from the light absorption of the fine-grained 
sulphur sols (Fig. 63). Similar results have been arrived at in com- 
paring light absorption in colloid and molecular solutions of selenium 
and some dye stuffs. 
The relation between radius and the scattering of light for a cer- 
tain wave length can be used as a means of determining the degree 
of dispersity. For particles of very low light absorption Lord Ray- COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
161 
leigh found that the intensity of the scattered light was proportional 
to the square of the volume of particles divided by the 4th power 
of the wave length (197). 
v2 
Int. = const. 
i.e. the intensity of scattered light increases rapidly with decreasing 
wave length. For substances with high light absorption, gold for 
instance, similar formulae have been deduced by Mie. The experi- 
mental test has not been completed. However, we can give the rela- 
tion in the form of experimentally determined diagrams. Mecklenburg 
has constructed a so-called Tyndall meter which allows convenient 
measurements of the scattered light (198). By means of a Lummer- 
Brodhun photometer cube, the intensity of the Tyndall light is com- 
pared with a constant light intensity. Light filters can be used so as 
to enable measurements in different parts of the spectrum. Mecklen- 
burg has shown that it is possible by means of his instrument to make 
comparative measurements of size of particles of such sols that possess 
only a slight light absorption, e.g. sulphur sols (199). 
The scattered light can be photographed by means of a spectro- 
photometer of very high aperture and the intensity measured. This 
method, which gives more reliable results than Mecklenburg's is now 
in use in the writer's laboratory. 
When we have determined experimentally the relation between 
radius on one hand and scattered light and absorption on the other, 
we would be able to determine the size of particles of gold sols by 
measuring the scattered light and the absorption. The difficulty is, 
however, that both the amount of scattered light and the light ab- 
sorbed depends not only on the size but also, probably, on the structure 
and shape of the particles. Using different methods of preparing 
sols, we get particles of different shapes and different structures. Gold 
sols that consist of aggregated particles give a light absorption curve 
of quite another kind than a solid gold particle. A sol built up of 
solid gold particles is red provided the particles are not very large. 
Sols containing aggregated particles are blue in color. 
The study of the amount of scattered light when the sol is under 
the influence of certain external forces enables us to get some informa- 
tion about the shape of the particles (200). It is a well-known fact 
that a suspension or a coarse grained colloid that contains rod shaped 
particles shows a peculiar optical effect when stirred-the lines of 162 
COLLOID CHEMISTRY 
flow in the sol being marked by light and dark stripes. A suspension 
of fine grained asbestos having rod shaped particles shows this phe- 
nomenon when stirred. Freundlich has studied this "schlieren-effect" 
in detail (201,202). By giving the liquid a constant motion, the 
phenomenon can be studied quantitatively. Now when a rod shaped 
or a disk shaped particle is carried by the flow in a liquid where there 
is a fall in velocity in some direction, the particles will be oriented 
so that in the case of disk or leaf shaped particles the plane of the 
disk coincides with a surface of constant velocity in the liquid. The 
rod shaped particles will probably be oriented so that their axis is 
Fig. 64.-Freundlich's cell for studying the intensity of the light scattered from 
a streaming sol at different directions. 
along the lines of flow. The cell shown in Fig. 64 was used by 
Freundlich for the study of the intensity of the scattered light. The 
streaming sol could be illuminated with linear polarized light from 
three different directions and the scattered light could also be observed 
from three different directions. 
The intensity of the scattered light in a certain direction depends 
on the way in which the particles are oriented, and on the position of 
the electrical vector and the direction of the illuminating beam (203). 
If the illumination comes from A (Fig. 65) and we observe it from B, 
and if the electrical vector is in a plane orthogonal to the plane of 
the paper, we will get very little scattered light. If we observe it 
from the front and if the electrical vector is in the plane of the paper, COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
163 
we will get more scattered light from the disk shaped particles than 
from the rod shaped ones. This way of observation can be varied 
so that we are able to get at least some idea of the shape of particles 
in different sols. By using this method, Freundlich found that gold 
and silver sols and arsenious sulphide sols contained almost spherical 
Fig. 65.-Scattering of light from needle shaped and from leaf shaped particles. 
particles. Disk or leaf shaped particles were found in ferric oxide 
sols and in blue gold sols. Rod shaped particles were found in vana- 
dium pentoxide sols and in some dye stuffs such as aniline blue and 
benzopurpurine. 
Double refraction.-Another method of getting information about 
Fig. 66.-Diagram of arrangement for measuring magnetic double refraction 
in sols. 
the shape and structure of particles is to measure the double refrac- 
tion in a sol in which the particles have been oriented, the sol being 
allowed to stream or being placed in a field of force such as a gravity 
field, an electric or a magnetic field. One of the most simple methods 
is to measure the double refraction of the sol in a magnetic field. 
There is no danger of contamination by electrolysis as in the case of an 164 
COLLOID CHEMISTRY 
electric field. Bjornstahl in the laboratory of the writer studied the 
double refraction of gold sols in magnetic fields (204). He used the 
Brace method of measurement. A monochromatic beam of light (Fig. 
66) passes the sol S placed between the poles of a powerful electro- 
magnet. At each side of the sol is a polarizing prism Pi, P2, the 
principal planes of the prisms being at right angles and at 45° with 
the lines of force of the field. If the sol becomes double refractive, it 
Fig. 67.-View of arrangement for measuring magnetic and electric double 
refraction in sols. 
means that there is a certain phase difference between the two com- 
ponent rays into which the original plane polarized ray is split up. 
To measure this the mica compensator C is turned until the image 
of the so-called sensitive strip m, a very thin mica leaf, as viewed 
in a telescope vanishes. 
Fig. 67 gives a photographic view of the apparatus. 
Ordinary gold sols show a very marked double refraction down to 
sizes of about 10 pp. The effect is probably due to orientation of the COLLOID PARTICLE AS A MOLECULAR KINETIC UNIT 
165 
particles in the field, indicating that they are dissymmetrical in shape. 
Bjornstahl found that the phase difference A was proportional to the 
square of the field intensity H2. The quantity is therefore inde- 
pendent of the field. It increases rapidly with increased size and for 
gold sols it seems to reach a maximum value at a radius of particles 
Fig. 68.-Formation of a gold sol as measured by the variation of double 
refraction with time. 
of about 60 pp. It then goes down to a minimum and increases again 
with increasing size. The process of formation (Fig. 68) and of 
coagulation (Fig. 69) of sols can be studied by means of measuring 
the double refraction in a magnetic field. 
Fig. 69.-Coagulation of a gold sol as measured by the variation of double 
refraction with time. 
Some determinations on colloid sulphur showed that ordinary sul- 
phur sols prepared by chemical reactions give no double refraction, 
while sulphur sols prepared by grinding sulphur crystals to a very 
fine powder showed double refraction. This probably means that the 
particles of the latter are still crystalline and dissymmetrical in shape 
while the particles in the chemically prepared sulphur sols are spheri- 
cal, perhaps amorphous droplets of sulphur. PART III 
THE COLLOID PARTICLE AS A MICELL 
In the first section we studied the formation of the particle and in 
the second section we studied the particle from the point of view of the 
molecular kinetic theory. We have studied the energy of motion of 
the particles or the Brownian movements, the diffusion, the fluctua- 
tions, and the other phenomena connected with the Brownian move- 
ments. We have studied the methods of determining size, structure, 
and shape of particles. In all those measurements we only take into 
account the particle itself. We do not take into account e.g. in light 
absorption the action of the ions and the molecules adsorbed on the 
surface. Now we are going to study the particle together with its 
surrounding or adsorbed molecules and ions and probably a part of 
the surrounding liquid or gas. The particle, together with the atoms, 
molecules and ions, is called a micell, a term introduced by the French 
colloid chemist Duclaux. 
Under this heading come the phenomena of adsorption, cata- 
phoresis, electro-endosmosis, and the various phenomena of coagula- 
tion, gel formation and changes of structure which we may have in 
colloid systems. 
Adsorption 
The first phenomenon is adsorption in disperse systems. Quite a 
number of investigations have been carried out and various theories 
presented to account for the figures observed. I will try to outline 
some of the important points, such points as are of especial interest 
in the study of colloids. 
The phenomenon of adsorption was discovered in 1777 by Scheele, 
the Swedish chemist. He observed the adsorption of different gases 
by charcoal. A few years later, 1791, a German, Lowitz, found the 
same phenomenon in solutions-i.e. that charcoal takes up dissolved 
substances. 
If we try to define adsorption it is obvious that in the extreme, 
167 168 
COLLOID CHEMISTRY 
adsorption is very different from chemical reaction, but also that there 
are cases where the difference is not so marked. A very striking 
feature is that adsorption often takes place in cases where we hardly 
would expect any chemical reaction-e.g. the adsorption of the noble 
gases by charcoal and the adsorption of different inactive substances 
by the noble metals, platinum, etc. Even in cases where we have 
never found any chemical compounds-e.g. in helium and argon-there 
is very marked adsorption. The volume of argon adsorbed by one 
gram of cocoanut charcoal at 9° C. is 12 cc., with hydrogen only 4 cc. 
and with nitrogen 15 cc. (205) 
This shows that the forces involved in the adsorption phenomena 
are, as a rule, rather different from the forces in ordinary chemical 
compounds. We have never been able to isolate a chemical com- 
pound containing argon, yet we have in it such a marked adsorption. 
If we try to imagine the forces involved, we might assume that 
at the boundary surface part of the valences binding the atoms 
together are free in the form of secondary or partial valences and 
that they are responsible for adsorption. That would make possible 
a certain distinction between chemical compounds and adsorption 
compounds, the former being built up chiefly by means of primary 
valences. Naturally, in the future when we are able to calculate 
the force between the electrons and the positive nuclei in the atoms, 
the difference between chemical compounds and adsorption compounds 
will probably be less marked than it is now. At least, we hope that 
it will be possible to account for all phenomena, physical and chemi- 
cal, by calculating the forces between the molecules and electrons and 
atoms. If those forces are all electrical in nature, the force holding 
the atoms together in a chemical compound such as NaCl and the 
force binding argon atoms at the surface of charcoal, would be of 
the same nature. 
If we study the relation between the adsorbed quantity and the 
concentration in the solution, we find that if we plot the quantity of 
substance taken away from the solution or the amount adsorbed on 
the surface against the concentration of the solution, we get a curve 
concave to the concentration axis (A in Fig. 70). 
Freundlich (206) has tried to express this by means of the ex- 
ponential law 
x - k c n THE COLLOID PARTICLE AS A MIC ELL 
169 
Co/?ce/?fa7fio/? 
Fig. 70.-Adsorption curves. 
where x is the amount adsorbed per gr. adsorbing substance, c is 
the concentration in the solution, and k and n are constants. This 
equation holds fairly well. He found that 
x = 2.606 . c0 425 
gave the relation between adsorbed mass and concentration in the case 
of adsorption of acetic acid on charcoal in the following way: 
Adsorption of Acetic Acid on Charcoal 
TABLE XXIX 
c 
x Values Observed 
x Values Calc. 
0.00092 
2.07 
2.19 
0.00259 
3.10 
3.01 
0.00669 
4.27 
4.15 
0.01708 
5.44 
5.73 
0.02975 
6.80 
6.87 
A few years later, Schmidt (207) and Marc (208) discovered that 
if the adsorption is followed to rather high concentrations, x sometimes 
reaches a maximum value (B in Fig. 70) that cannot be explained by 
the exponential curve (Table XXX). 
Adsorption of Acetic Acid on Charcoal 
TABLE XXX 
c 
X 
0.00884 
0.005223 
0.03217 
0.01006 
0.0372 
0.01259 
0.2116 
0.03224 
1.161 
0.05879 
3.759 
0.07952 
3.752 
0.08105 
5.602 
0.08284 
9.175 
0.09010 
12.65 
0.09526 
16.60 
0.09049 
25.73 
0.08819 
29.38 
0.09019 
30.60 
0.09039 170 
COLLOID CHEMISTRY 
To explain the relation and in order to account for this saturation, 
Schmidt (207) suggested the following formula, where s = saturation 
or the value of the absorbed quantity at saturation. The change of 
absorbed quantity with concentration should be proportional to the 
distance from the saturation point, or 
4^=k(-«). 
It soon became evident that this formula did not express the experi- 
mental values very well. It became necessary to assume that the k 
was a function of the adsorbed quantity; i.e., that k was not really 
constant. Arrhenius (209) suggested to put 
d x klz . 
de x 
which means that we assume k in Schmidt's formula inversely propor- 
tional to the adsorbed quantity. It seemed at first to fit in fairly well 
W'ith the experimental results, but Schmidt soon showed (210) that, 
in certain cases, the Arrhenius formula was quite unable to account 
for the experimental results. He therefore assumed a still more com- 
plicated relation between his original k and x and finally arrived at a 
formula that expressed the values ver^ well, viz. 
A (s - x) 
s i 
x . e = k . c . s 
where e is the basis of the nat. log. and A is a constant. 
This equation gave a very satisfactory agreement between experi- 
mental and calculated values, but the weakness of such a formula is, 
of course, that it is almost purely empirical. 
An attempt to get a theoretical basis for the adsorption was made 
many years ago by Gibbs (211). We can deduce his formula (212) 
which gives the relation between adsorbed quantity and change of 
surface tension with concentration, if we make a thermodynamic 
cycle with a system composed of the pure solvent separated by a 
semi-permeable membrane which can be moved up and down, which, 
at the same time, is provided with a sort of impermeable diaphragm 
so that we can change the surface between the solution and the pure 
solvent as well as the concentration of the solution. If we change 
the surface and volume of the solution, we get, obviously, the same 
results in whatever order we perform those operations. It means THE COLLOID PARTICLE A MIC ELL 
171 
that the sum of the work done by the surface tension and the osmotic 
work, must be independent of the order of performance. Or, 
ids - (p + ds) dv = - pdv + (c + dv) ds 
ds dv 
do- _ dp 
dv - ds 
where p is the osmotic pressure, s the surface, v the volume, and a- 
the surface tension. This formula means that if there is a change in 
surface tension with volume, the osmotic pressure must change with 
the surface, and that is only possible if the change in surface changes 
the concentration. From that, we get the well-known formula, 
_ c do- 
X""rt ' de * 
It expresses that if the surface tension is lowered as the concentra- 
tion increases, positive adsorption takes place. We are especially 
interested in solid adsorbing surfaces-i.e. an interface of a solid and a 
liquid. But in such cases we do not know anything at all about 
surface tension. Therefore, we have not really been able to apply 
the Gibb equation to the ordinary adsorption experiments. 
This was the state of things when Langmuir's theory of adsorp- 
tion was suggested (213). The Langmuir theory and the Eucken- 
Polanyi theory are now the two leading theories for adsorption and 
I think that probably the Langmuir is more useful than the other. 
Langmuir's theory of adsorption involves the assumption that the 
forces acting in adsorption were of nearly the same kind as all forces 
causing chemical combination. From the point of view of the modern 
conception of the atom, we might say that atomic forces seem to 
be developed from the deviations of the orbits of the outer electrons 
in the atoms. The forces acting in ordinary chemical compounds 
would be due to very strong deviations of those orbits. In adsorp- 
tion phenomena the forces acting should be due to comparatively 
small deviations. When we come to measurements of adsorbed gases 
at high pressures, we find considerable deviation from the values cal- 
culated from Langmuir's formula. 
The basis for Langmuir's theory is that on the surface of a crystal 
there are a certain number of what he calls elementary spaces, points 
where there is residual valency. The forces acting in adsorption are 
concentrated at those points and adsorption consists of a fixing of 172 
COLLOID CHEMISTRY 
the adsorbed atoms in the elementary spaces for a certain time, the 
average life of an adsorbed atom or molecule on the surface. He 
also assumes that those spaces can, as a rule, hold only one atom 
or molecule, i.e. that the adsorbed layer is only one molecule thick. 
That means that the force between the atoms of the surface and the 
atoms of the adsorbed substance decrease rapidly with the distance 
between the atoms. They will only act when the atoms are very 
close together. He arrives at an expression between the concentra- 
tion in the solution and the adsorbed quantity by assuming that there 
is equilibrium between the rate of adsorption and the rate of dead- 
sorption, or in the case of a gas the rate of condensation on the sur- 
face and the rate of evaporation. 
After the adsorption process has started and only part of the 
surface has been covered, the rate of adsorption should be equal to 
(1 - 0), if we call the fraction covered 0. It should be propor- 
tional to the number of atoms or molecules p striking the surface and 
also proportional to the fraction a of the molecules that actually stick 
to the surface, or a p (1 - 0). This rate must be equal to the rate of 
evaporation. If we call the rate of evaporation from a completely 
covered surface v, we get for the rate of evaporation Ov. And accord- 
ingly when equilibrium is reached, a p (1 - 0) = Ov, or 
v -f- a p 
. ot 
Langmuir introduces another constant y = - and gets 
9==-^- 
1 + yh 
This constant y which gives the relation between that fraction of 
atoms striking the surface which actually stick to the surface, and 
the total number of atoms striking the surface represents the average 
time that an atom stays on the surface. Langmuir has calculated for 
oxygen molecules adsorbed on mica at 9O°K y = 97,000 sec. and at 
155°K 69,000 sec. If we want to express the absorbed quantity in 
N 
mols M, we have the relation M = 0 . where No is the number 
of elementary spaces per unit area and N the Avogadro constant. 
Hence M = . 
N 1 + y p THE COLLOID PARTICLE AS A MIC ELL 
173 
Langmuir assumes that there are cases where there are more than 
one kind of such elementary spaces. He means that the forces that 
hold the atoms or molecules adsorbed are different for different kinds 
of elementary spaces. In order to express the adsorption in such a 
case, we use a formula of the same kind, viz. 
M = + + ) 
NV 1 + Yi P 1 + Y2 P / 
if we multiply by p1; p2, . . . to express the fraction of each of those 
kinds of elementary spaces. The sum of all those constants is 
Pi + P2 + Pa + - 1 
There may be cases where there is an infinity of different elementary 
spaces and here we obtain 
1 
m=1 p ■ dp 
N J 1 + y p 1 
o 
d p meaning the relative number of elementary spaces corresponding 
to a certain value of y. 
If . we look for the experimental verification of Langmuir's theory, 
we find that he himself has made a series of determinations on adsorp- 
tion of gases at comparatively low pressures on plane surfaces, of 
mica, glass, and platinum, and in those experiments he actually ob- 
tained better agreement between experimental and calculated values 
using his formula than when using Freundlich's exponential formula. 
N" V Ll 
For a gas the law M = . --Lt- can be written in the form 
N 1 -f- y p 
x - _ a^P . where x is the adsorbed mass per unit surface and a and b 
1 + ap 
are constants. Table XXXI gives some of Langmuir's determina- 
tions together with the values calculated from his own and from 
Freundlich's formula. It is remarkable that the Langmuir formula 
does not contain more constants than Freundlich's. 
Investigators before Langmuir could get better agreement only by 
introducing more constants in their formulae. At higher pressures, 
the experimental values do not agree so well with Langmuir's formula. 
In such cases Langmuir assumes that more than one kind of elemen- 
tary spaces come into action. That, of course, is difficult to prove, 
and might be looked upon as a weakness of his theory. 174 
COLLOID CHEMISTRY 
TABLE XXXI 
Pressure in 
dyn/cm2 
Adsorbed Volume in cmm. at 20° C. and 760 mm. 
Obs. 
Calc, from Langmuir's 
Formula x = - ■ 
1 + ap 
a = 0.156 b = 38.9 
Diff. 
Calc, from 
Freundlich's Formula 
x = S+p0417 
Diff. 
34.0 
23.8 
17.3 
13.0 
9.5 
7.4 
6.1 
5.0 
4.0 
3.4 
2.8 
33.0 
30.0 
28.2 
25.5 
23.9 
21.6 
19.0 
17.0 
15.1 
13.4 
12.0 
32.8 
30.7 
28.4 
26.0 
23.2 
20.8 
19.0 
17.0 
15.0 
13.5 
11.8 
- 0.2 
- 0.1 
+ 0.2 
+ 0.5 
- 0.7 
- 0.8 
0.0 
0.0 
- 0.1 
+ 0.1 
- 0.2 
36.8 
31.6 
27.3 
24.2 
21.2 
19.1 
17.7 
16.3 
14.9 
13.9 
12.9 
+ 3.8 
+ 0.8 
- 0.9 
- 1.3 
- 2.8 
- 2.5 
- 1.3 
- 0.7 
- 0.2 
+ 0.5 
+ 0.9 
Adsorption of Nitrogen on Mica 
Some recent experiments on the thickness of the adsorbed layer 
have also confirmed Langmuir's views. Paneth (214) succeeded in 
measuring the actual surface of a crystalline powder-the surface of 
lead sulphate-by using a radioactive isotrope of lead. If we have 
a suspension of lead sulphate in the saturated solution and if we 
introduce an isotrope the relation between the concentration of this 
isotrope on the surface and the concentration in the solution, must 
be equal to the relation between the Pb on the surface and in the 
solution. In that way he could actually measure the number of Pb 
molecules in the surface of the powder and calculate the free surface 
of the lead sulphate powder. In some adsorption experiments with 
the dyestuff ponceau, he found that only 31 per cent of the total sur- 
face calculated in that way was actually covered with molecules of 
the dye. 
From Oden's determinations of the amount of sodium chloridf 
held by the reversible sulphur coagulum-a quantity that is inde- 
pendent of the concentration of the NaCl in the solution when com- 
plete coagulation has taken place-Gustaver calculated the surface 
covered by adsorbed molecules (215). For sulphur particles of 
r = 50 pp Oden found 2.79 gr. NaCl per 100 gms. of sulphur. One 
particle would therefore adsorb 3 X 105 molecules NaCl. If we take 
the diameter of the NaCl molecule to 3.5 X IO-8 cm., we get for a THE COLLOID PARTICLE AS A MICELL 
175 
monomolecular layer of 3 X 105 molecules NaCl 3.87 X 10"10 em.2, 
while the surface of the sulphur particle is 3.14 X 1(P10 cm.2 Those 
values are as near as we can expect from such a calculation, which 
shows that NaCl is actually very nearly one layer thick on the 
sulphur particles. 
Some experiments by Gustaver (215) on the adsorption of picric 
acid by charcoal seem to be in favor of Langmuir's theory. If we 
have a case where 
M = - 
N 
S Y1H IB Y2^ 
P1* 1 + y^+P2' l + y2p 
Gustaver assumes that the second term only comes in action when 
the first group of elementary spaces is completely covered. The 
values he obtained on adsorption of picric acid on charcoal now seem 
to show that adsorption takes place in steps so that the curve is 
abrupt in certain points and that would be in accordance with Lang- 
muir's view that we have adsorption points of different activity on 
a surface. 
Another adsorption theory which I would like to mention is one 
representative of quite the opposite point of view and that is the 
Eucken-Polanyi theory. The leading ideas in this theory were first 
published by Eucken (216) and then worked out by Polanyi (217). 
The basic assumption is that the adsorbed layer does not consist, as 
in Langmuir's system, of a single layer of atoms or molecules, but 
it consists of a polymolecular layer with a density varying con- 
tinually from the adsorbing surface out into the free gas or liquid- 
a sort of an atmosphere of adsorption. He assumes that the condi- 
tion near the surface is like the atmosphere around the earth. At 
every point, we can define a function that expresses what he called 
the adsorption potential. By this, we mean the work done by trans- 
porting the mass unit of the adsorbed substance from the point in 
question to infinity. By means of the adsorption potential and 
by the Van der Waals' equation, or, in the case of very low pressures, 
the simple Boyle's law, he has actually been able to account for 
adsorption phenomena in gases. Experimental evidence at present 
is not sufficient to decide which of those theories will prove to be the 
most useful one. In certain cases, perhaps, the Polanyi point of 
view will be the most suitable one, but, on the whole, Lang- 176 
COLLOID CHEMISTRY 
muir's theory gives a more definite formula, and is easier to prove 
experimentally. 
Most adsorption experiments have been carried out with organic 
substances or with substances which are not ionized. For the colloid 
chemist, the adsorption of ionized substances or electrolytes is very 
important, and before we leave the subject of adsorption I will men- 
tion some of the experimental work done on the adsorption of elec- 
trolytes. Only a few reliable investigations have been made because 
most of the electrolytes are so slightly adsorbed that it is difficult 
to measure the adsorption accurately. 
