Monographs on Physics Skssskh m PHYSICAL PROPERTIES OF OLLOIDAL SOLUTIONS E, F. BURTON ALBERT R. MANN LIBRARY New York State Colleges of Agriculture and Home Economics Cornell University Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924002981904 MONOGRAPHS ON PHYSICS EDITED BY Sir J. J. THOMSON, O.M., F.R.S. MASTER OF TRINITY COLLEGE, CAMBRIDGE AND FRANK HORTON, Sc.D. PROFESSOR OF PHYSICS IN THE UNIVERSITY OF LONDON MONOGRAPHS ON PHYSICS. Edited by Sir J. J. THOMSON, O.M., F.R.S., Master of Trinity College, Cambridge, and FRANK HORTON, Sc.D., Professor of Physics in the University of London. THE SPECTROSCOPY OF THE EXTREME ULTRA- VIOLET. By Theodore Lyman, Ph.D., Assistant Professor of Physics in Harvard University. With Diagrams. RELATIVITY, THE ELECTRON THEORY, AND GRAVI- TATION. By E. Cunningham, M.A., Fellow and Lecturer of St. John's College, Cambridge. THE EMISSION OF ELECTRICITY FROM HOT BODIES. By O. W. Richardson, F.R.S., Wheatstone Professor of Physics, King's College, London. MODERN SEISMOLOGY. By G. W. Walker, A.R.C.Sc, F.R.S., Deputy University Lecturer in Astrophysics in the University of Cambridge. With Plates and Diagrams. RAYS OF POSITIVE ELECTRICITY AND THEIR APPLI- CATION TO CHEMICAL ANALYSIS. By Sir J. J. Thomson, O.M., F.R.S., Master of Trinity College, Cam- bridge. With Illustrations. THE PHYSICAL PROPERTIES OF COLLOIDAL SOLU- TIONS. By E. F. Burton, B.A. (Cantab.), Ph.D. (Toronto) ; Associate Professor of Physics, University of Toronto ; formerly 1851 Exhibition Scholar of the University of Toronto ; and Research Student of Emmanuel College , Cambridge. With 18 Illustrations. LONGMANS, GREEN AND CO. 3 g PATERNOSTER ROW, LONDON NEW YORK, BOMBAY, CALCUTTA, AND MADRAS THE PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS BY E. F. BURTON, B.A. (Cantab.), Ph.D. (Toronto) ASSOCIATE PROFESSOR OF PHYSICS, UNIVERSITY OF TORONTO FORMERLY 18S1 EXHIBITION SCHOLAR OF THE UNIVERSITY OF TORONTO AND RESEARCH STUDENT OF EMMANUEL COLLEGE, CAMBRIDGE WITH 18 ILLUSTRATIONS SECOND EDITION LONGMANS, GREEN AND CO. 39 PATERNOSTER ROW, LONDON FOURTH AVENUE & 30th STREET, NEW YORK BOMBAY, CALCUTTA, AND MADRAS l 9 2 J 0b ^f "Br 7 Q~ s"]x PREFACE TO SECOND EDITION The book has been thoroughly revised for this new edition. Certain parts, particularly the chapters on introduction to the subject, and on the Coagulation of Colloids have been almost entirely rewritten in the light of recent work. No attempt has been made to alter the last chapter on the practical applications of the study of colloidal solutions, as such a topic requires a whole treatise to itself. The Reports on Colloid Chemistry and its General and Industrial Applications now being issued by the British Association for the advance- ment of Science are mines of information on this phase of the subject. I desire to thank Dr. D. A. Keys of Corpus Christi College, Cambridge, for his assistance in the proof-reading for this edition. E. F. BURTON. Department of Physics, University of Toronto, Toronto, Canada, November, 1920. PREFACE TO FIRST EDITION The present attempt to give an outline of the study of colloidal solutions has to do particularly with its interest to the student of Physics. Both by aim and necessity the writer has kept in mind the relation of colloids to the development of Physics. For this reason rather extended treatment is given of the development of the ultramicroscope and the confirmation of the kinetic theory of matter afforded by the theoretical and experimental study of the Brownian movement. When we come to deal with the phenomena of the charge possessed by the colloidal particle, the surface tension between the particle and the surrounding medium, and the mechanism of coagulation, we approach the most important problem of physics and chemistry, namely, the unfolding of the interaction of the ultimate particles of matter on one another. The plan of the book is apparent from the table of contents. Under the head of preparation and classification, I have attempted to offer systematic tables of various classes of colloids having something in common, and have quoted types of methods of preparation to enable the reader to find out where to look for detailed information. Chapters III. to VII. inclusive might be called the physics of colloidal study ; they embrace the greater part of the book and will probably appeal particularly to the student of pure physics. In dealing with the question of the coagulation of sols, we come to the part of the subject on which probably the greatest amount of work has been done and from which we may expect most definite ideas as to the reason for the stability of colloidal solutions. PREFACE TO FIRST EDITION vii As to the arrangement of the bibliography, the numbers in each chapter refer to the list immediately following the chapter. Although this entails a few repetitions, it is hoped that it will prove of more immediate value to the reader than a general bibliography for the whole at the end of the volume. In addition to the references throughout the book, the following treatises should be listed as standards of refer- ence in colloidal study : — Zsigmondy, "Zur Erkenntnis der Kolloide" I9°5- (English translation by Alexander. 1909.) Cotton et Mouton, " Les ultramicroscopes et les objets ultramicro- scopiques" 1906. Arthur Miiller, " Allgemeine Chemie der Kolloide " 1907. Wo. Ostwold, " Grundriss der Kolloidchemie ". 1909. The. Svedberg, " Herstellung Kolloider Losungen ". 1909. Freundlich, " Kapillarchemie ". 1909. van Bemmelen, " Die Absorption ". 191 1. Zsigmondy, "Kolloidchemie". 191 2. The. Svedberg, " Die Existenz der Molekiile". 191 2. Side by side with these, one must mention the " Zeitschrift fiir Chemie und Industrie der Kolloide (Kollpid-Zeitschrift) " and the " Kolloidchemische Beihefte," published by Wo. Ostwald ; anyone hoping to have any complete conception of the subject should be familiar with these journals from their beginnings. The few references made to these journals in the bibliographies do not represent adequately one's real indebted- ness to them. I desire to express here the sense of gratitude I feel to Sir J. J. Thomson, who first suggested the subject of colloids to me, and who has invariably shown a keen and sympathetic interest in the work, and also to Mr. W. B. Hardy, F.R.S., one of the pioneers of the modern work on colloids who, during the writer's residence in Cambridge, was a continual source of help and inspiration. E. F. BURTON. University of Toronto, Toronto, Canada, August, 1914. CONTENTS CHAP. PAGE I. Introduction ......... i II. Preparation and Classification of Colloidal Solutions 7 III. The Ultramicroscope 28 Limitations of the ordinary microscope — Invention of the ultramicro- scope — Various forms of ultramicroscopes. IV. The Brownian Movement 5 1 Historical — Velocities observed in Brownian motions — Suggested causes of the motion— Kinetic Theory of the motion — Perrin's distribution law — Values of molecular constants. V. The Optical Properties of Colloidal Solutions .... 96 Colour and absorption of light — The blue colour of the sky — The Tyndall phenomenon — Theoretical work on the scattering of light by small particles — Double refraction induced in colloids. VI. Measurement of the Sizes of Ultramicroscopic Particles . . 122 Direct methods, counting— Methods involving the use of Stokes' law- Application of formulae from optical properties — The sire of mole- cules. VII. Motion of Colloidal Particles in an Electric Field, Cata- phoresis .132 Cationic and anionic solutions — Theory of cataphoresis — Experi- mental measurement of mobilities— Values of the mobilities for various solutions — The effect of the medium. VIII. The Coagulation of Colloids 155 By electrolytes, coagulative power — Schulze-Linder-Picton law — Electrokinetic effects of electrolytes — Electrolytes and electroendos- mose — Ultramicroscopic observation of electrolytic action — Changes in physical properties due to electrolytes, colour, viscosity — Ions entrained by the coagulum — Adsorption — Mixing of oppo- sitely charged colloids — Schutzkolloide — Action of j8-rays, X-rays, and ultraviolet light on colloids. IX. Theory of the Stability of Colloids 196 The production of colloids — Disperse phase — Cause of stability when produced — The mechanism of coagulation. X. Practical Applications of the Study of Colloidal Solutions . 209 Various manufacturing processes — Dyeing — Clay as a colloid — Purification of effluent waters — Colloids of the soil — Agriculture — Physiological applications — Conclusion. Subject Index . . . . . . . . .215 Name Index 318 CHAPTER I. INTRODUCTION. RECENT advances in many branches of scientific research have tended to emphasize the essential unity of all the sciences in the struggle to unfold the mysteries of the phenomena of life and nature. Biology, physiology, biochemistry, physical chemistry, and pure physics deal fundamentally with the same laws, and it is becoming more and more difficult to delimit the region peculiar to each. Few lines of recent research exhibit such ramifications of interest as that dealing with colloidal solutions. The rapid development in our knowledge of these solutions is due to the confluence of some three or four lines of investi- gation, each having its beginning early in the last century. 1. For several hundred years biologists have observed and studied the motions of microscopic animalcules in liquids. About the year 1827, Robert Brown, 1 the English biologist, found that even inanimate fine particles in liquids possessed a similar characteristic motion — a continual zig-zag movement which has come to be called the Brownian movement. This curious motion has been studied continuously since Brown's time, and has recently contributed important quantitative con- firmation of the kinetic theory of matter. 2 2. Faraday carried out many experiments to show the connexion between electricity and light. He at one time sought to find the effect exerted on light by very fine particles of metals suspended in liquid or solid media, e.g. in water or glass. 8 Faraday prepared several aqueous (colloidal) solutions of gold, and first suggested what is now believed to be the ' true constitution of these solutions. A few years later Tyndall 4 developed the experiment by which such small 1 2 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS particles may be revealed by the lateral diffusion of a beam of light traversing the solution, the so-called Tyndall phenom- enon. This led to the theoretical work on the blue colour of the sky and, later, to the investigation of the optical ab- sorption of colloidal solutions. 3. About 1850, English microscopists, in their endeavour to increase the magnifying power of the microscope, introduced the method of illumination known under the name of dark background illumination. 6 The characteristic of this method is that the direct illuminating beam is screened off, and the object is made visible by the light which it diffuses up the tube of the microscope. Although these early investigators used this method for the lateral illumination of ordinary micro- scopic objects, e.g. diatoms, after the invention of the slit ultra- microscope by Zsigmondy and Siedentopf, 6 the early method of dark background illumination was revived in the forms of other recent ultramicroscopes. 4. The most direct antecedent of the modern work on col- loidal solutions is found in the investigations of Graham 7 on the rates of diffusion of various substances in water. He found that all substances fall into two classes — those with very slow diffusion (which he called colloids), and those with a higher order of diffusion rate (crystalloids). Using permeable septa, such as employed by early workers on osmosis, he found that his colloids did not diffuse through them at all, while the crystalloidal materials went through the septa quite readily. On account of these diffusion experiments, Graham sug- gested that the " colloidal molecules may be constituted by the grouping together of a number of smaller crystalloidal molecules". But it was just such aggregates which should show the Tyndall phenomenon when the solution is illumin- ated by a narrow beam of light. Such tests were applied to these solutions by Linder and Picton 8 ; they prepared a series of solutions of arsenious sulphide in which, by the use of the Tyndall phenomenon, the rate of diffusion, and the velocity of settling under gravity, they were able to grade the sizes of the • particles from aggregates visible in an ordinary microscope to INTRODUCTION 3 those just bordering on the upper limit of the size of mole- cules. This direct proof of the existence of comparatively large aggregates of molecules offered a challenge to the microscopist to attempt to extend the range of the ordinary microscope to bring much smaller particles into view than he had hitherto done. In answer to this challenge, Zsigmondy and Siedentopf set themselves to apply the principle of the Tyndall phenomenon to the illumination of the ordinary microscope ; the result was the production of the first so-called ultramicroscope. There soon followed from various optical manufacturers and scientific workers the simpler types of ultramicroscope, which adopted, consciously or unconsciously, the method of dark background illumination of the early English microscopists. The use of the ultramicroscope has given direct visual evidence of the existence of discrete particles of matter in suspension in solids, liquids, and gases of sizes ranging all the way from that of the largest molecule to that seen in compar- atively coarse suspensions ; the definite determination of the sizes of such particles has led to the modern definition of a colloidal solution. Generally, a colloidal solution may be defined as a suspension, in a liquid medium, of fine particles which may be graded down from those of microscopic to those of molecular dimensions ; these particles may be either homogeneous matter, solid or liquid, or solutions themselves of a small percentage of the medium in an otherwise homo- geneous complex. 9 Such solutions may be prepared in almost numberless ways, and, in their properties, may betray variations as numerous as the methods of preparation. The one property common to all such solutions is that the suspended matter will remain almost indefinitely in suspension in the liquid, gener- ally in spite of rather wide variations in temperature and pressure ; the natural tendency to settle due to gravity is over- balanced by some other force tending to keep the small masses in suspension. The ultramicroscope showed that the particles in sus- pension in colloidal solutions possessed a very lively Brownian movement, much more rapid than that shown by ordinary 4 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS microscopic particles since the rate of motion increases very rapidly as the size of the particles decreases. The discovery made many years ago that the Brownian movement was usually destroyed by the addition of electrolytes to the solution, indicated some connexion between these particles and electrically charged ions. In common with coarse suspensions of such materials as clay, graphite, quartz, amber, etc., in various fluids, generally speaking, these colloidal particles are found to be electrically charged; that is, they will move in an electrical field maintained between two elect- rodes placed in the solution. In some cases the particles are positively charged, in others, negatively. Again, although these solutions are very stable and when left undisturbed will remain practically unchanged, the suspended matter may be precipitated in a variety of ways ; as a general rule, the addition to the solution of electrically conducting solutions (electrolytes) will induce coagulation in a short time. The chapters which follow will deal with the physical as- pect of colloidal solutions from four points of view: (i) their preparation and classification ; (2) the general properties of such solutions ; (3) the theoretical importance of the study of such solutions, and (4) the practical importance of colloids, as for example in physiology and technology. As will be seen in the description of the methods of pre- paration of colloidal solutions, the process of formation of the particles follows one or other of two directions : either very small (molecular) units combine to form large particles, or large masses break down to the size of the small particles of the colloidal solution. In either case, the final permanent size of the particle seems to be fixed by an equilibrium of forces, the analysis of which forms one of the most fascinating problems in physics and chemistry. As a result of the inter- action of such forces as crystal-forming tendencies, surface tension, and electrical attraction or repulsion, the particles either grow or diminish to a certain size dependent on the material of the particle and of the medium. Apart from the analysis of the forces contributing to the stability of colloidal solutions and the explanation of the INTRODUCTION 5 effect of the addition of electrolytic ions on this stability, the chief interest in the study of these solutions for the physicist may be indicated under two heads. In the first place, the work of Einstein, 10 Smoluchowski, 11 and Langevin, 12 in offering exact mathematical formulae whereby the Brownian movement may be quantitatively tested, and the investigations of Perrin 13 on the distribution of the particles near the surface of a liquid, afford most striking evidence of the truth of the fundamental hypotheses of the kinetic theory of liquids and gases, and of the existence of the molecule. Secondly, following out Faraday's and Tyndall's work on the optical properties of these solutions, many interesting researches have been carried out dealing with the colour and light absorption of such solutions, and leading to suggestions as to the form and structure of the particles." Judging by the literature on the subject and considering the composition and action of the constituent fluids of the animal body, we may conclude that the study of colloidal solutions is of surpassing interest to the biologist. The invention of the ultramicroscope has brought into view bodies, e.g. certain germs, which were theretofore undiscovered. The abundance and ubiquity of natural colloids in the human body brings into prominence the work on semi-permeable mem- branes, surface tension, and the r61e played by the protective colloids. Indeed, Perrin 15 has suggested a colloidal explanation of the process of primary cell growth and cell division, an idea which is somewhat supported by the phe- nomenon of galvanotropism of microscopic animals. 16 ' 17 A mere enumeration of the use of colloids in technology would occupy too much space at this point. 18 Dyeing, tan- ning, glass making, cement hardening, and rubber manufacture afford examples of the way in which the properties of these solutions were made use of before their real constitution had become a subject of theoretically important work. In reality there are very few modern manufacturing processes which do not employ such solutions. Equally important is the r61e of such solutions in the process of nature ; as an instance of this, as emphasized by van Bemmelen, 19 the retentive power of rich soils for the salts necessary to the growth of plants is due 6 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS directly to the existence of colloidal solutions in the humus and clay of the soil. Although there is, as yet, little finality in the study of these solutions, the vast amount of work that has been and is being done will probably justify attempts from time to time to re-state a summary of our knowledge of them. BIBLIOGRAPHY. 1 Brown : " Pogg. Ann." 14, 1828,. p. 294 ; Roy. Soc. Vol. I, 1866. ' Perrin : "Ann. Chim. Phys." (8), 18, 1909, pp. 5-1 14; "Jour, de Phys." (4), 9, 1910, pp. 5-39; "Jour. Chim. Phys." (8), 1910, pp. 57-91 ; "Bull. Fr. Phys. Soc." 1909, pp. 15, 50, 189. 3 Faraday: "Proc. Roy. Inst." II, 1854-8, pp. 310, 444 ; "Phil. Mag." (4), 14, 1857, PP- 401, 512; "Phil. Trans." 147, 1857, P- US- 4 Tyndall : "Phil. Mag." (4), 37, 1869, p. 384. 6 Wenham; "Jour. Micros. Soc. Lon." II, SB 54, p. 145 ; 1" Trans. Mic. Soc. Lond." (Quar. J. Mic. Soc), IV, 1856, p. 55 ; "Amer, Quar. Mic. Jour." I, 1879, P- 2 35 ; "Jour. Roy. Mic. Soc." August, 1879, p. 520. 6 Zsigmondy and Siedentopf: "Phys. Zeit." 6, 1905, p. 855; 8, 1907, p. 850; "Zs. f. Wiss. Mikros." 24, 1907, p. 13. 'Graham: "Phil. Trans." 1861, p. 183; "Proc. Roy. Soc. Lon." XIII, P- 335- "Linder and Picton : "Jour. Chem. Soc. Lon." LXI, p. 148; LXVII, p. 63 ; LXXI, p. 568 ; LXXXVII, p. 1906. 9 Ostwald and Fischer : " Theoretical and Applied Colloid Chemistry " (Wiley, New York, 191 7), p. 20. 10 Einstein : "Ann. der Phys." 17, 1905, p. 549 ; 19, 1906, p. 371. 11 Smoluchowski : " Bull. Intern. Acad. d. Sci. Cracovie," 7, July, 1906, PP- 577-6o2 ; "Ann. Der. Phys." 4, B., 21, 1906, pp. 756-80. "Langevin: "C. R." 146, 1908, p. 530. "Perrin: "Bull. Soc. Fr. Phys." 3, 1909, pp. 155-89; "Zs. fur Elektro-ch." 15, 1909, p. 269. 14 Cotton and Mouton : " Les Ultramicroscopes et les objets ultramicro- scopiques," Paris, 1906, p. 166 et seq. 16 Perrin : "Jour, de Chim. Phys." XI, ic, 1904, p. 607. 18 Miller: "Jour, of Physiology," XXXV, 3, March 25, 1907, p. 215. 17 Buxton and Rahe : "Zs. f. d. ges. Biochemie," XI, n-12, p. 479. 18 Rohland: (Britland and Potts) "The Colloidal and Crystalloidal State of Matter" (Van Nostrand), 191 1. 19 Van Bemmelen : " Vide Zsigmondy, Uber Kolloid-Chemie " (Barth) Leipzig, 1907. CHAPTER II. PREPARATION AND CLASSIFICATION OF COLLOIDAL SOLUTIONS. The term, colloid, was used first by Graham about 1861, to denote a class of substances, many of them of a gummy con- sistency, which had an extremely low rate of diffusion through media in which they were dissolved. As the result of an ex- tensive series of experiments on the rates of diffusion of various compounds, he was led to divide all substances into two classes, the rate of diffusion of materials in one of the groups being much larger than the rate of those belonging to the other group. He found that such substances as silicic acid, soluble alumina, and certain organic compounds, viz. gum-arabic, tannin, dextrin, caramel, and albumen, possess extremely slow rates of diffusion into pure water, compared with the rates of such compounds as sodium chloride, common acids, etc. The former group he called colloids, while the latter he designated crystalloids on account of the fact that they usually crystallize from saturated solutions. Further examination of the properties of the substances in the two classes showed him that there was a very general line of cleavage between the two groups. "They appear like different worlds of matter, and give occasion to a corresponding division of chemical science. The distinction between these kinds of matter is that subsisting between the material of a mineral and that of an organized mass. " The colloidal character is not obliterated by liquefaction, and is, therefore, more than a modification of the physical con- dition of solid. Some colloids are soluble in water, as gelatine and gum-arabic ; and some are insoluble, like gum-tragacanth. Some colloids again form solid compounds with water, as 7 8 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS gelatine and gum-tragacanth, while others like tannin do not. In such points the colloids exhibit as great a diversity of pro- perty as the crystalloids. A certain parallelism is maintained between the two classes notwithstanding their differences. " The phenomena of the solution of a salt or crystalloid probably all appear in the solution of a colloid, but greatly reduced in degree. The process becomes slow ; time, indeed, appearing essential to all colloidal changes. The change of temperature usually occurring in the act of solution becomes barely perceptible. The liquid is always sensibly gummy or viscous when concentrated. The colloid, although often dis- solved in a large proportion by its solvent, is held in solution by a singularly feeble force. Hence colloids are generally displaced or precipitated by the addition to their solution of any substance from the other class. Of all the properties of liquid colloids, their slow diffusion in water, and their arrest by colloidal septa are the most serviceable in distin- guishing them from crystalloids. Colloids have feeble chemical reactions, but they exhibit at the same time a very general sensibility to liquid reagents. . . . "The inquiry suggests itself whether the colloidal mole- cule may not be constituted by the grouping together of a number of smaller crystalloidal molecules, and whether the basis of colloidality may not really be this composite character of the molecule." 