Freundlich in his theory of coagulation assumed that the adsorp- 
tion of ordinary inorganic salts was about the same. The actual 
measurements by Osaka (218) in Japan and by Oden (219) in Sweden 
have shown that although the difference in adsorption is not so very 
large between the different salts, it is, however, marked enough to 
be well measurable. We find certain relations between atomic weight 
and adsorption. In a series of adsorption experiments with the nitrates 
of the alkali metals and charcoal, as the adsorbing substance, Oden 
got a series of curves given in Fig. 71. 
Cor7centrcjt/o/? 
Fig. 71.-Adsorption curves for different cations. 
Thus the alkali ions are adsorbed in the following order 
Li <Na <K < Rb <NH4 <Cs. 
If we compare solutions of the same kation and different anions, we 
get the diagram Fig. 72. THE COLLOID PARTICLE AS A MIC ELL 
177 
Fig. 72.-Adsorption curves for different anions. 
Concerrtraf/o/i 
Within the series of the halides adsorption also increases with atomic 
weight. Other salts with more complicated anions give the following 
result in order of decreasing adsorption: 
KOH 
KCNS 
KC103 
kno3 
K2CrO4 
K4(CN)6Fe 
K2SO4. 
It is obvious that the two ions of one and the same electrolyte tend 
to be adsorbed in different amounts. If we have a surface on which 
an electrolyte is adsorbed, e.g., HC1, and if we assume that the posi- 
tive ion, the H ion, is adsorbed more than the Cl ion, there must 
be an equilibrium between the electrical force which tends to drive 
the H ion from the surface and the adsorption force which tends to 
fix it to the surface. Experiments by Rona and Michaelis (220) have 
shown that the amount of an electrolyte, e.g., HC1 adsorbed depends 
on the amount of other electrolytes present. If we make adsorption 
experiments in low concentration of HC1, the amount of H ions ad- 
sorbed will not only depend on the force between the H ions and the 
molecules of the adsorbing surface but also on the forces between 
the H ions and the Cl ions. If we increase the concentration of the 178 
COLLOID CHEMISTRY 
Cl ions very much, the H ions should be, so to speak, free-i.e. the 
Cl ions will not interfere with them. The adsorption of the HC1, 
if the Cl ion concentration is very high, will not change the Cl con- 
centration markedly. We can do this by adding KC1 to the liquid. 
In such a case, we actually get a much higher adsorption of the 
hydrogen ion than in pure HC1. For instance, if we have HC1 of 
0.0095 norm, and the quantity of H ions adsorbed was 0.35 m. mol. 
per gm. charcoal, and if we take the same HC1 and add N/l KC1, 
the adsorption increases to 0.45 m. mol. At higher concentrations of 
NaCl the limit value, 0.46, is reached. Similar experiments can be 
made with the adsorption of the hydroxyl ions. If we have KOH 
in 0.1 norm, concentration the adsorbed quantity of hydroxyl ions 
is 0.27 m. mol. and if we add 2 normal KC1 it increases to 0.47 m. 
mol. It is interesting to note that the limiting value for the adsorp- 
tion of OH ions and of H ions on charcoal is about the same at 
equal concentrations in the solution. 
Another important phenomenon is the adsorption of the dispersion 
medium. It probably plays a prominent role in colloid chemistry, but 
so far we do not know very much about it. The so-called hydration 
of the particles comes under this heading. In some cases of nega- 
tive adsorption, i.e., where we get an increase in the concentration 
of the solution, it is probably due to adsorption of the dispersion 
medium (215, 221). According to various investigations in electro- 
chemistry, we are inclined to believe that most of the ions are hydrated, 
that they carry water molecules with them. If ions are adsorbed on 
the surface of the colloid particle, those ions carry water molecules 
with them and accordingly concentrate water around the particle. 
One would be inclined to think that those molecules would be arranged 
closer than they are in the free liquid, and that the density in that 
layer would increase. Some determinations of the density or the 
specific volume of a sol seem to indicate this (222). If vs is the 
specific volume of the sol, i.e. the volume of one gram of sol-we have 
vs = xvp + (1 - x)vm where vp is the specific volume of the particles, 
vm the specific volume of the dispersion medium, and x the weight 
of the particles in one gr. of the sol. If we calculate the specific 
volume of the disperse phase from this equation, we find lower values 
than in the case of macroscopic pieces of the same substance. The 
increase in the density of the particles may be due to the adsorbed 
layer of the solvent around them. 
Density determinations on gelatin sols under various conditions THE COLLOID PARTICLE AS A MIC ELL 
179 
seem to indicate that the hydration is a function of the hydrogen 
ion concentration and is strongly influenced by salts but only slightly 
by non-electrolytes added. 
The Electrokinetic Phenomena 
A series of phenomena closely connected with adsorption are elec- 
tro-endosmosis, cataphoresis, and the reverse of these phenomena- 
the streaming potential and the migration potential. 
Electro-endosmosis means that if we have a vessel divided into 
two parts by means of a diaphragm and establish a potential across 
that membrane, we get a flow of liquid from one part to the other. 
Cataphoresis means the migration of the small particles when ex- 
posed to the action of an electric field. 
If we apply a pressure to force the liquid through the membrane, 
we get a potential difference-the streaming potential. We also get 
a potential because of the migration of the particles in the liquid, 
if we are able to force particles through a liquid, e.g. by means of 
gravity. 
The important thing for the colloid chemist is that we are able 
to calculate the potential difference between the colloid particle and 
the liquid from measurements of (1) cataphoresis, or (2) the migra- 
tion potential, (3) the potential between the diaphragm and the 
liquid in the first two phenomena. This potential difference plays a 
very important role in coagulation phenomena. 
The two first phenomena, electrical endosmosis and cataphoresis 
were discovered about 1809 by the Russian physicist Reuss (223). 
Reuss' first experiment was arranged as follows (Fig. 73). He took 
a piece of wet clay and forced down two open glass tubes into the 
mass. At the bottom of the tubes he placed a layer of sand to pre- 
vent the clay particles from being stirred up, poured water into the 
tubes, and put in two electrodes. When a potential difference was 
applied, he found that the water level was raised in the tube con- 
taining the minus pole so that there was a flow of water in that 
direction. At the same time clay particles migrated to the other- 
the 4- electrode. 
Endosmosis, endosmotic currents, cataphoresis.-The theory of 
the electro-kinetic phenomena has been developed by Helmholtz (224) 
and improved by Perrin (225) and Smoluchowski (226). Helmholtz 
introduced the conception of the so-called double layer to explain 180 
COLLOID CHEMISTRY 
those phenomena. Let us consider first the electroendosmosis in a 
capillary. We assume that there is a negative charge located in the 
surface of the capillary and a positive charge located at a certain 
distance & out in the liquid-that is that we have a double layer of 
electricity at the interface forming'a sort of condenser (Fig. 74). 
-water 
- water 
-water 
-day part rates 
■saap 
c/ay 
Fig. 73.-Reuss' discovery of electro endosmosis and cataphoresis. 
If a potential difference is applied to the ends of the tube, the charged 
water will glide along the wall of the tube, i.e. an endosmotic flow 
will appear. Let us consider the process taking place at the unit sur- 
face of the tube. The electrical force acting is eE, if e is the charge 
on the unit surface and E the fall of potential. The frictional force 
Fig. 74.-Helmholtz' double layer in a capillary. 
is u/h.q, where u means the velocity of the column of liquid, and 
q the viscosity of the liquid and 6 the thickness of the double layer. 
When equilibrium is reached, those forces are equal or 
T- U 
eE = s -n- 
The potential of the condenser represented by the double layer is 
4;t&e 
P - IT 
where K is the dielectric, constant of the liquid. THE COLLOID PARTICLE AS A MICELL 
181 
TT 4jtnu 
Hence p = ~. 
lx lb 
If we desire to express p by means of the endosmotic flow, we have 
u = v/r2jt where v, the endosmotic flow, is the volume of liquid that 
passes through a section of the capillary per second. 
Thus p = 
and for a bundle of capillaries or a diaphragm of total section q, we 
have 
4xqv 
P - qEK 
but E = -4- = - 
jtr-x qx 
where i is the electric current and x the conductivity of the liquid 
hence 
4;tnxv 
An important application of the equation for the endosmotic flow 
is the deduction of a formula for the endosmotic pressure. If we have 
a tube divided into two parts by a diaphragm, there will be an 
endosmotic flow through the membrane and a certain transportation 
of liquid. When this has reached a certain value, an equilibrium will 
be established and the endosmotic flow of liquid through the mem- 
brane in one direction will be balanced up by the hydrostatic flow in 
the opposite direction. For the simple case of a capillary, we can 
express the flow by means of Poiseuille's law 
jtPr4 
V - T- 
8ql 
where P = hydrostatic pressure, and 1 = length of capillary. Now 
we had for the endosmotic flow 
KEr2p 
v = -i-- 
4q 
and therefore when equilibrium is reached 
JtPr4 KEr2p 
8ql 4q 
, 2pEKl 
or ' P - 5. 
jtr- 182 
COLLOID CHEMISTRY 
The formula for the cataphoresis can be deduced simply by re- 
garding the liquid phase as fixed and the wall as movable. 
For the sake of simplicity, take a system consisting of a capillary 
filled with liquid and having an inner solid cylinder concentric with 
the capillary. If a potential difference is maintained at the ends of 
the tube we will have an endosmotic flow in the space between the 
two cylinders. Now keep the liquid in rest but allow the inner 
cylinder to move. It will migrate in the direction opposite to the 
endosmotic flow with a velocity equal in magnitude to the velocity 
of endosmotic flow, i.e. 
4rcnu 
or P=EK-' 
In this formula the size of the particle does not enter, i.e. the 
velocity of cataphoretic migration u is independent of the size. 
If a liquid is pressed through a capillary, a potential difference, 
the streaming potential, can be observed at the ends of the capillary. 
According to Helmholtz and Smoluchowski this potential is 
V = PPK 
4jiqz 
where P is the pressure. 
Thus p = ^. 
If the above theory is correct we have three different methods of 
determining the potential difference of the double layer: viz. endosmo- 
sis, streaming potential and cataphoresis. 
An interesting test of the theory has been carried out by 
Saxen (227). He measured both the endosmosis and the streaming 
potential by means of the same apparatus and using the same liquids. 
According to the theory, we ought to have 
y _ v 
P ~ i 
because they are both equal to 
pK 
4raqx * 
Saxen obtained the values tabulated in Table XXXII showing that 
the above equation actually holds. THE COLLOID PARTICLE AS A MICELL 
183 
TABLE XXXII 
Saxen's Endosmotic Experiments 
Solution 
v/i 
V/P 
0.0174 
ZnSO« 
0.360 
0.352 
0.0261 
Ci 
0.382 
0.379 
0.0348 
u 
0.346 
0.344 
0.0195 
CdSCh 
0.582 
0.588 
0.0390 
<1 
0.116 
0.115 
0.0400 
CuSCh 
0.385 
0.385 
0.0800 
a 
0.233 
0.237 
One of the apparatus used by Freundlich and his co-workers (228) 
for the study of the streaming potential is shown in Fig. 75. The 
liquid is pressed over from B to B' through the capillary K. The 
ends of the capillary are connected up to the calomel electrodes E 
Fig. 75.-Freundlich's apparatus for the streaming potential 
and E' by means of tubes filled with a KCl-agar jelly. For the 
measure of the potential a binant-electrometer is used. 
Cataphoresis is obviously the electrokinetic phenomenon that the 
colloid chemist is most interested in. There are quite a number of 
different methods of measurement which have been worked out. They 
all belong to one of the following types: (1) rate of migration of 
boundary between sol and dispersion medium measured, (2) change 
in concentration of disperse phase in a volume Hear the boundary 
measured, (3) migration ot the individual particles measured directly 184 
COLLOID CHEMISTRY 
in the ultramicroscope. The third method is supposed to be the 
more accurate. In cases where we are unable to see the particles in 
the ultramicroscope, we must, of course, use the first or the second. 
Fig. 76 shows the apparatus used by Burton (229). Part of the 
u-tube is filled with dispersion medium and a quantity of the sol 
is run down slowly through the funnel and the tube, so as to form a 
layer under the pure dispersion medium. Platinized electrodes are 
introduced and a potential difference applied. The whole apparatus is 
to be kept at a constant temperature. If the sol is colored the rate 
of migration of the two boundaries can be measured, and the rate of 
cataphoresis calculated if the fall of potential in the tube is known. 
In order to obtain accurate values, it is essential that the conduc- 
Fig. 76.-Burton's cataphoresis apparatus. 
tivity of the sol and the dispersion medium should be equal, a con- 
dition which is usually fulfilled in the case of dilute sols. 
Difficulties arise in such cases where the sol is colorless so that 
the position of the boundaries cannot be seen. By using an apparatus 
of the form shown in Fig. 77 constructed by Michaelis (230) at least 
the sign of migration can be determined. The sol is poured into 
part B and dispersion medium into A and C. The current is intro- 
duced by means of reversible electrodes, e.g. silver in NaCl and 
copper in CuCl2. After the current has been flowing for some time 
the stopcocks D and E are closed and the amount of colloid in A 
and C determined by analysis. This method has found extensive 
use in the study of proteins. 
It is difficult to get the absolute values of the velocity of cata- 
phoresis by means of method 2. In view of the important position THE COLLOID PARTICLE AS A MIC ELL 
185 
which the proteins at present occupy in the field of colloids it has 
seemed worth while to try to work out a procedure permitting ac- 
curate determinations of the absolute values of cataphoretic migra- 
tion. The writer in co-operation with Jette and with Scott made 
use of the fluorescence that proteins show when illuminated with 
ultraviolet light. A modification of method 1 could be used and the 
position of the boundaries photographed. The rate of movement of 
the boundaries was then measured on the pictures (231). 
In Fig. 78 A is the ordinary form of U-tube with the capillary B 
Fig. 77.-Michaelis' cataphoresis apparatus. 
entering at the bottom, and the container C for allowing the sol 
to reach the same temperature as the solution in A before being run 
into A. The reversible electrodes DD' consist of zinc rods im- 
mersed in a saturated zinc sulfate solution. The electrode vessels 
were connected to the U-tube by the intermediate vessels EE'. The 
tubes FF' allowed the air to escape from the intermediate vessels dur- 
ing the filling of the apparatus. 
The bulbs of the electrode vessels were filled with the saturated 
zinc sulfate solutions and the remainder of the apparatus with a buffer 
solution of the desired hydrogen ion concentration (except the con- 
tainer C). The solution containing the protein was placed in C and 
after reaching the proper temperature was slowly run into the U-tube 
under a slight pressure from an outside source. 186 
COLLOID CHEMISTRY 
pIQ. 78.-Cataphoresis tube for fluorescence photography of proteins. 
j\- 79.-Apparatus for measuring the cataphoresis of proteins by fluorescence 
photography. THE COLLOID PARTICLE AS A MIC ELL 
187 
The arrangement of the apparatus for photographing is shown in 
Fig. 79 in which A is an air thermostat, BB' the boxes containing the 
quartz mercury lamps, C the cataphoresis tube, DD' special glass 
screens and E is the camera. The glass screens were Wratten's new 
ultraviolet filters which pass practically only the wave length 
X = 366 pp and a small amount of X = 334 pp. The camera lens 
was a Zeiss-Tessar 1:4.5. To prevent the ultraviolet light reflected 
from the walls of the thermostat from entering the camera, a cell F 
2 millimeters thick filled with a 5 per cent solution of HC1 containing 
5 per cent quinine bi-sulfate, was placed before the lens. 
Fig. 80.-Fluorescence photography of cataphoresis of proteins 
Fig. 80 shows the position of the protein boundary before a and 
after b the current has passed through an eggalbumin sol containing 
0.3 per cent of dry albumin in an acetic acid -sodium acetate buffer 
solution with a pH of '3.90. The time interval between a and b was 
120 minutes. 
When we measure the cataphoresis directly in the ultramicroscope 
we obviously have to use different kinds of cataphoresis cells adapted 
to different kinds of ultramicroscopes. For the slit-ultramicroscope 
the writer (232) used the cell shown in Fig. 81. It is provided with 
platinum electrodes and two windows Wx and W2, one for the illumi- 
nating beam of light and one for the beam of observation. The cell 188 
COLLOID CHEMISTRY 
can be made thick enough so that the influence of the walls of the 
cell is not very marked. 
For use with the dark field condensers such as the Zeiss paraboloid- 
or cardioid- ultramicroscope we must have the sol enclosed in a thin 
cell. In such a case there are certain complications because of the 
small depth of the layer of the sol. Already early investigators have 
found that the particles moved with different velocities at different 
distances from the wall and, as a rule, they found that the particles 
moved in opposite directions in the midde and near the walls. To 
explain this phenomenon it was assumed that the charge of the 
particles was influenced by the walls. It is obvious that this is not 
the right explanation. In such a thin cell we have to take into ac- 
Fig. 81.-Cataphoresis cell for the slit-ultramicroscope 
count not only the migration of the particles but also the endosmotic 
flow of the liquid. Along the wall there is an endosmotic flow of the 
liquid and in a closed cell that flow must be compensated by a 
flow of liquid in the opposite direction in the middle part of the 
cell. Ellis (233) plotted the velocity of the particle obtained by 
direct measurement at different distances from the wall, and found 
a curve of the kind shown in Fig. 82. If u' = the velocity of the 
particle with regard to the wall, u = the actual velocity relative to 
the liquid, and v = the velocity of liquid we have 
u'= u -j- v 
hence u = u'- v 
and if we integrate over the whole thickness d of the cell 
d d 
ud = y u'dx - y vdx. 
o o THE COLLOID PARTICLE AS A MIC ELL 
189 
But the second integral must be zero in the case of a closed cell thus 
1 r M 
u = -t f u'dx. 
do 
From the curve Fig. 82 which gives u' as a function of x we can 
therefore calculate the velocity of cataphoresis. The value of the 
integral can easily be estimated graphically. 
Later, Smoluchowski (234) showed that the theory of cataphoresis 
and endosmotic flow in a thin cell can be worked out more in detail 
and that we can calculate the velocity of the particles relative to 
the liquid from measurements in twTo points, i.e. that it is not neces- 
Fig. 82.-Cataphoresis of particles in a thin cell 
sary to measure the whole u'x - curve, but only to find the u' values 
for two known distances. If the values of u' in the middle u'i^ and 
at the distance 1/6 from the wall u' % arc known we have according 
to Smoluchowski 
3 , . 1 , 
u = 4 u % + 4 u • 
There is a certain point between the walls where u' and u are 
equal and that is the distance from the wall of 
Vi 1 A 
X" d\2 ± V12 / 
Andersson and the writer (235) made a series of measurements of 
cataphoresis of gold particles in thin cells and we actually found that 190 
COLLOID CHEMISTRY 
the values of u which we obtained when calculating from the Ellis 
formula and from Smoluchowski's agreed fairly well. 
Two methods of measurement were used. In one of the pro- 
cedures, we photographed the path of the particles. The current was 
closed for a very short time only, in order to avoid electrolysis. In 
the photograph there are small lines indicating the part traversed 
by the particle in the time interval in question, and by measuring 
Fig. 83.-Diagram of voltage for ultramicroscopic measurements of cataphoresis. 
those on the plates and knowing the enlargement we obtained the 
values u'. In the second procedure we used alternating current and 
observed directly with the eye. If the oscillations are rapid enough 
we get the impression of a line of light, and by means of a scale 
in the ocular, we can measure its length. The alternating current 
was produced with a rotating commutator, giving voltage diagram 
of the type shown in Fig. 83. An alternating current of this type 
Fig. 84.-Cataphoresis cell for the cardioid ultramicroscope. 
has the advantage that the voltage is nearly constant during the 
whole half cycle. Fig. 84 indicates the construction of the cells used. 
Two platinum foils AA 0.01 thick are cemented to a microscopic slide 
by means of the cement "picein" and a coverglass B cemented on by 
simply placing it on top of the picein edges and warming slightly. 
After introducing the sol the cell is closed with vaseline CC. The 
thickness of the cell varied between 64 and 141 p. A diagram of the 
apparatus is shown in Fig. 85. Light from the arc lamp A passes 
the condenser lens B, the water cell C, the photographic shutter D and THE COLLOID PARTICLE AS A MIC ELL 
191 
the cardioid condenser E and illuminates the particles in the cell F. 
Further, G is the microscope, H the camera (which can be removed 
when direct observations are made), J the battery and K the com- 
Fig. 85.-Diagram of apparatus for ultramicroscopic measurement of cataphoresis. 
mutator. Fig. 86 gives a photographic view of the arrangement. The 
commutator together with its motor and speed reducer is at the left 
in the picture. 
Fig. 86.-View of arrangement for ultramicroscopic measurement of cataphoresis. 
The values for one and the same sol arrived at by means of the 
two procedures agreed on the whole fairly well. The accuracy of the 
procedure with alternating current is however markedly higher. 
Table XXXIII contains some of the determinations with alternat- 
ing current. 192 
COLLOID CHEMISTRY 
TABLE XXXIII 
Determination of Cataphoresis in Gold Sols by Means of Alternating 
Current (11 Cycles per Sec.) 
Distance from the Wall of 
the Cell in |a 
Displacement of Particle 
in Scale Div. of 2.306 p, 
A 
B 
A 
B 
0 = wall 
0 = wall 
- 9.7 
- 
10.2 
8 
8 
- 1.5 
0 
12 
17 
0 
+ 
6.2 
22 
24 
+ 5.2 
+ 
9.0 
32 
28 
+ 9.2 
+ 
8.8 
38 
37 
+ 9.5 
+ 
4.0 
42 
41 
+ 9.0 
0 
52 
46 
+ 7.6 
- 
5.2 
58 
48 - wall 
+ 3.2 
- 
10.2 
64 
0 
70 
- 3.7 
76 - wall 
- 9.7 
Formula 
Formula 
F ormula 
Mobility calculated from 
1 ' _L 
2 , 
3 , 
, 1 ■ 
graph, meas. of true u 
3 u y2 1 
u = 7 u h , 
4 % 
+ 4U 
y2 u 
- u at - 
average velocity of 
particle 
AB A 
B 
A 
B 
x = 
=d( 
A 
hvA) 
B 
1.75 1.60 1.79 
1.50 
1.79 
1.62 
1.79 
1.74 
Mobility Calculated from 
Fig. 87 gives a graphical representation of the relation between 
lengths of the track L' and x for the experiment A. The theoretical 
Fig. 87.-Cataphoresis curve for particles in a thin cell 
curve (dotted) calculated from Smoluchowski's equation almost coin- 
cides with the experimental one (full). 
Potential and charge of the particle.-Among the different results 
of the numerous experimental investigations of electro-endosmosis, THE COLLOID PARTICLE AS A MIC ELL 
193 
streaming potential, cataphoresis the following ones are of especial 
interest to the colloid chemist (236). 
The potential difference of the double layer is greatly influenced 
by the presence of electrolytes in the liquid. For mono- and di-valent 
ions the curve giving the relation between p and concentration of the 
electrolyte shows a maximum at low concentrations and then falls off 
Cb/7ce/?frafion of e/ecfro/yte 
Fig. 88.-Variation of electro-kinetic potential with concentration for various 
electrolytes. 
continually. The tri- and tetra-valent ions have their maximum so 
very close to the zero point that it can hardly be observed. The 
potential goes down very rapidly with increasing concentration re- 
versing its sign then reaches a minimum and rises again. In Fig. 88 
some such curves are given. How enormously the action of the ions 
increases with valency is illustrated by Table XXXIV (Freundlich) 
which gives the concentration necessary to lower the p of the glass- 
water interface from 0.089 to 0.039 volts. 
TABLE XXXIV 
Action of Cations of Different Valency upon the Electrokinetic 
Potential between Glass and Water 
Electrolyte 
Millimol electrolyte per lit. necessary to change 
the potential from 0.089 volt to 0.039 volt. 