1 As indicated above, Graham found that the solution of a colloid would not pass through a membrane of a solid colloid, while solutions of crystalloids do so with the utmost ease. This property is of the greatest importance as a practical means of freeing solutions of colloids from crystalloidal impurities, i.e. by so-called dialysis. While Graham called the particular substances — gelatine, gum-arabic, tannin, alumina, etc. — colloids, there is distinct indication in the above quotation that he was well aware of the intimate relation that must subsist between the solvent and the solute. Modern work has shown that it is incorrect to speak of colloidal substances as a particular class. Krafft 2 has observed that the alkali salts of the higher fatty acids — PREPARATION AND CLASSIFICATION 9 stearate, palmitate, oleate — dissolve in alcohol as crystalloids with normal molecular weights, but in water they are true colloids. The reverse is true of sodium chloride ; Paal 3 found that the latter gave a colloidal solution in benzol, while, of course, it gives a crystalloidal solution in water (Karczag 4 ). More recently, Von Weimarn 5 has demonstrated, by the preparation of colloidal solutions of over two hundred chemical substances (salts, elements, etc.), that, by proper manipulation, almost any substance which exists in the solid state can be produced in solution, either as a colloid or as a crystalloid ; and that, as shown by many other workers, in some cases it is merely a matter of the concentration of the reacting components whether one gets crystalloidal or colloidal solu- tions. Consequently, we now speak of matter being in the colloidal state rather than of certain substances as colloids — the essential characteristic of the colloidal state being that the substance will exist indefinitely as a suspension of solid (or, in some cases, probably liquid) masses of very small size in some liquid media, e.g. water, alcohol, benzol, glycerine, etc. According to the medium employed the resulting solutions or suspensions are called, after Graham, hydrosols, alcosols, benzosols, glycersols, etc. When a general treatment of the theory of such solutions is attempted, it is seen that they are related in their properties, on the one hand, to distributions, in finely divided state, of a solid through a solid medium, as for example, gold ruby glass ; and, on the other hand, to distributions of finely divided solids in gaseous media as, for example, smoke in air. To all such heterogeneous mixtures of solid, liquid, or gas in state of sus- pension in solid, liquid or gaseous media, the name dispersoid has been given ; the theory of the equilibrium of dispersoids in general has been treated by Freundlich, 6 Wo. Ostwald/ and Von Weimarn. 6 Following the nomenclature adopted by these writers, we shall call the finely divided masses, the disperse phase, while the medium through which the particles are distributed will be called the dispersion medium. Taking the three states of matter— solid, liquid, and io PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS gaseous — we should have the nine different kinds of dis- persoids indicated in the following table (Table I), in which is also given examples of the various systems : — TABLE I. Disperse phase. Dispersion medium. Examples. I Solid in Solid. Solid solutions, gold ruby glass, carbon, in steel, rock salt with sodium. 2 Liquid in Solid. Liquid in minerals, water of crystalliza- tion. 3 Gas in Solid. Gases in minerals, meerschaum, hydro- gen in various metals. 4 Solid in Liquid. Colloidal solutions of metals. 5 Liquid in Liquid. Emulsion of oil in water. b Gas in Liquid. Air in water, foam. 7 Solid in Gas. Smoke in air, salammoniac powder in 8 Liquid in Gas. Clouds, gases at their critical state. 9 Gas in Gas. Not a dispersoid, merely a mixture of molecules. So-called colloidal solutions are included under groups (4) and (5), chiefly the former. They include such of those dis- persoids as have the individuals of the disperse phase with diameters lying between two fairly definite limits. The upper limit is set by those particles which settle under gravitation in a short time ; the lower limit is fixed by the power of the ultramicroscope to render the particles visible. So we have, after Wo. Ostwald, the following classification of these disper- soids : — Dispersoids. [4] and [5]. Coarse suspensions \ Diameters of particles : >o'i p* Colloidal solutions. \ between o-i p and ro pit, p equals io- 3 mm. = io- 4 cm. pp = io- 6 mm. = 10-' cm. Molecular solutions. I s w o § 5 ° O O I— I < a. w a; p* w ►J •a v ££ O 3 « o<0 bo < bo EC .O' *s j» bS in 5 15 g_ W > cu C MO ■■.-•comfe. c w . j- .^ •2 _-<3 bo 6" « lo-^g"*! — . 3? " fa ^ ~ S .H-* a --,-"■ 4^< CO a > -„- JO £ C Oh bo .2 --B U ** CO O « 3 V a W a a s PhO 2 o ££ •8H O ■•■« . .2^-C IS no £»■« C 3 W'ijaio .o — s pfe g" o*-- 3 -° js -pq m 2 . bC" 1 to Sd " CO ■xs< bo a •a O 3" U 3" < •3 c 13 co 8 m " « ? -o.o aha & 2 J ■-• a S N .1 = co>- - " 1* u c •~.2 R bo"rt ^J^^ tip a5 • • c -X ,r ' ■G ! s £% a> I ° I P °"o o CO ,4J c_ c O rt « bOWcoS.wz'' 3 ■ 1 ;b *3 "s _ rt Mot C •SJg«a-S * -C o o o -■ m X r7! co '3 j? „- 5>: ■co . -- u-co u u tJo^ ■s si??!?" f-3 fj3 >cjM ' u ^ « PREPARATION AND CLASSIFICATION 15 (crystals of AuCl 4 . H . 3H 2 0) and 37 mgms. of the purest potassium carbonate. The gold chloride is reduced by about o - 5 c.c. of an ethereal solution of phosphorus, made by diluting a concentrated solution with five times its volume of ether. The formation of the hydrosol takes place slowly, the fluid becoming first bright brownish-red, and then gradually bright red, often with a tinge of brown-red, without showing the slightest turbidity in transmitted or reflected light. Particu- larly troublesome impurities in the water are the following : Phosphates of the alkaline earths, silicates from the containing glass vessel, colloidally dissolved substances in ordinary com- mercial distilled water. lb. Chemical Oxidation. This method is important on account of its use in the production of sulphur — a reaction employed by chemists for many years. The production of the hydrosol is more a matter of manipulation of an old experiment than any new development. Colloidal Sulphur (Raffo 21 ). 70 grms. sulphuric acid (d = I '84) are placed in a cylinder of about 300 ccs. capacity which is kept in cold water. A solution of sodium hyposulphite (50 grms. pure crystals in 30 ccs. distilled water) is added, drop by drop, while the acid is continually stirred. The hyposulphite must be added very slowly in order not to form too large masses of t:he insoluble sulphur, which is the end product of the reaction. When all the hyposulphite has been added, the whole is placed in a flask, 30 ccs. of distilled water added, the whole then shaken and warmed on a water bath for about ten minutes at 8o c C. At, this temperature, the original turbid, thick mass clears quickly and assumes the sulphur-yellow colour. The first purification consists in filtering the whole through glass wool in order to remove the undissolved sulphur. During the cooling the fil- trate deposits the sulphur again ; consequently it is set away in a cool place for some twelve hours. Heating and filtering is continued until all the insoluble sulphur is removed. The 1 6 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS solution is then centrifuged, the sediment washed in a little cold water, and then dissolved in as small a quantity of (hot) water as possible. The solution is neutralized by sodium car- bonate which precipitates the greater portion of the sulphur, leaving a stable sulphur solution containing about I per cent, sulphur and 6 per cent, sodium sulphate. Ic. Hydrolysis. By hydrolysis is meant the decomposition which many chemical compounds (soluble in water) undergo when dis- solved in water. The action may be represented by the equa- tion — Ct. An + H 2 OJH. An+Ct. OH. where Ct and An stand for the cation and anion respectively of the dissolved substance. When, in the course of the hy- drolysis, a compound of small solubility, with respect to the water, is formed, conditions are favourable to the production of a colloidal solution. Colloidal Thorium Hydroxide (Biltz 22 ). A solution of 7 grms. of purest thorium nitrate in 50 c.cs. water gives, after five days' dialysis, a hydrosol of thorium hy- droxide as clear as water. While the water is in the dialyser only a very slight osmotic rise is observed. The reaction of the solution is neutral ; with acidified ferrosulphate, nitrate can undoubtedly be recognized. Analysis gave o - i32 grm. thor- ium hydroxide per 100 c.cs. of solution. Evaporation on a water bath leaves a gummy shining mass, which does not again dissolve in water. The colloidal solution is stable even after boiling. Id. Double Decomposition. Under this heading, following Svedberg, 16 we may include chemical condensation reactions which are not included under the three previous methods. They include the production of sulphides by the action of hydrogen sulphide on metallic solu- tions, of certain acids by the action of strong acids on salts, e.g. silicic acid by the action of hydrochloric acid on sodium silicate, etc. PREPARATION AND CLASSIFICATION 17 Colloidal Metallic Sulphides (Linder and Picton "), Solutions of metallic sulphides may be prepared in the following ways :— 1. A solution of the metallic salts is allowed to run into sulphuretted hydrogen water, kept saturated by a stream of gas. It may then be freed from uncombined hydrogen sul- phide gas by a current of hydrogen, and dialysed to free it from salts. 2. The metallic hydrates are suspended in water and treated with hydrogen sulphide gas. The solutions obtained contain hydrogen sulphide com- bined, and are, in fact, solutions of hydrosulphides. By the first method one may obtain the solution of any metallic sulphide, provided no excess of acid be present. An arsenide, acidified with hydrochloric acid, if allowed to run into hydrogen sulphide water will readily give a solution contain- ing about 5 grms. of sulphide per litre. Ie. With Protective Colloid. Many substances added to pure water tend to retain any particles formed therein in a finely divided state of suspension. For example, if traces of gelatine be added to very dilute solutions of silver nitrate and potassium iodide, the insoluble silver iodide, obtained by mixing the solutions, remains in a state of fine suspension in the water. The gelatine seems to exert some sort of protecting action on the small particles, preventing their coalescence into larger masses. In addition to gelatine, gum-arabic, water-glass, dextrin, egg albumen, lysalbinic acid, protalbinic acid, tannin, starch, casein, and glycerine have served as the protecting or " schutz " colloid. The exact function of the protective colloid is one of the very perplexing problems of colloid chemistry. Colloidal Gold Sol with Tannin as Protective Colloid (Ostwald and Fischer 23 ). To 100 ccs. of ordinary distilled water add a few drops of a neutralised 1 per cent solution of gold chloride and, after stirring, a few drops of about o - i per cent solution of tannin. 1 8 Physical properties of colloidal solutions This mixture should be practically colourless. Heat over a Bunsen burner for a few minutes while shaking constantly. A cherry-red or reddish-black sol is obtained. The tannin not only acts as a reducing substance but also as a protective colloid. Ha. Mechanical Dispersion. Mastic in Water. — As an example of the mechanical dis- persion of a substance in water we may quote the usual method of producing hydrosols of many of the natural gums (such as mastic) which are themselves insoluble in water. 2 * A small quantity of mastic gum may be easily dissolved in ethyl alcohol ; a few drops of such a solution when mixed with, say, ioo ccs. of pure water gives a milky white permanent solution contain- ing ultramicroscopic particles. The mastic content per c.c. is very small, and the resulting hydrosol is exceedingly sensitive to the addition of electrolytes. lib. Electrical Pulverization. It has long been known that an arc passing between metal electrodes causes the disintegration of the electrodes, and, as Faraday 19 showed, the metal is deposited in very fine particles. Bredig 25 first applied this to the preparation of colloidal solutions by causing the arc to pass between two similar metal electrodes held below the surface of distilled water contained in a vessel of clean, very insoluble glass or porce- lain. He employed a current of from 4 to 10 amperes with a difference of potential at the arc of from 30 to 100 volts, and used as electrodes chemically pure metals. Care should be taken that electro-negative metals are not alloyed with electro- positive metals in the electrodes used. In practice the arc may be made by some device giving intermittent sparking between the electrodes. If contamination is rigidly avoided, the pulverized metal distributes itself through the liquid, giving rise to a transparent coloured solution which, in the pure state, will remain stable for any length of time. The intensity of the current used in the Bredig method is harmful when the electrodes used are made of the softer metals, PREPARATION AND CLASSIFICATION 19 or when sols are attempted in organic liquids. For this reason, Svedberg 26 has made use of an oscillating discharge from an induction coil between specially constructed electrodes of the metals. The currents used were of the order of 10 milliamperes up to one or two amperes, the voltage being from 30 to 200 volts, so that the heating action of the spark was much re- duced. By this means he greatly extended the number of both hydrosols and organosols produced electrically. (See also Morris-Airey and Long. 27 ) Chemical Dispersion Methods. In the two methods of preparation included under this head- ing, the substance to be produced in the colloidal state is first precipitated in an ordinary chemical reaction and the precipitate so treated as to induce its dispersion throughout the liquid medium. In the first subdivision, the precipitant is freed from some coagulant (electrolyte) by washing with pure water ; in the second, the reverse takes place — some electrolyte being added to the precipitate to bring the latter to the dispersoid state. He. Washing of Precipitates. Soluble Molybdic Acid (Berzelius 2S ). This hydrate, e.g. precipitated from molybdic chloride by ammonia, is soluble in water. When one precipitates the acid with ammonia, one sees that at first the precipitate re- dissolves ; finally this action ceases and the hydrate is then completely precipitated, because it is insoluble in water contain- ing salts, particularly the ammonium salts. When these are eliminated by washing out the precipitate, the hydrate begins to dissolve again, and finally it completely dissolves to produce a reddish-yellow liquid — a hydrosol. lid. Peptization. By the addition of acids or alkalies to the precipitate (hydrogel) from some colloidal solutions, Graham x was able to bring the substance into the hydrosol state again. From the analogy between this action and the solution of insoluble a* 20 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS colloids during the process of animal digestion, Graham called the above operation peptization. It is a method which has been employed with a great variety of reagents by many chemists since the time of Berzelius. Colloidal Aluminium Oxide (Miiller 18 ). 50 ccs. of an aluminium chloride solution of 2*448 per cent A1 2 3 content was placed in a flask, diluted with water and precipitated with ammonia at the boiling-point in the manner usually pursued in analytical chemistry. The solution was filtered and the precipitate carefully washed with hot water and then emptied into a flask to which some 250 ccs. of water was added. By means of a burette small quantities of 1/20 N hydrochloric acid solution were added and, after each such addition, the flask was again brought to the boiling-point, the water lost by evaporation being constantly supplied. The following phenomena were noticed : after the addition of the first traces of the acid, the precipitate was apparently un- changed ; with further addition, it assumed a slimy consistency ;. finally, the point was reached where the original hydrogel which lay at the bottom of the flask in masses, distributed it- self in a completely uniform manner through the liquid, where- upon the latter assumed an opalescent aspect and passed easily and completely through a filter paper. 4. Classification according to Physical Properties. The first attempt to classify colloids under this head is due to Hardy, 9 who divided all colloidal solutions into ^wo classes which he called reversible and irreversible. Although not the original intention of Hardy, this division now depends on the characteristics of the dried residue left after evaporating the solution. If, as in the case of gelatine, the residue will dissolve again in water and reproduce the colloidal state, the solution is said to be reversible ; if, on the other hand, as in the case of the Bredig metal sols, the dried residue cannot be redissolved in the liquid so as to give the dispersoid, the solution is said to be irreversible. These two classes are almost, but not entirely, co-existent with those of the other classifications PREPARATION AND CLASSIFICATION 21 indicated in Table II. This classification contemplates dried residues. However, in the solutions of the irreversible class there are great differences of behaviour of the residue when the latter is not thoroughly dried. Some solutions, such as copper ferrocyanide, can be reproduced if, to the moist co- agulum, a particular stabilizing ion be added ; in fact, the dis- persion method of peptization is this Operation on a moist coagulum. On the other hand, it is impossible to redissolve the coagulum from a Bredig metal sol, even if it is treated in the moist state. A second characteristic by which these solutions may be differentiated is their action when electrolytes are added to them. " Colloidal solutions differ in their relation to small con- centrations of salts, some, such as the hydrosols of metals, of silica and of alumina, are precipitated — and others depend for their stability upon the presence of salts " (Hardy 9 ) ; others, such as sols with protective colloids, do not seem to be affected by the addition of electrolytes. A close study of the methods of preparation suggests wide differences in the electrolytic content of different solutions, and consequent differences in their behaviour toward added electrolytes. A third important physical property of the particles of the solutions is the sign of the charge which they bear. Solutions belonging to any sub-group might ultimately be divided into two sets, according to whether the particles are positively or negatively charged. No very exact rule may be laid down in this regard, except that, in general, oxides, hydroxides, and sols of easily oxidizable metals, usually have positively charged particles, while materials which do not easily oxidize give negatively charged particles. In the case of globulin, if the sol is acidic, the particles are positively charged ; if basic, negatively charged. As indicated in Table IV, the most general classification of colloidal solutions is that into the two large classes, suspen- soids and emulsoids. We have seen that these two classes are almost co-extensive with other pairs of classes as given in Table II, and, roughly speaking, are differentiated from one another by the nature of the coagulum formed ; that is, the 22 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS emulsoids give a residuum which is a gel as in the case of gelatine 1 , while the coagulum for those of the other class are non-gelatinous powders as in the case of gold sols. The name emulsoid has been suggested on account of the analogy which exists between these sols and ordinary emulsions. The principal members of this class are the sols of substances which make up the majority of the substances which Graham primarily denoted by the name colloid, i.e. gummy substance. They are gelatine, natural gums, tannin, dextrin, caramel, agar- agar, starch, concentrated soap solutions, rubber latex, col- lodion, cellulose, serum .albumen, casein, and most other protein bodies. On account of their importance in investi- gations in physiology and biochemistry, there has been a tendency in the past to look upon these solutions as colloids par excellence, and their characteristics have been in a popular way recognized as the peculiar properties of colloidal solutions. There is evidence to show that the structure which exists in the solid gels obtained from these solutions really exists to a certain extent in the liquid solution 29 ; at any rate these solu- tions have properties as regards viscosity, reversibility, sensi- tivity to added electrolytes, electrical charge on the disperse phase, etc., which are of quite a different order from corre- sponding properties of the dispersoids. This has led to considerable misunderstanding on the part of some scientists who may be inclined to question the advisability of including all the varieties of these solutions under the one heading — colloidal solutions. But, in spite of the great differences existing between these two classes, we do meet with both kinds side by side in many technical operations, as for example dyeing, while in the case of a mixture of a suspen- soid and an emulsoid, where the latter acts as a protective colloid, we have a solution which retains many of the characteristics of sols of both classes. With regard to the sub-class, suspensoids, their behaviour as to reversibility and irreversibility, and their sensitiveness to added electrolytes, leads us to a classification which may be useful in helping us to understand colloidal solutions in general. I. First, we may group together those which have the PRE PA RA TION AND CLA SSIFICA TION 2 3 appearance of very fine suspensions of quite simple uniform particles; they are noticeable in their extreme sensitiveness to added electrolytic solutions, and have usually a very low electrical conductivity. Under this class are included the Bredig metallic solutions, Zsigmondy's gold solutions, etc. They have in general a very small amount of the disperse phase present per c.c. of solution ; Bredig sols have metal present to the order of 10 mgms. per 100 c.cs. II and III. Closely allied to those named above, we have a large class which depend for their stability upon a trace of salt absorbed by the colloidal particle. For example, Duclaux 30 prepared his solutions of colloidal copper ferrocy- anide by the reaction of potassium ferrocyanide on cupric chloride and found that the colloidal particle (copper ferrocy- anide) entangled a certain quantity of potassium ; as the percentage of potassium was decreased the stability of the colloid decreased, and the particles tended to coagulate when the potassium content was reduced to zero. The coagulating power of electrolytes appeared to him to be due to the substitu- tion of a new ion for the potassium of the particle, although it is not quite clear how this action results in coagulation. As to additional members of this class we may cite the following facts : — (a) Hardy gives the example of acid and alkali globulin as a true example of this class — the acid globulin retaining the negative radical of the acid, etc. (b) The historically important ferric hydrate colloidal solution depends for its stability on a trace of the retained ferric chloride, as dialysis to remove the chloride brings about coagulation. (c) Purified egg-albumen always contains chloride enough to react on silver nitrate. (d) Silicic acid nearly always contains traces of potassium, sodium, and hydrochloric acid ; continued dialysis produces coagulation. (e) The metallic sulphides, e.g. arsenious sulphide and antimony sulphide, probably depend for their stability upon a slight trace of entrained hydrogen sulphide. 24 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS Mrt fS 2 o3 3 2 -as* » 3 "S — '32 5b. -is cu3 I -s-g S3 >, ■Q o ■O u »a ;rj a .O rt rt CO c W C CJ o to O S .SP:3 •2 f i co rt c b Cu ■s lag 00' ~ S O rt Oi rt o rt > O - rt ° «• w> •d3 M .- O II " . rt 'o e " ,2 3 5.J 51. mQ 8w -§!.£.§ ,Too 38 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS The highest numerical aperture (with homogeneous im- mersion) catalogued by Zeiss is i"40, so that the maximum number of lines per cm. (or inch) will be reduced in the pro- portion of I "53 to 1*40. With an immersion objective of N. A. 135 and an immersion condenser of i'30, both care- fully adjusted and with useless light excluded by a suitable stop, Johnstone Stoney 8 found that the practical limit of proximity at which particles in a row may be placed consis- tently with our seeing them as separate objects (with wave- length 0'45 //,), is somewhere about 0-20 fi or O'lQ fi, i.e. 2 - or i-a x io~ 6 cm. or about 1/130,000 of an inch. He has also shown that a pair of objects can be seen as two, when distant from one another about # of the interval at which a row of such objects must be spaced in order to make it possible to resolve them with a given microscope. Again, as shown by Gordon, 3 if an object of uniform structure be illuminated by light which is already diffracted, the resolution is much better than for ordinary illumination. While the above limit is in reality the limit of the interval between two points which may just be differentiated and does not represent the limit of smallness of particles just visible, it may be looked upon also as the limit of small particles for which it is possible to detect any detail by microscopic vision. The attempt to advance our knowledge of still smaller particles led to the invention of the ultramicroscope. The prominence given in recent years to colloidal sub- stances has created the desire to render visible finer and finer particles. The true nature of such substances in very finely divided state was forecasted by Faraday in his work on gold ruby glass and colloidal gold solutions. At the Royal Institution in 1856, 9 Faraday "had been led by certain con- siderations to seek experimentally for some effect on the rays of light, by bodies which when in small quantities had strong peculiar action on it, and which also could be divided into plates and particles so thin and minute as to come far within the dimensions of an undulation of light, whilst they still retained more or less of the power they had in mass. . . . When a solution of gold is placed in an atmosphere of phos- THE ULTRAMICROSCOPE 39 phorus vapour the gold is reduced, forming films that may be washed, and placed on glass without destroying their state or condition. . . . When gold wires are deflagrated by the Leyden discharge upon glass plates, extreme division into particles is effected, and deposits are produced, appearing by transmitted light, of many varieties of colour, amongst which are ruby, violet, purple, green, and grey tints. By heat many of these are changed so as to transmit chiefly ruby tints, retain- ing always the reflective character of gold. ... If a piece of clean phosphorus be placed beneath a weak gold solution, and especially if the phosphorus be a clear thick film, obtained by the evaporation of a solution of that substance in sulphide of carbon, in the course of a few hours the solution becomes coloured of a ruby tint ; and the effect goes on increasing sometimes for two or three days. At times the liquid appears clear, at other times turbid." Faraday believed " this fluid to be a mixture of a colourless, transparent liquid, with fine par- ticles of gold. By transmitted light it is of a fine ruby tint ; by reflected light, it has more or less of a brown-yellow colour. That it is merely a diffusion of fine particles is shown by two results ; the first is, that the fluid being left long enough the particles settle to the bottom ; the second is, that whilst it is coloured or turbid, if a cone of sun's rays (or that from a lamp or candle in a dark room) be thrown across the fluid by a lens, the particles are illuminated, reflect yellow light, and become visible, not as independent particles but as a cloud. Sometimes a liquid which has deposited much of its gold re- mains of a faint ruby tint, and to the ordinary observation, transparent ; but when illuminated by a cone of rays, the sus- pended particles show their presence by the opalescence, which is the result of their united action. . . . Some specimens, however, of the fluid, of a weak purple or violet colour, remain for months without any appearance of settling, so that the particles must be exceedingly divided ; still the rays of the sun or of a candle in a dark room, when collected by a lens, will manifest their presence. The highest powers of the microscope have not as yet rendered visible either the ruby or the violet particles in any of these fluids. . . . Glass is 40 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS occasionally coloured of a ruby tint by gold ; such glass, when examined by a ray of light and a lens, gives the opalescent effect described above, which indicates the presence of separate particles. It becomes a question whether the constitution of the glass and the ruby fluids described is not, as regards colour, alike. Whether the gold is in the state of the pure metal, or of a compound, has yet to be decided. It would be a point of considerable optical importance if they should prove to be metallic gold ; from the effects presented when gold wires are deflagrated by the Leyden discharge over glass, quartz, mica, vellum, and the deposits subjected to heat, pressure," etc., Faraday inclines to believe that they are pure metal. The determination of the exact structure of these particles presented itself to Zsigmondy almost fifty years later; the method of rendering them visible, inaugurated and perfected by Zsig- mondy and Siedentopf, 10 is essentially a refinement of the rough method used by Faraday himself. Whereas Faraday was enabled to recognize only the cloud of particles, Siedentopf and Zsigmondy, by elaborate illumination and the application of the microscope, succeeded in making individual particles visible. Since the original Siedentopf and Zsigmondy ultramicro- scope was brought out, many other forms of ultramicroscopes have been invented, or rather re-invented; the underlying principle of all forms of the instrument is the same ; the whole purpose of the ultramicroscope is to render the particles so self-luminous, in contrast to a dark background, that they may be seen as points of light by an ordinary microscope. In the discussion of the various forms it is necessary to differentiate the two beams of light involved, viz. : — 1. The illuminating bundle of rays. 2. The image forming bundle of rays. The incident illuminating rays are never allowed to enter the objective; the particles are rendered visible by the light which they scatter out of the main illuminating beam. This result is obtained, with varying success, in one of the four following ways : — I. Orthogonal illumination — the particles viewed by a THE ULTRAMICROSCOPE 41 microscope the axis of which is at right angles to the direction of the illuminating beam (Fig. 3). II. Oblique illumination, arranged either by the incident direction or by means of internal reflections so that no direct light enters the objective (Fig. 5). Fig. 3. III. Oblique illumination by an axial beam through a sub-stage condenser with central stop, or through a specially constructed, reflecting condenser provided with central stop (Fig. 6). IV. Axial illuminating beam with small aperture and direct light cut out by means of a stop back of the objective. I. Orthogonal Illumination. The slit ultramicroscope of Zsigmondy and Siedentopf is the outstanding example of the successful application of this form of illumination and vision. The following is Zsigmondy's description n : — " The solar rays reflected from a heliostat enter the darkened laboratory through an iris diaphragm. In the room is an optical bench about 1*5 metres long, having a metal flange, P (Fig. 4), supported on an adjustable stand G. . . . " On this, by means of carefully adjusted brackets, are mounted the individual parts of the apparatus. The light rays first enter the telescope objective Fj, having a focal length of about 10 mms., which throws an image of the sun about 1 mm. in diameter on a finely adjusted slit head S, which is modelled after Engelmann's microspectral objective. 12 By the horizontal bilateral slit, this image can be re-* duced to the range from 5 to 50 hundredths of a millimetre, as desired. The width of the slit may be read off from an 42 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS index on the drum connected with the screw. The edges limiting the height of the slit are movable horizontally, and may be placed from i/io to 2 mms. apart. A polariser N may be placed behind the slit when desired. The iris dia- phragm J shuts off any side-light which may be reflected from the edges of the slit. By means of the chisel-shaped diaphragm B one-half of the beam of light may be cut off; this is necessary when immersion objectives are used, in order to prevent objectionable reflection from the mounting of the front lens, due to the closeness of the objective. A second Fig. 4. telescope objective F 2 of 80 mm. focal length forms a quarter- size image of the slit at the focal plane E of the condenser K. By means of the microscope objective AA, used as a condenser, this picture E (reduced to £ its size) is projected into the pre- paration. It should be seen that full use is made of the aperture of the condenser system K, by controlling the illumination of its rear focal plane. The upper half of the rays emerging from the objective AA are cut out when the picture of the semi-diaphragm B, thrown by the telescope objective F 2 into the after-focal plane of AA, darkens the upper half of this plane. By means of two micrometer THE ULTRAMICROSCOPE 43 screws, working in a horizontal plane, and perpendicularly to each other, the condenser-objective may be readily centred in the optical axis of the microscope proper." By means of this apparatus the particles in a very shallow layer of the specimen — solid or liquid — are intensely illumin- ated by sunlight (or arc lantern) and none of the direct illuminating rays reach the eye. II. Simple Oblique Non-axial Illumination without Central Stop. It had been noticed by English microscopists early in the last century that the resolving power of an objective in- creased with the obliquity of the illuminating beam. By gradually increasing the obliquity it was noticed that the micro- scopic picture suddenly changed completely ; it became bright on a dark ground instead of dark on a bright ground. 13 This led to the development of the so-called dark-ground illumination. Table VI shows the chronological development of the simplest form of dark-ground illumination, adapted first to ultramicroscopic purposes by Cotton and Mouton. The object is illuminated by a beam incident in such a direction as to be out of line of the aperture of the objective, and usually totally reflected at the under side of the cover glass in order not to enter the objective. The illuminating source is brought to a focus as nearly as possible at the point of total reflection, at which point the specimen is placed ; as TABLE VI.— OBLIQUE ILLUMINATION WITHOUT CENTRAL STOPS. No. Year. I 1793 2 1838 3 1856 4 1856 5 1869 6 1877 7 1881 8 1903 9 1905 Experimenter. Dellebare. Rev. J. B. Reade. F. H. Wenham. F. H. Wenham. F. H. Wenham. J. J. Woodward. Hyde. Cotton-Mouton. O. Scarpa. Method. By system of mirrors. Single plano-convex lens. Lens, amici prism, total reflection prism. Half prism and lens. Half cylinder, lens and mirror. Same principle as in No. 2. Same principle as in No. 3. Internal reflection in glass block. Same principle as in No. 2. References. 14 15, 16, 17 15. 18, i. 15 IS, 20 15.21 15. 19 15, 22 15.23 44 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS particles are brought into the path of the light at the point of total -reflection, some of the light which they scatter passes into the microscope. As the principle involved in all these cases is the same, it will probably suffice to describe the apparatus of Cotton and Mouton. The diagram, Fig. 5 22, 24, exaggerates the relative sizes of the smaller parts of the Cotton-Mouton apparatus. A drop of the solution to be examined is enclosed beneath a thin cover glass on a microscopic slide. The plate is placed on a special block of glass, ABCD, good optical contact being made by an intervening thin layer of cedar oil, the Fig. 5. refractive index of which does not differ much from that of glass. The block ABCD (for which a Fresnel rhomb serves very well) allows the direction of a beam of light to be adjusted easily so that, after being internally reflected at the under surface CD, the succeeding internal reflection at the upper surface may be made to take place at the critical angle. The proper adjustment of the lens L and the block allows the beam to come to a focus just at the drop of the liquid. As the particles in the solution come into the path of the beam, the light striking them is now no longer totally reflected, but is scattered into the microscope. As the field of view is other- THE ULTRAMICROSCOPE 45 wise dark, the appearance is that of a dark sky filled with moving stars — the Brownian movement being at once recog- nizable. III. Oblique Illumination from Axial Beam by Means of Sub-stage Condenser with Central Stop. The forms of dark background illumination given in the above class have the disadvantage that the illuminating system is not made a simple attachment to the microscope stage. Wenham and others remedied this defect in their forms of co-axial dark-ground condenser; the various forms are in- dicated in Table VII. TABLE VII.— OBLIQUE ILLUMINATION WITH SUB-STAGE CONDENSER. No. IO Year. Experimenter. Method. References. Th. Ross. Spot lens. 15, 1. 16 II Nachet. Prism with multiple reflections. 25 12 1850 Wenham. Two Nachet prisms and lenses. 15.26 13 1850 Wenham. Hollow reflecting paraboloid and spot lens. I5> 1. 26 14 1852 Shadbolt. Annular condenser. 15, 16, 27 15 1854 Wenham. Solid paraboloid and stop. 15. 1. 28, 29 16 1855 Nobert. Truncated plano-convex lens. 15. 16 *7 1856 Wenham. Solid paraboloid and spot lens. 15, 18, 1 18 1856 Wenham. Solid truncated paraboloid. 15. 18, >■ 19 1861 Rev. J. B. Reade. Hemispherical lens with spot. 30 20 — J. Mayall. Semi-cylinder and spiral diaphragm. 1 21 1872 Wenham(Wells). Reflex illuminator. 15,31.32,33 22 1876 Nachet. Glass truncated cone. 15,34 23 1877 J. Edmunds. Solid truncated cone and revolver. 15,35 24 1877 Stephenson. Catoptric illuminator. 15,36 25 1878 J. Woodward. Truncated right-angled prism. 37 26 1879 Stephenson. Catadioptric immersion illuminator. 15,38 27 1883 Abbd Sternblende Kondensor. 28 1906 Heimstadt. Similar to No. 24. 15, 39 29 1907 Riechert. Similar to No. 22. 15, 40 3° 1907 Siedentopf. Paraboloid condenser (Nos. 18, 23). 41 3 1 1908 Ignatowski. Bispherical condenser. 42 32 1910 Siedentopf. Cardioid condenser. 43 33 igio Jentzsch. Concentric condenser. 44 It will be noticed that some of the earliest of these forms are quite identical with the most recent. Originally they were used for oblique illumination of ordinary microscopic material, and were replaced, under the advice of Abbe, by the 46 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS central stop accessory on the ordinary condenser. This con- denser afforded an easy method of varying at will the obliquity and the aperture of the illuminating beam. It was forgotten that the older forms possess the advantage of colour-free, oblique illumination and, consequently, for the special aim of dark-ground illumination, are superior to Abb6's central stop condenser. 15 In the methods of oblique illumination given under the second class (Table VI), the appearance of the object depended on the azimuth of the incident light. In order to make the illumination more uniform, Edmunds 35 arranged to have the light fall on the object from four sides. Early in his Fig. 6. work Wenham, by the use of the paraboloid, produced uniform illumination in all directions. The principle of these methods is shown in Fig. 6 (Paraboloid, Wenham-Siedentopf ). The incident light, reflected by the plane microscope mirror, has its central portion screened off, while the outer rays are brought by a series of reflections to be focussed on the object where they are internally reflected as nearly as possible at grazing incidence. As the fine particles come into the path of the light, they scatter part of the light into the microscope, as in the case described above. As in all forms of ultramicroscope, the aim here is to illuminate the particles as intensely as possible, relatively to their background. This requires (i) the aperture of the il- luminating cone of light to differ as greatly as possible from THE ULTRAMICROSCOPE 47 that of the image-forming cone, (2) the light source to be exactly focussed at the point of the specimen under observation, i.e. perfect union at a point A of the rays of the illuminat- ing pencil (Fig. 6), (3) the condenser to be free from spherical difference of magnification, i.e. fulfilment of the sine condition. 42 These ideals have led to the improvements recently suggested by Siedentopf, Ignatowski, and Jentzsch. IV. Axial Illumination with Central Stop back of the Objective. In this case the axis of the illuminating cone of light and that of the rays diffracted by the object are in the same straight line, and not inclined at a great angle to one an- other, as in the other methods. The direct illuminating rays are stopped out either by a carefully centred stop behind the objective, or by a method, suggested by Abbe, 13 by which a stop is formed by grinding flat and blackening a small central portion of the curved surface of the front lens of the objective. The portion ground away is exactly calculated to suit the aperture of the illuminating objective (condenser). This method obviates difficulties of centring and prevents decentring, while at the same time the objective may be used for observation in the ordinary way without dark-ground illumination. The difficulty which has thrown this method of dark-ground illumination into disuse, is that the central screen changes destructively the distribution of the brightness in the diffraction fringes, as pointed out by Siedentopf 46 and Jentzsch. 44 3. Limitations of the Ultramicroscope. Lord Rayleigh 46 has shown that the intensity of the light diffused from a particle, small in all dimensions in com- parison with a wave-length of light, varies directly as the quantity [$ - ■] where fi and /*' are the indices of refraction of the medium and the particle respectively. On account of this factor one 48 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS cannot set a definite limit to the smallest particle visible by- means of the ultramicroscope ; if the index of refraction of the particles is very nearly the same as that of the surround- ing liquid, they will remain invisible, no matter what the intensity of the illuminating pencil. Thus small particles of gold, silver, and copper in their colloidal mixtures are easily visible because the refractive indices of these metals are greatly different from that of the medium in which they are em- bedded, while in the case of colloidal solutions of such sub- stances as silicic acid, oxide of aluminium, and albumen, the particles are not easily visible on account of the very slight differences between the indices of refraction of these substances and that of water. 13 However great the difference between the refractive in- dices of the particles and the medium, there is a lower limit to the size of the particles which can possibly be made visible, due merely to the intensity of the illumination. In Table XVI (p. 122) is recorded the difference in size between the smallest gold particles visible to Zsigmondy t0 ' n with arc-light illumi- nation and sunlight illumination. As pointed out by Sieden- topf, 13 single molecules could be rendered visible if they could be separated sufficiently from their neighbours and illuminated intensely enough ; however, the illumination necessary in this case would have to be so strong as to be quite beyond the possibility of attainment. The smallest particle of gold observed by Zsigmondy, using sunlight illumination, was 17 x io~ 7 cm. in diameter. Keeping in mind the favourable circumstance of the large difference of index of refraction between gold and water, we may cite this as the smallest particle ever observed. BIBLIOGRAPHY. 1 Hogg, J. : "The Microscope," 15th ed. (London, Routledge), 1912. "Beck: "The Microscope," Cantor Lectures, Roy. Soc. Arts, Lon., Nov. and Dec. 1907. 3 Gordon: "Proc. Roy. Inst.'' 18, 1905-7, p. 11. 4 Lewis Wright : "English Mechanic," Sept. 7, 1894, p. 49. 5 "Jour. Roy. Mic. Soc." 1875-80. THE ULTRAMICROSCOPE 49 6 Rayleigh: "Sc. Papers," IV, p. 222; "Jour. Roy. Mic. Soc." 1903, p. 447 ; "Phil. Mag." 5, 42, 1896, p. 167. 7 Abbe" : "Jour. Roy. Mic. Soc." June, 1881, p. 388. 8 Stoney: "Jour. Roy. Mic. Soc." 1903, p. 564. 9 Faraday : " Proc. Roy. Inst." II, 1854-8, pp. 310, 444. 10 Zsigmondy : "Erkenntnis der Kolloide," 1905. 11 Zsigmondy (Alexander) : " Colloids and the Ultramicroscope," 1909. 12 Engelmann : "Zs. f. Wiss. Mikros." 5, 1888, p. 289. 13 Siedentopf : "Jour. Roy. Mic. Soc." 1903, p. 573. 14 Ch. Robin : "Traite" du Microscope," 2nd ed. (Baillie're, Paris), 1877. 1D Siedentopf: "Zs. f. Wiss. Mikros." 24, 1907, p. 382. 16 Queckett, J.: "The Microscope," 3rd ed., London (Baillie're), 18551 p. 220. 17 Goring and Pritchard : " Micrographia," London (Whittaker), 1837. 18 Wenham, F. H. : "Trans. Mic. Soc." Lon. N.S. 4, 1856, p. 55. 19 Hyde : "Jour. Roy. Mic. Soc." Lon. 1, 1881, p. 524. 20 Wenham, F. H.: " Mon. Mic. Jour." 2, 1869, p. 158. 21 Woodward, J. J. : "Trans. Roy. Mic. Soc." Lon. 18, 1877, p. 61. 22 Cotton and Mouton : " Les Ultramicroscopes et l'objets ultramicro- scopiques"; "C.R." 136, 1903, p. 1657; "Bull. Soc. Fr. Phys." i9°3, P- 54- 23 Scarpa: "Arch, di Fisiologia," 2, 1905, p. 321. 24 Burton : " Univ. of Toronto Studies" (Physics, No. 36), 1910, pp. 24-25. 26 Nachet: "C.R." 4, 24, 1847, p. 976. 26 Wenham, F. H. : "Trans. Mic. Soc." Lon. 1, 3, 1852, p. 83. 27 Shadbolt : "Trans. Mic. Soc." Lon. 1, 3, 1852, p. 152. 28 Wenham : " Quar. Jour. Mic. Sci." 2, 1854, p. 145. 29 Mayall, J. : "Jour. Roy. Mic. Soc." 2, 1879, PP- 22, 837. 30 Reade, J. B. : "Trans. Mic. Soc." Lon. N.S. 9, 1861, p. 59. 31 Wenham : "Mon. Mic. Jour." 7, 1872, p. 237. 32 Schulze: "Jour. Roy. Mic. Soc." 1, 1878, p. 45. 33 Wells : "Boston Jour, of Chem." June, 1875, p. 140. 34 Pelletan: "Le Microscope" (Masson, Paris), 1876, p. 109. 36 Edmunds, J. : "Trans. Mic. Soc." Lon. 18, 1877, p. 78; "Jour. Roy. Mic. Soc." Feb. 1879, p. 32. 36 Stephenson : " Jour. Roy. Mic. Soc." Lon. 2, 1879, P- 36- 37 Woodward, J. J. : "Jour. Roy. Mic. Soc." Lon. 2, 1, 1878, p. 246, Oct. 1879. "* 88 Carpenter : " The Microscope," 7th ed., Dallinger (London, Churchill), 1891. 39 Heimstadt : "Zs. f. Wiss. Mikros." 24, 1907, p. 233. 40 Riechert : "Osterr. Chem. Zeitung," 10, 1907, p. 5. 41 Siedentopf: "Zs. f. Wiss. Mikros." 24, 1907, p. 104. 42 Ignatowski : "Zs. f. Wiss. Mikros." 24, 1908, pp. 26, 64; 1909, p. 387. 4 50 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS 43 Siedentopf: "Ber. d. d. Phys. Ges." i, 1910, p. 6. 44 Jentzsch : "Ber. d. d. Phys. Ges." 22, 1910, p. 975. 46 Siedentopf: "Ber. d. d. Phys. Ges." 21, 1909, p. 574. 