KC1 
25 
BaCL 
0.87 
AlCb 
0.02 
ThCL 
0.015 194 
COLLOID CHEMISTRY 
These results throw some light on the nature of the double layer. 
It is always the valency of the ion of opposite charge to the electric 
layer in the adsorbing phase that lowers the potential difference. This 
indicates that the electrokinetic potential is due to adsorption of ions. 
From such a point of view the existence of the double layer is easy 
to understand. We know that the two ions of an electrolyte are 
adsorbed with different strength and that means a certain separa- 
tion of the positive and negative charges in the vicinity of an interface. 
Gouy (237) assumes that the double layer is built up of two diffuse 
layers of ions; the concentration of e.g. the negative ions decreasing 
and the concentration of the positive ions increasing with increasing 
distance from the interface. He calculated the thickness 5 of the 
double layer that would be equivalent to such a mixed atmosphere of 
ions and found that 6 decreases when the concentration of the electro- 
lyte increases. 
In the case of a surface charge e = 10 el. stat, units he found 
& = 0.96 pp, in 1/10 n. solution 
8 = 9.6 pp, " 1/1000 n. solution 
8 - 1010 pp, " pure water. 
For ordinary sols the thickness of the double layer would therefore 
be of the order of a few p.p. 
The particle with its double layer can be regarded as a charged 
condenser. The potential of a condenser consisting of two concentric 
spherical layers is 
_ e(rx - r) _ e& 
P " Kr^ - Kr(r + &) 
where rx is the radius of the outer sphere, r the radius of the inner 
sphere and 8 = rx - r = the thickness of the double layer. But 
4jtnu 
. 4;nmr(r 4- 8) .u 
hence e = -!--- . 
E8 
That is if we know the size of the particle, the thickness of the double 
layer, the cataphoresis velocity and the viscosity we can calculate the 
charge of the particle. The thickness of the double layer has never 
been measured but we may assume it to be of the order of magnitude 
given by Gouy. Von Hevesy (238) has calculated the charge for 
gold particles of different size taking p=0.070 volts, K=81, 8-5 p,p 
and obtained the following values THE COLLOID PARTICLE AS A MICELL 
195 
TABLE XXXV 
E'lectric Charge and Size of Particle 
Charge of Particle in 
r in up. 
Number of Electrons 
1 
6 
2 
14 
10 
120 
24 
550 
100 
8550 
240 
47000 
This shows that for ordinary colloid solutions the number of charges 
is comparatively high, for instance, with a radius of 10 p.p, a rather 
common size, the number is 120. The mobility of the colloid particles 
u/E = ux as calculated from cataphoresis experiments is of the same 
order of magnitude as those we obtain for ions. The mobility of 
sodium ions, for instance, is at 18° = 4.4 X IO-4 cm. per sec. a mobility 
often found in sols. For very large ions of low valency such as the 
ions of the higher fatty acids, the mobility is even lower than for 
normal colloid particles. Such ions might be compared with colloid 
particles, the charge of which has been partly neutralized. 
It is obvious that the migration of the particles in cataphoresis 
must give the sol a certain conductivity, the mobility of the particles 
being of the same order as that of the ions. 
Smoluchowski (239) has calculated the conductivity which we 
would expect in a pure sol and he finds 
4jtr]vr(r + 8) Ui2 
N8 
where v - number of colloid particles per unit volume, r = radius, 
8 = the distance between the charges, uL = the mobility and N = the 
Avogadro constant. 
If we calculate from that formula the conductivity that we would 
expect, for instance, with a gold sol having a radius of particles r of 
10 41, a mobility of 5.2 X 10 * and with a distance between charges 
- 5 pp. we get for the conductivity value 1.2 X IO-7, which 
is obviously very low. In most cases there are electrolytes present, 
and at least in most inorganic sols and especially in metallic sols 
which are rather dilute, the conductivity of the particles does not play 
a very prominent role (240). It has always been found that the 
conductivity of the sol decreases as the purity increases. In some 
cases the conductivity of the sol has been found to be even less than 196 
COLLOID CHEMISTRY 
the conductivity of the dispersion medium. If we disperse mercury 
in pure conductivity water by means of the oscillatory arc, the con- 
ductivity decreases (241). That, probably, is due to the adsorption 
on the Hg-particles formed of the impurities present. The conduc- 
tivity therefore decreases. The small contribution to conductivity 
from the particles can of course be disregarded. 
In some organic colloids, the conductivity caused by the particles 
present is more important. A very interesting investigation has been 
carried out by McBain in the case of soap solutions (242). McBain 
found that if we measure the relation between the conductivity and 
concentration for soaps derived from different fatty acids we obtain 
Mo/ar ca/nft/tf/y/ty 
Co/?ce/7fTof/o/? of <5oap 
Fig. 89.-Variation of molar conductivity of soap solutions with concentration. 
the family of curves represented in Fig. 89. For the potassium salts 
of fatty acids of low molecular weight, e.g. acetates and laurates, 
he obtained curves of the ordinary shape, the conductivity decreasing 
with concentration as the dissociation is lowered. For the higher fatty 
acids after a certain concentration was reached, he obtained a max- 
imum and then a decrease again. This probably was due to the 
formation of colloid particles with higher mobility than the fatty 
acid ions. In the case of a fatty acid, the mobility of the anions is 
very low, because of the large surface and the low charge which gives 
a comparatively low conductivity. As some of those ions, together 
with undissociated molecules, aggregate to a colloid particle, the 
number of charges relative to the surface is increased and therefore 
the mobility of the colloid is higher than for the isolated ion. 
One might be inclined to assume that the potential difference dis- THE COLLOID PARTICLE AS A MIC ELL 
197 
played in cataphoresis is the same one as the substance of the particle 
would show when used as an electrode in a galvanic cell. A metallic 
particle immersed in a very dilute solution of one of its own salts 
would then give a potential difference according to its solution 
pressure. 
A few years ago, some scientists actually held the above view 
and Billiter (243) tried to determine the absolute zero potential by 
means of a method based upon such an assumption. We know now, 
however, that the potential difference which causes cataphoresis is 
not the same as the interface potential between the particle and the 
liquid, as measured in a galvanic cell. An experiment in favor of this 
view is that the electrokinetic potential difference is changed by the 
addition of ions-especially such ions as are strongly adsorbed, and 
it is therefore natural to assume that this potential difference is to a 
large extent due to the difference in adsorbed charges-to the differ- 
ent adsorption of ions. 
Freundlich and his co-workers have thrown some light upon this 
question (244). They have measured statically the potential be- 
tween the surface of the particle and the liquid, and also determined 
the electrokinetic potential for the same substance. Take for in- 
stance a glass tube and blow a very thin bubble at the end. Then 
immerse it in a solution and fill the inner part with an electrolyte. 
The interior of the glass bubble is connected to one side of an electrom- 
eter by means of a platinum wire and the outer liquid to the other 
side over a reversible calomel electrode. This combination enables 
us to measure the potential difference between the interior of the 
glass and the outer liquid. Freundlich also measured the electro- 
kinetic potential for the same kind of glass by measuring the stream- 
ing potential in a capillary. In that way, he found that the inter- 
face or static potential between the glass and the liquid is higher 
than the electrokinetic, and that the interface potential is not af- 
fected by small additions of ions which cause a very great change 
in the electrokinetic potential difference. 
In order to explain why the electrokinetic potential 'is so much 
smaller than the static one, Smoluchowski (245) assumed that part 
of the liquid is carried on with the particle in its movement, and 
that the potential difference we measure in cataphoresis is, there- 
fore, that from a point out in the liquid to the infinity point. If 
this is actually the case, it is possible to explain how the small addi- 
tions of electrolytes can affect the electrokinetic potential without 198 
COLLOID CHEMISTRY 
affecting the other potential, and that such additions can even reverse 
the sign of the potential, as in the curve given in Fig. 90. If x in 
Fig. 90 denotes the distance from the surface of the particle and 
the ordinates the potentials and if we assume that in cataphoresis 
we only measure the potential from the point x' and not from x = 0 
it is easy to see that the electrokinetic potential p can be lower than 
the statically measured potential. The former can also be of op- 
posite sign to the latter as shown by the dotted curve. As a rule 
the electrokinetic potential is only about 1/10 of the ordinary static 
potential. 
The isoelectric point.-If the potential difference between the layer 
of water or layer of dispersion medium which the particle has con- 
Fig. 90.-Diagram showing variation of potential with distance from the interface 
densed around it and the outer liquid is zero then the particle is 
at the so-called isoelectric point. The most common way of getting 
the potential difference down to zero is to introduce such ions of 
opposite charge to that of the particle as will be adsorbed around 
the particle. Now in the case that the particle itself can produce 
ions of opposite charge, the zero potential or the isoelectric point 
might be reached by changing the dissociation of the particle. At 
least, that is what Michaelis claims to be the case with most of the 
proteins. His theory of the isoelectric point has played an important 
role in the study of proteins (246). 
If we have an amphoteric electrolyte with the acid and basic 
dissociation constants ka and kb equilibrium gives 
(A-) (H+) = ka.x 
(A+) (OH-) = kb.x THE COLLOID PARTICLE AS A MIC ELL 
199 
where (A-) is the concentration of the ampholyte anions, (A+) the 
concentration of the ampholyte cations and x the concentration of 
the undissociated parts. 
Now Michaelis defines the isoelectric point as the point where the 
concentration of the anions and the cations of the ampholyte is equal, 
hence, 
(H+) _ka 
(OH-) ~ kb 
but (H+) (HO-) = kw = dissociation constant of water. Thus 
/ 
(H+) = . kw 
which equation defines the hydrogen ion concentration at Michaelis' 
isoelectric point. 
From this theory it would follow that if we knew the dissociation 
constants of the substance of the disperse phase we would be able 
to calculate the hydrogen ion concentration that corresponds to the 
isoelectric point. The trouble is that we have never been able to 
test this proposition, because of the fact that there is no case where 
we know the two dissociation constants. It has never been proved 
that the electrokinetic isoelectric point is identical with Michaelis' 
isoelectric point. As shown by Michaelis it follows from his defini- 
tion of the isoelectric point that the undissociated part of the ampho- 
lyte should have a maximum at the isoelectric point. 
If we call x/(A) = p the dissociation rest where (A) is the total 
concentration of the ampholyte we have 
x= (A) - (A+) - (A-) 
i x _ _ 1 
d <A> ~e~ 1 . k. । kb ' 
1 + (H*) + k, ' (H ' 
After forming the derivative of the denominator and putting it equal 
to zero we get 
-(W+fe = ° OT = 
which latter expression was the condition of the isoelectric point. 
Now in all cases that we know of, the solubility of the undis- 
sociated ampholyte is less than the solubility of the dissociated one 
and that means that the ampholyte should show a minimum of 200 
COLLOID CHEMISTRY 
solubility at the isoelectric point. For ordinary ampholytes which 
give a molecular solution when dissolved, this relationship probably 
holds but in the case of the proteins where we do not know if there 
is any solubility in the ordinary sense of the word it is safer not 
to apply this equation. It would be a very interesting problem to 
try to find out if or when Michaelis' isoelectric point is identical with 
the electrokinetic isoelectric point. Michaelis has pointed out that 
the shape of the curve giving the relation between p and pH (pu = the 
neg. logarithm of the hydrogen ion-concentration) is determined by the 
product ka. kb while the curve is just shifted along the abscissee axis 
if ka changes and ka . kb remains constant. For values of ka. kb higher 
than 10~12 the dissociation rest is so small that the isoelectric point 
would be imperceptible while for values of ka. kb lower than 1018 
Fig. 91.-Diagram showing the change of ionization of an ampholyte with hydro, 
gen ion concentration for different values of the dissociation constants. 
the ampholyte is completely undissociated over quite a wide range 
of hydrogen ion concentrations (Fig. 91). 
That would mean that a very sparingly dissociated ampholyte if 
present as a colloid would be isoelectric over a wide range while a 
strongly dissociated ampholyte would show practically no isoelectric 
behavior at all. Michaelis believes that the proteins all fall within 
the range of ka . kb = IO-12 to 10-18 because they all have fairly well 
defined isoelectric points as determined by cataphoresis. As already 
pointed out it is, however, possible that the isoelectric point which 
we get by measuring the cataphoresis is not identical with Michaelis 
isoelectric point. 
As a matter of fact, we do not know very much about the dis- 
sociation of proteins. For some proteins we can calculate the ratio 
between the dissociation constants from determinations of the iso- 
electric point from the relation 
<H'> = kw THE COLLOID PARTICLE AS A MIC ELL 
201 
but we have no means of determining their product. If we make 
certain assumptions, we obtain some idea of the order of magnitude 
of this product and from that it follows that most of the proteins 
actually have a product of dissociation constants falling within the 
range: ka . kb = IO12 to IQ18. 
Michaelis' theory of the isoelectric point of the amphoteric elec- 
trolytes is based on the assumption that it is only the H ions and 
the OH ions that determine the isoelectric point. As we know from 
measurements of cataphoresis of colloids, the isoelectric point also 
depends on the other ions present. We must therefore be careful in 
applying Michaelis' theory to colloid solutions because of the influence 
of other ions. 
Osmosis and membrane-equilibrium.-We have previously studied 
the osmotic pressure of sols in connection with the Brownian move- 
ment, but in that case, we considered the osmotic pressure purely 
from the standpoint of the colloid particle itself without taking into 
account the action of the adsorbed molecules or ions. The investiga- 
tion of the Brownian movement, of sedimentation equilibrium and of 
diffusion of dilute sols show that in cases where the sols are dilute 
and where we measure the osmotic pressure by such methods as the 
Brownian movement where no membranes are introduced, we have 
RT 
the simple relation p = . n, where n = number of particles per 
unit volume. When we measure osmotic pressure by means of mem- 
branes, however, the action of the crystalloids present, the adsorbed 
ions, or the ions dissociated aw'ay from the particle, play a very im- 
portant role. 
If we have a colloid sol separated from the dispersion medium by 
a membrane permeable to the dispersion medium but not to the 
particles of the sol, there is, of course, an osmotic flow but it is diffi- 
cult to tell whether this flow is actually due only to the presence of 
the particles, i.e. to the osmotic pressure measured by the Brownian 
movement, or if some other factors are involved. One factor pointed 
out as being possibly involved is the swelling (247). If the particles 
are to be considered as pieces of gel, the swelling pressure might 
figure in the expression for the total osmotic pressure and as the 
swelling pressure of the gel is usually an exponential function of con- 
R T 
centration we would have p = - . n -|- Po. cgk where Po and k 
are constants and cg the concentration of the gel. The part played 202 
COLLOID CHEMISTRY 
by the swelling has not, however, been experimentally investigated 
so far. 
Another phenomenon of importance is observed in cases where we 
have a colloid solution separated from the dispersion medium by a 
membrane and at the same time one or several electrolytes present. 
Here we get the so-called Donnan equilibrium (248, 249). Suppose 
we have a vessel divided into two parts by a membrane, on one side 
a solution of an electrolyte Na+ R" such that the positive ions can 
diffuse through the membrane but the negative ions cannot and on 
the other side of the membrane Na+ Cl'. One might think that equi- 
librium would be reached when the concentration of NaCl would be 
equal on both sides, but on second thought, we find that this is 
impossible. Both parts of the vessel must be electrically neutral. If 
we already have those negative ions that cannot diffuse through the 
membrane on one side of the membrane an equal distribution of the 
NaCl solution would cause an unequal distribution of the charges. 
The condition for equilibrium has been expressed by Donnan. 
The distribution of the ions must be such that the total work done 
when we transport the very small quantity Sq mol of Na ions and 
8q mol Cl ions from part 1 to part 2 is zero. If the concentrations 
of the ions for different sides are denoted by the indices 1 and 2 
we have 
8q R T In ^a^2- + Sq R T In = 0 
(Na )x (Cl-)i 
That can only be the case when 
(Na+)2 _ (Cl'), 
(Na+)t " (Cl')2 
or when 
(Na+)i . (Cl-)x= (Na+)2 . (Cb)2. 
This condition is needed to fulfill the membrane equilibrium. 
Instead of an electrolyte Na R with the non-diffusible ion R we 
can have a colloid with its non-diffusible particle carrying a certain 
charge and its diffusible ions of opposite charge. In measurements 
of osmotic pressure of sols against a semipermeable membrane it is 
therefore necessary to take into account the effect due to the Donnan 
equilibrium. 
Call the original concentrations on side 1 cx and on side 2 c2 and THE COLLOID PARTICLE AS A MICELL 
203 
the concentrations of the ions that have diffused over from 2 to 1 x, 
then we get for the osmotic pressure in 1: 
p = RT(2cx + 2x) - RT(2c2 - 2x) 
or p = 2 R T (cx - c2 + 2x) 
If we desire the expression for the relation between ths osmotic pres- 
sure when equilibrium is reached p and that which the colloid would 
have given if no electrolytes were present p0 we have 
p0 = 2 R T Ci 
p _ Ci - c2 2x 
Po Ci 
The value of x can be expressed by the Donnan equilibrium 
(c2 - x)2 = x(Ci + x). 
If we solve this and substitute the value for x, we get 
x - C22 or - - C1 + C2 
Cx + 2 c2 ' p0 cx + 2c2* 
When the amount of the colloid is large compared with the amount 
of the electrolytes, i.e. when cx c2, and upon dividing by cx we 
obtain 
1 + - 
lim - - 1 
1 + 2- 
Ci 
In such a case, we get the same osmotic pressure as if no electrolyte 
was present. If the electrolytes are present in high concentration 
compared to the colloid, i.e. when cx c2, we have 
- + 1 ! 
r C2 _ 1 
im c - 2' 
C2 
That is the osmotic pressure of the colloid is only the value we 
would expect-that is we obtain the osmotic pressure of the non- 
diffusible part. 
Another consequence of the membrane equilibrium is that we 
must get a potential difference across the membrane because of the 
unequal distribution of the ions. Suppose we have the "colloid elec- 
trolyte" RC1 and also HC1 and suppose we measure the potential 204 
COLLOID CHEMISTRY 
difference by means of an electrode reversible with regard to the Cl 
ions. Then we have for the potential difference 
RT (Cl')2 
F (CT)/ 
And if we measure the potential difference with the aid of a hydrogen 
electrode 
RT (H+)2 
F m (H+)x' 
But according to the Donnan equilibrium 
(CT)2_ (H+)x 
(CT)! - (H+)2 
hence 
RT (Cl')2 _ RT (H+)j 
F (CF)^ R (H+)2 
The Donnan equilibrium has been applied to some cases where 
there is still some doubt as to whether it can be applied or not. 
Procter and Wilson have tried to explain the behavior of gels by 
assuming that the swelling is controlled by the Donnan equi- 
librium (250). Loeb has applied the Donnan equilibrium to protein 
sols (251). They emphasize that the important point in the Donnan 
equilibrium is not that there must exist a regular membrane but that 
a certain portion of the ions present must be non-diffusible with 
regard to the other ions. It is the disturbance of the electroneutrality 
by the non-diffusible ions that is responsible for the Donnan equi- 
librium. Procter and Wilson believe that if some electrical charges 
are fixed to the walls of the cells in the gel, that must mean the 
establishment of a Donnan equilibrium. Now the structure of most 
gels, especially the protein gels, is probably fine enough to permit us 
to speak of a definite concentration of the diffusible ions inside the 
gel in contradiction to the concentration outside of the gel and it is 
therefore quite possible that we really have a right to apply the 
Donnan equilibrium to the swelling of a gel. 
When we try to apply the Donnan equilibrium to the single parti- 
cles in sols as has been done by Loeb we meet with certain difficulties 
which have not as yet been overcome. The main difficulty is that 
the two regions of different concentration have no tangible meaning. 
Loeb has shown that measurements of osmotic pressure of gelatin 
sols by means of a collodion membrane can, to a certain extent, be 
accounted for theoretically by the Donnan equilibrium (252) (Fig. 92). THE COLLOID PARTICLE AS A MICELL 
205 
Sorensen (253) studied the osmotic pressure of egg albumin at the 
isoelectric point in the presence of a large excess of ammonium sul- 
phate and found that the pressure decreased with increasing concen- 
tration of salt (253). In his experiments the salt concentration was 
always high compared with the concentration of the colloid so that 
the osmotic pressure measured was the pressure of the non-diffusible 
particles as indicated by Donnan's formula. The decrease in pres- 
sure with increasing salt concentration shows that the degree of dis- 
persity of the system decreased. 
G5/7X^/C 
Fig. 92.-Variation of osmotic pressure with hydrogen ion concentration in a 
protein sol. 
The only case where we might say with some degree of certainty 
that measurements of osmotic pressure against semi-permeable mem- 
branes have enabled us to calculate the size or molecular weight is 
in the case of haemoglobin. The osmotic measurements give us the 
molecular weight 16300 while computation from its chemical com- 
position suggests 16700. That would correspond to a size of particles 
of about 1.7 pp (254). 
Loeb has made some attempts to measure the potential difference 
between the particles and the liquid in protein colloids by measuring 
the membrane potential (255). A gelatine sol of a certain hydrogen 
ion concentration was allowed to set inside a collodion bag then im- 
mersed in hydrochloric acid of the same concentration and the potential 206 
COLLOID CHEMISTRY 
between the inside and the outside measured. Loeb first believed that 
the potential difference measured in that way corresponded to the 
electrokinetic potential that governs the stability of most sols. Quite 
recently, however, Loeb has made some new measurements and actually 
compared the potential difference arrived at by measuring the cata- 
phoresis and by measuring the membrane potential and found that 
those values did not coincide. He found a certain relationship be- 
tween them, however, so that it appears that in the case of proteins 
those two potentials are more closely connected than in the case of 
inorganic sols (256). Freundlich showed that in the case of glass, 
those two potential differences are not at all equal-that the total 
potential difference between the inside of the particle and a point out 
in the liquid is much higher than the potential difference measured 
in cataphoresis. 
In case of proteins, it seems that such ions which influence the cata- 
phoresis potential also influence the membrane potential to a certain 
extent as observed by Loeb. 
Viscosity .-Another property connected with the surface field of 
the particle which has been used very much in studying of colloid 
systems is the viscosity. According to a formula deduced by Ein- 
stein (257), the viscosity of a sol should be equal to the viscosity of 
the dispersion medium multiplied by the factor 1 -|- 2.5 V, or 
qs = T]m (1 -f- 2.5 V) where V is the volume of the particles contained 
in 1 cc. of the sol. According to this formula, the viscosity of a sol 
should be independent of the size of particles. It should only depend 
on the total volume of the particles per unit volume of sol. The 
actual determinations of viscosity have shown that the viscosity 
changes considerably when changes take place in the colloid. In 
some cases when we have been able to compare the viscosity of the 
same kind of particles, at different degrees of dispersity we have found 
that the viscosity actually varies with the size of particles. In the 
case of sulphur sols, Oden found that if we plot the viscosity against 
sulphur concentration we obtain different curves for sols of different 
size of particles (258). Fig. 93 shows two such curves, one for a sol 
of about 10 pp. particles and the other for a sol of about 100 pq, 
At the same concentration the viscosity of the fine grained sol is higher 
than the viscosity of the coarse grained sol. 
Smoluchowski (259) has shown theoretically that if the particles 
are charged-i.e. if there is a potential difference between the particles 
and the medium-that this must influence the viscosity. We have to THE COLLOID PARTICLE AS A MIC ELL 
207 
multiply the term 2.5 in Einstein's equation by the expression that 
gives the correction for the potential difference, 
r i i /Kp vi i 
ns = n™ i + 2.5 v u + --2 (H 
I xqmr2 \ 2a / J 
but this formula has never been tested experimentally. 
In the case of proteins, the viscosity changes very much with the 
conditions under which the proteins are placed. It is well known 
that the viscosity of a protein depends on the hydrogen ion concen- 
tration or the ph. The viscosity of the hydrogen ion concentration 
has a minimum at the isoelectric point and a maximum at both sides 
of it (260). We do not know very much about the changes that take 
WsCO3/ty 
^5c//pbur concentro/zon 
Fig. 93.-Viscosity of sulphur sols 
place in the protein particles when we change the hydrogen ion con- 
centration, so that it is difficult to tell how this change in the viscosity 
is brought about. According to a theory suggested by Pauli the 
change in viscosity should be due to an actual change in volume of 
the particle, by condensation of water around it, i.e. the so-called 
hydration of the particle (261). In this way, according to Einstein's 
formula, the viscosity ought to go up when the volume of particles 
increases. Hatschek suggested the same explanation in the case of 
Oden's sulphur sols of different degree of dispersity (262). 