40 Rayleigh: "Sc. Papers," I, pp. 87, 104, 518; IV, p. 397; "Phil. Mag." 41, 1871, pp. 107, 274, 447 ; 12, 1881, p. 81 ; 47, 1899, p. 375- CHAPTER IV. THE BROWN IAN MOVEMENT. i. Historical. This discovery of Brown* 1 was really a development from the observations of the movements of microscopic animalcules in various liquid media. We have references to such observa- tions as far back as Leeuwenhoek (1632-1723), Stephen Gray (d. 1736), and Comte de Buffon (1707-1788). Up to 1827 many microscopic objects suspended in water had been ob- served to be in rapid motion, but this phenomenon was sup- posed to be connected always with living matter. This view was disproved by Brown's series of experiments. He began by mixing in water pollen from ripe anthers of Clarckia Pul- chella and from those of Qnagrariae CEnothera and observed that the pollen appeared as very minute spherical bodies which were in rapid motion in the liquid — a phenomenon of pollen dust already known to Needham and Gleichen. In order to prove whether or not this motion was a phase of life, Brown examined for similar action the spore dust of mosses and equiseti that had been dry for a century. Surprised to find just as lively a motion with these, he tested, in finely di- vided state in water, such inanimate substances as gums, resins, wax, coal, glass, rocks, manganese, lead, bismuth, nickel, anti- mony, arsenic, and sulphur. He found the same unique motion in every case ; his conclusions may be summed up best in his own words : — "Extremely minute particles of solid matter, whether ob- tained from organic or inorganic substances, when suspended in pure water or some other aqueous fluids, exhibit motions * An interesting reference is made to Brown's paper in George Eliot's story, '« Middlemarch," Book II, Chap. XVII. 51 4* 52 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS for which I am unable to account and which from their irregu- larity and seeming independence resemble in a remarkable degree the less rapid motions of some of the simplest animal- cules of infusions. The smallest moving particles observed, and which I have termed active molecules, appear to be spherical, or nearly so, and to be between I /20,000th and 1 /30,000th of an inch in diameter ; other particles of considerably greater and various size, and either of similar or of very different figure, also present analogous motions in like circumstances. " I have formerly stated my belief that these motions of the particles neither arose from currents in the fluid containing them, nor depended on that intestine motion which may be supposed to accompany its evaporation. " These causes of motion, however, either singly or com- bined with others — as the attractions and repulsions among the particles themselves, their unstable equilibrium in the fluid in which they are suspended, their hygrometrical or capillary ac- tion, and in some cases the disengagement of volatile matter, or minute air bubbles — have been considered by several writers as sufficiently accounting for the appearances. Some of the alleged causes here stated, with others which I have con- sidered it unnecessary to mention, are not likely to be over- looked or to deceive observers of any experience in microscopi- cal researches : and the insufficiency of the most important of those enumerated may, I think, be satisfactorily shown by means of a very simple experiment (referring to evaporation)." Although, as is indicated by the above extract, the ques- tions underlying this phenomenon are to a great extent physical in their nature, physicists do not seem to have attacked them for a great many years after Brown's work was published. About 1868, some experiments, which were in a sense a repetition of those of Brown, were reported to the Manchester Philosophical Society by Dancer 2 : the new facts which he brings out are that gamboge in water gives good results and that the smallest globules of oil in milk show the Brownian movement. At about the same time" before the same Society, Jevons 3 communicated the results of his epoch-making experiments. Briefly, his conclusions are as THE BRO WNIA N MO VEMENT 5 3 follows: (1) repeating Brown's observations with many sub- stances, he finds that the motion depends on the size of the particles, and very little, if any, on the nature of the material in the particles : (2) with powdered clay or glass, in water, the motion seems to exist parallel with the stability of the suspension: (3) pure water gives the best movement, while addition of salts usually causes its cessation : (4) the action of acids, alkalies, and salts seems to be independent of their chemical constitution : (5) ammonia and boracic acid do not affect the motion, acetic acid stops it, while sodium silicate seems to increase it : (6) albumen, dextrin, cane and grape sugar, starch and alcohol seem to have little effect, while gum- arabic increases the motion and the stability of the solution. His work on the effect of added electrolytes led Jevons to as- scribe the stability of the particles to their possession of elec- trical charges. On the continent these phenomena were being investigated by Wiener, Exner, and Schultze, who also tried to single out the cause of the motion from among the various explanations offered. A resume" of their work is to be found in the Jahres- berichte of 1867, as follows : — "Chr. Wiener instituted microscopic observations of these movements, and came to the conclusion that this trembling, irregular, unsteady motion of solid molecules, which alter their direction in the briefest fraction of time in their zig-zag course, has for its basis the continual movements, which, by virtue of their" molecular constitution, belong to fluids. He learned through his investigations that (1) the movements are not those of infusoria ; (2) the movement is not communicated to the fluid ; (3) the trembling movement is not in any way derived from the varying attraction or the collisions of the various oscillating molecules ; (4) the movement is not derived from changes in temperature; (5) the movement is not derived from evaporation. Consequently, there remained, in his opinion, nothing to account for the peculiar movements but the constitution of the fluid itself. This explanation received direct confirmation from Wiener's observation, that the speed of the movement has a certain relation to the size of the 54 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS molecule. Lately S. Exner has extended the investigations of Wiener. Exner sought to test with reference to the mole- cular motion whether or not either chemical causes or mechan- ical ones, such as pressure, vibration, and so forth, could in any way produce an acceleration or a retardation of the effect. Only by exposure to light and heat did the motion become accelerated, and then in such a manner as, in the case of gly- cerine, to give freer motion to the molecules on account of de- creasing the viscosity of the liquid. Exner also experimented on properties of fluids in which solid molecules remain sus- pended. The results of his investigation resolve themselves into the following points: (i) the liveliness of the molecular movement is heightened by light and heat, and by radiant as well as by conducted heat ; (2) one of the consequences of the molecular movement is, that the molecules, in a specifically lighter fluid, not only do not sink to the bottom, but overcome the force of gravitation to such a degree as to spread themselves equally throughout the fluid ; (3) the velocity of this scattering is influenced by light and heat. It should be mentioned here that Fr. Schultze had already stated that substances, when most finely divided, especially such as seemed under the microscope to be amorphous, and exhibited the Brownian movement, re- main suspended in pure water and in many other fluids for days, weeks, and months at a time, so that the fluid containing them presents a cloudy or at least an opalescent appearance." Wiener 4 and Exner 6 are the first to give definite figures for the velocities with which particles of various sizes move (see Table VIII). Gouy 6 extended the number of suspensions viewed and also contributed extensively to the experimental work deter- mining the cause of the motion. Reserving until later the experiments bearing on the theory of the motion, we may note here that he observed that the Brownian movement was shown by mineral and organic particles in water, salt solutions, acids, alcohols, ethers, hydrocarbons, oils and glycerine, and found that in general electrolytes added to aqueous solutions caused cessation of the movement and coagulation. As a result of his many experiments, he was driven to ascribe the motion to the thermal vibrations of the molecules of the liquid. THE BRO WNIAN MO VEMENT 5 5 Ramsay 7 and Cantoni 8 disagree with the statements of Jevons and Gouy that the velocity of the particles in aqueous solutions does not depend on the material of which the particle consists, but merely on the size of the particle. Ramsay says that the velocity depends on the size and density of the particles : he thinks that the particles in pure water do not touch one another at any time and, in fact, that they do not appear to influence one another in their motion. Spring 9 also believes that, when the particles appear to collide, they do not touch one another, as each particle in pure water is surrounded by a special liquid layer which is destroyed only by the addition of electrolytes. In fact it seems that neighbouring particles do influence one an- other (see Zsigmondy 10 ) ; this view was also put forward by Malt6zos. u The latter points out that the movement is complex, consisting of the ordinary zig-zag motion which he calls Brownian alone, a vibration about a line and a ro- tation. He also states that the general action of added electrolytes causes a retardation of the motion and gives evidence of the presence of ultramicroscopic particles in the solutions which he examined — ordinary water containing a trace of clay or highly diluted ink. The above outline brings us to the time of the invention of the ultramicroscope, which afforded most valuable infor- mation regarding the motion of the very fine and, conse- quently, fast moving ultramicroscopic particles. Recently the first reliable velocity measurements have been made, but these can best be dealt with in examining later the confirmations of the kinetic theory of the Brownian movement. 2. Samples of Solutions in which the Brownian Movement may be Observed. 1. Gamboge, as prepared by Perrin, 12 has the advantage of giving both microscopic and ultramicroscopic particles. It is made by the desiccation of the .milk secreted by a gutti- ferous plant from Indo-China. A part of the dry residue is rubbed under distilled water, in the manner of making soapy water; the gamboge dissolves giving a yellow solution con- taining spherical particles of various sizes. Or, the yellow dry 56 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS residue may be completely dissolved in alcohol, giving rise to a transparent true solution. This alcoholic solution, when poured quickly into a large excess of pure water, produces an emulsion with spherical grains. One can separate these grains by centrifuging from the alcoholic water which contains them and then dilute them in excess of pure water, a process re- sulting in an emulsion with grains of different sizes, usually of diameter less than icr 4 cm. 2. Spring 9 prepared mastic solutions in a manner anal- ogous to the preceding. 4 grams of mastic were dissolved in 100 c.cs. of alcohol; 10 c.cs. of the alcoholic solution were stirred slowly into a litre of pure water and the whole was filtered. This gives a solution with various sized particles. 3. Meade Bache 13 finds that a solution containing car- mine from cochineal gives much more brilliant particles than gamboge, or, one would gather, than mastic. It contains very brilliant microscopic particles which show much better with weak illumination than do the particles of gamboge. " With a weak aqueous solution of carmine one may see by daylight on a background of faint blue, or with artificial light on a golden background, thousands of tiny particles, bright as sparks of ruby, shimmering and performing their independent evolu- tions over the field of view." 4. Zsigmondy 10 and Svedberg 14 and others have ob- served the movement of the particles in the solutions made by the methods recorded in chapter II. 3. Velocities of Particles of Various Sizes. In Table VIII are arranged the various determinations of the velocities of particles' of various sizes in different solutions. The names of the observers are placed in chronological order and, naturally, greater weight must be accorded to the later results. The experiments of Exner, Wiener, and Ramsay were carried out before the ultramicroscope came into use and consequently deal only with particles above io -6 cm. diameter. Their measurements were made apparently with a micrometri- cally divided glass scale and watch. ^s is pointed out by Zsigmondy, the absolute motion of THE BROWNIAN MOVEMENT 57 the particles is very hard to observe directly, although dif- ferences in motion may be recognized very easily. The diffi- culties of direct observation have been overcome by the application of the cinematograph to the microscope by Victor Henri. 15 The latter made with each solution examined a series of exposures each of duration of i/320th of a second at intervals of i/20th of a second, .and was thus enabled to get very reliable results of the motion in pure solvents and also in these solvents after impurities were added. A somewhat Fig. 7. analogous photographic method has also been used by Seddig 16 in his experiments on the influence of temperature on the Brownian movement. Perrin, assisted by two of his colleagues, Chaudesaigues 17 and Dabrowski, 17 applied a new method of direct observation ; they marked on squared paper according to scale the position of a given particle at intervals of thirty seconds, tracing one particle for periods of twenty or thirty minutes. Svedberg 1 * followed a somewhat unique course in 58 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS observing the motion. A glance at Fig. 7 (V. Henri) and Fig. 8 (Perrin) shows that a particle oscillates in a haphaz- Fig. 8. ard fashion about a mean position during a short interval of time. Svedberg, by keeping a slow current of the colloidal Fig. 9. solution passing through the cell in which he was observing the particles, gave to all the particles a slow velocity of trans- THE BROWNIAN MOVEMENT 59 lation in parallel straight lines across the field of view. The effect of this motion is to give the impression that the par- ticle is describing a wavy line — so that Svedberg speaks of the amplitude (a) and wave-length (A.) of the particle. Fig. 9 (Svedberg) shows the appearance that V. Henri 18 would have observed if he had introduced Svedberg's constant velocity of translation. The time interval between the points on Henri's figure is i/20th of a second, and consequently each of Svedberg's composite curves corresponds to 1/2 second of time. Knowing the time, t, required for the impressed velocity to carry the particles the distance \, then the mean absolute velocity of the particle would be 4A/t. Perrin's objection to the acceptability of Svedberg's results seems to be well founded ; not particularly because the latter's experi- mental results are " 6 or 7 times too great," by which Perrin probably means that much greater than the results of other workers, but because of the assumption that the motion can be treated as oscillatory. Certainly some of the particles may wander continuously away to one side of Svedberg's axial line and give a correspondingly disproportionate value of the wave-length and amplitude. 19 In Table VIII are arranged all the available results giving the velocity, material, and the diameter of the particle examined, the medium, its temperature, the observer, and the method. Care must be exercised in comparing results such as we have in the above table, for the velocity found in any particular case depends on the time interval which elapses between two observations of the same particle. A glance at Figs. 7 and 8 will show that, as a result of the zig-zag motion, a particle may after a comparatively long interval return very nearly to its original position. In dealing with the verification of the kinetic theory formula, Smoluchowski 20 says : " Let us imagine that we could make two series of cinematographic pictures of a given particle, one corresponding to intervals of one second and the other to intervals of i/ioth of a second. The velocity calculated from the second series would be kJio times greater than that from the first series. This is probably 60 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS why Exner, who used a very highly perfected method, ob- tained results about twice as great as those by Wiener." TABLE VIII.— BROWNIAN MOVEMENT VELOCITIES. Observer. Material. Diameter x io B cms. Medium. Temper- ature. Velocity. xio B cms./sec. Method. f Quartz, Gamboge, IO'O Water. 18 23 - o Micrometer. Wiener 4 . Salicic Acid, [White Lead. l6'0 n 18 50 (Sulphur, Mastic, 4'° J» 21 380 Mica, Cinnabar, g-o j 21 33° Scale Exner 5 . Gamboge, Char- go i 71 510 and coal. 130 400 1 21 21 27'0 No motion Watch. Ramsay'* . *■ !4'o 1 14-0 Zsigmondy 10 . Gold. 0-06 » 20(?) t 700 '0 »> O'l , It 1 280 '0 Estimated „ 0'35 1 11 t 200 with Dust particles. 20 » No motion the eye. Svedberg 14 Platinum. 0-4 to Aceton 18 39000 »» °-5 Ethylacetate 19 28000 From wave- )i Amylacetate 18 2200 form under ,, n-Pro. Alco. 20 2goo'o impressed i» Water. 20 3200-0 velocity. Henri 15 . Rubber Emulsion. io-o Water. 17 124-0 Cinematograph Chaudesaigues 1 ' Gamboge. 4'5 »l 20 + 2-4 Observations n 2'13 11 20 t3-4 made on single »» 2'13 Sugar Sol'n. # t 3 -l particles at i) 2-13 n * ti'5 intervals of Perrin and Dab- 30 sees. rowski " Mastic. lO'OO Water. 20(?) i'55 t These results calculated from rather indefinite data. * Viscosity of first solution 1-2 times that of water at same temperature. Viscosity of the second solution 4-6 times that of water at the same temperature. 4. Suggested Causes of the Brownian Movement. As is shown by the quoted summary of Brown's work, the question uppermost in his mind was the cause of the motions which he observed ; the same quest has engaged all the workers on this phenomenon up to the present. As a result of the work of Brown and his successors we may discard a number of theories which have been suggested. While the whole mechanism of this movement is by no means clear, we believe that the shocks of the molecules of the liquid medium are the main cause ; still it is hard to imagine that the particles are not affected by such factors as surface tension and electrical forces. Before dealing with the treatment from THE BRO WNIAN MO VEMENT 6 1 the point of view of the kinetic theory, we may enumerate the other theories, some of which have been definitely dis- carded. i. The motion is not due to infusoria. — This proposition dif- ferentiates the experiments of Brown from those of his pre- decessors : he found that the motion exists with such inanimate objects as resins, glass, rocks, and various metals. This point is also dwelt on by Wiener who observed the motion in particles of finely divided quartz after it had been heated to a temperature sufficiently high to destroy all life. 2. The motion is not due to such external agencies as mechanical vibrations from surrounding bodies, or incident light and heat. — Wiener, Exner, and Gouy all record experiments which show that the motion is not due to mechanical vibrations. The first named observed a sample of sol for twelve days but was unable to detect any change in the motion, while Gouy placed a sample in a cellar completely free from vibration and still found no change. It is doubtful whether the effect of external vibrations' would have even a secondary effect on the particles of a drop of liquid such as was usually examined under the microscope. Wiener believed the motion was caused primarily by the light and heat-waves passing through the medium, because the particles which he examined were of dimensions about the same as the wave-length of the red light of the spectrum. On examining further into this phase of the question, Exner found that the motion was affected to some extent by the incident light and heat but not sufficiently to account for the whole motion. For example, using sunlight, first with the heat rays shut off by a liquid cell, and secondly with the heat rays allowed to pass freely, the ratio of the rates of motion of the particles was 8 -25 : 1 1 -5. Exner showed that this difference was due merely to a change of temperature of the medium, as the velocity of any particle at a given temperature above the initial temperature was the same whether the heat was conveyed to the liquid by conduc- tion or by radiation. Taking Exner's numbers for the velocities of certain particles -at 20° and 71°, the difference may be completely accounted for by the change in the 62 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS viscosity of the liquid. Gouy maintained a sample of sol in a constant temperature bath without noticing any change, show- ing that the motion is not due to temperature changes. Exner, Gouy, and Meade Bache each exposed samples to light of various wave-lengths and intensities and found little or no change in the movement; Bache kept a sample in the dark for a long period and still the motion persisted. Zsigmondy arranged the light cone so that it could be moved quickly from one region of the liquid to another but found the motion just as lively in one place as in the other. 3. The motion is not due to convection currents or to disturb- ances induced by evaporation of the liquid. — Regarding the former of these two causes, Exner points out that the motion of neighbouring particles is not what would be expected if they were moved along by convection currents; even the motion of two neighbouring particles appears to be utterly haphazard. Varying the intensity of the heat rays allowed to fall upon the solution does not give any startling change in the motion, and Gouy found that the motion persists even under constant temperature conditions. Under a uniform temperature of 4" C, at which point the convection currents in an aqueous solution should be at a minimum, Bache found very little difference in the motion. Gouy also points out that in such a small space as that in a droplet 1/10 of a mm. in depth the convection currents should be enormously re- duced : still the motion is apparently independent of the volume of liquid under examination. To show that evaporation has no effect on the motion, Brown shook up some of an aqueous solution in oil so as to obtain, distributed through an oily medium, small drops of water containing the fine particles ; although evaporation was thus prevented, the particles in the aqueous drops possessed the customary motion. By preventing the evaporation of the liquid under examination by hermetically sealing it, this possible cause was shown by Wiener, Bache, and Cantoni, to have no effect. Cantoni observed one sealed sample at in- tervals during a whole year but was unable to observe any change. Evaporation promoted artificially was shown by Wiener to have no effect. THE BRO WN1AN MO VEMENT 63 With the causes enumerated above, we eliminate all effects which have to do with the liquid as a whole, and are now confined to the consideration of the mutual actions of the particles themselves, and the more intimate relation between the particles and the molecules of the liquid medium. 4. Influence of the gases absorbed by the particles. — It is a phenomenon of common observation by mineralogists that the small bubbles of gas contained in liquids enclosed in spaces in certain minerals, are in constant motion. Gouy 6 quotes from de Lapparent's "Trait6 de Geologie," p. 549, as follows: " The mobile bubbles, or libelles, are the distinctive char- acteristics of the ' inclusions liquides ' . . . ; whenever the dimensions of the libelles are below 0002 mm., we observe that they are subject to a constant quivering motion, quite analogous to the motion of corpuscles known as the Brownian movement. The quivering of the libelles appears to be com- pletely independent of external circumstances, such as the rigidity of the supports and temperature variations." The explanation, given by Carbonnelli and Thirion, 21 for the motion of these libelles, is founded on a supposed incessant interchange between the molecules of vapour in the libelle and those of the liquid surrounding the libelle. Mahizos 11 imagined an analogous cause for the Brownian movement of solid particles — an incessant interchange between the gaseous molecules dissolved in the liquid medium and those of the air imprisoned in small pores in the surface of the solid particles : or, again, continual evaporation of the surrounding water into, these small imprisoned air-bubbles and condensation of the vapour molecules into liquid. However, Malt6zos disproved this himself, because, after boiling a solution for an hour to drive off the gases, sealing it, and then allowing it to cool, not in contact with the air, he found the motion as lively as ever. 5. Influence of gravitational, electrical, and magnetic forces between the particles. — The decision with regard to these mutual actions of the particles depends to a great extent on their apparent motions in respect to each other. Wiener con- cluded that the collisions of one particle with others could have little effect because diluting the solution made no change 64 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS in the motion. However, Zsigmondy says " that the particles appear to influence each other and that for the most part the activity of the motion of gold particles is somewhat decreased by the dilution of the gold solution". Ramsay believed that the particles did not influence one another. Direct observa- tion will justify the conclusion that the motion is not funda- mentally due to the collision of the particles. The appearance is very much in accordance with Spring's suggestion, viz. : " It is to be remarked that when two droplets (of gamboge emul- sion) collide they rebound without coming into contact ; there must be, then, surrounding each droplet, an adherent liquid layer which prevents contact at the moment of collision. That the cause of the motion lies in the electrical forces acting between the particles was first suggested to Jevons by the influence of electrolytes in producing the coagulation of these solutions. The Brownian movement always exists when particles are in suspension, and since, as Jevons thought, only electrolytes produced a cessation of the movement and consequent coagulation, electrolytes must have some electrical effect in stopping the motion, and, therefore, the motion must be due primarily to electrical forces between the particles. It has been found almost invariably that the addition of electrolytes stops the Brownian movement. The truth of this statement is asserted by Jevons, Gouy, Ramsay, Maltezos, Bliss, 22 Spring, Zsigmondy, Henri, and others ; these men worked with a large variety of colloidal solutions and tried the influence of both electrolytes and non-electrolytes. Jevons mentions that sodium silicate increases the movement, ammonia or boracic acid does not affect the motion or cause coagu- lation, while acetic acid . produces precipitation, although it is a weak electrolyte. Testing cinematographically the action of various substances on rubber emulsion, Henri found that the Brownian movement is retarded by the addition of a coagulative reagent before the phenomena of coagulation appear ; acetic acid, which has an especially keen coagulant effect on this rubber emulsion, produced retardation before coagulation ; alcohol acts similarly ; the addition of urea, which does not coagulate the solution, has no effect on the motion THE BROWNIAN MOVEMENT 65 of the particles. Bliss records that the addition of extremely small traces of alkalies to suspensions of clay and finely divided sand accelerates the Brownian movement, but with increasing doses the movement is retarded : the addition of acids and neutral salts always causes flocculation. Maltizos holds that we get different appearances under different circum- stances ; in some cases the particles unite to form large masses and the Brownian movement ceases at once, while in other cases the particles increase in size slightly and the motion persists. Svedberg alone maintains that the Brownian move- ment is independent of the electrical charge. In his method of impressing a velocity on the particles, he found that the am- plitude of a silver particle was independent of the direction of its cataphoresis, which can be changed by the addition of salts, e.g. aluminium sulphate. According to Smoluchowski 23 electrical forces between the particles " would be able to produce a certain grouping of the particles, but not a continuous motion ''. While this objection would hold for a system of particles held in a state of equili- brium, it seems hardly justifiable when applied to a liquid medium, because there always would be influences at work tending to disturb the particles, so that the system would be striving towards, but never attaining to, an equilibrium state of rest. At any rate, the motion resulting from such a state of affairs would show a much more intimate interaction between the suspended particles than is apparent to the eye. It seems justifiable in view of all the evidence to as- sume that the charge on the particle exerts some influence in keeping the particles in a finely divided state, while it is prob- ably only rarely that the electrical forces can intervene to alter the motion of the particle. The cessation of the Brownian movement, when it takes place, is due not to the addition of impurity to the liquid, per se, but merely to the impossibility of the forces at play making a visible effect on the large masses produced in flocculation. In the process of flocculation the particles coalesce gradually and, if the growth is not too rapid, the alteration in the Brownian movement may be ap- parent, as in Henri's results. 