Loeb assumes that the particles in protein solutions are little 
clumps of gel and that the change in viscosity is due to the swelling 
of those little gel clumps. According to Loeb the amount of swelling 
and therefore also the amount of change in viscosity can be calculated 
from the Donnan equilibrium (263). 
When we try to measure the viscosity of colloids, we find especially 208 
COLLOID CHEMISTRY 
in such cases as proteins that the viscosity is not very well defined. 
We find that it changes with the velocity of the sol (264). If we 
use an ordinary viscosimeter which consists of a capillary tube through 
which the sol flows we find that the value of the viscosity we get 
depends on the speed of the liquid through the capillary. An instru- 
ment constructed by Couette has given a means of determining the 
viscosity at different rates of flow (265). The principle of the instru- 
ment is demonstrated by Fig. 94. A metallic cylinder A is suspended 
Fig. 94.-Couette's viscosimeter 
by the wire B and surrounded by another cylinder D containing the 
liquid to be studied. D can be rotated at different speeds by means 
of a motor. The inner cylinder then will be turned a certain angle 
which can be read off by means of the mirror H and a scale and 
telescope. When equilibrium is reached the force of torsion in the 
wire ought to equalize the frictional force which in turn is proportional 
to the viscosity and to the angular velocity of D. According to meas- 
urements by Hatschek this relation holds very well for water but not 
for gelatin sols. In the latter case the viscosity decreases with in- 
creasing angular velocity and reaches a limiting value. THE COLLOID PARTICLE AS A MIC ELL 
209 
It is rather difficult to explain why the viscosity depends on the 
velocity of the rotation, but probably a gel network is formed spon- 
taneously and destroyed by the motion. A modification of the Couette 
instrument as worked out by Sheppard is used in the Eastman Kodak 
Laboratory for testing gelatin sols for photographic work (266). 
Coagulation 
The phenomenon of coagulation is one of the most important things 
in colloid chemistry, and quite characteristic of the colloid state. By 
coagulation we understand the aggregation of the particles of the dis- 
perse phase to secondary units of different size and structure. Those 
units may be either reversible or irreversible. In its first stage, prob- 
ably, all coagulation is reversible but in many cases the particles very 
soon grow together so that the bonds between them cannot be broken 
unless the particles themselves are destroyed. With regard to coagu- 
lation we distinguish between lyophobe and lyophile sols (267), or in 
the case of water as the dispersion medium between hydrophobe and 
hydrophile sols (268). Hydrophobe means that the particles hate the 
water, they have only little affinity to the water and are easily coagu- 
lated) upon addition of electrolytes. The term hydrophile means that 
the particles love the water, that the sol is not easily coagulated by 
electrolytes. There is no very sharp distinction between those two 
classes, but in the extreme, they are rather charactersistic. 
Hydrophobe sols.-We shall first study the coagulation of the 
hydrophobe sols. Here the action of the electrolytes predominates. 
According to our studies of the electrokinetic phenomena the particles 
are surrounded by an electrical double layer. It has been found that 
the electrokinetic potential difference is closely connected with coagu- 
lation. If we compare the curve connecting the concentration of 
electrolyte with the potential difference as measured by cataphoresis, 
we remember that in certain cases we found that the potential differ- 
ence was diminished or even reversed by adding electrolytes. When 
we compare the stability of the sols at those different concentrations 
corresponding to different values of the potential difference, we usually 
find that when the potential difference has been brought down to a 
certain value, the particle loses stability and the colloid coagu- 
lates (269). The corresponding concentration of the electrolyte is 
called the coagulation value. In Fig. 95 the dotted areas represent 210 
COLLOID CHEMISTRY 
the regions within which the sol is stable. If we follow the concen- 
tration curve along, we find that when the potential difference has 
dropped to a certain value the sol loses stability and when the poten- 
tial difference has reached the same value of the opposite sign, we 
get into the region where the sol is stable again. It has also been 
found that the different kinds of electrolytes seem to have about the 
same coagulating effect at such points where they have lowered the 
potential difference to the same degree (270). This means that in 
order to coagulate the hydrophobe sols it is necessary to lower the 
electrokinetic potential difference to a certain extent, but we can do 
that with different ions. The nature of the ions seems to be without 
influence. 
If we compare coagulating electrolytes containing ions of different 
Crit/co/ 
Coog of e/ectro/yfs 
Fig. 95.-Diagram showing the relation between electrokinetic potential 
and stability. 
valencies we find that those of high valency have a much higher 
coagulating power than one would expect from the increase in 
charge (16). Freundlich has tried to explain this fact in the follow- 
ing way (271). The lowering of the electrokinetic potential and the 
coagulating effect is supposed to be due to the adsorption of ions of 
opposite charge to that of the particle. Now in a series of inorganic 
electrolytes such as KC1, BaCl2, A1C13, ThCl4 and a negatively charged 
sol such as As2S3 Freundlich assumes that practically equimolecular 
amounts of the cations are adsorbed. Let the absorption curve com- 
mon to all be represented by Fig. 96. In order to lower the potential 
to the same degree it would be necessary to have equal numbers of 
charges adsorbed or if the number of mols of the monovalent ions 
necessary is x, we must have of the divalent ions x/2 mols of the THE COLLOID PARTICLE AS A MIC ELL 
211 
trivalent ions x/3 mols, etc. If we calculate from our absorption 
curve the concentrations cx, c2, c3, in the liquid that correspond to the 
adsorption of those quantities we find that the concentration necessary 
to give the same charge adsorbed decreases much more rapidly than 
would be expected from the increase in valency. Now we know from 
recent measurements by Oden that those ions are not adsorbed exactly 
in equimolecular concentrations but the differences are not so very 
great, so that Freundlich's theory, even if it does not explain this 
phenomenon completely, actually gives the main points. 
Freundlich has also shown that some very strongly adsorbed 
organic ions have an exceptionally strong coagulating action. So 
Fig. 96.-The relation between adsorption and coagulation. 
for instance the anion of salicylic acid coagulates the positively 
charged A12O3 sol much more intensely than the anion Cl, and the 
cation of morphine chloride has a much stronger coagulating action 
upon the negatively charged As2S3 sol than has the cation K. 
It is very remarkable that in such cases where the curve giving 
the relation between electrokinetic potential difference and the con- 
centration of the electrolyte has such a shape that the critical poten- 
tial appears thrice (Fig. 97) there are actually two different con- 
centrations at which coagulation occurs. Such so-called irregular 
series of coagulation have only been observed in the case of tri- or 
tetravalent ions. Table XXXVI gives some of Buxton's and Teague's 
determinations on the coagulation of a platinum sol by FeCl3 (272). 212 
COLLOID CHEMISTRY 
Cone of e/ecfro/^e 
Fig. 97.-Diagram explaining the existence of two coagulation pointe 
TABLE XXXVI 
Coagulation of a Platinum Hydrosol by FeCL 
Millimol FeCL 
per Lit. 
Degree of Coagulation 
Direction of Cataphoresis 
0.0208 
no coagulation 
to anode 
0.0417 
CC 
0.0557 
CC 
0.0833 
complete coagulation 
no cataphoresis 
0.1633 
Cl 
0.2222 
Cl 
0.3333 
no coagulation 
to cathode 
0.5567 
cc 
0.8333 
Cl 
1.633 
Cl 
3.333 
cc 
6.667 
IC 
16.33 
complete coagulation 
no cataphoresis 
33.33 
CC 
83.33 
Cl 
163.3 
cc 
333.3 
ll 
666.7 
ll 
The coagulating action of mixtures of electrolytes has been studied 
and in most cases the action is additive. So for instance in the coagu- 
lation of gold sols by LiCl mixed with other salts (273). Table 
XXXVII gives some of Freundlich's determinations. The sum of the 
percentage values is about 100 in all cases showing that the coagu- 
lants act independently of each other. THE COLLOID PARTICLE AS A MICELL 
213 
TABLE XXXVII 
Coagulation of Gold Sol by a Mixture of Two Electrolytes 
Concentration of LiCl in per 
Coagulation concentration in per cent 
cent of the coagulation con- 
of 
the coag. 
cone, in 
the pure 
solution 
centration in the pure solu- 
of 
tion 
KC1 
MgCL 
BaCL 
A1C13 
CeCl3 
0 
100 
100 
100 
100 
100 
20 
66 
73 
60 
62 
36 
40 
55 
66 
46 
30 
60 
50 
60 
38 
38 
23 
80 
33 
50 
30 
25 
20 
In some sols that come nearer to the hydrophile sols, we get a differ- 
ent result. For As2S3 sol we find that the addition of the first elec- 
trolyte diminishes the action of the second one. For instance, if we 
add LiCl to a As2S3 sol and then add MgCL we find we must add 
more MgCL than if there was no LiCl added, so there seems to be 
an antagonistic action between the two (Table XXXVIII) (273). 
TABLE XXXVIII 
Coagulation of As2Ss Sol by a Mixture of Two Electrolytes 
Concentration of LiCl in per cent of 
Coagulation concentration 
in per cent 
the coagulation concentration in the 
of the coag. cone, in the 
pure solu- 
pure solution 
tion of 
MgCL 
AlCls 
0 
100 
100 
24 
200 
110 
48 
220 
133 
70 
233 
166 
The addition of a positive sol to a negative sol corresponds to 
the addition of cations of high valency to the same sol. Mutual 
precipitation of the two sols takes place within certain ranges of 
concentration. The following experiments by Billiter (274) illustrates 
this (Table XXXIX). 
TABLE XXXIX 
Mutual Coagulation of Negative As2Sa and Positive Fe2O3 Sols 
Milligram Milligram 
FCaOa ASaS» 
per 10 cc. 
of the Mixture 
0.61 20.3 
almost no coagulation, particles neg. 
9.12 
14.5 
coagulation. 
27.4 
2.07 
no coagulation, particles positive. 214 
COLLOID CHEMISTRY 
In most investigations of coagulation, the so-called coagulation 
value or limiting value of the concentration of the electrolyte sufficient 
to cause coagulation has been studied but apparently that value is 
not so very well defined. It is interesting to follow the attempts that 
have been made to study coagulation on a quantitative basis, by 
measuring the velocity of coagulation. The best way to do this is 
to measure the actual number of particles present at different times 
in the ultramicroscope. In some cases it is not possible to follow 
directly the change in the number of particles, and attempts have been 
made to follow the coagulation by studying the change in light absorp- 
tion or in viscosity. It is, however, difficult to interpret those other 
measurements and it seems that at the present time the only way to 
study the velocity of coagulation quantitatively is to count the number 
of particles in the ultramicroscope. 
Some preliminary experiments on the velocity of coagulation were 
carried out by Zsigmondy (275). As a measure of the process he 
took the time necessary to change the color of a gold sol from red 
to violet. When varying the concentration of the coagulating electro- 
lyte he found that the time of color change at first decreased rapidly 
with increased concentration and then became constant (Table XL). 
TABLE XL 
Concentration in Millimol 
NaCl per Liter 
Time of Color Change 
5 
>150 sec. 
10 
12 
20 
7.2 
50 
7 
75 
6.5 
100 
7 
150 
6 
200 
6.5 
300 
7.5 
500 
7 
Coagulation of a Gold Sol with NaCl 
Experiments by Zsigmondy and Reitstotter also showed that the 
limiting value of time of color change is independent not only of 
the concentration but also of the valency and nature of the coagu- 
lating ions. The range of concentration within which this holds is 
called the range of rapid coagulation and the range below those 
concentrations, the range of slow coagulation. By comparing his 
measurements on coagulation with those of Galecki (276) on cata- 
phoresis, Zsigmondy was able to show that the isoelectric point lies THE COLLOID PARTICLE AS A MICELL 
215 
within the range of rapid coagulation. A gold sol the particles of 
which normally had a mobility of 1.35 p/sec. began to show slow 
coagulation at about 0.50 p/sec. and rapid coagulation at about 
0.18 p/sec. He assumes that in the case of rapid coagulation of 
spherical particles of equal size particles that approach another 
particle within a certain minimum distance become permanently 
fixed to it. The minimum distance is defined as the radius of 
the sphere of action of the particle (Fig. 98), i.e. the particles 
become aggregated as soon as their centers are at a distance less 
than A. 
Smoluchowski (277) showed that it is possible to deduce the 
formulae for the decrease in the number of particles with time as a 
function of this radius of action A, of the diffusion constant D, and 
Fig. 98.-The sphere of action in coagulation 
of the original number of particles per unit volume of the sol v0. 
The general outline of his way of reasoning is as follows. He first 
takes into account a single particle in the sol and calculates the 
probability for any other particle to enter its sphere of action and 
the probability that within the time t no particle shall enter the 
sphere of action. This can be done simply by applying the equation 
given for the Brownian movement. From that probability he cal- 
culates the decrease in number of the single particles. He then takes 
into account that the number of single particles also decreases owing 
to similar processes around every particle in the sol. The result is 
still defective, for in the first place the particles or nuclei around 
which coagulation is supposed to take place are not at rest but carry 
on Brownian movements and in the second place also the aggregates 
already formed act as coagulating nuclei to help diminish the number 
of primary or single particles. He calculates the corrections due to 216 
COLLOID CHEMISTRY 
those two phenomena and finally arrives at the following system of 
equations: 
11 v v° 
V1 + v2 + = Iv - 
1 + T 
Vo 
V1= 7 Tv 
t 
Vo?p 
V2"7 Tv 
0+t) 
/ t \k -1 
V° \T ) 
where 
vx - number of primary or single particles 
v2 = " " double " 
v3 = " " triple " 
T = 1 
4 it D A v0 
These formulae are sufficiently correct only at the beginning of the 
coagulation because of the uncertainty involved in estimating the 
radius of the sphere of action of the aggregates built up of several 
particles. 
If we measure the time in units of T and the number of particles 
in units of v0 we get the simple and interesting diagram shown in 
Fig. 99. 
The total number of particles is reduced to half its value after 
the time T and the number of primary particles is reduced to y± in 
the same time. The curve for double particles has a maximum equal 
4 
to - . vo at the time T/2, etc. 
z i 
Smoluchowski's theory has been tested in experiments carried out 
by Zsigmondy, Reitstotter and Westgren. As already pointed out 
Smoluchowski's original theory of coagulation applies only to the 
so-called rapid coagulation, i.e. within the range of concentration THE COLLOID PARTICLE AS A MIC ELL 
217 
where the velocity of coagulation has become independent of the con- 
centration of the coagulant. According to Smoluchowski that would 
mean that every such collision between the particles which brings 
them within their mutual sphere of action would cause aggregation. 
v 
Zsigmondv (275) first tested the equation Vx -- --by meas- 
(1 + t) 
uring, in the ultramicroscope, the decrease in the number of primary 
particles in a gold sol. He was able to distinguish between the pri- 
mary or single particles and the aggregates, because the single particles 
Fig. 99.-Variation in the relative number of particles in a sol during coagulation 
emit green light, while the aggregates emit yellow light. This series 
of experiments by Zsigmondy are, so far, the only ones in which the 
decrease in the number of single particles has been measured. In 
most cases, it is impossible to distinguish between primary particles 
and aggregates, but in gold colloids the color is quite distinguishable. 
To be able to determine the number of primary particles accurately 
the coagulation of a series of equal sols was interrupted at different 
times by means of adding gum arabic (protective action). He found 
the following values (Table XLI). 
Westgren and Reitstbtter (278) studied the change in the total 
number of particles in gold sols and used their values to determine 218 
COLLOID CHEMISTRY 
TABLE XLI 
Decrease in the Number of Primary Particles During Coagulation 
Vi 
t in Sec. 
Obs. 
Calc. 
0 
1.97 
1.97 
2 
1.35 
1.65 
5 
1.19 
1.31 
10 
0.89 
0.93 
20 
0.52 
0.64 
40 
0.29 
0.25 
the ratio between the radius of particles and the radius of the sphere 
of action. The coagulation was stopped by addition of gelatin solu- 
tion. They found, for instance, the following values in the case of a 
gold sol of radius r = 76 pp (Table XLII). 
TABLE XLII 
Decrease in Total Number of Particles During Coagulation 
t in Sec. 
S v per cc. 
A/r 
0 
5.27 X 
108 
- - - - 
60 
4.46 
44 
2.15 
120 
3.68 
44 
2.54 
240 
3.11 
44 , 
2.07 
420 
2.50 
44 
1.87 
600 
2.10 
44 
1.78 
900 
1.49 
44 
2.02 
1200 
1.23 
44 
1.97 
The average value for A/r, 2.20, is not very far from 2, i.e. the radius 
of the sphere of action is the double of the radius of the particle. 
That means that in a gold sol coagulation only occurs when the 
particles come so close together that they are practically in contact. 
Smoluchowski's original theory was developed for the case where 
the velocity of coagulation is independent of the concentration of the 
electrolytes present. Later on, he tried to modify his theory so as 
to include the case where the coagulation velocity is dependent upon 
the concentration. He assumes that the difference between the rapid 
and the slow coagulation is that in the case of slow coagulation every 
collision does not lead to a permanent aggregation, but only a certain 
fraction of them. He showed that the same general kind of formulae 
would apply to slow coagulation. The only difference is that in the 
constant T, the so-called time of coagulation, there would appear a 
certain factor x, i.e. we would have T = --=^-4 . 
Ln: D A v0. x THE COLLOID PARTICLE AS A MIC ELL 
219 
According to Zsigmondy's determinations the region of slow coagu- 
lation of gold sols by NaCl is 5 to 50 millimol per lit. Westgren found 
that T is independent of the concentration of the electrolytes above 
about 50 millimol but increases with decreasing concentration below 
about 50. At a certain concentration T is constant, i.e. T is inde- 
pendent of the time, as shown in Table XLIII. 
TABLE XLIII 
Slow Coagulation of a Gold Sol with NaCl (9.5 Millimol per Lit.) 
r = 120 mi 
t in Min. 
2 v per cc. 
T in Min. 
0 
4.35 X 108 
5 
4.02 " 
60.9 
10 
3.78 " 
66.3 
15 
3.69 " 
83.9 
20 
3.32 " 
64.5 
30 
2.79 " 
64.6 
Westgren (279) studied the action of different electrolytes in the 
case of slow coagulation of gold sols. If we plot the time of coagu- 
Time m mmaTes 
Coecenfmf/o/? of e/ec/ro/yfe 
in m/hrno/s per /iter 
Fig. 100.-Action of cations in slow coagulation of gold sols 
lation T against the concentration of the coagulating electrolyte we 
get a diagram that expresses the coagulating power of an electrolyte 
fairly well. Fig. 100 and Fig. 101 give some of Westgren's curves 
for different cations and different anions. 220 
COLLOID CHEMISTRY 
It is of interest to note that the NaCl curve cuts the KC1 curve 
and the NaOH curve, showing that the order of the coagulating action 
of electrolytes might be different at different concentrations. With 
Time m m/n^es 
Cone, of e/ec/ro/yfe //? mz/imo/s per ///-er 
Fig. 101.-Action of anions in slow coagulation of gold sols 
regard to the cations of the alkali metal we find if we compare the 
coagulating action at comparatively high concentrations that we have 
the following series 
H> Kb>Na>Li . 
That is the same series as the electrolytical mobility 
H = 318 > ™ ~ 6£ > Na - 44 > Li = 33. 
111) = bo 
Westgren also tried to find out whether the influence of tem- 
perature on the coagulation of gold hydrosols was only due to the 
change in the diffusion constant, or whether the specific action of the 
electrolyte as it manifests itself in the slow coagulation really changes 
with temperature. In the case of 10 millimol NaCl as coagulant he 
found, for instance, that when the temperature was changed from 
13.2° to 39.5° the time of coagulation decreased from 69.0 min. to 
24.1 min. while from the change in the diffusion constant one would 
expect 35.5 min. The coagulating action of the electrolyte appar- 
ently increases with temperature. 
In some recent measurements of velocity of slow coagulation car- 
ried out by Kruyt (280) certain discrepancies have been found be- 
tween the theoretical and experimental values. The time of coagu- 
lation was not constant within a series and he therefore thinks that THE COLLOID PARTICLE AS A MIC ELL 
221 
Smoluchowski's theory cannot be applied to slow coagulation. The 
system that Kruyt and his co-workers used were, however, not so 
well defined. They used Se sols which undoubtedly were very in- 
homogeneous. There were probably particles of different sizes pres- 
ent, some perhaps so small that they could not be seen in the ultra- 
microscope. Those would cause considerable complication because 
in the course of coagulation they would gradualy become visible in 
the form of aggregates and would therefore apparently tend to slow 
down the rate of coagulation. 
The process of reversing coagulation is called peptization. The 
name was introduced before we knew much about the process and 
originally stood for processes analogous to the action of pepsin upon 
proteins. Now we look upon peptization as merely a reverse of coagu- 
lation. Peptization can be caused in many cases by simply adding 
a suitable ion so that the potential difference between the particle 
and the liquid is raised. Or, in cases where the concentration of the 
ions is too high, peptization can be brought about by washing out 
some of the ions. An example of this kind is the peptization of 
arsenious sulphide by washing. The coagulum precipitate of ferric 
oxide can be peptized, e.g. by adding Fe ions. There have not been 
many quantitative investigations of peptization of hydrophobe sols 
so far (281). 
A curious case of the coagulation of hydrophobe sols observed by 
the writer is that which occurs in some organosols of noble metals 
when the temperature is changed (282). The mechanism of this 
process is not cleared up as yet. 
If we try to prepare, say a platinum sol in pure ethyl ether by 
striking an oscillatory arc within the liquid at low temperature, the 
sol usually coagulates immediately, if the ether is pure enough, but 
if we had added a little water to the ether it would have been stable. 
Upon raising the temperature slowly we find that the sol coagulates 
rather suddenly at a certain temperature. If we plot in a diagram 
the temperature of coagulation against the concentration of the water 
we get the diagram (Fig. 102). That is the coagulation temperature 
rises rapidly with increase in concentration of the water added. When 
we have added a little more than % per cent of water, the sol is stable 
at the boiling point. It is not very easy to imagine how this trace 
of water is able to stabilize the sol. One might try to explain it by 
assuming that the water is adsorbed by the particles and forms a 
sort of protective film. When the temperature is raised the adsorp- 222 
COLLOID CHEMISTRY 
tion of this water film probably goes down. Recent investigations 
by Lindeman and the writer (283) have shown that the velocity of 
raising the temperature has some influence. If we warm up a sol 
very quickly, we can raise it to a higher temperature than if we warm 
it slowly. The time during which the sol remains at a certain tem- 
perature is therefore of importance. It is remarkable that this phe- 
nomenon only occurs in a sol of a noble metal and in such dispersion 
Coagu/arw? 
Fig. 102.-Coagulation temperatures of platinum sols. 
media that do not affect the particles chemically. You will find it in 
platinum and gold sols, but with silver, the point of coagulation is 
very indistinct. 
Hydrophobe sols can also be coagulated by certain radiations. 
Ultraviolet light has a coagulating effect and so have X-rays, and the 
radiations from radium, but as yet we do not know very much about 
the mechanism of the process. Nordenson (284) studied the influence 
of ultraviolet light, X-rays and P-rays on gold sols and found that 
the coagulative action of the rays was independent of the sign of the 
charge of the particle, i.e. negative and positive sols were coagulated 
at about the same rate. Any perceptible chemical change did not take 
place, but as Nordenson suggests, it is possible that the light changes THE COLLOID PARTICLE AS A MIC ELL 
223 
the surface of the particles so as to depress the adsorptive power and 
therefore also the stability. 
Hydrophile sols.-We will now consider briefly the coagulation of 
the hydrophile sols-that is the sols with particles of high affinity to 
water. Evidently there is no very distinct difference between those 
two classes, but it is convenient to use those names for the more 
extreme cases. 
The best known of the hydrophile sols is the sulphur sol, pre- 
pared by the reaction between hydrogen sulphide and sulphur dioxide 
or by decomposition of thiosulphate by an acid and the most im- 
portant ones are the protein sols. Oden working in the laboratory 
of the writer has made a very detailed investigation of the sulphur 
sol (285). He found that the coagulation of such a sol is completely 
reversible, that is, the number of particles that we have before coagu- 
lation and after coagulation is quite the same. Table XLIV. 
TABLE XLIV 
Repeated Coagulation of a Sulphur Sol 
Number of 
Number of Coagulations 
Particles per 384 p3 
0 
2.54 
1 
2.55 
2 
2.52 
3 
2.53 
This shows that those sulphur sols when coagulated, form aggre- 
gates within which the particles preserve their individuality, and when 
peptized, the aggregates are dissolved, the bonds between the particles 
loosened and the particles become free again. 
The coagulating power of the electrolytes was found parallel to 
the degree of dissociation. Electrolytes that are very slightly dis- 
sociated, such as HgCl2 or Hg(CN)2 had little coagulative action, 
while Hg(NO3)2 coagulated strongly. In Table XLV a list of coagu- 
lation values as determined by Oden are given. 
The sulphur particles are negatively charged and one would con- 
sequently expect that they are coagulated by the cations. This is 
actually the case but there are evidently also other factors than the 
charge of the cations that play a part in this coagulation. The 
valency rule is not at all so pronounced as in the case of the hydro- 
phobe sols. Arranged according to the coagulating action of their 
chlorides the monovalent cations give the following series. 
Cs > Rb > K > Na > NH4 > Li > H 224 
COLLOID CHEMISTRY 
TABLE XLV 
Coagulation of a Sulphur Sol by Different Electrolytes 
Electrolyte 
Molar Concentration When Coagulation Occurs 
HC1 
6 
LiCl 
0.913 
NH4CI 
0.435 
NaCl 
0.153 
KC1 
0.021 
RbCl 
0.016 
CsCl 
0.009 
CaCL 
0.0041 
BaCL 
0.0021 
A1C13 
0.0044 
If we compare this series with the one determined by Westgren for 
gold sols 
H> > Na > Li 
Rb 
it is striking that the H ion which has such a strong coagulating action 
in the case of gold has the lowest coagulating action in the case of 
sulphur. 
When coagulating a sulphur sol with say NaCl Oden found that 
if he added the electrolyte in successive portions and collected each 
coagulum separately the first precipitate contained the coarsest parti- 
cles and the last the finest. By dissolving the precipitates again and 
repeating the coagulation he was able to divide the original sol into 
a series of sols of different sized particles. Determinations of the 
coagulating values for those sols showed that they vary with the 
degree of dispersion. 
A consequence of this phenomenon is that the coagulating values 
become more and more sharp as the sizes of the particles in a sol 
become uniform. Table XLVI and Table XLVII give the content 
of colloid sulphur as a function of the concentration of the coagu- 
lating electrolyte for a non-uniformly-or polydisperse-and for a 
uniformly-or monodisperse-sol. 
The coagulating action of two or more electrolytes present at the 
same time is not additive as in the case of a hydrophobe sol such as 
gold. If we measure, say the coagulation value of KC1 in presence 
of various amounts of LiCl we will find that in certain concentrations 
of LiCl it takes more KC1 to coagulate the sulphur than when there 
is no LiCl present. Fig. 103 shows diagrammatically such a series of 
determinations made by Oden. THE COLLOID PARTICLE AS A MIC ELL 
225 
TABLE XLVI 
Coagulation of a Polydisperse Sulphur Sol 
Gr. S per 100 cc. 
Mol. NaCl per Lit. Liquid 
17.25 
0.187 
17.24 
0.195 
15.72 
0.262 
14.50 
0.296 
12.93 
0.337 
11.35 
0.354 
8.51 
0.354 
5.81 
0.356 
3.64 
0.381 
2.49 
0.400 
1.88 
0.426 
1.43 
0.445 
0.64 
0.515 
TABLE XLVII 
Coagulation of a Monodisperse Sulphur Sol 
Gr. S per 100 cc. 
Mol. NaCl per Lit. Liquid 
60.6 
0.248 
59.9 
0.258 
53.4 
0.359 
10.70 
0.404 
6.14 
0.405 
4.10 
0.423 
2.56 
0.443 
0.90 
0.498 
Oden believed that this antagonistic action between the two electro- 
lytes were entirely due to the antagonism between the cations and 
-Co/xeofrof/ao offf<!7 
Fig. 103-Antagonistic action of ions in coagulation, 
Co/7ceofrof/o/? of f/Cf 
the anions. According to recent experiments by Freundlich, there is 
probably also an antagonistic action taking place between the differ- 
ent cations. He found that the coagulative power of cations of high 
valency is reduced quite enormously by the presence of say Li2SO4. 226 
COLLOID CHEMISTRY 
In a Li2SO4 solution containing 65 per cent of the concentration 
necessary to coagulate the sulphur, it was necessary to raise the con- 
centration of CeCl3 to 15000 per cent of the coagulation value in a 
Li-free sol in order to get coagulation. Such a phenomenon could 
hardly be ascribed to the peptizing action of the anions only. 
Sulphur sols have a very peculiar behavior when the temperature 
is changed. If we take a clear sulphur sol and cool it with ice, it 
is partially coagulated, and when it is warmed, it is peptized again. 
We can repeat this as many times as we desire to and the coagulation 
and peptization will occur again and again. The writer studied this 
action of temperature and found that there is a real temperature 
'Su/ppyr concertf/oT/b/? 
7en?pen?fyre 
Fig. 104.-Variation of sulphur concentration with temperature in a sulphur sol 
in contact with its coagulum. 
equilibrium between the concentration of the colloid sulphur in the 
liquid and in the coagulum, determined by the temperature and the 
nature and concentrations of the electrolytes present (286). The con- 
centration of sulphur in sol form can be expressed by the following 
formula S = e where t is the temperature and k and t0 are 
constants (Fig. 104). It was also found that a certain point on that 
curve could be reached from both sides, by lowering the temperature 
and by raising it, so that this is actually a true equilibrium from 
the ordinary point of view. 
If we have only a limited amount of colloid present, we will 
of course upon raising the temperature come to a point where all 
the sulphur has gone into solution. Oden found that sols of differ- THE COLLOID PARTICLE AS A MIC ELL 
227 
ent sized particles gave different curves. Curve A in Fig. 105 might 
represent a fine grained and B a coarse grained sol. If we mix these 
sols, it is obvious that they will both go into solution and the con- 
Su/p/wr 
7e/??per<7^re 
Fig. 105.-Temperature coagulation of sulphur sols of different degree of 
dispersity. 
centration go up along say the line C. When the point F is reached 
the fine grained sol is completely in solution, and only -part of the 
coarse grained sol is left. That is from the point F upwards we 
c#/?ce/?fa7to/7 
Fig. 106.-Temperature coagulation of a mixed sulphur sol 
"77/T7& 
move along the curve of the pure sol B. If we make up a sol of a 
great number of different sized sulphur colloids, we get an equilibrium 
curve of the type shown in Fig. 106. If the number of size classes 
increases infinitely we will get a continuous curve as the limit. 
Oden also showed that the exponential curve becomes more and 228 
COLLOID CHEMISTRY 
more steep as the sol becomes more and more equally sized, and it 
is therefore possible that if we had a sol of absolutely equally sized 
particles, the coagulum would be dissolved at quite a distinct point 
of temperature and not along an exponential curve as in the case 
we have investigated. The behavior of the sulphur sol with regard 
to changes in electrolyte concentration is very interesting because it 
shows that colloid systems can give the same type of solubility dia- 
gram as ordinary solutions. It is not at all unlikely that in some 
cases where we have measured the solubility of proteins, the figures 
arrived at only represent a colloid equilibrium of the same kind as 
found for the sulphur sols. 
Freundlich has shown that sulphur sols prepared by mixing an 
alcoholic solution of sulphur with water are hydrophobe (287). The 
hydrophile behavior of the sulphur sols prepared by chemical re- 
actions is according to him due to an adsorbed layer of pentathionic 
acid. He found that by treating a hydrophile sulphur sol with am- 
monia an amount of about 0.450 millimol pentathionic acid per gr. 
sulphur was set free. 
Other hydrophile sols that have been studied with regard to 
coagulation and peptization are the sol of silicic acid, SiO2 and the 
sol of stannic acid SnO2. They resemble the sulphur sol to some ex- 
tent, but are more difficult to study in detail. In the case of SnO2, 
the coagulum can be peptized by addition of an alkali. According to 
Zsigmondy peptization is probably due to the peptizing action of 
the SnO3 ions which are strongly adsorbed on the particles (288). 
Probably those ions are responsible for the raise in electrokinetic 
potential necessary for the peptization. In the series of the oxides of 
Si, Sn, Pb the hydrophile behavior decreases as the electropositive 
character increases. Thus the SiO2 sol is perhaps the most pronounced 
hydrophile of all inorganic sols, the SnO2 sol is still very markedly 
hydrophile while the PbO2 sol is distinctly hydrophobe. 
It seems that the degree of hydrophile behavior of those oxide 
sols also depends to some extent upon the method of preparation. 
Mecklenburg prepared stannic acid sols of apparently different hydro- 
phility by hydrolyzing stannic sulphate at different temperatures. 
The sols formed at low temperatures seemed to contain smaller par- 
ticles and seemed also to be more hydrophile than those formed at a 
higher temperature (289). 
Among the hydrophile sols there is a group that is perhaps more 
important than any other group of sols. They have been studied THE COLLOID PARTICLE AS A MIC ELL 
229 
very much but the results are not of the same accuracy as the results 
arrived at in the study of inorganic colloids. This important group 
of colloids is the proteins. 
One of the important points in the coagulation of proteins is that 
the stability is very low at the isoelectric point. Now this is also 
the case in ordinary inorganic colloids, or at least we find that stability 
decreases rapidly when the potential difference between the particle 
and the liquid goes down below a certain limit. In the case of the 
proteins, however, the sols are most unstable just at the isoelectric 
point. The isoelectric point in its turn depends to a great extent upon 
the hydrogen ion concentration in the sol. If we take a fairly pure 
sol, e.g. dialyzed egg albumin which is not very far from its isoelectric 
point, we find that upon adding alcohol, the opalesence increases con- 
siderably. The protein is partly coagulated when near the isoelectric 
point. If we remove another sample of the same protein from the 
isoelectric point by adding acetic acid, and then adding alcohol, we 
will find that there is practically no coagulation at all. Coagulation 
experiments with alcohol have therefore been used to determine the 
isoelectric point of proteins. Table XLVIII gives some determinations 
made by Pauli (290). 
TABLE XLVHI 
Coagulation of Serum Albumin by Ethyl Alcohol at Various Hydrogen Ion 
Con centration s 
Hydrogen. Ion Cone. 
Degree of Coagulation by Alcohol 
0.6 X 10-3 
+ 
0.9 X IO-3 
-I-F 
1.8 X 10'5 
+ + + = maximum of coag. 
3.6 X 10"3 
-j 1" 
5.4 X 10'5 
+ 
7.2 X 10'3 
- 
Some proteins are so unstable at the isoelectric point that they can- 
not be had as colloid solutions there unless some peptizing electrolyte 
is present (291). This is the case with most of the globulins. They 
are held in colloid solution in the juices of the animals by the salts. 
Many proteins show mutual coagulation when mixed with in- 
organic colloids of opposite charge (292). If we take ferric oxide 
which is positively charged and add some protein, e.g. dialyzed egg al- 
bumin, we find that as long as the ferric oxide is in excess, there 
will be practically no coagulation. If we add more of the protein, 
we will reach the point where the charges of the particles are 230 
COLLOID CHEMISTRY 
mutually neutralized and there coagulation will occur. Even within 
the range of concentration where no direct coagulation takes place 
the sol has lost some of its original stability. If we determine the 
salt concentration necessary to coagulate a ferric oxide sol with and 
without albumin present we find that within a certain range the 
ferric oxide sol with albumin is more sensitive to the coagulant. 
The ferric oxide sol has been "sensitized." The sensitizing action 
is different for different proteins and determinations of this kind- 
determinations of the "iron number" (293)-has been used to char- 
acterize abnormal changes in the blood plasma. In a certain case 
where a ferric oxide sol could be coagulated by 37.5 millimol per lit. 
NaCl the addition of paraglobulin from normal human blood de- 
pressed the coagulation value to 4.69 while the addition of para- 
globulin from tetanus serum depressed it to 1.17 (294). 
The mutual precipitation of different proteins such as toxins and 
antitoxins, bacteria and agglutinins is also probably to be regarded 
as a colloid phenomenon. A maximum of coagulation is often ob- 
served at a certain concentration as illustrated by Table XLIX 
(Bechhold) (295). 
TABLE XLIX 
Agglutination of Bacteria by an Immune Serum 
Concentration of Serum 
State of Suspension after 2 Hours 
1/100 
no agglutination 
1/1000 
almost complete agglutination 
1/25000 
complete agglutination 
1/30000 
marked flocculation 
1/45000 
no agglutination 
When we mix a protein sol with an inorganic sol of the same 
charge of particles, we get a so-called "protective action"-that is, 
the protein sol protects the particles of the inorganic sol from coagu- 
lation by electrolytes. One of the. best known examples of this is 
the action of gelatin on gold sols. 
The color of a red gold sol when coagulated with say NaCl, 
changes to blue. If a sufficient amount of gelatine is added no 
coagulation and no change in color takes place. Zsigmondy has de- 
fined the so-called gold number as the number of milligrams of the 
hydrophile colloid per 10 cc. of gold sol that just suffices to prevent 
the color change to occur when 1 cc. of a 10 per cent NaCl solution 
is added (296). The determination of this gold number has often THE COLLOID PARTICLE AS A MIC ELL 
231 
proved to be a valuable help in characterizing different proteins or 
in detecting changes in the composition of liquids containing mixtures 
of different proteins (297). The highest protective action is found 
with the euglobulins. Paraglobulins protect less and albumins still 
less (298). Such changes in the blood plasma as occur, e.g. in tetanus 
where almost all the albumins are transformed into globulins can 
therefore easily be detected by determining the gold number. The 
changes that gradually take place in protein solutions with time, the 
aging effect, can also be studied by this method. In Table L some 
gold numbers are tabulated. 
TABLE' L 
Gold Numbers of Some Hydrophile Colloids 
gelatin 
0.005-0.01 
casein 
0.01 
haemoglobin 
0.03-0.07 
gum arabic 
0.15-0.25 
dextrin 
6-20 
With regard to the mechanism of the protective action it is of 
interest to note that the charge of the gold particles is not markedly 
changed by the protein. Probably the protein particles form a kind 
of protective layer around the gold particles thus conferring upon 
them a more hydrophile behavior. 
Hydrophile sols can often be changed to hydrophobe. An ex- 
ample of this is the so-called denaturation of an ordinary protein. 
If we take a dilute solution of dialyzed egg albumin and heat it, 
the protein is changed, the hydrophile colloid goes over to a hydro- 
phobe, i.e. it becomes much more unstable, and at the isoelectric point 
it coagulates. If we add some suitable electrolyte, e.g. acetic acid, 
before heating it, the sol does not show coagulation, but if a salt such 
as Na2SO4 is added after the heating, coagulation takes place show- 
ing that the albumin was actually denatured and transformed into a 
hydrophobe sol also in the presence of the acetic acid but that the 
coagulation was prevented (299). The isoelectric point of a denatured 
protein is situated nearer neutrality than that of the native protein. 
So, for instance, the isoelectric point of natural serum albumin is 
2 X 10 5 while the denatured product has 4 X 10"". The denaturation 
by heat seems to take place rather suddenly at a certain temperature. 
Recent investigations, however, have shown that it is a time process 
occurring at any temperature, but that the velocity of denaturation 232 
COLLOID CHEMISTRY 
rises very rapidly with increase in temperature. So, for instance, the 
velocity increases 564 times between 69° and 79° in the case of egg 
albumin (299). 
There are, of course, many other examples of transformations 
of hydrophile sols into hydrophobe. The hydrophile sulphur sols, pre- 
pared, e.g. by dissociation of thiosulphates with an acid, can be trans- 
formed to hydrophobe sols by removing the traces of pentathionic 
acid which the particles held adsorbed (287). 
Oden found that the change brought about by addition of NaOH 
can be expressed by the formula y = a. cb where t is the time before 
opalescence appears, c is the concentration of NaOH and a and b 
are constants (285). Table LI gives some of his determinations. 
TABLE LI 
Transformation of a Hydrophile Sulphur Sol into a Hydrophobe 
Time for Opalescence 
to Appear in Min. 
Millimol NaOH per Lit. 
Observ. 
Calc. 
10 
about 100 
100 
15 
" 60 
53 
20 
" 35 
34 
25 
" 20 
24 
40 
" 12.5 
12 
45 
" 10 
9.5 
50 
" 6.5 
8 
70 
" 5 
4.7 
75 
" 4.5 
4.3 
80 
" 4 
3.8 
90 
" 3 
3.2 
Gels 
The coagulation of colloids does not always lead to precipitation. 
It sometimes leads to a setting of the whole system to a gel. The 
study of the formation of gels is rather important to the bio-scientists 
and it has also some bearing on soil and geological problems. 
Probably the formation of a gel-the complete settling of the sol- 
is much more common than we would expect. In many cases, there 
are probably formed very weak gels at first and the coagulum or 
precipitate is probably due often to a destruction of a very weak 
gel. If we have a sol say in a large beaker and it sets to a very 
weak gel, the gel is easily broken, but in cases where the sol is en- 
closed in narrow channels-in capillary spaces-such as in the tis- 
sues and cells of plants and animals, the formation of weak gels is THE COLLOID PARTICLE 48 A MICELL 
233 
probably much more important than is generally supposed. The study 
of weak gels is therefore a problem of considerable importance. 
The properties of a gel depend to a large extent on its structure. 
In the case of a sol or a colloid solution, there is only one structure 
possible, if the sol is dilute enough, i.e. we have a complete hap- 
hazard distribution of the particles according to the probability theory. 
But when we come to the formation of a gel which probably is ac- 
companied by an aggregration of particles, the same kind of particles 
can, by arranging themselves to different structures, give rise to dif- 
ferent kinds of gels. In the study of the gel, even in the cases where 
the particles, when in sol form, would give off light enough to be 
seen in the ultramicroscope, the concentration or number of parti- 
cles in unit volume is so great that they cannot be resolved by the 
ultramicroscope. We therefore know very little of the structure of 
the gels. The particles in almost all gels studied so far give off too 
little light to be seen even in the sol form. Such is the case with 
the gelatin gel, the agar gel, the ferric oxide gel. The gel formation 
is much more common among the hydrophile sols than among the 
hydrophobe. It is not, however, improbable that in the future we 
will be able to study the formation of gels out of typically hydro- 
phobe particles such as metallic particles and that would certainly 
help us very much to elucidate the structure of gels in general. 
In cases where we are unable to follow the formation of a gel 
directly by means of the ultramicroscope, studies of the Brownian 
movements of foreign particles added to the sol before setting, 
e.g. gold or mercury particles, large enough to be seen in the ultra- 
microscope, might be of considerable value. By measuring the average 
square of displacement of those particles as a function of time one 
would be able to decide whether the foreign particles could move 
freely within the network of the gel or whether they were confined 
to move only within little closed cells in the gel, etc. Measurements 
of this kind are now in progress. 
Gelatination.-The setting of a gel is accompanied by an enormous 
rise in viscosity. There is, however, no break in the curve giving 
the relation between viscosity and degree of setting, when the vis- 
cosity is measured by ordinary methods. It is not clear whether 
this is due only to inappropriate methods of measurement or whether 
it is a true expression of the transition between sol and gel. On one 
hand it is possible that in the ordinary methods of viscosity measure- 
ment we break up the gel network as it is formed and thus create 234 
COLLOID CHEMISTRY 
the continuity artificially. On the other hand it is possible that the 
formation of the gel structure starts far below the setting point and 
that the gradual increase in viscosity measures this increase in rigidity 
of the network. Measurements of the elastic properties of very weak 
gels when setting would allow us to solve this question. The fact that 
//scos/fts 
gelatin 
TempenaTure 
Fig. 107.-Relation between viscosity and temperature for the system 
gelatin water. 
the temperature-viscosity curves for gelatin give a sharper and 
sharper knee as the concentration decreases is in favor of the former 
assumption (Fig. 107). 
The transition of sol to gel and vice versa shows considerable 
hysteresis or lag. If we warm up a gelatin gel quickly, that has 
W5COS/ft/ 
Temperature 
Fig. 108.-Hysteresis in gel-sol transformation. 
reached equilibrium, from point A Fig. 108 it does not reach the 
equilibrium point B in the sol region corresponding to the new tem- 
perature at once but moves to the point C in the gel region and then 
gradually goes up to B. If we then lower the temperature quickly 
we come to the point D in the sol region and after some time we 
finally come back to the starting point A in the gel region. The 
changes are very slow and they are never quite reversible. The THE COLLOID PARTICLE AS A MICELL 
235 
properties of a gel always depend upon the history of it to some 
extent. 
The velocity of setting or gelatinization depends on various fac- 
tors. It is quite striking that in such a case as with a gelatine gel 
where the lowering of temperature causes a setting of the solution, the 
velocity of gelatinization rises with increasing temperature. That 
is, if we have say 1.5 per cent gelatine solution and if we keep 
it at 20°, it would set to a gel in 3 days but if the same gel were 
kept at a lower temperature say 2° C. it would still be liquid after 
14 days (300). The velocity of the setting goes down when the tem- 
perature is lowered, so that it seems as if the rise in temperature 
should correspond to a rise of the setting point, but it only means 
that equilibrium has not been reached. The velocity of gelatiniza- 
tion also depends on the electrolytes present. If we take a gelatine 
solution, about 10 per cent, in two test tubes and add to one am- 
monium sulpho-cyanide and to the other an equal amount of water 
and cool with ice, the pure gelatine will set much more rapidly than 
the one containing the sulpho-cyanide. Some other electrolytes, such 
as sulphates and acetates, seem to accelerate the velocity of setting. 
There is a certain analogy between narcotic action of some organic 
substances and their action upon the setting of gels (301, 302), 
Table LIL 
TABLE LII 
Gelatinization and Narcotic Action 
Increase in Time of 
Narcotic Action 
Substance 
Setting of a Gelatin Gel 
According to Overton 
Ethyl ether 
+ 240 min. 
1000 
Chloroform 
+ 70 " 
714 
Chloralhydrate 
+ 55 " 
167 
Isoamulalcohol 
+ 48 " 
43 
Isobutylalcohol 
+ 25 " 
22 
Of course, it is difficult to tell whether this connection is a real one 
or only accidental. It may be that the narcotic action of a sub- 
stance means that the transition from the gel to the sol state is 
slowed down. Now it is not unlikely that many physiological proc- 
esses depend on transformations of parts of the protoplasm from sol 
to gel and vice versa and that would account for the analogy in 
question. 
The real mechanism of the formation of gels is very incompletely 
known. Recently some attempts have been made to study the factors 236 
COLLOID CHEMISTRY 
that determine whether a gel or a precipitate is formed. Kraemer 
investigated in Freundlich's laboratory the influence of different fac- 
tors upon the formation of manganese arsenate gels. A very pro- 
nounced anion effect was found. The following molar concentrations 
of potassium salts were necessary to prevent precipitate formation 
and allow a gel to be formed. 
C2O4 0.005 
SO4 0.003 
CNS 0.093 
Cl 0.333 
NO3, C1O3 0.500 
Tartrate and acetate favor precipitate formation. 
Such investigations are of great value for our understanding of 
the gels. One must, however, bear in mind that there is probably no 
sharp distinction between the formation of a gel and a flocculant pre- 
cipitate. Most coagula, especially the flocculant precipitates, are to 
be regarded as fragments of shattered weak gels. 
The following experiment made by Borjeson in the writer's lab- 
oratory illustrates this view very strikingly. A 0.5 per cent cadmium 
ethyl alcosol produced by the oscillatory arc in the presence of a 
slight amount of CO2 if allowed to stand for some days at constant 
temperature often (not always) sets to a gel. This gel is exceedingly 
unstable and at once disintegrates separating out the cadmium as a 
flocculant precipitate when touched with a glass rod. Had this sol 
been kept in a less undisturbed condition during setting the gel net- 
work formed would have been gradually destroyed and we would 
never have observed the gel. We would have classified this process 
as a case of formation of a precipitate and not of a gel. In this 
particular case the gel formation is favored by a slight oxidation 
or carbonate production on the surface of the cadmium particles. 