5 66 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS Under the belief that electrical forces might be the cause of the motion, Gouy 6 and Bache 2i examined the effect when the solution under observation was exposed to a strong magnetic field but they found no change. Of course this does not apply to the action of a magnetic field on various iron solu- tions (see Cotton and Mouton 26 ). 6. The influence of surface tension. — In the production of the Brownian movement there is experimental evidence of several contributing causes, each bearing its part in the action. While the majority of the workers, from Brown onward, have hinted that the cause lies in the molecular motions in the liquids, there have been other suggestions strongly supported, as, e.g, electrical forces (Jevons) and surface tension (Maltizos). I know of no valid reason for maintaining that these two forces have not a very intimate relation to the Brownian movement : on the other hand, there appears to be insurmountable diffi- culty in proving that these forces, either alone or combined, would cause the motion. One undisputed property of the Brownian movement is that, for a given solution, the motion varies inversely as the size of the particles; io _4 cm. seems to be the maximum di- ameter of a particle showing the motion. There are really two conditions for the maintenance of the Brownian move- ment : in the first place, the particles must be kept less than a certain size in order to have a motion visible to us, and in order to keep the suspended matter from sinking to the bottom of the containing vessel ; in the second place, the particles must be made to move. Taking the experiments as a whole, we may ascribe the regulation of the size of the particle to surface tension effects, influenced, as they must be, by the electrical charges on the particles ; and to the kinetic theory we must look for the explanation of the motive power necessary to give the particles their curious random paths. The r61e of surface tension in deciding whether small particles will unite to form larger ones or still further sub- divide, is definitely laid down in two laws stated by Fucks 26 :— I. If the molecules of the liquid are attracted more strongly THE BRO WNIAN MO VEMENT 67 by those of the solid than they are by neighbouring molecules of the liquid or than the molecules of the solid attract one another, the potential energy will be a minimum when each particle of solid is surrounded by a shell of liquid of thickness equal to the radius of molecular forces. The two particles will then repel each other if brought closer together than twice this distance. 2. If either of the forces, solid-solid or liquid-liquid, is greater than the force solid-liquid, the potential energy will be least when the two particles are made to approach as closely as possible. They will then attract each other. Such facts as these are undoubtedly of importance in regulating the size of the particles. We have unmistakable evidence in the work of Jevons, Malt6zos, Bliss, and Henri, that certain substances added to colloidal solutions have the effect of producing finer subdivision of the suspended particles and more rapid Brownian move- ment. The influence of the electrical charge relative to the surface tension has been developed by Bredig, 27 and it is quite apparent that we have here tremendous forces capable of altering the sizes of the particles. On the other hand, to establish the proposition that the motion is caused by surface tension, leads to hypotheses so artificial as to be untenable. In attempting to do this, Maltezos sums up the forces acting on the particles as follows : " We have then the excess of the weight of the particle (over that of an equal volume of the liquid), the hydrodynamic forces, and the forces of internal friction of the liquid : these two latter do not remain invariable during the continuance of the motion inasmuch as they de- pend on the velocity and the surface of the particle. These, forces all tend to retard the Brownian movement. The surface tension (between the particle and liquid) being the same all round the particle, its effect will be zero, except in one of the following cases : (1) when there are traces of foreign matter about the particle; (2) when there are pores in the surface filled with gas, or with the vapour of the liquid ; (3) if near the particle the liquid is not pure." In a later paper Maltizos pins his faith to the last of these conditions. 68 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS Mensbrugghe 28 suggests a similar explanation from the sup- posed analogy of the action of small pieces of camphor on the surface of water. However, as Smoluchowski 23 points out, any explanation which postulates the existence of the unequal distribution of impurities, assumes tacitly that a state of equili- brium should be reached eventually, at which time the motion would cease. This explanation is consequently put out of court by the unchangeableness of the movements observed throughout long intervals of time. 5. The Kinetic Theory of the Brownian Movement. 1. Development of the theoretical formula. — Although nearly every observer of the Brownian movement has ascribed it to the molecular action of the liquid, it is only of recent years that this theory of the motion has been given mathematical form. Smoluchowski, 23 Einstein, 29 and Langevin 30 have attacked the problem by independent avenues and have been led to practi- cally the same formula, which gives the relation between the distance moved by a particle in a certain time, the radius of the particle, the temperature and viscosity of the liquid, and the duration of the observation. A kinetic theory of this motion was first stated definitely by Wiener, 4 and Exner, 5 and later by Clausius. Afterwards Gouy * wrote " the Brownian movement, of all physical phenomena, shows us visibly that there is a constant state of internal agitation in liquids, even in the absence of all external causes " — a statement by which he replaces the dictum of Maxwell that " under the most powerful microscopes bodies show the most perfect repose ". Maltezos n quotes from a lecture by Boussinesq : " The whole of a liquid is at a certain definite temperature and not at absolute zero. It is necessary that the thermal agitation should reach a given value in order that the bodies may become liquid, when the molecular vibrations shall have reached an amplitude sufficient to disengage the mole- cules from one another. It is probable that the movement called Brownian is due to this thermal motion of the mole- cules." Regarding the same question Zsigmondy 10 wrote: "Although the causes of this remarkable phenomenon may be THE BROWNIAN MOVEMENT 69 manifold, it is the kinetic theory of fluids which appears to be of prime importance in explaining the motion, which persists uninterruptedly in the fluid for months and years ". In treating of the development of the kinetic theory of this motion one could not do better than adopt the language of Smoluchowski who gives the following direct treatment of this phase of the subject : — " The direct observation of this movement, by means of the microscope, produces an impression analogous to our im- agination of molecular motions. It is not a vibration, nor a simple progressive movement, but it is rather a trembling, or, as Gouy expresses it, a swarming. The particles pursue an irregular zig-zag course, in all directions in space, as if they were pushed here and there by accidental collisions with the mole- cules. In reality their progress is very slow in spite of their feverish activity. Many physicists have considered this pheno- menon as a visible proof of the truth of the kinetic theory. . . . " We shall study here the simplest kinetic theory ; we shall assume that what we see in this motion is the result of ac- cidental collisions between the particles and the molecules of the liquid. One qbjection often considered as fatal to this theory was first raised by Nageli. He shows that the velocity transmitted to a spherical particle of diameter CVO03 mm. by collision with one molecule of hydrogen is only 2 x 10 ~ 6 mm. per second, which would not be visible in the microscope ; in addition, the shocks received on the various sides of the particle would annul each other and give no perceptible result. "This conclusion is comparable to that error which one makes who pursues a game of chance, if one expects never to have a loss or a gain more than the simple wager. One knows that, in general, the chances do not balance exactly and that the amount of the sum lost or gained increases with the number of plays. We have in the problem before us to discuss the excess in the number of shocks given to a particle by the mole- cules in a certain direction. Now we have the simple result that the velocity transmitted to a particle of mass, M, in repose, by a direct collision with a molecule of mass, m, which is moving with a velocity, c, will be : C = mcjM. which is of the 70 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS order given by Nageli : and further the absolute value along a fixed direction, X, will be still smaller. But it is necessary to consider that the particle M suffers more than io 16 collisions per second in a gas and more than io 20 in a liquid, of which the effect will be annulled in general : but there will always be an excess, + or - , of io 8 or io 10 collisions, by virtue of which the particle will attain a velocity of from io to iooo cms. per second in the direction of X ( + or - ). " This proves that the objection of Nageli is not justified, but the final result, on the other hand, is not exact. For (a) the absolute value of the change in the velocity of M will not be the same for each collision, but will depend on the absolute value of C at the time, and (b) the probability of collisions re- tarding will be greater than that of collisions accelerating for large values of C. These two factors oppose an unlimited in- crease in the value of C : the final result which one can readily foretell for the kinetic theory is that the mean kinetic energy of translatory motion of M will become equal to the mean kinetic energy of a molecule. For the equalization of this value is precisely the characteristic condition of the thermal equilibrium of bodies, according to the theory of Boltzmann and Maxwell. In the same way we conclude that the particles play the rdle of highly polyatomic molecules of some dissolved substance, and that they would consequently have the same kinetic energy as a molecule of a gas at the temperature of the medium. Then one can calculate the value of C according to the ordinary formula of the gas theory C-cJ^fW . . . . (i) which for a particle of diameter equal to crooi mm. and a density I, gives for C, 0*4 cm. per sec. How are we to re- concile this result with the observed values, which are of the order of 3 x io~ 4 cm. per sec. ? This obstacle seems at first sight a serious matter for the kinetic theory. However, the ex- planation is very simple. It would be impossible to follow the movement of such a particle if it were endowed with a velocity of 04 cm. per sec, for in a microscope of magnification 500 it would be moving with a velocity of 2 metres per sec. " That which we see is the mean position of the particle, THE BROWNIAN MOVEMENT 71 pushed io, 20 times per second with this velocity, each time in a different direction. Its centre describes a capricious, zig- zag path, composed of straight pieces each very small in com- parison with the dimensions of the particle. Its displacement is visible only when the geometrical sum of its paths is raised to an appreciable value. In addition there is the minor cor- rection that it is not the movement in space we observe but the projection of this movement on a plane ; consequently, we shall have to multiply observed results by 4/77." Smoluchowski then proceeds to determine the mean dis- tance, T) x , traversed in one second by a spherical particle of mass M under the influence of n collisions with molecules each of mass m. What he really calculates is the square root of the mean square of the distance, but, as he points out, the numerical difference is small and may be left out of consideration. There are two main cases, according as the radius, a, of the particle is (1) small compared with the mean free path, X, of the mole- cule of the medium, or (2) large compared with the value of X ; the latter is the case in point for the Brownian movement in liquids. The rigid treatment of the first case leads to the following equation : — D *=T -Jn- ■ ■ ■ (2) where c is, as above, the mean velocity of the molecules of the medium. This leads to the rather surprising result that the value of D^. does not depend on the mass of the particle, but only on the nature of the medium and the number of collision per second. The essential assumption made in deducing the above formula is that one may neglect the reaction of the movement of the sphere M on the distribution of the velocities of the neighbouring molecules. Then the collisions with M will be independent, accidental events, and the curvature of the path which M traverses will be, with equal probability, in any plane whatever, determined by the instantaneous direction of the movement of M. When we come to deal with the second case, in which a is comparable with X, the shocks of the 72 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS molecules against M will no longer be distributed with equal probability in all directions, since layers of the liquid con- tiguous to the sphere will participate in the motion — a circumstance which will have the effect of preventing abrupt changes in the direction of motion of M and, consequently, the effect of increasing the value of D x . This circumstance led Smoluchowski to use a second method of attacking the problem — a method not so exact as the former, but simpler. "Suppose a particle, M, launched in a medium with an initial velocity C ; it will suffer retardation of movement (of the resolved part of the velocity parallel to the original direction) according to the formula v = C.e-' 1 * where t is equal to the mass of the particle divided by the co- efficient of resistance, or M/S. But the kinetic energy of the centre of gravity of the particle will not diminish if C has the value given in (i). The sphere loses its original velocity but in return gains velocity normal to that direction, so that the resultant velocity does not change. "We may regard the time of relaxation, t, as a measure of the continuance of rectilineal motion, and the paths r . C = MC/S, as a measure of the rectilineal path. The movement of M can then be expressed as the movement of a gaseous molecule, which travels out from its initial position in a zig-zag fashion, its path being composed of short, straight parts of length equal to the apparent mean free path. "The mean distance attained in time, t sees., by such a molecule, is given by the gas theory as H M = \Jnt=r .C. JnTt^CjVTi^C . Jr^.t cj m . I . . gr . t since t = - . (3) b n This calculation is not exact in all points but the order of the result is true." Applying this formula to the case of a particle moving in a rare gas and reckoning S by means of the gas theory, Smolu- chowski finds that in l second THE BRO WNIAN MO VEMENT 73 D,-,.^ .... (4) g If this value of D is multiplied by the numerical factor — -=■ we get the value given by the exact theory (2). This then may be treated as a modifying factor in a result obtained by the use of equation (3), and we have given as the general equation D = Jl> ■ • .8) 3x/3 In the case of a small sphere moving in a liquid, we have S given by Stokes' law, viz. : S = 6-rrrjav. The displacement, D^, described by M becomes D 2 = 32 A«£ (6) 27 3-ima The motion considered above is that parallel to one particular direction and, since the kinetic energy of a molecule due to its motion parallel to a given direction is RT/2N, mi? = RT/N. Substituting in the above equation we have finally 2 = 3 _2 RT^ 27 N 37r V a WJ Independently of Smoluchowski, Einstein 29 developed a similar formula for the motion of small spheres suspended in a liquid medium ; he applied the laws of osmotic pressure to particles and evaluated their diffusion in the medium. The diffusion coefficient, d, of a material suspended in the form of small spheres in a liquid is given by ^=¥-^- .... (8) Again, the mean value of the displacement, D I( of a sphere along the X-axis in time t is D, = J2d. t . . . (9) From (8) and (9) we get D,"-|.Iil. . . .(10) 74 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS This formula differs from Smoluchowski's by the dropping of the numerical factor 32/27. More recently, Langevin 30 offered a very simple solution of the same problem, and obtained the same result as Einstein. If a particle is moving with a component velocity parallel to the axis of X equal to £ = dxjdt, under the action of a force X due to molecular shocks, it will suffer a resistance given by 6TTfja^, according to Stokes' law. The equation of motion will then be d 2 x , dx , T The force X is varying and is indifferently positive and negative, but maintains the motion which would otherwise be stopped by the viscosity of the liquid. Multiplying through by x, the equation may be written m d\x 2 ) „„ dx 2 v Taking the mean of a large number of identical particles, the term in X.z disappears on account of the variation in X : dx 1 writing — = «, we obtain m da F — . -=- + ^TTTjas = mt'. 2 dt Now \m% 1 is the average kinetic energy of a particle, due to the component of its velocity parallel to the axis of X. On the kinetic explanation of the Brownian movement, this energy is equal to that of a single molecule of the liquid, or to that of a gaseous molecule, parallel to a given direction. 5 RT , m ds RT and _._ +3wvM -_ r The general solution of this differential equation is RT 1 ^ _ 6 j^it. ■s = — — . h L . e »> When the motion reaches a steady state THE BRO WNIAN MO VEMENT y 5 RT a = 37T»/aN from which, by integration, we get D^ from the equation D 2 = R Tt N ' 37T77« a result identical with that of Einstein. As is emphasized by Smoluchowski, we should not expect very exact correspondence between this theoretical formula and observation, for, in addition to simplification of the prob- lem mathematically, we have made two assumptions,. the im- portance of which cannot be gauged very exactly in the case of liquids, viz. : — (a) that the particles may be regarded as rigid spheres, and. (£) that the forces of surface tension need not be con- sidered. Nevertheless, the tests which have been made up to the present justify the formula as regards its dependence on temperature, time, viscosity, and the radii of the particles : while many of the exact determinations of the absolute values of D,. do not depart very much from the theoretical value. (a) Experimental verification of the theoretical formula. — a. Observed_yalues of D x . In the formula for D^, putting N, the number of molecules in a gram molecule, equal to 7 x io 23 and R = 83 x io 6 c.g.s. units, T t D/= 12-6 x io~ 18 . — : — r) . a In Table IX are arranged the calculated and observed values of D„, from some of the data given in Table VIII. In the above calculations, the values for t, the interval dur- ing which the displacement was observed, were as follows : 1 sec. for Wiener and Exner, 1/7 sec. for Zsigmondy, 1/20 sec. for Henri, and 30 sees, for Chaudesaigues. It has been pointed out already that the value of the velocity in cms. per sec. depends on the interval of time through which the particle is observed. If D, is the distance traversed in time t, then the velocity, v, in cms. per sec. will be DJt: therefore, 76 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS TABLE IX.— CALCULATED AND OBSERVED VALUES OF D3. (D*s = 12-6 x 10-18. Tt/ V a.) Name of Experimenter. Radius in cms. x 10 5 . Viscosity. Temp. Cent. Dz (calculated) in cms./sec. Xio 5 . Da: (observed) in cms./sec. X I0 6 . Wiener 4 . 5-o •0107 18 8-2 23-0 1} 8-o . '0107 18 6-5 5-0 Exner" 2 - •01 21 13-6 38-0 .1 4 - 5 •01 21 9-0 33'° >> • 4'5 •004 71 *4'3 Si-o »* 6-5 •01 21 7 - 5 27-0 Zsigmondy 10 ■°5 •01 (?) 20(?) 227-5 280-0 Henri 15 . 18 5"° •on J 7 36-0 124-0 Chaudesaigues 17 2-13 •01 (?) 20(?) *3-4 * 3 -e Perrin and Dabrowski 17 5-00 ■0I(?) 20(?) 1-56 1 "55 under given constant conditions, v 2 - t = a constant ; i. e. the smaller t, the larger will be v. Svedberg's 14 confirmation of the formula was carried out with platinum particles in various liquid media, by observations using a value of t of the order of 2 or 3 one-hundredths of a second. In Table X are arranged the values taken from Sved- berg's paper (see Perrin 19 ). TABLE X.— SVEDBERG'S RESULTS FOR PLATINUM PARTICLES. Medium. Radius in cms. X io 5 Temp. Cent. Time, t in sees. Viscosity. D*in cms. x io 5 Velocity cms./sec. XIO* icalcul.). Velocity in cms./sec. X io 5 (observed). Aceton . Ethylacetate . Amylacetate . Water . Propyl alcohol 0-25 0-25 0-25 0-25 0-25 18 19 18 20 20 0-032 0-028 0-O26 0-013 O-OOOg t •0023 •0046 •0059 •0102 •0226 14-2 9'4 8-o 4"3 2-4 444 336 308 324 266 390O 2800 2200 3200 2goo In order that a reliable comparison may be made with the results of Table IX, the velocities in Table X have been ex- pressed in cms. per sec. and the same value of N has been used as that in working out Table IX. (Svedberg took N equal to 4 x IO 23 .) The only conclusion that we can draw from these results is that the order of the displacements given by Einstein's * These results were calculated from Chaudesaigues' statement that his re- sults satisfy Einstein's formula with the value 6'4 x io 23 for N, and from a similar statement by Perrin. THE BR WNIAN MO VEMENT 7 7 formula is correct. Smoluchowski's formula gives results a little more in conformity with the observed facts than that of Einstein. (b) The influence of the viscosity of the medium and the tem- perature. — Referring to the outline of Svedberg's method of observation, given on page 58 and in Fig. 9, if we put in Einstein's formula, D* = 4A, t will be the time required for the particle to make one complete oscillation. Therefore we have (4A) —N-^a-V Now, if we treat of the same sized particles in various liquids at the same temperature, A 2 = k.