Swelling and imbibition.-Many gels show very marked swelling, 
that is, a concentrated gel containing a small amount of dispersion 
medium has a tendency to take up more dispersion medium. The 
gelatine gel is a representative of the gels which swell and silicic 
acid is one of the gels which do not swell very much. Fig. 109 shows 
the swelling curve for gelatine. When we approach the vapor pressure 
of pure water the composition of the gel changes very rapidly with 
small changes in the vapor pressure (303). THE COLLOID PARTICLE AS A MIC ELL 
237 
If we enclose the gel in a sort of semi-permeable vessel so that 
it is surrounded by some material that is permeable to the dispersion 
medium but not to the gel and fill the space above the gel with 
mercury or some other suitable liquid, we can measure the swelling 
co^e/7/- o/ge/ 
uopor 
/?/2R5i5^7e' 
Fig. 109.-Relation between swelling and vapor pressure. 
pressure, by exerting a gas pressure of known height to balance the 
swelling (Fig. 110). The swelling pressures are comparatively high, 
of the order of several atmospheres. It has been shown that the 
swelling pressure P can be expressed as an exponential function of 
Presses? 
"/'bfoc/s 
posce/a//? 
Fig. 110.-Posnjak's apparatus for measuring swelling pressure. 
the concentration of the gel P = Po.ck, where P and k are constants. 
The agreement between experimental and calculated values is fairly 
good (304). 
The thermodynamics of swelling has been worked out by Freund- 
lich and Posnjak (305). We can find an expression for the swelling 238 
COLLOID CHEMISTRY 
pressure as a function of the vapor pressure of the gel and the vapor 
pressure of the pure liquid-performing a reversible cycle. If we 
have two gels of different vapor pressures, we arrange it so that a 
small amount of liquid can be transferred from the diluted to the 
concentrated one by using some semi-permeable membrane. The 
same amount of water is then transferred back into the dilute gel by 
isothermal distillation. The result is 
p - RT i i 
P " MV0 n h 
where M is the molecular weight, Vo the specific volume of the liquid 
and h the vapor pressure of the gel relative to the vapor pressure of 
the pure liquid. 
It is of interest to analyze a little more closely the work A which 
a gel can perform when swelling. If we take into account a volume 
change equal to unity the work is 
A - P P - jn 
A _ Px P2 - MVo in . 
This work therefore can be calculated from the vapor pressures. On 
the other hand we can measure the heat change U which accompanies 
swelling. These measurements have shown that the energy repre- 
sented by mechanical work as done by swelling is almost exactly 
equal to the heat change, that is that the heat of dilution of a gel 
is almost exactly equal to the energy represented by the work of 
swelling (305). In the case of cellulose, the following figures were 
found 
A U 
47 50 
22 23. 
This means that the mechanical work performed by a swelling gel 
is surprisingly economical. Now probably most of the muscular work 
is performed by swelling of gels, and it is remarkable that it has been 
found by physiologists that a very large amount, at least 60 per cent, 
of the heat produced by the body can be transformed into mechanical 
work of the muscles. 
Swelling in solutions has been studied to a great extent. The 
electrolytes present-especially the hydrogen ions-play a very promi- 
nent part in the swelling of protein gels. It was found rather early 
in the investigations that the swelling shows a minimum at the iso- THE COLLOID PARTICLE AS A MICELL 
239 
electric point and then goes up (306). According to the work of 
Procter and Wilson (250) and Loeb (307), this relation between the 
isoelectric point and the swelling is caused by the Donnan equilibrium. 
The gel, according to the view of these investigators, should be con- 
sidered as a colloid meshwork holding a solution of certain concentra- 
tion and that there should be a membrane equilibrium between this 
inner solution and the outside solution. According to Loeb, the swell- 
ing caused by acids should be almost entirely dependent upon the pu 
value. In some early work by Hofmeister and other chemists it was 
found that different acids had a very pronounced different influence 
on the swelling. According to Loeb, this action of different acids is 
to be ascribed to differences in hydrogen ion concentrations. 
fr'eppre vapor pressure 
Wafer confer# of ffe/ 
Fig. 111.-Variation of water content with vapor pressure for a silica gel. 
With respect to such gels as do not swell, or only swell to a very 
small extent, it has been found, e.g. in the case of SiO2 gel that if 
we start with a gel that has taken up much water (A in Fig. Ill) and 
decrease the vapor pressure around it, the concentration of the water 
in the gel falls continually and uniformly until we reach a point B 
where the gel begins to look opalescent and cloudy. The water is here 
(B - C) given off at about constant vapor pressure. Then the con- 
centration goes down again with decreasing vapor pressure. If we 
try to transfer the gel back to the first condition by moving in the 
opposite direction, we find that there is a certain hysteresis. This 
process was first studied by van Bemmelen (308). 
Zsigmondy has suggested the following explanation of van Bem- 
melen's curve (309). The gel of SiO2 is probably built up of a net- 
work of aggregates of SiO2 particles and water. When we remove the 240 
COLLOID CHEMISTRY 
water from it, the small cells within the gel decrease in volume until 
we reach the point of opalescence (B in Fig. 111). Here the volume 
change of the gel stops (Table LIII), i.e. the volumes of the cells or 
capillaries in the gel become almost constant. 
TABLE LIII 
Relation between Content of Water and Volume of SiO2 Gel 
Water Content in Mol 
Volume 
122 
29 
75.7 
18 
45.2 
11 
23.2 
4 
11.3 
3 
2.8 
1 
2.2 
0.86 
1.7 
0.75 
1.0 
0.73 opalescence begins 
0.39 
0.73 
0.3 
0.73 
The further removal of water is then accompanied by an emptying 
of some of the capillaries and that would cause opalescence. At the 
point C of the curve the water held by the capillaries is completely 
removed and it is only the adsorbed water that is present. This water 
is given off along the line CD. When we go the other way, the capil- 
laries begin to be filled with water and at higher vapor pressure (C'). 
Zsigmondy has suggested the explanation that if we compare the dif- 
ferent processes with the emptying and filling of an ordinary capillary, 
the first process-downward-corresponds to the evaporation of the 
water from a curved surface of a certain radius. When we go upward 
again and attempt to fill the capillaries, the wetting is less complete 
and the curvature of the meniscus is greater, and therefore the vapor 
pressure is higher according to the formula which we have deduced 
for vapor pressure of a curved surface, viz. 
RT. p 2a 
In - = - 
M pr pr 
where p and pr are the vapor pressures over the plane surface and 
over the concave surface of radius r resp., a the surface tension and 
p the density of the liquid. If we apply this equation to the above 
problem we obtain the radius of the capillaries corresponding to the 
vapor pressure of the gel during a period where the volume of the 
gel was constant. If we calculate the radius of the capillaries from 
this assumption we get about 2.8 pp which is a very fine ultramicro- THE COLLOID PARTICLE AS A MIC ELL 
241 
scopic structure. The interesting thing is that if we determine this 
radius of one and the same gel with different kinds of dispersion 
medium, e.g. SiO2 and alcohol or benzol instead of water we 
get about the same value for the radius, viz., 2.6 and 2.99 pp 
respectively (310). 
Elasticity.-The elasticity of a gel depends, of course, also on the 
different substances present. Therefore, the study of elasticity is a 
means of studying the influences that various electrolytes and non- 
electrolytes have on the structure of the gel. So far different investi- 
gations of elasticity have not led to any more definite conception of 
the structure. 
Until quite recently only macroscopic methods of measuring elas- 
ticity were used. In the case of stiff gels the compression or exten- 
sion of a block of the gel was measured. In the case of a weak gel 
the angle of rotation of a cylinder or of a sphere immersed in the gel 
and exposed to a known force was measured. Rohloff and Shinjo (311) 
studied the elasticity of gelatin gels by means of a sphere of radius 
Ri rotating in the gel which was contained in an outer concentric fixed 
sphere of radius Ro. According to Hooke's law the displacement is 
equal to the elasticity modulus E times the force acting and we there- 
fore have after integrating over the whole volume of the gel: 
R 3 R 3 
moment of force = 4jtEcp * ' V 
Ro - Ri3 
where cp is the angle of rotation of the sphere. 
In the case of bifilar suspension of the sphere this moment of force 
in the gel is balanced by the torque of the bifilar suspension 
mgab . 
--j-sin 0 
where a and b are the distances between the upper and lower ends and 
1 the lengths of the wires, g the gravity constant and m the apparent 
weight of the sphere, 6 the angle of torsion, or 
p mgab /. Ri3 \ sin 0 
K -4jtlRi3 \ 1 " R? / * 
Now if Ro Ri the expression can be simplified and we get for a 
sphere of radius R suspended in an unlimited liquid 
„ _ mgab sin 0 
4n:lR3 cp 242 
COLLOID CHEMISTRY 
Rohloff and Shinjo found that the modulus increases with time (Fig. 
112) and with concentration. 
When working with very weak gels it is often difficult to manipu- 
late the torsion head without destroying the gel. Kraemer and the 
writer therefore devised an arrangement which permits to rotate the 
suspension point of the bifilar wire by means of an electromagnet. 
The bifilar wire was fixed to an iron rod and this in its turn was sus- 
pended by a wire. The magnetic field was supplied by two coils with 
iron cores, forming an electromagnet around the iron rod. By rotat- 
ing the electromagnet the iron rod which forms the torsion head can 
ge/Qf/r? 
Mody/us 
Time i/? dags 
Fig. 112.-Variation of modulus of elasticity with time in gelatin gels 
be rotated. The rotation of the torsion head and the sphere could 
be read off in the ordinary way by means of mirror and scale. The 
work undertaken by means of this method has not yet been finished. 
Recently Freundlich and Seifriz (312) have worked out a very 
promising method of studying the elasticity of gels. They introduce a 
little particle of magnetic material, e.g. nickel particles of 7 to 18 p, 
in the gel to be studied and observe in the microscope the displace- 
ment of this particle when exposed to the influence of a magnetic 
force. We have the relation 
Where P is the force and A the displacement. THE COLLOID PARTICLE AS A MIC ELL 
243 
Freundlich's micromethod also enables us to study the elasticity of 
sols. Freundlich and Seifriz found that such sols that show double 
refraction when streaming, e.g. benzopurpurin sol and vanadium 
pentoxide sol, were elastic while an old Fe2O3 sol and viscous liquids 
such as glycerin and saturated sugar solutions were not elastic. 
In the case of gelatin the modulus increases with concentration. 
Leick found by means of the macroscopic method the values given 
in Table LIV (313). 
TABLE LIV 
Relation between Modulus and Concentration in Gelatin Gels 
Concentration in Per Cent 
Modulus (kg/sqmm. .103) 
10.0 
2.42 
10.2 
2.66 
18.6 
9.78 
19.9 
9.77 
30.0 
15.45 
32.0 
21.57 
45.0 
29.44 
By means of the micromethod Freundlich found for dilute gelatin 
gels the following values (Table LV, Fig. 113). 
Relation between Modulus and Concentration in Gelatin Gels 
TABLE LV 
Modulus in 
Concentration 
Relat. Units 
0.8 
1 
0.9 
4 
1.0 
4 
1.1 
19 
1.2 
56 
1.3 
43 
1.4 
77 
1.5 
67 
1.6 
83 
1.7 
91 
1.8 
227 
1.9 
333 
2.0 
400 
It is interesting to note that Freundlich found the gels very inhomo- 
geneous when studied by the micromethod. In different parts of one 
and the same gel different values were obtained. This fact partly 
accounts for the discrepancies in these values. 
The elasticity of gelatin gels is changed markedly by addition of 244 
COLLOID CHEMISTRY 
foreign substances. Leick found that chlorides and nitrates lower 
the modulus while sulphates and cane sugar raise the modulus. 
Freundlich also studied the elastic limit as a function of concen- 
Modo/us of e/asfc/ty 
6e/ot/o co/x&rf/zrf/ov 
Fig. 113. Variation of modulus of elasticity with concentration of a gelatin gel. 
tration by means of his micro method and found that it shows a 
maximum at the concentration where gel formation occurs (Table 
LVI). 
TABLE LVI 
Relation between Elastic Limit and Concentration for Gelatin 
Concentration 
Elastic Limit in n 
0.7 
18 
0.8 
130 
0.9 
115 
1.0 
76 
1.1 
49 
1.2 
54 
1.3 
36 
1.4 
36 
1.5 
38 
1.6 
32 
1.7 
29 
1.8 
18 
1.9 
18 
2.0 
18 
The elasticity of a gel depends, of course, also on the different 
substances present. Therefore, the study of elasticity is a means of 
studying the influences that various electrolytes and non-electrolytes 
have on the structure of the gel. So far different investigations of 
elasticity have not led to any more definite conception of the structure. THE COLLOID PARTICLE AS A MIC ELL 
245 
Diffusion and chemical reactions in gels.-A problem of consid- 
erable importance is that of the diffusion in gels (314). In the first 
place there is the possibility that studies of the rate of diffusion in 
different gels might give us some information about their structure 
and in the second place the question of the rate of diffusion of differ- 
ent substances in gels is of fundamental importance in physiology. 
Graham pointed out that the rate of diffusion of crystalloids in 
weak gels was about the same as in the pure dispersion medium. Later 
on it was shown that there actually is a certain action of the gel upon 
the rate of diffusion. Chlorides of the alkaline and the alkaline earth 
metals diffuse without much disturbance while on the other hand 
most acids and bases with the exception of ammonia diffuse slower; 
the diffusion of sulphates is also slowed down. In more concentrated 
gels there is a marked influence on the diffusion of all substances. The 
diffusion of high molecular substances and colloids is of course very 
much influenced by the gel. To a certain extent the depression of 
the rate of diffusion by the gel seems to be due to a simple mechanical 
action of the pores of the gel. When the average size of the pores 
decreases, e.g. upon using a gel of higher concentration, the rate of 
diffusion decreases rapidly (315). In many cases, however, there is 
a specific action between the particles of the gel and the diffusing 
molecules or particles, e.g. when marked adsorption takes place (316). 
Most of the membranes we find in living beings or use in the 
laboratory are gels and the question of their permeability is therefore 
to a great extent a question of rate of diffusion in the material of 
the membrane. The action of a gel membrane is, however, also de- 
pendent on other phenomena. The diffusing substance might be 
soluble in the disperse phase of the gel and penetrate the membrane 
diffusing through the material of the very network of the gel. 
A potential difference might exist across the membrane and if at 
the same time there is a potential difference between the free movable 
and the adsorbed part of the liquid in the pores of the membrane, 
an osmotic flow of liquid will take place through the membrane. 
This latter phenomenon, the so-called anomalous osmosis, has been 
studied by Bartell (317) and by Loeb (318). Fig. 114 gives, accord- 
ing to Loeb, the osmotic flow through a collodion membrane impreg- 
nated with gelatin for various solutions. 
The question of chemical reactions in gels is of great importance 
especially in physiology. The fact that mixing and convection cur- 
rents are excluded gives to the reactions in gels a special character. 246 
COLLOID CHEMISTRY 
All transport of material takes place by diffusion. When working 
in gels it is therefore possible to locate the reactions much better than 
when working in solutions or sols. If properly conducted, chemical 
reactions of quite different type might take place side by side in a 
gel separated only by spaces of microscopic dimensions. This fact 
is probably the explanation of the highly differentiated chemical 
activity of the protoplasm of the living cell. 
A special type of chemical reaction in gels, the so-called Liesegang 
phenomenon, has been the object of extensive investigations (319). 
When a substance is allowed to diffuse into a gel containing another 
f/PtV 
Co/7cer?^f/^ 
Fig. 114.-Anomalous osmosis. 
substance which forms a precipitate with the former substance, a 
rhythmic process is often observed. The classic experiment first per- 
formed by Liesegang can be arranged as follows. A test tube is 
partly filled with a gelatin gel containing say 0.1 per cent K2CrO4 
and a solution of say 8.5 per cent AgNO3 is poured on top of the gel. 
The diffusion of the silver nitrate down into the chromate gel gives 
rise to a series of stratifications of silver chromate. Instead of making 
the experiment in- a test tube one can put a drop of the silver nitrate 
solution on a film of the chromate gelatine supported by a glass plate 
and get a series of concentric rings of silver chromate (Fig. 115). 
Such rhythmic reactions are supposed to be of importance in physio- 
logical processes and probably also to some extent in certain geo- THE COLLOID PARTICLE AS A MIC ELL 
247 
logical processes. The banding of agate might be explained as the 
result of rhythmic precipitations caused by diffusion and chemical 
reactions in a silica gel. As to the theory of the Liesegang phenome- 
non we are still very much behind. It is obvious that an explana- 
tion might be based upon the fact that the formation of the precipi- 
tate requires a certain supersaturation and after precipitation has 
once started at a certain point, the region around this point will by 
virtue of diffusion be deprived of most of its material so that a new 
starting point of precipitation can only be reached some way off from 
Fig. 115.-Liesegang rings of silver chromate in gelatin, 
the first point and so on. We have not, however, so far been able 
to account for the various facts observed in connection with the 
Liesegang stratifications. In the opinion of the writer a better under- 
standing of this important phenomenon can only be obtained by using 
a microtechnic. So far only semi-qualitative methods have been 
adopted. The character of the banding under different conditions 
and with different substances has been observed and recorded. Quan- 
titative measurements of the change of concentration at various points 
during the process by means of micro measurements of light absorp- 
tion and electric conductivity would probably be of great value. PART IV 
THE DESTRUCTION OF THE COLLOID 
PARTICLE 
We have now followed the colloid particle from its formation to 
coagulation and gel formation and studied its properties. There is 
one thing left and that is the study of the destruction of the colloid 
particle. The study of this process may turn out to be very important 
in the future, but so far, very few investigations have been attempted 
along this line. Part IV of this outline of Colloid Chemistry therefore 
only serves the purpose of calling attention to the problem of the 
destruction of the colloid particle. 
The destruction of the particle can be brought about by dif- 
ferent means. The particle can be dissolved to molecules by adding 
a suitable solvent or, which is still more important, different particles 
might crystallize together and form a complete crystallization unit 
instead of a loose aggregate. The particle can, of course, also be 
destroyed by chemical reactions. The growing together of the indi- 
vidual particles plays an important part in the changes that some 
gels undergo. Probably this destruction of the particle is of impor- 
tance in geological, as well as in biological problems. 
249 BIBLIOGRAPHY 
1. Graham, Phil. Trans. 151, 183 
(1861). 
2. See Svedberg, Herstellung kolloi- 
der Lbsungen, p. 14 (Dresden, 
1909). 
3. Berzelius, Lehrb. der Chemie, 3 
Aufl. 3, 65 (1834). 5 Aufl., 2, 
269 (1844). 
4. Selmi, Nuovi Ann. di Scienze 
Natur., Bologna (2), 8, 404 
(1847). Cf. Koll.-Zeitschr., 8, 
113 (1911). 
5. Faraday, Phil. Trans., 147, 145 
(1857). 
6. Tyndall, Phil. Mag. (4), 37, 384 
(1869). 
7. Linder and Picton, Journ. Chem. 
Soc., 61, 114, 137 and 148 (1892); 
67, 63 (1895). 
8. Siedentopf and Zsigmondy, Annal. 
Phys. (4), 10, 1 (1903). 
9. Brown, Phil. Mag., 4, 161 (1828). 
10. Zsigmondy, Zur Erkenntnis der 
Kolloide, p. 106 (Jena, 1905). 
11. Einstein, Annal. Phys. (4), 17, 549 
(1905). 
12. Quincke, Annal. Phys. (2), 107, 1 
(1859). 
13. Davy, Phil. Trans. 1809, p. 78; 
Berzelius, Annal. Phys. (2), 4, 
122 (1825). 
14. Oden, Nova Acta, Upsala (4), 3, 
No. 4, p. 124 (1913). 
15. Schlbsing, Comptes rend., 70, 1345 
(1870). 
16. Schulze, Journ. prakt. Chem. 25, 
431 (1882); 27, 320 (1883). 
17. Wo. Ostwald, Koll.-Zeitschr., 1, 291 
(1907). 
18. Svedberg, Herstellung kolloider 
Lbsungen (Dresden, 1909); For- 
mation of Colloids (London, 
1921). 
19. Svedberg, Nova Acta, Upsala (4), 
2, No. 1, p. 3 (1907). 
20 See Freundlich, Kapillarchemie, p. 
1069 (Leipzig, 1922). 
21. Kasperowicz and Schoop, Das 
Electrometallspritzverfahren, 
(Halle, 1920). 
22. Zsigmondy, Kolloidchemie, 3 Aufl., 
p. 34 (Leipzig, 1920). 
23. Kohlschiitter, Erscheinungsformen 
der Materie, p. 143 (Leipzig, 
1917). 
24. v. Weimarn, Dispersoidchemie, pp. 
69 and 77 (Dresden, 1911). 
25. Berzelius, Annal. Phys. (2), 32, 1 
(1834). 
26. KuSel, Osterreich. Patent, KI. 12b, 
No. A, 2573 (1906); See also 
Lottermoser, Koll.-Zeitschr., 2, 
347 (1908). 
27. v. Weimarn, Dispersoidchemie, p. 
82 
28. Pihlblad, Zeitschr. phys. Chem. 81. 
420 (1912). Lichtabsorption und 
Teilchengrbsse, Diss. Upsala, p. 
46 (1918). 
29. v. Weimarn, Koll.-Zeitschr., 11, 
315 (1912); Utzino, Japanese 
Journ. Chem. 2, No. 1 (1923). 
30. See Kenney, Chem. and Met. Eng. 
27, 1080 (1922). 
31. Clayton, The theory of emulsions 
and emulsification (Philadel- 
phia, 1923). 
32. Nordlund, Quecksilberhydrosole, 
Diss. Upsala, p. 18 (1918); Koll.- 
Zeitschr. 26, 121 (1920). 
33. Hamburger, Koll.-Zeitschr., 23, 177 
(1918). 
34. W. Thomson, Phil. Mag. (4), 
448 (1871). 
35. Cf. Freundlich, Kapillarchemie, 
p. 63 (1922). 
36. J. J. Thomson, Conduction of 
Electricity through Gases, p. 149 
(1903). 
37. C. T. A. Wilson, Phil. Trans. A189, 
265 (1897); A192, 403 (1899); 
Proc. Roy Soc. A85, 285 (1911); 
A87, 277 (1912). 
38. Andren, Ziihlung und Messung der 
komplexen Molekiile einiger 
Dampfe nach einer neuen Kon- 
densationstheorie, Diss. Upsala, 
p. 28 (1918). 
39. Cf. Freundlich, Kapillarchemie, p. 
437 (1922). 
251 252 
COLLOID CHEMISTRY 
40. Kohlschutter and Ehlers, Zeitschr. 
Elektrochem., 18, 373 (1912). 
41. Kohlschutter and Noll, Zeitschr 
Elektrochem., 18, 419 (1912); 
Kohlschutter, Jahrb. Radioakt. 
9, 355 (1912). 
42. Nordlund, Quecksilberhydrosole, 
Diss. Upsala, p. 22 (1918); 
Koll.-Zeitschr, 26, 121 (1920). 
43. Svedberg, Meddel. Nobelinst, 
Stockholm, 5, No. 10, p. 3 (1919). 
44. Bredig, Zeitschr. angew. Chem, 
1898, p. 951; Anorganische Fer- 
mente (Leipzig, 1901); Zeitschr. 
phys. Chem, 32, 127 (1900). 
45. Svedberg, Meddel. Nobelinst, 
Stockholm, 5, No. 10, p. 4 (1919). 
46. Borjeson, Electric Synthesis of 
Colloids, Diss. Upsala (1921). 
47. Svedberg, Ber. Deutsch, chem. 
Ges, 39, 1705 (1906); Nova 
Acta, Upsala (4) 2, No. 1 (1907). 
48 Bodforss and Frolich, Kolloid- 
chem. Beih, 16, 301 (1922). 