-, V where k is a constant. Since, by this kinetic theory, the average kinetic energy of a particle is the same as the average kinetic energy of a mole- cule, and since the molecules of all fluids at the same tempera- ture have the same average kinetic energy, we should expect the average velocity of all the particles to be the same, provided their masses are the same, whatever the liquid in which they may be moving. Svedberg remarks that the num- bers in the last column of the above table may be taken as sensibly constant and, therefore, Einstein's formula demands that the product 17 . a should also be constant. Svedberg gives the curve, Fig. 10, showing the relation between the numbers in the fifth and sixth columns, from which we see that the demand of the formula is practically met. The objection raised on page 59 need not be urged here, as these results are merely relative and not absolute determinations as in the case of the velocity. Results of measurements made at temperatures of 20 C. and 71 C. are given by Exner and will be found in Table IX : the ratio of the values of D,. in these two cases is 1 : 1 - 6, while the ratio of the corresponding values of \ZTJt) (for water) at these two temperatures is 1 : 1 7. Seddig 16 has shown by means of a photographic method 78 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS in conjunction with the microscope, that finely divided cinna- bar in water obeys Einstein's formula, the greatest departure from the theoretical value being 6 per cent; as is the case with nearly all the results, the observed velocity exceeds the cal- culated. Seddig changed the temperature over a long range but found that the value of */T/t? was practically constant. Chaudesaigues, 17 working with an emulsion of gamboge, varied the viscosity of a solution by adding sugar. In this way he carried out observations on two solutions containing the same sized particles at the same temperature, the vis- cosities of which were in the ratio of i : 4 and found that the motion was twice as fast in the less viscous solution as it was in the solution of higher viscosity. JsebutylaUtotwl Aceton flmylaceUt Fig. 10. (c) Relation of the radius of the particles. — Table IX shows that the velocities observed are greater for the small particles than for the large ones. Chaudesaigues also tested this point by observing the velocities of particles of gam- boge with radii respectively 4-5 x io -5 cm. and 2-13 x io -6 , practically a ratio of 2:i, and found that these velocities varied inversely as the square of the radii. (This result may be calculated from Table IX.) (d) Relation of the time interval, t. — We are indebted to Chaudesaigues 17 also for a direct test of this point. He ob- served the distances described by 50 grains, each of diameter 2-13 x io -5 cm. during successive intervals of 30 sees, each THE BROWNIAN MOVEMENT 79 and obtained the following results : the particles moved over on the average 6"7» 9 '3, 1 1 '8, and 13-95 microns in 30, 60, 90, and 120 seconds. The square roots of the times are proportional to the numbers, 67, 9*46, 1 1 '6, and 13-4, giving a good con- firmation of this point. (e) The velocity independent of the material and mass of the particle. — This brings up a debatable question. Gouy 6 and Jevons 3 maintain that the motion is independent of these two circumstances, while Cantoni 8 and Ramsay 7 hold that the motion depends on the material and density of the particle. Physically, Smoluchowski explains the motion being indepen- dent of the mass by the fact that the smaller velocity which would be communicated to the particle of larger mass, M, would be counterbalanced by a greater persistency of velocity possessed by the larger particle once it is moving. When it is borne in mind that the theory deals with the particles as if they were rigid spheres, and that in reality this cannot be realized, we may expect the motion to depend to some extent on the material of the particle ; consequently we need not bring the essential truth of the theory into doubt if we do find that the material of the particle affects the movement. In fact, Zsigmondy states that the " nature of the subdivided sub- stance appears to influence the motion : for example, the ultra-microscopic dust particles of distilled water do not show an appreciable motion ". (/) The Brownian motion of rotation. — Considering the rota- tions which should be produced in the particles by the mole- cular shocks, as well as the translation, the energy of rotation of a particle will be, on the average, equal to its mean energy of translation. Einstein obtained the following equation for the mean square of the angle of rotation, d, in a time, t, relatively to an arbitrary axis : — N 47rr)a 3 Perrin 31 has made this test of the theory by observing the time of rotation of comparatively large grains of mastic (diameter 80 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS 1 3 /a). These particles could be seen in the ordinary microscope and the time of rotation was noted by the periodic appearance of certain defects in the surfaces of the particles. The difficulty of coagulation was overcome by suspending the particles in a solution of urea of the same density as the particles. The re- sults of substituting observed values of a, r\, a and t in the above formula gave a value of N equal to 6'5 x io 23 , which confirms the theory. After the foregoing rather rigorous comparison of theory and observation, we are justified in regarding the Brownian movement, in the words of Smoluchowski, "as a visible proof of the reality of our molecular and kinetic hypotheses. If we reduce the Brownian movement to a kinetic phenome- non, we have no longer to inquire for the source of the energy of the motion, since the energy dissipated by viscosity has its origin in the energy of the heat motion. Gouy remarked that this motion would be a contradiction of Carnot's principle, if one were able to concentrate the mechanical effects of the movements of the particles. In effect this would be a way of transforming heat into work, which is not practical on account of the grossness of our instruments ; but it is more interesting in that it does not seem as impossible as the pursuit of the molecules by the aid of Maxwell's demons." 23 6. Perrin's Law of the Distribution of Particles in a Colloidal Solution. The work of Perrin and his collaborators on the ex- perimental and theoretical application of the results of the kinetic theory to colloidal solutions is probably the most com- plete exposition of this most interesting phase of modern work. 32 In the course of the work Perrin shows that we should expect a law of distribution of the particles in a colloidal suspension analogous to that regulating the dis- tribution of the molecules of the air in the atmosphere. His fundamental assumption is that the colloidal particle may be treated as a large molecule so that the mean kinetic energy of the particle in a state of equilibrium of the solution may be THE BRO WNIAN MO VEMENT 8 1 taken equal to the mean kinetic energy of a molecule of the medium. Suppose we have a uniform emulsion in equilibrium in a vertical cylinder of cross-section s. The state of a thin section of the liquid comprised between the levels h and h + dh would not be changed if the section be enclosed between two pistons permeable to the water molecules but impermeable to the granules themselves. On each of these pistons there would be an osmotic pressure due to the bombardment by the granules which they enclose. If the emulsion is- dilute, this osmotic pressure may be calculated in a manner similar to that employed in the case of dilute solutions, according to which, if at a height h there are n grains per unit volume, the osmotic pressure, P, will be -=^r- . n. Similarly at a height RT h + dh the value of the osmotic pressure will be -^=- . (n + dn). Now since the granules in the section do not fall, there must be equilibrium between all the forces acting on them, viz. (i) the difference in the osmotic pressures at h and h + dh, (2) the total weight of the granules, and (3) the buoyant force due to the liquid. If V = the volume of each granule, d = the density of the granule, w = the density of the intergranular liquid, the above conditions of equilibrium give us the following equation : — RT s . -=^- .dn - n . s . V(d - w)g . dh. Integrating from depth h to h, we have ~N~ ' log n = V ^ ~ V * )8 ' ^ " k ^ where « and n are the values n at depths h and h. This equation shows that the concentration of the granules of a uniform emulsion should increase in an exponential fashion as a function of the depth, or, in other words, if the depths in- crease in arithmetical progression the rate of distribution of the granules should increase in geometrical progression. If one 83 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS could obtain a uniform dispersoid of any material, i.e. one in which the granules are identical in size and in shape, these granules should arrange themselves in the liquid at rest ac- cording to the same law that is obeyed by the molecules of a gas under the action of gravity. For the same reason that the air is more dense at sea-level than at the tops of mountains, the granules of the emulsion, whatever may have been their initial distribution, will reach a steady state in which the con- centration will diminish as a function of the height from the lowest layer; and indeed the law of rarefaction will be the same. Perrin tested the truth of this equation by measuring each of the quantities, u, a, and »„/» for certain values of h, using solutions of gamboge and mastic prepared by methods already recorded. (a) Determination of the density of the particles. — The density was determined in two ways, both of which depend on the fact that one can find the weight of solid substance in a given sample of solution, by evaporating the latter and weigh- ing the dry residue. The first method was simply to find the specific gravity of the dried vitreous mass in the ordinary way. In the second method the weights of water and of the emulsion required to fill a specific gravity bottle were found first; then the emulsion was evaporated and the weight of solid in the given weight of emulsion obtained. If m = the weight of water filling the bottle, tri = the weight of emulsion filling the bottle, m" = the weight of solid in weight m of emulsion, d = density of the water, \~7 - — -j — \ = volume of the solid in weight tri of solution. Therefore, the density of the solid is tri' (m m - m"\ \d 1 j " These two methods gave concordant results — 0^207 for the apparent density of gamboge, and 0-063 for that of mastic. THE BROWNIAN MOVEMENT 83 {b) Measurement of the radii of the particles. - — Three methods which gave results agreeing well among themselves were used in this determination. First, the rate of fall of the upper surface of the cloud of particles in a solution enclosed in a vertical capillary tube, and kept at a constant temperature, was measured and the radius determined from Stokes' law. As a second method, Perrin counted the number of particles in a given volume of emulsion : he noticed that in a slightly acidulated solution the granules of gamboge become fixed to the glass walls when they, approach near enough. After some hours the granules in a small volume viewed in a microscope stick to the wall and can then be counted. In the third place it was noticed that, in a slightly acid- ulated solution, the particles sometimes stick together in a string, which becomes attached to the wall : the length of this string of particles was measured and the number in it counted, from which the diameter could be deduced. Variously sized particles, from o*52/« to 0*14/4 in diameter, were measured by these means. In one case the three methods gave for the same particles, 0-45 /<,, 0-46 p, and 0*455 /m, respectively ; as a second example, the application of Stokes' law to a certain solution gave a diameter equal to 0*213 /*> while counting 11,000 granules in the second method gave 0*212 fi. Perrin uses the concordance of these results to support the hypothesis that the laws of internal friction, established for the displacements of large objects in a uniform fluid, apply to the displacements of small objects which show the Brownian movement. This is a very important point, as Stokes' law is used by Einstein, Smoluchowski, and Langevin in the de- duction of the formula for D/. ft (V) Relation between — and h. — In obtaining this relation • n Perrin viewed a cylindrical column of height 1/10 mm. under a microscope, which could be focussed at different heights in the liquid by turning the micrometer screw. When the liquid is first put in the apparatus the distribution of the particles is 84 PHYSICAL PROPERTIES OF COL'LOIDAL SOLUTIONS apparently uniform, but ir> a few minutes it is quite evident that in the lower layers the particles become more closely packed than in the upper layers. The distribution reaches a steady state, and the particles all remain in suspension ; Perrin found that the arrangement was the same at the end of fifteen days as at the end of three hours. He quotes two typical series of observations. 33 I. For gamboge particles 2-12 x io~ 5 cm. in diameter the number of particles at four different depths differing successively by 3 x io~ 3 cm. (30 p) were found to be proportional to the numbers 12 : 22'6 : 47 : 100, which numbers are almost the same as the geometrical pro- gression 1 1 -I : 23 : 48 : IOO. In all, some 13,000 particles were observed in this one experi- ment. II. For gamboge particles 5-2 x 10 " 5 cm. in diameter similar observations of depths differing by 6 x io~ 4 cm. (6 /i) gave numbers proportional to 305 : 530:940: 1880, approximately given by 280 : 528 :995 : 1880, which are in geometrical progression. If the above equation be written . log n - = P(A - A ) where P = A • Vfo - Pi )g (2) the two series of results give values for P as follows : — I. Pj = 1-5. II. P 2 = 80. As pointed out by Perrin, the concentration at a distance 9'6 x io -3 cm. from the bottom of the dish would only be 6 -jL of that at the bottom, and he adds, "hence, when permanent equilibrium has been reached, grains will hardly ever be found in the higher layers of such preparations ". It is interesting to note that the concentration drops to half value in about -03 mm. difference of level, whereas in the THE BROWNIAN MOVEMENT 85 atmosphere the same proportional decrease requires a difference of level of 6000 metres. Perrin tested this law for particles of gamboge of various sizes and, assisted by Dabrowski, 17 for particles of mastic of density I '063, and satisfied himself of the truth of the formula. •.:.*-. •:••;. v i v.- -; : -.••'/ Gamboge. Mastic. Fig. 11. In Fig. 11 (Perrin) are drawings of the distribution of the particles in gamboge and mastic ; in the former, the levels were at intervals of 10 /j, with particles o - 6 /a in diameter, while, in the case of the mastic, the intervals were each 12 fj, and the diameters I fi. 86 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS The evaluation of the constant N is the test which Perrin always applies to his experimental .observations. Determina- tion of the values of njn , {h - k ), T, and the radius and density of the particles enables one to get directly a value of N. Perrin 33 quotes as his best probable value of N, 68"2 x 10. , 22 7. Limitations of Perrin's Distribution Law. Perrin's experiments were carried out on gamboge particles which were large compared with the particles of ordinary colloidal solutions and observations were confined to samples of these gamboge suspensions of very small depth. " Successful observations with the emulsions I have used cannot be made through heights of several centimetres or even millimetres : heights of less than a tenth of a millimetre only are suit- able." 33 Whether so intended by Perrin or not, this formula has been taken to hold for all colloidal solutions and for all depths. A little consideration will contradict the possibility of such an extension of Perrin's work. For example, in a silver colloidal solution worked with by the author (p. 125), the value of P in the above formula would be given by substituting as follows in (2) : — RT u -^j- = approx. 4 x 10 Pi- P2 = 9"5 V = 22 x io -15 g ■= 980 . \ P = approx. 5000. The ratio of the concentrations at any two levels one cm. apart would be given by the equation log -* = 5 000, which is a result quite out of all reason to one familiar with such solutions. If there is any remarkable variation in the distribution of the particles in an ordinary colloidal solution, it should be shown by allowing the solution to stand in a long vertical tube for some time. In a paper by Burton and Bishop Si results of such tests THE BRO WNIAN MO VEMENT 87 are given which show that the concentration at different heights in colloidal solutions is practically constant, and that, certainly for distances of the order of some centimetres, the distribution demanded by Perrin's law does not hold. That the concentration of such solutions tends to become uniform in any given sample and to reach a maximum for various samples of the same colloid has been shown experimentally, and these facts point to the existence of some interaction between the particles which determines how close they can be to one another and still be in equilibrium (see Bancroft 36 ). In his first paper on electrically prepared colloidal solutions, Bredig 86 reports sols of the following concentrations in milli- grams per 100 ccs.: platinum, 20; gold, 14; iridium, 7. With many similar sols of platinum, gold, silver, and copper which the author has prepared at various times the con- centration has invariably been in the neighbourhood of 10 mgms. per 100 ccs. Zsigmondy 37 notes that such limiting concentrations are reached in the production of platinum and gold sols by many different methods, and the work of Schulze 38 on arsenious and antimony sulphide sols indicates a limiting concentration for these solutions under given conditions of preparation. The uniformity of these results points to some cause limiting the amount of material which a given liquid will retain in the colloidal state. A large volume of silver colloidal solution of known concentration was evaporated over sulphuric acid and calcium chloride by the author, 39 so as to reduce its volume successively to $, \, and i of the original volume, and the concentration of the silver measured at various stages in the operation. The numbers obtained showed that the con- centration tended to an upper limit at about 14 mgms. per 100 ccs. Perrin deduced his distribution equation on the basis of the simple kinetic theory, which leaves out of consideration any mutual action of the particles themselves. Since these particles bear like charges they will repel one another; in fact, long continued observation of such particles by means of the ultramicroscope does not show collisions taking place 88 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS between the particles at all. In introducing a correcting term in Perrin's equation to take account of this electrical repulsion, we have to calculate the electrical force on the particles in the layer dh in thickness due to the rest of the solution. Various approximations to the evaluation of this force suggest that it will be of the form k . n . e per unit charge in the layer dh, where k may be taken as a constant, at any rate for regions near the surface, and e is the charge in electrostatic units on each particle. Consequently the total force on the layer of particles dh will be (k . n i . e) . (n . e . s . dh) or k . s . n 2 . e 2 . dh. A term of this form may be taken to represent the excess electrical repulsion of all the particles below dh over that due to those above dh. Perrin's equation then becomes — s .JQ.dtt + i.s. n 2 e 2 dh = n . V . s (d - w) . g . dh. Writing this in the form : A . dn = (C« - B« 2 ) . dh, where A = ^, B = ke> and C = V . (d - w) .g, and solving, we get n given by the equation — C- n = ! B + K*~ in which K = - . In this equation for n, for large values of h, the value of c, K . £~a is small and can be neglected. This value of h will be fixed by the values of £, calculation of which for ordinary -~h colloidal solutions shows that the value of e" A becomes negligible at a short distance below the surface. At such a distance the value of n becomes constant, as given in the above experiments, and of value given by _ C _ \'(d - w)g M ~B k.e> where k is a constant. We see that the determining factor in fixing the distribution of the particles is the charge borne by the particles, and further, the less the charge the greater the THE BROWNIAN MOVEMENT 89 concentration of the particles — a circumstance in agreement with the properties of known colloidal sols. In the region near the surface where the distribution is not uniform, we have to consider the relative value of B and K ; although we do not know all the quantities involved, it is quite possible that K may be large compared with B. Since, when h is very small, e * approaches unity, if K is large compared with B, then K = - and the equation for n becomes — which is in the form of Perrin's equation, but is applicable for only very small values of h. The above limitation introduced into Perrin's original formula does not at all invalidate his calculations for the range over which he observed the distribution, nor does it call in question his determination of the value of the constant N. 8. Brownian Movement in Gases. It was pointed out first by Smoluchowski 23 that we should expect to have the Brownian movement in gases as well as in liquids, and he quotes from Bodaszewski 40 and O. Lehmann 41 references to the dancing movements executed by the particles of fumes of ammonium chloride, acids, phosphorus, etc., which they compared to the Brownian move- ment in liquids and interpreted as molecular movements. The formulae of Smoluchowski and Einstein, given in section 5 (equations 7 and 10), are, in accordance with their proof, true whenever Stokes' law is applicable (vide Zeleny and McKeehan, 42 Perrin, 19 Millikan, 43 and Lamb 44 ). This law probably holds, approximately at least, for the smallest particles visible in the ultramicroscope ; for liquids this will be true independently of the pressure, but for gases the truth of the statement depends on \, i.e. on the pressure of the gas. Smoluchowski points out that, when the ratio of \ : a be- comes very large, the law of Stokes no longer holds, and the go PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS resistance to the motion of the particles must be determined by another method (Boltzman 45 ) ; formula 4, p. 73, then applies. In the motions in gases to which alone this formula applies, it may be used either for extremely small particles or for larger particles if the gas pressure is very much reduced. Ehrenhaft 46 was the first to carry out direct measurements on the Brownian movement of particles in gases. He found that, as theory predicts, there is a much livelier motion in gases than in liquids ; at the same time the action of gravity in causing vertical descent of the particles is also much more apparent in gases than it is in liquids. For comparatively large particles in the smoke of cigars and cigarettes and in the fumes of ammonium chloride, he observed an undoubted zig-zag Brownian movement, while with smaller particles obtained by a spark discharge between zinc, platinum, or silver electrodes, he found the motion very rapid. Ehrenhaft concludes that he has " proved without a doubt the existence of a motion in gases completely analogous to the Brownian movement in liquids ". As was predicted by Smoluchowski, it is more difficult to re- cognize this motion in gases on account of disturbing convection currents and the action of gravity. For the heavier particles, the velocity due. to the force of gravity completely overshadows that due to the molecular shocks, while with the very small particles the opposite is the case. Table XII gives the velocities impressed by molecular shocks and by the force of gravitation, respectively, on silver particles of various sizes (density 10-5). TABLE XII.— BROWNIAN MOVEMENT IN GASES. Radius of the particles in cms. Velocity in cms. per sec. due to molecular shocks. Velocity in cms. per sec. due -to gravity. v _2 ai.it. a 9 ' n I X 10- 7 6'3 x 10- 3 12 X 10- 8 5 x 10- 7 2'8 x 10- 3 3 x 10- 6 1 X 10- B 2'0 X I0~ s 12 X 10 -" 5 x 10- 6 8-g x i -4 3 x io-« I X io- s 6 - 3 x 10- 4 12 X IO- 4 5 x 10- 5 2-8 x 10-* 3 x 10- 2 1 x 10- 4 2"o x 10- 4 12 x 10- 2 For air, 77 = 1 9x10"' (Poynting an d Thomson <"). THE BRO WNIAN MO VEMENT g i These numbers show that, when we reach particles having diameters of the order of the wave-length of light, the two velocities do not differ materially. As we deal with smaller particles, the velocity induced by gravity soon becomes negligible, while with particles increasing above io -5 cm. the motion due to gravity soon dominates the situation. This is in keeping with what Ehrenhaft found: "Particles, the linear dimensions of which were of the order of the size of the mean free path of a gas molecule (i x io -5 cm.), and somewhat larger particles fall in a zig-zag line, the velocity due to gravitation being greater than that due to molecular shocks. Particles which near the limit of visibility in the ultramicroscope (i x io -7 cm.) are in such lively mole- cular motion that the vertical gravitational velocity is com- pletely masked." Ehrenhaft viewed silver particles that remained in lively motion in the air of his ultramicroscopic cell for some thirty minutes. His measurements on the cigarette smoke particles gave a mean velocity of 2-5 x 10 " 3 cm. /sec, and on the smaller particles of silver, 4-6 x io~ 3 cm./sec. Much interesting work has been done • in this field by De Broglie. 48 Both Ehrenhaft and De Broglie have found that these silver particles, suspended in air, are charged and, by measuring the velocity impressed on them by a known electric field, have come to the conclusion that the charge is that of one electron. The values that they find for this charge, e, are respectively 4-6 x io -10 and 4-5 x icr 10 electrostatic units (see also Millikan 43 ). 9. Comparison of the Values of N Found in Various Ways. As we have seen, each of the formulae deduced in relation to the Brownian movement involves the quantity N, the number of molecules in one gram-molecular weight of any substance. This number is associated with the theoretical explanation of a great variety of physical phenomena ; some of these calcu- lations are collected in Table XIII, along with certain other constants depending on N. The number of molecules in 9* PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS TABLE XIII.— VALUES OF THE MOLECULAR CONSTANTS.— N, », and e. N.B. — The numbers in italics are those deduced directly from given experimental data. The other numbers are found from the two relations : N . e = zg x io ls and N = n . 224 x io 2 . Name. Method. Nx 10-22 « X IO- 19 e x ioio Maxwell . Mean free path and density of liquid (Mercury). 45 2'0 6-5 Maxwell . Kinetic theory of gases. 42-7 i-g 6-8 Clausius-Mosotti Dielectricconstantofa gas. 200 9"o 1 '4 Van der Waals . Value of " b " — oxygen and nitrogen. 45 2 - 6-5 — Argon. f62 + 27 t 4 -6 7 Meyer General results of kinetic theory. 138 6-1 2 1 Einstein- Perrin . Diffusion coefficient. 40-90 i - 8-4 - o 7-2-3-2 Rayleigh-Kelvin Blue colour of the sky. 54-9 2 "5 5 "2 Rayleigh-Langevin . it »» 90 4-0 3'2 Planck Distribution of energy in the spectrum of hot bodies. i6V7 t2-8 t4"6g Lorentz . Electron theory of radia- " tion, long waves. 77 3'4 3-8 Lorentz-Fery . Same as above — Fery's nos. f66 t2 - 9 + 4'39 Pellat Electrolytic ion. 60-150 27-6-6 4-8-1-9 Townsend Cloud experiment. 95 '4 4"3 3-0 J. J. Thomson . ij »> 84-3 3-8 3-4 H. A. Wilson . j» tj 93 "2 4-2 3-1 Millikan . i» )* + 62-3 t2-8 f4-65 Begeman 49 ») u f62'o t2-8 \4-67 Dewer- Rutherford . No. of rays in 1 c.c. of He. i57-3 t2"56 t5'05 Boltwood-Rutherford No. of atoms in the weight of Ra disintegrated per yr. and the atomic wt. of Ra. -f68-8 t3-i + 4-21 Rutherford-Geiger . Direct determination of the charge on a particle. t62'3 t2-8 \4-65 Regener M Same as above. f6o-5 t27 f4-79 Moreau 51 . Charge on ions in flames. t°73 t3-o \4-3 Perrin Brownian movement of rotation. 65 2-g 4 '5 Perrin- Dabrowski Brownian movement in liquids. ■\71-5 t3'2 t4"°5 Perrin Distribution of coll. particles. t68-2 + 3"2 t4'n Chaudesaigues . Brownian movement in liquids. f64 t2-g + 4 '52 Ehrenhaft Brownian movement in gases. f63-o t2-8 f4-6 De Broglie Brownian movement in gases. t6 4 -3 t2-g ■{4-5 one c.c. of a gas at normal pressure and 0° C, directly from the relation N = 22400 . n. comes THE BROWNIAN MOVEMENT 93 N is also simply connected with the charge (e) on a univalent electrolytic ion, e.g. of hydrogen. The decomposition by an electric current of one gram-molecule of hydrochloric acid requires a quantity of electricity equal to 96,550 coulombs — one faraday. Thus, one gram-atom of hydrogen (N atoms), in the state of ions carry one faraday and, therefore, in elec- trostatic units, N . e = 96,550 x 3 x io 9 = 29 x io 13 . Consequently, having given one of the three quantities N, n, or e, we may easily -determine the other two. In the results given in the table on the opposite page these two relations have been used in deducing two of the three quantities from the third. The numbers marked with a dagger are those which we have chosen as being, from an experimental point of view, of the greatest weight. Millikan, 43 in suggesting a similar set of results, discards Perrin's numbers for reasons which the latter 62 shows are due to misconceptions. The average values suggested by Rutherford, 53 Millikan, and from the above table are as follows : — TABLE XIV. Average. NX 10-22 « X IO" ls X IO 10 Rutherford Millikan From Table 62-3 6i-8 64-2 277 276 2-g 4-65 4-69 4'5I The general tendency of the results of recent electrical determinations of e has been to increase its value : 4-6 x io -10 is probably not far from the true value of e. The corresponding value of N would be 63 x io" 22 . We have then all the data required to give the other im- portant "gas constants. The kinetic energy of agitation of a molecule equals 3/2 . RT/N. The constant of molecular energy, 3/2. R/N, equals 1-98 x io -16 erg. The mass of an atom of hydrogen equals I . 008/N = I "6 x io -24 gram. The striking coincidence in the various best values of N, as shown in Table XIV, leaves little room for doubt that the 94 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS Brownian movement, in both liquids and gases, is a direct result of molecular shocks on the suspended particles ; con- versely, the kinetic theory receives the most convincing "visible proof of its fundamental truths. The vast ramification of the kinetic theory in the domain of physics can hardly be illustrated better than in the work summarized in the results recorded in Table XIII (vide Larmor 5 *). BIBLIOGRAPHY. 1 Brown: "Phil. Mag." 2, 4, 1828, p. 161. Complete Works, Ray. Soc. Pub. Vol I, 1866 ; " Pogg. Ann." 14, 1828, p. 294. 2 Dancer : "Trans. Mane. Phil. Soc." 1868, p. 162 ; 1870, p. 37 ; 1870, p. 82. 3 Jevons : "Trans. Mane. Phil. Soc." 1870, p. 78. 4 Weiner : " Pogg. Ann." 118, 1863, p. 79. 6 Exner: "Wien. Sitz-Ber. Natur-Wissen." 56, 1867, p. 116. Gouy : "Jour, de Phys." 7, 1888, p. 561 ; "C.R." 109, 1889, p. 102. 7 Ramsay : "Chem. News," 65, 1892, p. 90. 8 Cantoni : " Nuovo Cimento," 27, 1867, p. 156. 9 Spring : " Rec. Trav. Chim. Pays-Bas," 1900, p. 204. 10 Zsigmondy : "Zur Erkenntnis der Kolloide," pp. 106-m; "Colloids and the Ultramicroscope," Zsigmondy and Alexander, 1909, pp. 134-40. "Maltezos: "Ann. Chim. Phys." 7, 1, 1894, p. 559; "C.R." 121, 1895, p. 303. 13 Perrin : "Bull. Soc. Fr. Phys." 3, 1909, p. 170. 13 Bache, Meade: " Proc. Amer. Phil. Soc." 33, 1894; "Chem. News," 71, 1895, pp. 47, 83,96, 107. 14 Svedberg: "Zs. f. Electroch." 12, 1906, pp. 853, 909; "Zs. f. Phys. Chem." 71, 1910, p. 571. 16 Henri : "Bull. Soc. Fr. Phys." 4, 1908, pp. 45, 61. 16 Seddig: "Phys. Zeit." 9, July 15, 1908, p. 465; " Habilitationsschrift. Frankfort a. M." 1908. 17 Chaudesaigues : "C.R." 147, 1908, pp. 1044-1046; Dabrowski (and Perrin) : "C.R." 149, 1909, p. 477. 18 Henri : "C.R." 147, 1908, p. 62. " Perrin: "Atoms" (tr. Hammick, Constable, 1 916), p. 120. 20 Schmoluchowski : " Bull. Intern. Acad, des Sci. Cracovie," 7, July, 1906. 21 Carbonnelli and Thirion : "Rev. d. Ques. Sci. Bruxelles," 1880. 52 Bliss: "Phys. Rev." 2, 1894-1895, pp. 241, 373. 23 Schmoluchowski : " Bull Intern. Acad, des Sci. Cracovie," 7, July, 1906, pp. 577-602; "Ann. der Phys." 4, 21, 1906, pp. 756-80. THE BRO WNIAN MO VEMENT 9 5 24 Bache, Meade: " Proc. Amer. Phil. Soc." 33, 1894; "Chem. News," 71, 1895. 25 Cotton and Mouton : " Les Ultramicroscopes," Masson et Cie, Paris, 1906. a6 Fuchs : "Exner's Rep.'' 25, pp. 735-42. 27 Bredig: " Anorganische Fermente" (Leipzig), 1901. 28 Mensbrugghe : "Pogg. Ann." 138, 1869, p. 323. 29 Einstein : "Ann. der Phys." 17, 1905, p. 549 ; 19, 1906, p. 371. S0 Langevin: "C.R." 146, 1908, p. 530. 51 Perrin: "C.R." 149, 1909, p. 549. 52 Perrin: "C.R." 147, 1908, p. 530; "C.R." 147, 1908, p. 594; "Ann. Chim. Phys." 8, 1 8, 1909, pp. 5-114; "Bull. Soc. Fr. Phys." 3, 1909, p. 155 ; "Zs. f. Electroch." 15, 1909, p. 269. 33 "Atoms" (tr. Hammick, Constable, 1916). 34 Burton and Bishop: "Proc. Roy. Soc. Canada," 192 1 (in print); "Jour. Phys. Chem." (in print). 36 Bancroft: "Jour. Phys. Chem." 18, 1914, p. 558. 36 Bredig: "Anorganische Fermente". 37 Zsigmondy and Spear : " Chemistry of Colloids " (Wiley, N.Y. 1917), pp. 92 and 1 1 4. 38 Schulze: "Jour. f. prak. Chem." 25, 1882, p. 431 ; 27, 1883, p. 320; 32, 1884, p. 390. 39 Burton : "On the Physical Aspect of Colloidal Solutions," "Univ. of Toronto Studies," 36, 1910, p. 48. 40 Bodazewski : "Beiba." 8, 1883, p. 488. 41 Lehmann, O. : " Molekularphysik," II, p. 5. 42 Zeleny and McKeehan : "Brit. Ass. Rep." Winnipeg, 1909, p. 406; "Phys. Rev." 30, May, 1910, p. 535. 43 Millikan : "Phil. Mag." 6, 19, 1910, p. 209. 44 Lamb: "Hydrodynamics," 3rd edition, 1906, pp. 551-54. 45 Boltzmann : " Gastheorie," I, p. 65. 46 Ehrenhaft : "Wien. Sitz-Ber. Natur-Wissen." 116, ia, 1907, p. 11 39. 47 Poynting and Thomson : "Properties of Matter". * s De Broglie : "C.R." 148, pp. 1163, 131 5; "C.R." 146, pp. 624, 1010; " Bull. Soc. Fr. Phys." 1909, p. 67. 49 Begeman : "Phys. Rev." 31, July, 1910, p. 41. 50 Regener: "Sitz-Ber. d. K. Pr. Akad. Wissen." 1909, p. 948. " Moreau : "C.R." 148, 1909, p. 1255. 62 Perrin : "Phil. Mag." 6, 19, 1910, p. 438. 53 Rutherford : " Brit. Ass. Rep." Winnipeg, 1909, p. 373. 54 Larmor: "Nature," 83, 1910, p. 478. Additional papers by Konstantinowski, Smoluchowski, Frank, and Fiirth in "Ann. der Phys." Vols. 46, 48, 52, and 53 ; and by Smolu- chowski, "Phys. Zeits." 191 5 and 1916. CHAPTER V. THE OPTICAL PROPERTIES OF COLLOIDAL SOLUTIONS. APART from the interest developed by the ultramicroscope the chief importance of colloidal solutions optically lies in their action on light which is incident upon them. The presence of the disperse phase in the medium changes the optical constants of the latter due to the absorption of the light ; when the light absorbed lies in the visible region of the spectrum we have the colour of the solution by transmitted light determined chiefly by this absorption. This has led to much work on the colour of colloidal solutions. At the same time the light which is reflected, or scattered diffusely from these solutions, is found to be, in general, par- tially polarized, and often completely plane polarized in a certain plane. This polarization of the scattered light is the second point of interest. Some work has been done on the phenomenon of double refraction, both inherent in the solutions and artificially pro- duced, and on the magneto-optical properties of the solutions containing the ferromagnetic elements. I. Colour, Absorption, Scattering and Polarization of Light by Colloids. The theoretical work on the optics of colloidal solutions deals almost entirely with the light which is scattered from a given sample ; on the other hand, the experimental tests of the theory depend, with a few exceptions, on the determination of the curve of the absorption of the given sample. There is not necessarily a simple relation between these two quantities of light (see Steubing *). If we were dealing merely with the emer- ge OPTICAL PROPERTIES OF COLLOIDAL SOLUTIONS 97 gent transmitted light and the portion of the light which is prevented from passing through, we should have the relations shown in the accompanying table between the colour which is the result of the transmitted light (subjective) and the colour which would result from the combination of the light shut out (absorbed). TABLE XV.— CORRESPONDING ABSORBED AND SUBJECTIVE COLOURS. 2 Wave- length in 70 •65 •60 •55 •53 •50 •48 •45 •43 •40 Absorbed colour. Purple Red Orange Yellow Green yellow Green Green blue Blue Indigo Violet Sub- jective colour. Green Green blue Blue Indigo Violet Purple Red Orange Yellow Green yellow Wave- length in •5° ■48 •45 "43 •40 •70 •65 •60 "55 '53 V- However, this does not mean that the absorbed colour noted in the above table will give the colour of the scattered light ; the latter is generally of a composite character, due partly to ordinary absorption and reflection and partly to se- lective reflection, and depends also on the refractive index of the supporting medium. 1 . Transmission, A bsorption, and Reflection. s — When a beam of light is allowed to pass through a layer of unit thickness of an absorbing substance a certain fraction a of the light is absorbed ; a is known as the coefficient of transmission of the substance. If I denotes the intensity of the initial beam and I the intensity of the beam after passing through a layer of thickness x cms., then I = I a*. The quantity a varies with the wave-length of the light and the nature of the ab- sorbing medium. If the incident beam consists of a mixture of light of various wave-lengths of intensities I 15 I 2 , I 3 , etc., for which the coefficients of transmission are a v a 2 , a s , etc., then I = I x . a x x + I 2 . a 2 x + I 3 . a* + etc. The quantity and quality of the transmitted light varies with the composition of the incident beam, i.e. with the nature of 7 9 8 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS the source, with the nature of the absorbing medium, and with the thickness traversed. On account of the fact that a depends on the wave-length, light of different colours will be absorbed to different extents, and, consequently, the emergent light will be coloured ; this colour will be, in general, the same for all thicknesses traversed, the tint deepening as the thickness of the absorbing layer is in- creased. A curious result ensues if the values of I and a for the various component wave-lengths are such that the correspond- ing values of I . cf change relatively to one another as the thickness increases ; as a consequence, the colour of the emergent light may change completely as the thickness of the absorbing layer is increased. For example, cobalt glass, while transmitting both blue and red light, absorbs the blue more than the red ; when the thickness is large the blue rays are almost entirely cut out and the glass appears red by trans- mitted light ; when the thickness is small, the glass is blue by transmitted light (see also Wood 4 ). The sum total of the light cut off by an absorbing layer is composite in its nature — a part is extinguished in the medium itself, and a part is reflected from the surface or from the interior of the medium ; this reflected portion may consist of light in which all wave-lengths are reflected in the same proportion, or we may have, as in the case of some aniline dyes, gold, copper, etc., selective reflection, i.e. light of certain wave-lengths being reflected more strongly than that of other wave-lengths. Ordinarily, bodies are made visible by the light which is diffusely reflected from their surfaces and from structural in- equalities in the interior. The part that is reflected from the interior suffers absorption by the medium after such reflection and consequently the reflected light is in general coloured. If the medium consists of particles or films which have little depth of the substance, as in clouds or in the froth on a liquid, the absorption of the internally reflected light is negligible and the colour of the reflected light is white if the incident light is white. " Reflection then is the proximate cause of colour in these bodies, inasmuch as without reflection no light would reach OPTICAL PROPERTIES OF COLLOIDAL SOLUTIONS 99 the eye, but absorption is the ultimate cause, for it is thus that the reflected light is deprived of some of its constituents and becomes coloured " (Preston 3 ). Following out a similar line of reasoning, Wood says : "Absorption is not the only factor which determines this selective reflection, and we often find misleading statements in text-books on optics, it being frequently stated that the wave- lengths most copiously reflected are the ones most strongly absorbed. This is by no means the case. ... In the case of absorbing media, the reflecting power depends both on the refractive index and the coefficient of absorption. Now, ab- sorbing media have a high refractive index on the red side of the absorption band and a low index on the blue side ; conse- quently the spectrum of the reflected light will be brightest on the red side of the absorption band, since for these wave-lengths we have a large coefficient of absorption and a high refractive index. On the blue side, however, the low value of the index diminishes the reflecting power more than the augmentation due to the powerful absorption. The hue of surface colour thus depends on the refractive index of the medium in which the substance is immersed, for it is the relative and not the absolute refractive index with which we are concerned." 2. The Blue Colour of the Sky — Artificial Atmospheres. — The interest in the colours produced by turbid media was, in the first place, due to the repeated attempts to explain the blue colour of the sky. Various explanations of the latter phenomenon have been put forward ; that which is generally accepted at the present time was first suggested by Leonardo da Vinci s : namely, that the atmosphere is in reality a turbid medium, filled with particles of dust, globules of water, etc., and, in accord with the action of such media on light passing through them, it diffuses laterally light which is richest in blue tints, while the light which is directly transmitted tends to have the red most intense. This explanation has been experiment- ally confirmed by the action of artificial atmospheres of turbid liquids and vapours prepared by Brlicke, 6 Roscoe, and Tyndall, 7 and strengthened, on the theoretical side, by the mathemati- cal treatment of Rayleigh 8 ; indeed, Rayleigh's most recent 7* loo PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS contribution 9 to the subject is that the colour of the atmos- phere may possibly be explained by the scattering action of the air molecules themselves (see King u ). In one of his experiments on artificial atmospheres, Tyndall passed light through a tube into which he had introduced a mixture of air bubbled through nitrate of butyl and air (in excess) bubbled through hydrochloric acid, the total pressure in the tube being about I cm. of mercury. On allowing the light from an arc lamp to traverse the tube, chemical action of the two vapours ensued, and a very fine cloud of solid particles began to form. At first the particles were exceed- ingly small, and the colour observed laterally was a delicate blue, but as the experiment progressed, the particles gradually increased in size, the colour gradually brightened, " still main- taining its blueness, until at length a whitish tinge mingled with the pure azure, announcing that the particles were now no longer of that infinitesimal size which scatters only the shortest waves ". Similar artificial atmospheres may be made in water by the addition of a few drops of alcoholic solution of mastic, or by the production of fine sulphur particles due to the interaction of dilute solutions of sodium hyposulphite and hydrochloric acid. The light scattered by the incipient cloud is partially plane polarized — the maximum percentage of polarization being pro- duced at points in the plane at right angles to the direction of the incident light ; the plane of polarization in the scattered light is that containing the beam of light and the eye of the observer. As the particles in suspension grow in size, the polarization becomes less complete, while the lines along which it is a maximum shift away from the position of 90 to the direction of the incident beam. Tyndall found also that there always existed neutral points where the polarization was zero and such that in passing through the neutral point the planes of polarization turned through a right angle ; this is in keep- ing with the observations of Arago, 10 Babinet, 11 and Brewster, 12 on neutral points in the light from the sun. 3. Solutions and the Tyndall Phenomenon.' — The fact that the so-called Tyndall phenomenon is shown by particles OPTICAL PROPERTIES OF COLLOIDAL SOLUTIONS 101 very much below the microscopic, or even ultramicroscopic, limit was used by Linder and Picton 13 in their experiments on arsenious sulphide solutions. By preparing such solutions with different grades of dispersion they offered strong evidence of the continuity of the transition from coarse suspensions to crystalloidul solutions ; they classified their various arsenious sulphide solutions thus : — As 2 S 3 (a) — aggregates visible under the ordinary micro- scope, As 2 S 3 (/3) — aggregates invisible but not diffusible, As 2 S 3 (7) — aggregates diffusible but held by filter, As a S 3 (8) — aggregates diffusible and not held by filter but showing the Tyndall phenomenon. More recently still Spring, 1 * Lobry de Bruyn 15 and their co-workers have examined all types of solutions for the Tyndall effect. Tyndall himself remarked that almost all liquids have motes in them sufficiently numerous to polarize the light sensibly ; and very beautiful effects may be obtained by simple artificial devices. When, for example, a cell of dis- tilled water is placed in front of the electric lamp, and a narrow beam permitted to pass through it, scarcely any polarized light is discharged, and scarcely any colour produced with a plate of selenite. But while the light is passing through it, if a piece of soap be agitated in the water above the beam, the moment the infinitesimal particles reach the beam the liquid sends forth laterally almost perfectly polarized light ; and if the selenite be employed, vivid colours flash into existence. A still more brilliant result is obtained by adding to the water a small amount of mastic dissolved in alcohol. "The selenite rings constitute an extremely delicate test as to the quantity of motes in a liquid. Commencing with distilled water, for example, a thickish beam of light is necessary to make the polarization of its motes sensible. A much thinner beam suffices for common water; while with Briicke's precipitated mastic, a beam too thin to produce any sensible effect, with most other liquids, suffices to bring out vividly the selenite colours." 7 102 PHYSICAL PROPERTIES OF- COLLOIDAL SOLUTIONS By this effect Spring showed the presence of the aggre- gates of hydrates resulting from the hydrolysis of dissolved salts, and suggested the Tyndall effect to explain gold ruby glass and other metal glasses ; he defined a true solution to be one which does not show the Tyndall effect. Lobry de Bruyn and Wolff found that aqueous solutions of saccharose, raffinose, etc., in high concentration, gave this diffusely scattered light. Doubtless the recognition of the scattered light has depended on the intensity of the illumination from the source and on the sensitiveness of the apparatus used by the various workers for detecting the same. It has been shown recently that, as already "noted by Tyndall, it is exceedingly difficult to get even distilled water which does not show some faint indication of the Tyndall phenomenon (see Martin). 