49. Borjeson and Svedberg, Koll.- 
Zeitschr, 25, 154 (1919). 
50. Nordlund, Quecksilberhydrosole, 
p. 86. 
51. Borjeson, Electric Synthesis of 
Colloids. 
52. Tammann, Zeitschr. anorg. Chem, 
87, 248 (1914). 
53. Freundlich, Kapillarchemie, p. 
437 (1922). 
54. Wilh. Ostwald, Zeitschr. phys. 
Chem, 34, 503 (1900); comp. 
Freundlich, Kapillarchemie, p. 
208 (1922). 
55. Tammann, Kristallisieren und 
Schmelzen (Leipzig, 1903). 
56. Freundlich, Kapillarchemie, p. 449 
(1922). 
57. Walton and Brann, Journ. Amer. 
Chem. Soc, 38, 317 (1916); 
Brann, Journ. Amer. Chem. Soc, 
40, 1168 (1918). 
58. Marc, Zeitschr. phys. Chem. 68, 112 
(1910); 73, 708 (1910). 
59. Reinders, Zeitschr. phys. Chem. 77, 
680 (1911). 
60. Wo. Ostwald and v. Weimarn, 
Koll.-Zeitschr, 6, 181 (1910). 
61. Svedberg, English Patent, No. 
12108 (1908). 
62. v. Weimarn, Dispersoidchemie, p. 
67. 
63. Cf. Svedberg, Herstellung kolloider 
Losungen, p. 222. 
64. Nordenson, Ueber die Bedeutung 
des Lichtes fiir die Bildung und 
Stabilitat kolloider Losungen, 
Diss. Upsala, p. 107 (1914); 
Svedberg, Formation of Colloids, 
p. 61 (1921). 
65. Reitstotter, Kolloidchem. Beih, 9, 
248 (1917); Zsigmondy, Kolloid- 
chemie, p. 148 (1920). 
66. Doerinckel, Zeitschr. anorg. Chern. 
63, 344 (1909). 
67. Naumoff, Zeitschr. anorg. Chem., 
88, 43 (1914); Vanino and Hartl, 
Koll.-Zeitschr, 1, 272 (1907). 
68. Zsigmondy, Kolloidchemie, p. 144 
(1920). 
69. Hiege, Zeitschr. anorg. Chem. 91, 
145 (1915). 
70. Svedberg, Koll.-Zeitschr. 5, 318 
(1909). 
71. Nordenson, Diss., p. 122. 
72. Zsigmondy, Zur Erkenntnis der 
Kolloide, p. 128 (1905); Sieden- 
topf and Zsigmondy, Annal. 
Phys. (4), 10, 1, (1903). 
73. Kohlschutter, Zeitschr. Elektroch., 
14, 49 (1908); Koll.-Zeitschr., 12, 
285 (1913). 
74. Kohlschutter and Fischmann, Lie- 
bigs Annal., 387, 86 (1911). 
75 Liippo-Cramer, Koll.-Zeitschr., 7, 99 
(1910). 
76. Carey Lea, Amer. Journ. Science 
(3), 37, 476 (1889). 
77. Oden, Zeitschr. phys. Chem., 78, 
682 (1912). 
78. Kohlschutter, Koll.-Zeitschr., 12, 
289 (1913). 
79. Billiter, Ber. Deutsch, chem. Ges., 
35, 1929 (1902). 
80. Svedberg, Formation of Colloids, 
p. 80. 
81. Nordenson, Kolloidchem. Beih., 7, 
130 (1915). 
82. Svedberg, Koll.-Zeitschr., 6, 129 
(1910). 
83. Nordenson, Kolloidchem. Beih., 7, 
91 (1915). 
84. Paal, Ber. Deutsch. Chem. Ges., 
35, 2224. 2236 (1902); 37, 124 
(1904); 38, 526, 534, 1398 (1905); 
39, 1550 (1906); 40, 1392 
(1907); 50, 722 (1917). 
85. Oden, Nova Acta, Upsala (4), 3, 
No. 4 (1913). 
86. Freundlich and Scholz, Kolloid- 
chem. Beih., 16, 234 (1922). 
87. Oden, Nova Acta. BIBLIOGRAPHY 
253 
88. Wa. Ostwald, Koll.-Zeitschr., 15, 
204 (1914); Hatschek and 
Thorne, Koll.-Zeitschr., 33, 1 
(1923). 
89. R. Lorenz, Zeitschr. anorg. Chem., 
91, 46, 57, 61 (1915); Koll.- 
Zeitschr., 18, 177 (1916). 
90. Siedentopf, Phys. Zeitschr., 6, 855 
(1905). 
91 Svedberg, Photogr. Journ., April, 
1922. 
92. Trivelli, Richter and Sheppard, 
Photogr. Journ., September, 
1922. 
93. Svedberg, Zeitschr. wiss. Photogr., 
20, 36 (1920). 
94. Slade and Higson, Proc. Roy. Soc. 
A. 98, 154 (1920). 
95. Svedberg and Andersson, Photogr. 
Journ., August, 1921. 
96. Svedberg, Photogr. Journ., July. 
1922. 
97. Svedberg, Photogr. Journ., April 
and July, 1922. 
98. Clark, Britt. Journ. Phot., 69, 462 
(1922). 
99. Svedberg, Photogr. Journ., July, 
1922 
100 Toy, Phil. Mag. (4), 44, 352 
(1922). 
101. Silberstein, Phil. Mag. (4), 44, 257, 
956 (1922); 45, 1062 (1923). 
102. Oden, Arkiv for Kemi, Stockholm, 
7, No. 26 (1920). 
103. Picton and Linder, Journ. Chem. 
Soc., 61, 137 (1892); 67, 63 
(1895). 
104. Borjeson, Koll.-Zeitschr., 27, 18 
(1920). 
105. Svedberg, Die Existenz der Mole- 
kiile, p. 24 (Leipzig, 1912). 
106. Lottermoser, Journ. pract. Chem., 
(2), 75, 293 (1907). 
107. Paal and Kuhn, Ber. Deutsch, 
chem. Ges., 39, 2859, 2863 
(1906); 41, 51. 58 (1908). 
108. Wolski, Kolloidchem. Beih., 13, 
137 (1920). 
109. Martin, Journ. phys. Chem., 24- 
478 (1920). 
110. Sorensen, Meddel. Carlsberg Lab., 
Kjdbenhavn, 12, 25 (1917). 
111. Zsigmondy and Heyer, Zeitschr. 
anorg. Chem., 68, 169 (1910). 
112. Malfitano, Comtes rend., 139, 1221 
(1904). 
113. Duclaux, Comptes rend., 140, 
1468, 1544 (1905). 
114. Bechhold, Zeitschr. phys. Chem., 
60, 257 (1907); 64, 328 (1908). 
115. Wegelin, Koll.-Zeitschr., 18, 225 
(1916). 
116. Oden, Nova Acta, p. 66. 
117. Kroger, Koll.-Zeitschr., 30, 16 
(1922). 
118. Westgren, Zeitschr. anorg. Chem., 
94, 193 (1916). 
119. Wi. Ostwald, Zeitschr. phys. Chem., 
64, 508 (1908). 
120. Einstein, Annal. Phys. (4), 17, 549 
(1905). 
121. Zsigmondy, Kolloidchemie, p. 406 
(1920). 
122. Stefan, Sitznngsber, Akad. Wiss. 
Mathem.-Nat. KI, Wien, 79 II. 
161 (1879). 
123. Scheffer, Zeitschr. phys. Chem., 2, 
393 (1888) 
124. Kawalki, Anal. Phys. (3), 52, 185 
(1894). 
125. Svedberg, Die Existenz der Mole- 
kule, p. 78 (1912). 
126. Westgren, Zeitschr. phys. Chem., 
89, 63 (1914). 
127. Smoluchowski, Annal. Phys. (4), 
21, 756 (1906). 
128. Perrin, Comptes rend., 146, 968 
(1908). 
129. Westgren, Arkiv for Matematik, 
Stockholm, 9, No. 5 (1913); 
Zeitschr. phys. Chem., 89, 63 
(1914). 
130. Perrin, Comptes rend., 147, 530, 
594 (1908); 152, 1165, 1380 
(1911); Ann. de chim. et de 
phys. (8), 18, 5 (1909). 
131. Westgren, Zeitschr. anorg. Chem., 
93, 231 (1915). 
132. Porter and Hedges, Phil. Mag. (6), 
44, 641 (1922). 
133. Burton, Proc. Roy. Soc. A. 100, 414 
(1922). 
134. Constantin, Comptes rend., 158. 
1341 (1914). 
135. Brown, Phil. Mag., 6, 161 (1829). 
136. Wiener, Annal. Phys. (2), 118, 79 
(1863). 
137. Thirion, Revue des questions 
scient., Bruxelles, 7, 44, 53 (Jan., 
1888). 
138. Langevin, Comptes rend, 146, 530 
(1908). 
139. De Haas-Lorentz, Die Brownsche 
Bewegung (Braunschweig, 1913). 
140. Smoluchowski, Phys. Zeitschr., 17, 
557 (1916). 254 
COLLOID CHEMISTRY 
141. Svedberg, Zeitschr. Elektrochem., 
12, 853, 909 (1906); Nova Acta, 
Upsala (4), 2, No. 1 (1907). 
142. Seddig, Sitzungsber. Ges. Naturw. 
Marburg 1907, p. 182. Phys. 
Zeitschr., 9, 465 (1908). 
143. Henri, Comptes rend., 146, 1024; 
147, 62 (1908). 
144. Comptes rend., 147, 1044 (1908); 
149, 477 (1909); Ann. de chim. 
et de phys. (8), 18, 5 (1909). 
145. Perrin, Comptes rend., 149, 549 
(1909). 
146. Svedberg, Koll-Zeitschr., 7, 1 
(1910). 
147. Svedberg and Inouye, Arkiv for 
Kemi, Stockholm, 4, No. 19 
(1911). 
148. Svedberg, Die Existenz der Mole- 
kiile, p. 124. 
149. Siedentopf, Zeitschr. wiss. Mikro- 
skop., 26, 391 (1909). 
150. Svedberg, Die Existenz der Mole- 
kiile, l.c., p. 138. 
151. Nordlund, Zeitschr. phys. Chem., 
87, 40 (1914). 
152. H. A. Lorentz, Abhandl. iiber 
theor. Phys., 1, 23 (1906). 
153. Smoluchowski, Phys. Zeitschr. 13, 
1069 (1912). 
154. Cf. Fiirth, Schwankungserschei- 
nungen in der Physik (Braun- 
schweig, 1920). 
155. Svedberg, Zeitschr. phys. Chem., 
73, 547 (1910). Die E'xistenz der 
Molekiile, p. 155. 
156. Westgren, Arkiv for Matematik, 
Stockholm, 11, No. 8 (1916). 
157. Constantin, Comptes rend., 158 
1341 (1914). 
158. Svedberg, Die Existenz der Mole- 
kiile, p. 181. 
159. Smoluchowski, Sitzungsber. Akad. 
Wiss. Mathem.-Nat. KI. Wien, 
123, 2381 (1915); Phys. Zeitschr., 
16, 321 (1915); Koll.-Zeitschr., 
18, 48 (1916). 
160. Anding, Sechsstellige Tafeln der 
Besselschen Functionen imagi- 
naren Argumentes (Leipzig, 
1911). 
161. Westgren, Arkiv for Matematik, 
Stockholm, 11, No. 14 (1916); 
13, No. 14 (1918). 
162. Cf. Siedentopf, Zeitschr. wiss. 
Mikroskop., 26, 391 (1909). 
163. Zsigmondy, Phys. Zeitschr., 14, 975 
(1913); Kolloidchemie, p. 12 
(1920). 
164. Zsigmondy, Zeitschr. Elektrochem., 
12, 631 (1906). 
165. Siedentopf, Zeitschr. wiss. Mikro- 
skop., 24, 382 (1908); 25, 273 
(1908). 
166. Cotton and Mouton, Comptes 
rend., 136, 1657 (1903). 
167. Siedentopf, Zeitschr. wiss. Mikro- 
skop., 24, 104 (1907). 
168. Siedentopf, VerhandL Deutsch, 
phys. Ges., 12, 1 (1910). 
169. Jentzsch, Verhandl. Deutsch, phys. 
Ges., 12, 975, 992 (1910). 
170. Siedentopf, Zeitschr. wiss. Mikro- 
skop., 25, 273 (1908). 
171. Regener in Freundlich, Kapill- 
archemie, p. 1076 (1922). 
172. Zsigmondy, Zeitschr. phys. Chern., 
56, 65, 77 (1906). 
173. Westgren, Die Brownsche Bewe- 
gung, Diss. Upsala, p. 68 (1915). 
174. Borjeson, Koll.-Zeitschr., 27, 18 
(1920). 
175. Lindeman and Svedberg, KolL- 
Zeitschr., 29, 1 (1921). 
176. Stokes, Cambr. Phil. Trans., 8, 
287 (1847); 9, 8 (1851); cf. 
Smoluchowski, Intern. Congr; of 
Mathematics, Cambridge, Au- 
gust, 1912. 
177. Westgren, Diss. (1915). 
178. Faxen, Annal. Phys. (4), 68, 89 
(1922). 
179. Svedberg and Estrup, Koll.- 
Zeitschr., 9, 259 (1911). 
180. Svedberg and Rinde, Joum. Amer. 
Chem. Soc., 45, 943 (1923). 
181. Oden, Proc. Roy. Soc. Edinburgh, 
36, 219 (1916); Int. Mitt. Boden- 
kunde, 1915; Bull. Geolog. Inst. 
Upsala, 16 (1916). 
182. Sorensen, Meddel. Carlsberg Lab., 
Kjobenhavn, 12, 255 (1917). 
183. Duclaux, Journ. de chim. phys., 7, 
405 (1909). 
184. Biltz and v. Vegesack, Zeitschr. 
phys. Chem., 68, 357 (1910); 73, 
484 (1910). 
185. Herzog, Zeitschr. Elektrochem., 13, 
533 (1907). 
186. Herzog and Polotzsky, Zeitschr. 
phys. Chem., 87, 449 (1914); 
Zeitschr. Elektrochem., 17, 679 
(1911). 
187. Dabrowski, Bull. Acad. Sc., Cra- 
covie, classe math, et nat., A, 
Juin, 1912. 
188. Westgren, Zeitschr. anorg. Chem., 
94, 193 (1916). BIBLIOGRAPHY 
255 
189. Bechhold, Zeitschr. phys. Chem, 
60, 257 (1907); 64, 328 (1908). 
190. Scherrer in Zsigmondy, Kolloid- 
chemie, p. 387 (1920). 
191. Svedberg, Die Existenz der Mole- 
■ kiile, p. 5 (1912). 
192. Pihlblad, Lichtabsorption und 
Teilchengrbsse, Diss. Upsala, 
1918. 
193. See Svedberg and Rinde, Journ. 
Amer. Chem. Soc, 45, 943 
(1923) 
194. Mie, Annal. Phys. (4), 25, 377 
(1908). 
195. J. W. Strutt, Phil. Mag. (5), 12, 
81 (1881). 
196. Garnett, Phil. Trans, A 203, 385 
(1904); 205, 237 (1906). 
197. Rayleigh, Phil. Mag. (5), 4?, 377 
(1899). 
198. Mecklenburg, Koll.-Zeitschr, 14, 
172 (1914); 15, 149 (1914). 
199. Mecklenburg, Koll.-Zeitschr, 16, 
97 (1915). 
200. Freundlich, Zeitschr. phys. Chem, 
57, 385 (1907); cf. Kapill- 
archemie, p. 552 (1922). 
201. Freundlich and Diesselhorst, Phys. 
Zeitschr, 17, 117 (1916). 
202. Zocher, Zeitschr. phys. Chem, 98, 
293 (1921) 
203. Cf. Gans, Annal. Phys. (4), 37, 
881 (1912). 
204. Bjbmstahl, Phil. Mag. (6), 42, 
352 (1921). 
205. Dewar, Proc. Roy. Soc. 74, 124 
(1905). 
206. Freundlich, Kapillarchemie, p. 232 
(1922) 
207. G. C. Schmidt, Zeitschr. phys. 
Chem, 74, 689 (1910). 
208. Marc, Zeitschr. phys. Chem, 75, 
710 (1911); 81, 641 (1913). 
209. Arrhenius, Meddel. Nobelinst, 
Stockholm, 2, No. 7 (1911). 
210. G. C. Schmidt, Zeitschr. phys. 
Chem, 77, 644 (1911); 78, 667 
(1912). 
211. Gibbs, Thermodynam. Studien, 
p. 271. 
212. Milner, Phil. Mag. (6), 13, 96 
(1907). 
213. Langmuir, Journ. Amer. Chem. 
Soc, 38, 2267 (1916); 39, 1883 
(1917); 40, 1361 (1918); cf. 
Dushman, High Vacuum, p. 205 
(1922). 
214. Paneth, Zeitschr. phys. Chem. 
101, 480 (1922). 
215. Gustaver, Kolloidchem. Beih., 15, 
185 (1922). 
216. Eucken, Ber. Deutsch, phys. Ges., 
16, 345 (1914). 
217. Polanyi, Ber. Deutsch, phys. Ges., 
16, 1012 (1914); 18, 55 (1916); 
Zeitschr. Elektrochem, 26, 370 
(1920). 
218. Osaka, Mem. Coll. Sc., Kyoto, 1, 
No. 6 (1915). 
219. Oden and Andersson, Journ. Phys. 
Chem, 25, 311 (1911); Oden 
and Langelius, Journ. Phys. 
Chem., 25, 385 (1921). 
220. Rona and Michaelis, Biochem. 
Zeitschr., 97, 94 (1919). 
221. Cf. Zsigmondy, Kolloidchemie, p. 
97 (1920). 
222. Kruyt, Koll.-Zeitschr, 20, 239 
(1917). 
223. Reuss, Mem. Soc. Nat. Moscou, 2, 
327 (1809). 
224. Helmholtz, Annal. Phys. (2), 7, 337 
(1879). 
225. Perrin, Journ. chim. phys., 2, 601 
(1904). 
226. Smoluchowski, Bull. Acad. Sc. 
Cracovie, 1903, p. 182; cf. 
Graetz, Handbuch d. Elektr, 2, 
366 (1914). 
227. Saxen, Annal. Phys. (2), 4^, 46 
(1892). 
228. Freundlich and Rona, Sitzungsber. 
Preuss. Akad. d. Wiss, 20, 397 
(1920). 
229. Burton, Phil. Mag. (6), 11, 436 
(1906). 
230. Michaelis, Biochem Zeitschr., 16, 
81 (1908). 
231. Svedberg and Jette, Journ. Amer. 
Chem. Soc., 45, 954 (1923). 
232. Svedberg, Nova Acta, Upsala (4), 
2, No. 1, p. 149 (1907). 
233. Ellis, Zeitschr. phys. Chem., 78, 321 
(1912). 
234. Smoluchowski, in Graetz, Handb. 
d. Elektriz., 2, 382 (Leipzig, 
1914). 
235. Svedberg and Andersson, Koll.- 
Zeitschr, 24, 156 (1919). 
236. Cf. Freundlich, Kapillarchemie, p. 
349 (1922). 
237. Gouy, Journ. d. phys. (4), 9, 457 
(1910); cf. Billiter, Zeitschr. 
phys. Chem, 45, 307 (1903). 
238. v. Hevesy, Koll.-Zeitschr, 21, 129 
(1917). 
239. Smoluchowski, Phys. Zeitschr, 6, 
529 (1905). 256 
COLLOID CHEMISTRY 
240. Nordenson, Koll.-Zeitschr, 16, 65 
(1915). 
241. Nordlund, Quecksilberhydrosole, 
p. 86 (1918). 
242. MacBain, Britt. Assoc. Adv. Sc. 
3rd rep. on Coll. Chem, p. 2 
(1920); cf. Freundlich, Kapill- 
archemie, p. 775 (1922). 
243. Billiter, Zeitschr. phys. Chem, 45, 
307 (1903); 48, 513 (1904); 49, 
709 (1904); 51, 167 (1905); 
Annal. Phys. (4), 11, 913 (1903). 
244. Freundlich, Kapillarchemie, p. 340 
(1922). 
245. Smoluchowski, in Graetz Handb. 
d. Elektriz, 2, 393 (1914). 
246. Michaelis, see e.g. Die Wasser- 
stoffionenkonzentrationen, 1, 52 
(Berlin, 1922). 
247. Wo. Ostwald and Miindler, Koll.- 
Zeitschr, 24, 7 (1919). 
248. Donnan, Zeitschr. E'lektrochem, 
17, 572 (1911). 
249. Donnan and co-workers, Journ. 
Chem. Soc, 99, 1554 (1911); 
105, 1941 (1914); 115, 1313 
(1919). 
250. Procter and J. A. Wilson, Journ. 
Chem. Soc, 109, 307 (1916; J. A. 
Wilson and W. H. Wilson, Journ. 
Amer. Chem. Soc, 40, 886 
(1918). 
251. Loeb, see e.g. Proteins and the 
Theory of Colloidal Behavior, 
p. 120 (1922). 
252. Loeb, Proteins, etc, p. 177 (1922). 
253. Sorensen, Medel. Carlsberg lab, 
Kjobenhavn, 12, 255 (1917). 
254. Zsigmondy, Kolloidchemie, p. 382 
(1920). 
255. Loeb, Proteins, p. 150 (1922). 
256. Loeb and Kuntz, Journ. Gen. 
Physiol, 5, 665 (1923). 
257. Einstein, Annal. Phys. (4), 19, 289 
(1906); Koll.-Zeitschr, 27, 137 
(1920). 
258. Oden, Zeitschr. phys. Chem, 80, 
709 (1912).. 
259. Smoluchowski, Koll.-Zeitschr, 18, 
194 (1916). 
260. Pauli, see e.g. Colloid Chemistry 
of the Proteins, p. 39 (1922). 
261. Pauli, Colloid Chemistry, l.c, p. 
11. 
262. Hatschek, Koll.-Zeitschr, 11, 280 
(1912). 
263. Loeb, Proteins, etc, p. 195 (1922). 
264. Hatschek, Koll.-Zeitschr, 13, 88 
(1913). 
265. Couette, Ann. de chim. et de. phys. 
(5), 21, 433 (1890). 
266. Sheppard, Gelatin in Photography, 
p. 196 (1923). 
267. Perrin, Journ. chim. phys., 3, 84 
(1905). 
268. Freundlich, Kapillarchemie, p. 496 
(1922). 
269. Powis, Zeitschr. phys. Chem., 89, 
186 (1915). 
270. Powis, Journ. Chem. Soc., 109, 734 
(1916). 
271. Freundlich, Koll .-Zeitschr., 1, 321 
(1907); Zeitschr. phys. Chem., 
73, 385 (1910); Kapillarchemie, 
p. 575 (1922). 
272. Buxton and Teague, Zeitschr. phys. 
Chem., 57, 72 (1906). 
273. Freundlich and Scholz, Kollqid- 
chem. Beih., 16, 267 (1922). 
274. Billiter, Zeitschr. phys. Chem., 51, 
142 (1905). 
275. Zsigmondy, Nachr. Ges. d. Wiss. 
Gottingen, 1917, p. 1; Zeitschr. 
phys. Chem, 92, 600 (1917). 
276. Galecki, Zeitschr. anorg. Chem, 
74, 199 (1912). 
277. Smoluchowski, Zeitschr. phys. 
Chem, 92, 129 (1917). 
278. Westgren and Reitstbtter, Zeitschr. 
phys. Chem, 92, 750 (1918); 
Journ. Phys. Chem, 26, 537 
(1922). 
279. Westgren, Arkiv for kemi, Stock- 
holm, 7, No. 6 (1918). 
280. Kruyt and van Arkel, Rec. trav. 
chim. d. Pays-Bas (4), 39, 656 
(1920); 40, 169 (1921). 
281. Cf. Freundlich, Kapillarchemie, p. 
647. 
282. Svedberg, Koll.-Zeitschr, 2, 142 
(1907). 
283. Lindeman and Svedberg, Koll.- 
Zeitschr, 29, 1 (1921). 
284. Nordenson, Die Bedeutung des 
Lichtes Diss, Bedeutung, p. 138. 
285. Oden, Nova Acta, Upsala (4), 3, 
No. 4 (1913). 
286. Svedberg, Koll.-Zeitschr, 4, 49 
(1909). 
287. Freundlich and Scholz, Kolloid- 
chem. Beih, 16, 234 (1922). 
288. Zsigmondy, Kolloidchemie, p. 238 
(1920). 
289. Mecklenburg, Zeitschr. anorg. 
Chem, 64, 368 (1909); 74, 207 
(1912). 
290. Pauli, Colloid Chemistry of the 
Proteins (1922). BIBLIOGRAPHY 
257 
291. Cf. Freundlich, Kapillarchemie, 
p. 795. 
292. Brossa and Freundlich, Zeitschr. 
phys. Chem., 89, 306 (1915). 
293. Windisch and Bermann, Wochen- 
schr. f. Brauerei, 37, 130 (1920). 
294. Reitstbtter, Zeitschr. f. Immuni- 
tatsforsch, 30, 507 (1920). 
295. Bechhold, Colloids in Biology and 
Medicine, p. 203 (1919). 
296. Zsigmondy, Kolloidchemie, p. 173. 
297. Heubner and Jacobs, Biochem. 
Zeitschr, 58, 352 (1913). 
298. Reitstbtter, Zeitschr. f. Immuni- 
tatsforsch, 30, 468 (1920). 
299. Chick and Martin, Kolloidchem, 
Beih, 5, 49 (1913). 
300. Arisz, Kolloidchem. Beih, 7, 1 
(1915). 
301. Schryver, Proc. Roy. Soc, B. 83, 
96 (1911); 87, 366 (1914). 
302. Traube and Kohler, Intern. 
Zeitschr. phys.-chem. Biolog, 2, 
42 (1916). 
303. Katz, Kolloidchem. Beih, 9, 1 
(1917). 
304. Posnjak, Kolloidchem. Beih, 3, 
417 (1912). 
305. Freundlich and Posnjak, Kolloid- 
chem. Beih, 3, 443 (1912). 
306. Chiari, Biochem. Zeitschr, 33, 167 
(1911). 
307. Loeb, Proteins, etc., p. 189 (1922). 
308. van Bemmelen, Zeitschr. anorg. 
Chern., 13, 233 (1897); 18, 14, 98 
(1898); 30, 265 (1902); 59, 225 
(1908); 62, 1 (1909). 
309. Zsigmondy, Kolloidchemie, p. 224 
(1920). 
310. Anderson, Zeitschr. phys. Chem., 
88, 191 (1914). 
311. Rohloff and Shinjo, Phys. Zeitschr., 
8, 442 (1907). 
312. Freundlich and Seifriz, Zeitschr. 
phys. Chem., 104, 233 (1923). 
313. Leick, Annal. Phys. (4), 14, 139 
(1904). 
314. Freundlich, Kapillarchemie, p. 
1002. 
315. Herzog and Polotzky, Zeitschr. 
phys. Chem., 87, 449 (1914). 
316. Bechhold and Ziegler, Zeitschr. 
phys. Chem., 56, 105 (1906). 
317. Bartell, Joum. Amer. Chem. Soc., 
36, 646 (1914). 
318. Loeb, Joum. Gen. Physiol., 1, 717 
(1919); 2, 173 (1919); 2, 563 
(1920). 
319. Liesegang, Naturwiss. Wochen- 
schr, 11, 353 (1896); cf. 
Freundlich, Kapillarchemie, p. 
1009. 
GENERAL TEXT BOOKS 
Bancroft, Applied Colloid Chemistry, 
New York. 1921. 
Bechhold, Colloids in Biology and 
Medicine. New York, 1919. 
Burton, The Physical Properties of 
Colloidal Solutions. London, 1921. 
Freundlich, Kapillarchemie. Leipzig, 
1922. 
Hatschek, Laboratory Manual of Ele- 
mentary Colloid Chemistry. Lon- 
don, 1920. 
Hatschek, An Introduction to the 
Physics and Chemistry of Colloids. 
London, 1922. 
Holmes, Laboratory Manual of Colloid 
Chemistry. New York, 1922. 
Ostwald, Kleines Praktikum der Kol- 
loidchemie. Leipzig, 1920. 
Ostwald, A Handbook of Colloid 
Chemistry. London, 1919. 
Svedberg, Die Methoden zur Herstel- 
lung Kolloider Lbsungen. Dresden, 
1909. 
Svedberg, The Formation of Colloids. 
London, 1921. 
Zsigmondy, The Chemistry of Colloids. 
New York, 1917. 
Zsigmondy, Kolloidchemie. Leipzig, 
1920. AUTHOR INDEX 
Abbe, 127 
Anderson, 257 
Andersson, 75, 77, 189, 253, 255 
Anding, 254 
Andren, 32, 251 
Arisz, 257 
Arrhenius, 170, 255 
Bancroft, 257 
Rartpll 94^ 9W 
Bechhold, 85, 86, 153, 154, 253, 255, 257 
Bermann, 257 
Berzelius, 14, 24, 251 
Billiter, 62, 197, 213, 252, 256 
Biltz, 254 
Bjerrum, 111, 112 
Bjbrnstahl, 115, 155, 156, 164, 165, 255 
Bodfors, 45, 252 
Boltzmann, 120, 126 
Borjeson, 42, 43, 45, 79, 136, 147, 236, 
252, 253, 254 
Brann, 252 
Bredig, 35, 252 
Brossa, 257 
Brown, 17, 102, 251, 253 
Burton, 101, 184, 253, 255, 257 
Buxton, 211, 256 
Carbonelie, 103 
Chaudesaigues, 111, 112, 113 
Chiari, 257 
Chick, 257 
Clark, 253 
Clayton, 251 
Constantin, 122, 253, 254 
Cotton, 131, 254 
Couette, 208, 256 
Dabrowski, 111, 112, 254 
Davy, 251 
Debye, 155 
De Haas-Lorentz, 104, 253 
Dewar, 255 
Diesselhorst, 255 
Doerinckel, 252 
Donnan, 202, 256 
Duclaux, 167, 253, 254 
Dushman, 255 
Eastman Kodak Laboratory, 69, 77 
Ehlers, 252 
Einstein, 17, 92, 96, 104, 109, 110 
Electro Filtros Co., 88 
Ellis, 188, 190, 255 
Estrup, 140, 254 
Eucken, 175, 255 
Faraday, 15, 16, 17, 251 
Faxen, 138, 254 
Fischmann, 252 
Freundlich, 51, 64, 65, 127, 162, 163, 
168, 176, 183, 193, 197, 210, 211, 212, 
225, 228, 236, 237, 242, 243, 244, 251, 
252, 255, 256, 257 
Frohlich, 45, 252 
Furth, 254 
Galecki, 214, 256 
Gans, 255 
Garnett, 160, 255 
Gibbs, 170, 255 
Gouy, 194, 255 
Graham, 14, 15, 18, 83, 245, 251 
Gustaver, 174, 175, 255 
Hamburger, 29, 251 
Hartl, 252 
Hatschek, 207, 208, 256, 257 
Hedges, 253 
Helmholtz, 179, 182, 255 
Henri, 110, 254 
Herzog, 254, 257 
Heubner, 257 
Heyer, 253 
Hiege, 252 
Higson, 71, 253 
Hofmeister, 239 
Holmes, 257 
Hull, 155 
Inouye, 116, 254 
Jacobs, 257 
Jentzsch, 132, 254 
Jette, 185, 255 
Kasperowicz, 251 
Katz, 257 
Kawalki, 253 
Kenney, 251 
Kenrick, 83 
Kohler, 257 
259 260 
AUTHOR INDEX 
Kohlschutter, 33, 34, 60, 61, 251, 252 
Kraemer, 46, 236 
Kroger, 253 
Kruyt, 220, 221, 255, 256 
Kuhn, 253 
Kuntz, 256 
Kuzel, 24, 251 
Langelius, 255 
Langevin, 104, 107, 253 
Langmuir, 171, 172, 173, 174, 175, 255 
Lea, 61, 252 
Leick, 243, 244, 257 
Leitz, 132 
Liesegang, 246, 257 
Lindeman, 222, 254, 256 
Linder, 16, 79, 251, 253 
Loeb, 204, 205, 206, 239, 245, 256, 257 
Lorentz, H. A., 118, 138, 254 
Lorenz, R., 66, 68, 253. 
Lotterm oser, 81, 253 
Liippo-Cramfer, 61, 62, 252 
Macquer, 14 
Malfitano, 253 
Marc, 52, 169, 252, 255 
Martin, C. J., 257 
Martin, W. H., 83, 253 
McBain, 196, 256 
Mecklenburg, 161, 228, 255, 256 
Michaelis, 177, 184, 198, 199, 200, 255, 
256 
Mie, 159, 161, 255 
Millikan, 95, 124 
Milner, 255 
Mouton, 131, 254 
Miindler, 256 
Naumoff, 57, 252 
Nichols, 139, 143 
Noll, 252 
Nordenson, 59, 62, 222, 252, 256 
Nordlund, 26, 27, 34, 41, 116, 118, 146, 
147, 251, 252, 254 , 256 
Oden, 61, 63, 64, 65, 66, 78, 87, 144, 
146, 147, 174, 206, 211, 223, 224, 225, 
226, 227, 232, 251, 252, 253, 254, 255, 
256 
Osaka, 176, 255 
Ostwald, Wa., 253 
Ostwald, Wi., 252, 253. 
Ostwald, Wo., 18, 251, 252, 256, 257 
Paal, 63, 252, 253 
Paneth, 174, 255 
Pauli, 207, 229, 256 
Perrin, 89, 97, 98, 99, 102, 111, 113, 179, 
253, 254, 255, 256 
Picton, 16, 79, 251, 253 
Pihlblad, 25, 159, 251, 255 
Plauson, 25 
Polanyi, 175, 255 
Polotzsky, 254, 257 
Pope, 41, 48 
Porter, 101, 253 
Posnjak, 237, 257 
Powis, 256 
Procter, 204, 239, 256 
Quincke, 17, 251 
Rayleigh, 159, 160, 255 
Regener, 22, 23, 133, 134, 254 
Reinders, 52, 252 
Reitstotter, 214, 216, 217, 252, 256, 257 
Reuss, 179, 255 
Richter, 253 
Rinde, 139, 143, 147, 157, 254, 255 
Rohloff, 241, 242, 257 
Rona, 177, 255 
Saxen, 182, 183, 255 
Scheffer, 253 
Scherrer, 155, 156, 255 
Schlbsing, 251 
Schmidt, 169, 170, 255 
Scholz, 252, 256 
Schoop, 251 
Schryver, 257 
Schulze, 251 
Scott, 185 
Seddig, 110, 254 
Seifriz, 242, 243, 257 
Selmi, 14, 251 
Sheppard, 209, 253, 256 
Shinjo, 241, 242, 257 
Siedentopf, 16, 67, 91, 92, 103, 116, 129, 
131, 132, 134, 251, 252, 253, 254 
Silberstein, 77, 253 
Slade, 71, 253 
Smoluchowski, 92, 96, 104, 106, 109, 
110, 120, 121, 122, 123, 124, 125, 126, 
179, 182, 189, 197, 206, 215, 217, 253, 
254 255 256 
Sorensen, 83, 84, 149, 150, 205, 253, 254, 
256 
Stefan, 253 
Stokes, 136, 137, 254 
Strutt, 255 
Svedberg, 251, 252, 253, 254, 255, 256. 
257 
Tammann, 50, 60, 252 
Teague, 211, 256 
Thirion, 103, 253 
Thomson, J. J., 30, 251 
Thomson, W., 29, 251 AUTHOR INDEX 
261 
Toy, 76, 77, 253 
Traube, 257 
Trivelli, 253 
Tyndall, 16, 49, 251 
Van Arkel, 256 
Van Bemmelen, 239, 257 
Vanino, 252 
Von Hevesy, 194, 255 
Von Vegesack, 254 
Von Weimam, 24, 25, 251, 252 
Walton, 52, 252 
Wegelin, 86, 253 
Westgren, 89, 96, 99, 100, 102, 122, 124, 
135, 136, 152, 216, 217, 219, 220, 253, 
254, 256 
Wiener, 103, 253 
Wilson, J. A„ 204, 239, 256 
Wilson, C. T. R., 31, 251 
Windisch, 257 
Wolski, 253 
Zeiss, 131, 133 
Ziegler, 257 
Zocher, 255 
Zsigmondy, 16, 43, 56, 58, 60, 78, 83, 91, 
92, 93, 103, 129, 130, 135, 155, 214, 
216, 217, 219, 228, 239, 240, 251, 252, 
253, 254, 255, 256, 257 SUBJECT INDEX 
Absolute potential, 197 
Adiabatic expansion, 31 
Adsorption, 167 
Eucken-Polanyi theory of, 171, 175 
forces involved in, 168 
formulse, 168 
Gibbs' theory of, 170 
Langmuir's theory of, 171 
of acetic acid on charcoal, 169 
of dispersion medium, 178 
of electrolytes, 176, 211 
of ions, 177 
of nitrogen on mica, 174 
Agglutination, 230 
Aggregation, 18, 78, 209 
Alcogel, 18 
Alcosol, 18 
Amphoteric electrolytes, 198 
Aniline blue sols, 25, 163 
Anomalous osmosis, 245 
Arsenious sulphide sols, 14, 16 
coagulation of, 213 
formation of, 79 
peptization of, 221 
shape of particles in, 163 
size of particles in, 81 
Atomizer, 22, 23 
Aurum potabile, 14 
Avogadro constant, 91, 95, 99, 100, 112, 
113, 118, 124 
Barium sulphate sols, distribution of 
size of particles in, 78 
Bismuth sols, 63 
Blue rock salt, 67 
Brownian movement, 17, 91, 102, 149, 
153, 215 
experimental work, 109 
fundamental formula, 104 
history of, 103 
photographs of, 110, 116, 119 
distribution of displacements, 113 
rotatory, 102, 108 
time law, 115 
translatory, 102 
Cadmium sols, 42, 48 
size of particles in, 45, 136 
Cadmium gels, 236 
Cardioid condenser, 116, 131, 133, 
191 
Casein, 14 
Cataphoresis, 17, 179 
fluorescence method, 186 
formulae, 182, 189 
macroscopic methods, 184 
methods of measurements, 183 
of gold sols, 192 
of protein sols, 187 
ultramicroscopic methods, 187 
Cell for cardioid condenser, 133, 134, 
190 
slit ultramicroscope, 133, 188 
Centers, 28, 58, 73, 74, 75, 76, 77 
Centrifugal force, field of, 138, 139, 143 
Centrifuge, 139 
Centrifuging, 83, 138 
Charge of particle, 192, 194, 195 
Chemical reactions, in gels, 245 
formation of sols by, 53, 55 
Cleanliness, 17, 82 
Coagulation, 17, 18, 209 
action of alcohol in, 229 
action of P-rays in, 222 
action of electrolytes in, 209, 211, 214, 
223 
action of ions in, 18, 220, 223, 224 
action of mixtures of electrolytes, 
212, 213, 224, 225 
action of temperature, 220, 221, 226, 
227, 231 
action of ultraviolet light, 222 
action of X-rays, 222 
and adsorption, 211 
Freundlich's theory of, 210 
irregular series, 211 
mutual of sols, 213, 229, 230 
rapid, 214, 215 
reversible, 18, 209, 223 
sensitized, 230 
slow, 214, 218, 219, 220 
Smoluchowski's theory of, 215 
sphere of action, 215, 218 
value, 209, 212, 214, 224 
velocity of, 214, 216, 218, 219, 
220 
Colloid mill, 25, 26 
Colloid particle as a micell, 167 
as a molecular kinetic unit, 91 
destruction of, 249 
formation of, 21 
Colored flames, 22 
Condensation in gases, 28 
in liquids, 49 
262 SUBJECT INDEX 
263 
in vacuo, 28 
methods, 21, 27 
of metal vapors, 33, 35, 42 
of water vapor, 31 
Condensers, 131, 132 
Conductivity of sols, 195, 196 
Cooling, formation of sols by, 53, 54 
Copper sols, 63, 101 
Crystallization, action of additions, 51, 
52 
velocity of, 49, 51, 52 
Denaturation of proteins, 231 
Dialysis, 14, 15, 83, 86 
Dialyzer, 14, 15, 83, 84 
Diffusion, 14, 15, 93, 150, 151, 245 
measurement of, 94, 95, 96 
Diluting agent, 25 
Discontinuities in colloids, 18 
Disperse phase, 18 
system, 18 
Dispersion medium, 18 
methods, 21, 22 
Dispersion methods, in gases, 22 
in liquids, 24 
Dissociation, formation of sols by, 66 
of salts, 66 
Distribution curve, 22, 38, 39, 140, 146, 
151 
of concentration, 141, 143 
of size of particles, 22, 28, 139, 140, 
142, 143, 144 
Donnan equilibrium, 149, 202, 204, 
207 
Double decomposition, formation of 
sols by, 78 
Double layer, 179, 194 
Double refraction in sols, 163, 164, 165 
Egg albumin, 14, 187, 229, 231 
Elasticity, 241 
macromethods of measurement, 241 
micromethods of measurement, 242 
Elastic limit, 244 
Electric arc, 21, 29, 34 
alternating current, 38 
direct current, 34 
enclosed, 35 
free, 35 
high frequency, 39, 45 
low frequency, 38 
pulverization of metals, 44, 46 
Electro-endosmosis, 179, 182 
Electro-dialysis, 86, 87 
Electrokinetic phenomena, 179, 180 
potential, 193, 197 
Electrokinetic potential and stability, 
210 
Electrolysis, formation of sols by, 62 
Emulsification, 24, 26 
of mercury, 27 
Emulsifying agent, 26 
Endosmotic currents, 179 
Ferric oxide sols, coagulation of, 213 
formation of, 81 
peptization of, 221 
shape of particles in, 163 
Fluctuations in sols, 118 
and compressibility, 121, 122 
average duration of, 124 
average time of return of, 124 
magnitude of, 120 
velocity of, 122 
Fogs, formation of, 31 
Fractional coagulation, 61, 65 
Friction formulse, 118, 138 
Gamboge sols, 98, 111, 112 
Gas ions, condensation on, 31 
Gelatinization, 233 
action of salts on, 235 
hysteresis, 234 
velocity of, 235 
Gels, 14, 15 
chemical reactions in, 245 
diffusion in, 245 
structure, 233 
viscosity of, 234 
Gels, weak, 232, 233 
Globulins, 229 
Gold number, 230, 231 
Gold sols, movement of particles in, 
115 
blue, 163 
coagulation of, 213, 214, 219, 220, 
222 
color change in, 214, 230 
diffusion in, 95, 96 
double refraction in, 164 
fluctuations in, 122, 123, 124, 125 
formation of, 55 
light absorption in, 38, 158, 159 
sedimentation equilibrium in, 99 
shape of particles in, 115, 163, 165 
size of particles in, 45, 95, 155, 158, 
159 
Grinding, formation of sols by, 24, 25 
Halide crystals, reduction of, 69, 70 
Helmholtz' double layer, 180 
Hildebrand cell, 88 
Hydration, 178, 207 
Hydrogel, 18 
Hydrolysis, 81 
Hydrophile sols, 209, 223, 228, 231, 
232 
Hydrophobe sols, 209, 228, 231, 232 264 
SUBJECT INDEX 
Hydrosol, 18 
Hypsometric law, 97 
Illumination, coaxial, 130 
Imbibition, 236, 239, 240 
Immersion, 128 
Immersion ultramicroscope, 130 
Iron number, 230 
Isoelectric point, 198, 199, 214, 229, 231 
Liesegang phenomenon, 246 
Light absorption in sols, 37, 38, 142, 
143, 156, 158 
and size of particles, 159, 160 
methods of measurement, 156, 157 
Lowering of solubility, formation of 
sols by, 53, 54 
Lyophile sols, 209 
Lyophobe sols, 209 
Mastic sols, 112 
Maxwell's distribution curve, 33, 50 
Mercury lamellae, 27 
particles, movement of, 118 
sols, 34, 63 
Membrane equilibrium, 201, 202 
and potential difference, 203, 205 
Metal films, 29 
Microscope, theory of, 127 
Migration potential, 179 
Mobility of particles, 192, 215 
Molecular kinetic theory, 91 
Monodisperse sols, 78, 224, 225 
Narcotic action, 235 
Nickel sols, 66 
Nuclear limit, 56 
method, 28, 135 
Nuclei, 30, 33, 49, 50, 58, 61, 78, 80, 81 
Numerical aperture, 127 
Organosols, 47, 66, 221 
Oscillatory circuit, 39, 40 
Osmometer, 149, 150 
Osmosis, 201 
Osmotic pressure, 92, 149, 203, 205 
and Dorman equilibrium, 203 
Oxidation, formation of sols by, 63 
Paraboloid condenser, 131 
Partial dissolution, formation of sols 
by, 24 
Peptization, 24, 221, 228 
Photographic process, 68 
action of a-rays, 71 
action of P-rays, 72 
action of light, 66, 68, 75 
action of X-rays, 73 
developable centers, 73, 74 
statistic method of study, 71, 75 
theory of, 76, 77 
Platinum sols, 63, 109, 221 
coagulation of, 212, 221 
size of particles in, 45 
Polydisperse sols, 65, 224, 225 
Positive rays, 33 
Potential of particle, 181, 182, 192, 193, 
197 
Primary particles, 22 
Production of nuclei, velocity of, 49, 
50, 51 
Protective action, 230, 231 
Protein sols, coagulation of, 229 
Prussian blue sols, 14 
Pulverization of alloys, 42 
Purification of air, 23 
of colloids, 82 
Radio-active processes, formation of 
sols by, 53, 54 
Reduction, formation of sols by, 55 
Ruby glass, 16, 59 
Scattered light, 156, 160, 161 
in streaming sols, 162 
Secondary particles, 22 
Sedimentation, 89, 96, 136, 140, 141 
accumulation of sediment, 144, 147 
equilibrium, 96, 101, 149, 152 
Selenium sols, coagulation of, 221 
formation of, 63 
diffusion in, 96 
Serum albumin, 229 
Silver halide sols, 81 
Silver mirrors, formation of, 61 
Silver sols, formation of, 36, 60, 62, 63 
shape of particles in, 163 
Single-layer plates, 69 
Silicic acid sols, 81 
Size of particles, 37, 43, 45, 56, 65, 79, 
81, 127, 130, 153, 159, 160 
Shape of particles, 115, 127, 162, 163, 
165 
Slit ultramicroscope, 109, 113, 128, 129, 
133, 188 
Sodium sols, 47, 67 
Sols, 14 
degree of purity, 41, 48 
Solubility of particles, 51 
Spectrum of arc, 36 
Stannic oxide sol, peptization of, 
228 
Stokes' law, 137 
Streaming potential, 179, 182, 183 
Structure of particles, 127, 154 
Sulphur sols, 14 
coagulation of, 223 SUBJECT INDEX 
265 
formation of, 24, 25, 54, 63 
light absorption in, 160 
purification of, 83, 87 
size of particles in, 65, 160 
viscosity of, 206 
Supersaturation, 28, 31, 32, 33, 49, 53 
Surface condensation, 53 
Surface tension, 21, 26, 30, 51, 170 
Swelling, 236 
pressure, 201, 237 
work of, 238 
Tellurium sols, formation of, 24 
Tyndall effect, 16, 156, 160 
meter, 161 
Ultrafiltration, 85, 86, 153 
Ultramicroscope, 16, 103, 104, 109, 113, 
116, 127 
efficiency of, 129 
methods of measurement, 134 
Ultraviolet light, action in gold reduc- 
tion, 59 
action in silver reduction, 62 
coagulating action, 222 
Vanadium pentoxide sols, shape of par- 
ticles in, 163 
Van Bemmelen's curve, 239 
Vapor pressure of drops, 29, 30, 31 
Viscosity, 206 
and hydration, 207 
measurement of, 207 
Volcanic ashes, 23 
Volume condensation, 53 
Water, optically empty, 82 
properties of, 58, 82 
X-ray analysis, 154 
Zinc sols, size of particles in, 45