4. Theoretical Work on the Scattering of Light by small Particles. — The theoretical importance of the optics of colloidal solutions was first noted by Faraday, 16 and became a subject of his research about 1856. He gives the reasons which led him to this inquiry in the following language : — " Light has a relation to the matter which it meets with in its course, and is affected by it, being reflected, deflected, transmitted, refracted, absorbed, etc., by particles very minute in their dimensions. The theory supposes the light to consist of undulations, which, though they are in one sense continually progressive, are, at the same time, as regards the particles of the aether, moving to and fro transversely. The number of progressive alterations or waves in an inch is considered as known, being from 37,600 to 59,880, and the number which passes to the eye in a second of time is known also, being from 458 to 727 billions ; but the extent of the lateral excursion of the particles of the aether, either separately or conjointly, is not known, though both the extent and the velocity are very small compared to the extent of the wave and the velocity of its propagation. Colour is identified with the number of waves. Whether reflection, refraction, etc., have any relation to the extent of the lateral vibration, or whether they are dependent in part upon some physical action of the medium unknown to or unsuspected by us, are points which I understand to be as yet undetermined. OPTICAL PROPERTIES OF COLLOIDAL SOLUTIONS 103 " Conceiving it very possible that some experimental evidence of value might result from the introduction into a ray of separate particles having great power of action on light, the particles being at the same time very small compared to the wave-lengths, I sought among the metals for such. Gold seemed especially fitted for experiments of this nature because of its comparative opacity amongst bodies, and yet possession of a real transparency ; because of its development of colour in both the reflected and transmitted ray; because of the state of tenuity and division which it permitted with the pre- servation of its integrity as a metallic body ; because of its supposed simplicity of character ; and because known pheno- mena appear to indicate that a mere variation in the size of its particles gave rise to a variety of resultant colours. Besides, the waves of light are so large compared with the dimensions of the particles of gold which in various conditions can be subjected to a ray, that it seemed probable that the particles might come into effective relations to the much smaller vibrations of the aether particles ; in which case, if reflection, refraction, absorption, etc., depended upon such relations, there was reason to expect that these functions would change sensibly by the substitution of different sized particles of this metal for each other." Similar language might very well indicate the purpose of workers who have attempted, since Faraday's time, to explain optical properties of the metal sols from the electromagnetic point of view. Optically, the important points of Faraday's experiments on gold colloidal solutions are his proofs that such solutions containing the smallest particles of gold have red or ruby tints by transmitted light, while if, for any reason, the particles become larger and larger, the colour by transmitted light tends more and more to the blue. The first attempt to give a mathematical explanation of the action of turbid media on light is that of Rayleigh 8 - 9 , first in the language of the undulatory theory simply and later from the point of view of the electromagnetic theory. He assumes that the foreign obstructing matter, supposed to 104 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS be present in the form of electrically non-conducting particles, each small in comparison with the wave-length of the light used, loads "the ether so as to increase its inertia without altering its resistance to distortion. If the particles were away the waves would pass on unbroken, and no light would be emitted laterally. Even with the particles retarding the motion of the ether the same will be true if, to counterbalance the increased inertia, suitable forces are caused to act on the ether at all points where the inertia is altered. These forces have the same period and direction as the undisturbed luminous vibrations themselves. The light actually emitted laterally is thus the same as would be caused by forces exactly the oppo- site of those acting on the medium otherwise free from disturb- ance, and it only remains to see what the effect of such forces would be. In the first place there is necessarily a complete symmetry around the direction of the force ; the disturbance, consisting of transverse vibrations, is propagated outwards in all directions from the centre ; and in consequence of the symmetry the direction of the vibration in any ray lies in the plane containing the ray and the axis of symmetry ; that is to say, the direction of vibration in the scattered or refracted ray makes with the direction in the incident or primary ray the least possible angle. The symmetry also requires that the intensity of the scattered light should vanish for the ray which would be propagated along the axis. For there is nothing to distinguish one direction transverse to the ray from another. Suppose for distinctness of statement that the primary ray is vertical, and that the plane of vibration is that of the meridian. The intensity of the light scattered by a small particle is constant, and a maximum for rays lying in the vertical plane running east and west, while there is no scattered ray along the north and south line. If the primary ray is unpolarized, the light scattered north and south is entirely due to that component which vibrates east and west, and is therefore perfectly polarized, the direction of its vibration being east and west. Similarly any other ray scattered hori- zontally is perfectly polarized, and the vibration is performed in the horizontal plane. In other directions the polarization becomes less and less complete as we approach the vertical." OPTICAL PROPERTIES OF COLLOIDAL SOLUTIONS 105 As a result of the analysis, Rayleigh shows that the intensity I s of the scattered light varies according to the following law : — . T (D'-D) 2 2/0 ^.*"T 2 where I = intensity of the incident light, D' and D = the optical density of the particles and the dispersion media respectively (proportional to the squares of the corresponding indices of refraction), m = number of particles per unit volume, T = volume of a disturbing particle, X = the wave-length of the scattered light. /8 = the angle between the line of sight and the incident direction. It is at once apparent that from ordinary white light incident on such a medium, the percentage of red light (75 ^,) reflected would be about one-twelfth that of the violet (-40 /j.) ; for a given mass of the disperse phase per unit volume, mY = a constant, and therefore I s varies directly as T ; for the number of particles per unit volume constant, i.e. m = a con- stant, I s varies directly as T 2 . These conditions are. quite in agreement with the phenomena described by Tyndall in his experiments. When scattering alone is considered, the intensity of the scattered light I s varies inversely as the fourth power of the wave-length. 17 " Now the light which reaches the eye is scattered, and also transmitted (both before and after scattering) through some thickness x of the medium. Hence its composi- tion will be determined by finding the effect of transmission on the quantity I s . This problem is equivalent to that of finding the intensity of a pencil of light after transmission through an absorbing medium when the absorption varies inversely as the fourth power of the wave-length. Hence we have dl k . dx T = ~^T' where k is a constant, and dl the change of intensity in passing through a layer of thickness dx. The intensity of the 106 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS light reaching the eye, after suffering scattering as well as transmission through a total thickness x of the medium, is therefore hx 1 = 1,. «-*, and expressing I s in terms of — 4 , we have finally . A -** I = -i . e a«. " This expression exhibits the joint effects of scattering and transmission, and shows how I diminishes for large values of the wave-length as well as for small values. The maximum value of I corresponds to some intermediate wave-length X w given by the equation which gives the maximum value of I, I^A.X"*.*- 1 %- e . k . x while the intensity I corresponding to any wave-length X is related to l m by the equation T -4 T A « "is _ = ^» /" a 4 ' l m X*' The curve in Fig. 12 shows the relation between I and I m given by the last formula for the case of the maximum scattering taken arbitrarily at the wave-length of 5 x io -5 cm. The resulting curve is quite typical of the experimental curves obtained in the determination of the absorption of metal glasses and colloidal solutions. The Rayleigh formula has been tested as to the plane polarization being complete along a line at right angles to the incident light and quite well confirmed ; by Ehrenhaft, 19 who obtained for silicic acid 90°, and for arsenic sulphide 87 , by Bock 20 on particles in a steam jet and as to the polarization in various directions, i.e. yS varying, by Dimmer 21 on glasses of different sorts. The investigation of Professor J. J. Thomson 22 on the analo- gous effect of conducting particles scattered throughout a given OPTICAL PROPERTIES OF COLLOIDAL SOLUTIONS 107 medium, treated electromagnetically, leads to a variation in the position of the lines of maximum polarization. " The scattered light produced by the incidence of a plane polarized wave vanishes in the plane through the centre at right angles to the magnetic induction in the incident wave along a line making an angle of 120° with the radius to the point at which the wave first strikes the sphere and it does not vanish in any direction other than this. Thus, if non-polarized waves of light or of electric displacement are incident upon a sphere whose radius is small compared with the wave-length of the incident vibration, the direction in which the scattered light is plane polarized will be inclined at an angle of 1 20° to the I- as ox 1 03* J A 4 6 Fig. 12. 8 k jo cm. X direction of the incident light. The scattering of light by small metallic spheres thus follows laws which are quite different from those which hold when the scattered light is produced by non- conducting particles. In the latter case (Rayleigh, ' Phil. Mag.,' V. 12, p. 81, 1881) when a ray of plane polarized light falls on a small sphere, the scattered light vanishes at all points in the plane normal to the magnetic induction when the radius vector makes an angle of 90 , and not 1 20°, with the direction of the incident light. Thus when non-polarized light falls on a small non-conducting sphere, the scattered light will be com- pletely polarized at any point in a plane through the centre of the sphere at right angles to the direction of the incident light. 108 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS " When the light is scattered by a conducting sphere, the points at which the light is completely polarized are on the surface of a cone whose axis is the direction of propagation of the incident light and whose semi-vertical angle is 120°." This result was tested experimentally by Threlfall and Professor Thomson 23 with negative results, but on the other hand, it has been partially confirmed by the recent experi- mental results of Ehrenhaft 19 and Miiller. 24 In the light of the following comment by Professor Thomson on the above theory, it is easily possible that such a variation in experiments may still be quite consonant with the theory. " I made, about two years ago, some rough experiments on the polarization of light scattered by small particles of gold, the results of which were in agreement with those of Professor Threlfall. I regarded these experiments as confirming the re- sults of Maxwell and Wien, that the resistance of metals to very rapidly alternating currents which constitute light is much greater than to steady currents. " It is, moreover, very difficult to make these experiments so as to be a fair test of the theory, as it is only when the size of the particles is within narrow limits that the theory would be applicable, even supposing the resistance to be as low as for steady currents. To scatter the light the diameters of the particles must be small compared with the wave-length of light, while the theory given in my ' Recent Researches on Electricity and Magnetism ' requires that the depth to which the currents produced by the light penetrate the particle should be small fraction of the radius of the particle. Now at a depth d below the surface of the sphere the intensity of the in- duced current varies as e' M , where k = \2irfipja-f, fi being the magnetic permeability, a the specific resistance of the metal, and 27t//j the time of oscillation of the incident electrical vibration. Thus the currents at a depth \\k below the surface will be only I \e of their value at the surface ; we may therefore take \\k as the measure of the thickness of the film filled by the currents. For gold a = 2IOO for steady currents, fj, = I, and for the D line p = 27r x 5-097 x io u ; thus i/k = 3-2 x io -7 . The wave-length of the D line is 5'8ox io -5 , about 170 OPTICAL PROPERTIES OF COLLOIDAL SOLUTIONS 109 times 1 /k. Thus for the theory to be applicable, the diameter of the particles must be small compared with X arid large com- pared with ijk. As i/X is only 170 times i/k this makes the range of diameters very small. A more satisfactory test of the theory could be made with longer wave-lengths and larger particles ; for the thickness to which the currents descend varies as the square root of the wave-length, so that the ratio of the wave-length to the thickness of the current film increases as the wave-length increases." As pointed out here, and also in the discussion between Ehrenhaft and Pockels, 26 regarding the former's experimental confirmation of the theory, there is the indeterminate quantity, a, the specific conductivity of the metal spheres for the electric waves in the light waves which renders agreement with the theory rather fortuitous ; there is a very limited range of sizes of particles for which the maximum polarization will, even theoretically, be in a direction making 120° with the incident direction. The invention of the ultramicroscope with the consequent power afforded for measuring with considerable accuracy the size of the particles in colloidal solutions, both solid (metal glasses) and liquid, stimulated the interest in the optical pro- perties of these suspensions. The metal glasses and metal sols offer the greatest variety of colour effects ; many of the sols, the disperse phases of which are compounds, and practically all emulsoids, are either colourless or merely milky white; the latter probably contain particles which are too large to scatter the blue light sufficiently in excess to make the colour dis- tinctive, or the indices of the disperse phase and the medium may be so nearly equal that the term (D' - D)/D, in the Rayleigh formula, is nearly zero. The problem of the colour of the metal sols and glasses is rendered complex on account of the many varying influences to be taken into consideration. In the first place, the relation of the size of the particle to the wave-length of the light used is all-important ; to apply Rayleigh's or Thom- son's theory of scattering, the particles must be small in com- parison with the wave-length. For a given number of particles 1 10 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS per unit volume, the intensity of the scattered light varies directly as the sixth power of the diameter and inversely as the fourth power of the wave-length ; that is, it is the light of short wave-length that is most abundantly scattered, and the intensity of the scattered light, and therefore also of the absorption, increases rapidly with the diameter of the small particles. However, as the particles approach the dimensions of the wave-length, we shall have ordinary reflection pheno- mena (including selective reflection) coming into play ; in which case, the intensity of the diffused light (and therefore also the amount of the absorption) varies, in general, according to the law „ Constant R = ioo 7=~> for a given metal ; i.e. the greater the wave-length, the greater the scattered or reflected light ; in addition, the reflected light now varies as the square of the diameter. The transition from samples with extremely small particles to those with particles of microscopic size affords an infinite variety of possibilities in their absorption. Again, as a consequence of Rayleigh's formula (p. 105), there is some wave-length, not necessarily in the visible region of the spectrum, for which, with scattering alone, we should get a maximum intensity. In the third place, we must always take into consideration, not only the relation between the refractive indices of the metal particles and the supporting medium for a single value of the wave-length, but also the dispersions of the two substances. As pointed out by Christiansen, 26 if powdered glass particles (of dimensions comparable with the wave-length of light) be suspended in a liquid of identically the same refractive index for some standard wave-length, colour will still be produced, on account of the difference in the dispersions of the liquid and the glass. Similarly, with a suspension of copper particles in water, if there were no other modifying cause, only the wave-length for which the index of refraction of copper is equal to that of water would be transmitted unchanged (vide Garnett 27 ). Finally, in the discussion from an electromagnetic point of OPTICAL PROPERTIES OF COLLOIDAL SOLUTIONS m view, it is apparent that variations in such features as the sur- face, shape, etc., of the particles will make large changes in the optical constants of the solution, and consequent variations in the absorption of light. This complexity has necessitated the attack being made initially with very simple assumptions. The first of the more recent attempts to solve the problem of the variations in the colour of these suspensions is that of Garnett. 27 He dealt more particularly with metal glasses (gold, silver, and copper) and the metal sols of gold' and silver. The object of his work was " to obtain information concerning the ultramicroscopic structure of various metal glasses, colloidal solutions, and metallic films by calculating optical properties corresponding to certain assumed microstructures, and by comparing the calculated properties with those observed ". Calculations were made for three types of microstructure : (i) that in which the metal molecules were distributed at random (called by Garnett, amorphous), (2) that in which the metal molecules were arranged in small spherical groups, many to a wave-length of light (granular), and (3) that in which the small spheres were replaced by small spheroids (spicular). Following Lorenz, Hertz, and Rayleigh, Garnett first shows that a metal sphere, small compared with the wave-length of light, produces in all surrounding space the same effect as would be produced by a Hertzian doublet placed at its centre. If light of wave-length X falls upon a sphere of metal of radius a, of refractive index n, and of extinction coefficient k, then the complex dielectric constant e will be expressed by N = »(l - ik)= s/e; (i = s/ - 1). If there be M such spheres per unit volume, in vacuo, Garnett shows that considering a volume which in all its directions is great compared with the wave-length of light, this complex medium is optically equivalent to a medium of refractive index ri and extinction coefficient k' given by the equation N' = »'(i - *£') = x/? N 2 - 1 4 wMa\^r^- 2 where e = 1 + 3 N 2 +2 ii2 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS or, if fi = the volunie of metal per c.c. of the solution, N 2 - i 6 = 1 + N 2 N 2 - V 2 3/^ N 2 + 2v' 2 I - a. N 2 - __2 + 2 If the metal spheres be situated in glass of refractive index v instead of in vacuo, the equation becomes [»'(l - ik')f = e = v* + " The constants, ri and k' of the medium thus depend only on fx, the relative volume of metal, and not on the radii of the individual spheres. It is clear that the spheres may now be supposed to be of quite various radii, provided only that there be many to the wave-length of light in the medium." In the cases under consideration, metal glasses and metal sols, the fraction /* is always small ; neglecting in the latter N 2 - i> 2 equation /* . ^ 2 in comparison with unity, we may write N 2 - v 2 [ri(i - ik')f - v* = 3^ 2 ■ N 2 + 2v 2 = sav > 3^ S - 2z'/3). Equating real and imaginary parts, we get expressions for a and /S in terms of u, k, and v. Introducing at each step the. fact that fi is a small quantity, the analysis gives rik' = 3/W/3 and ri = i/(i + f/owi). That is, knowing the values of n and k for the metal (as found from other independent experiments), we may determine the values of ri H and ri for the complex medium. The above applies to the metal in what Garnett calls the granular state. For the amorphous state of subdivision of the metal, i.e. suspended as a molecular solution, taking for the constants of the solution ri' , k", N", e", we have N" = «"(l - ik") = >/7, and the corresponding equations : — OPTICAL 'PROPERTIES OF COLLOIDAL SOLUTIONS it 3 [*"(I - ik")J - v* = (2 + „> . *^ = say, (2 + *> . («' - 2 #J'). Again, equating real and imaginary parts, we may obtain a and /3' in terms of n, k, and v, and the resulting equations— >,,,, 2 + v 2 a , , „ ( 2 + V* A n k = . fip and « = i>( I + — ^- . fia ). Garnett shows that the expressions ri k' and n" k" measure the absorption in the granular and amorphous states respectively ; that is, " when light of a wave-length X traverses a thickness d of a metalliferous medium, the intensity of the light is reduced in the proportion K > according as the metal is in true solution or in spherical aggregates ". The above theory lends itself to experimental confirmation by the calculation of the absorption produced by a given solution containing what are known to be fine particles, and comparing these calculations with the results of experiment. A very exhaustive series of such experiments was carried out by Garnett on gold, silver, and copper glasses, and gold and silver colloidal solutions. In general there is a striking agree- ment between the calculated and the observed results. It will be noticed from Garnett's formulae that the re- fractive index of the complex medium which has the metal in molecular solution is different from that in which the metal is in the form of small spheres. Garnett's experiments on the refractive indices of colloidal silver solutions for the sodium yellow line gave values exceedingly near the value ri, calculated from the distribution of spheres ; he consequently concludes "that practically the whole of the silver must have been in suspension in the form of small spheres ". As the whole of Garnett's treatment relates to the phenomena observed with spheres small compared with the wave-length of light in the medium, Spence 28 extended it ex- perimentally by using infra-red rays, of wave-length up to 18 x io~ 5 cm. and determining the absorption of Bredig metal sols of gold, platinum and silver. However, there was the additional difficulty that the liquid media themselves absorbed 1 14 Physical properties of colloidal solutions these rays to a certain extent. Spence extended Garnett's theoretical work to include the case of the supporting media itself showing absorption of the rays used. If the complex dielectric constant of the medium be written e'" = v(l - ig\ we shall have the dielectric constant of this medium when the spheres are distributed in it given by the equation 3e "> • [rrb 77 ] -J p ~ 77) ^T Following out Garnett's analysis and keeping in mind the negligible quantities involved in relation to colloidal solutions, Spence gets for the refractive index, n, of the metal in the solution, the equation \ \_2a{t - w) J (a 2 - 2v 2 ) 2 -t2 za{t - w) — the root of a quadratic equation in n. where a = kn = the absorption coefficient of the metal, v = the refractive index of the medium itself, t = k'ri = the absorption coefficient of the colloidal solution, w = gv = the absorption coefficient of the supporting medium. When n is considerably less than I, the quadratic equation reduces to _ (t - w)(a 2 - 2y 2 ) 2 gav ft Two results are immediately deducible from the theory : (1) the value of {t- w), the difference between the absorptions of the colloidal solution and the supporting medium is directly proportional to fi, the concentration ; (2) the value of n ob- tained for a given metal should be independent of the sup- porting medium. Spence confirmed both of these points experimentally for wave-lengths up to 18 x io -5 cm. He ob- tained the indices of refraction for gold, silver, and platinum OPTICAL PROPERTIES OF COLLOIDAL SOLUTIONS 115 in solutions with water and ethyl malonate respectively, as the supporting media ; his values agreed well among them- selves and also with corresponding values found by other workers by more direct methods. As an additional test of his results, he calculated the value of R in Drude's equation _ Q 2 - I) 2 + a 2 („» + 1)8 + a v where R is the reflection coefficient and a the absorption coefficient and found close agreement between his results and those observed by others. By calculating the light scattered by small particles of a colloidal solution as a series of partial wavelets of two groups, viz. those corresponding respectively to the electric and magnetic vibrations of the particles, Mie a * has determined the optical properties of turbid media, in which the particles may be regarded as spherical and for which the turbidity is infinitely thin optically, such as is the case with ordinary colloidal solutions. Only a finite number of these partial waves need be taken into account in these cases ; in any case, the (r- i)th magnetic vibration is considered simultaneously with the rth electric vibration. For colloidal solutions with very fine particles only the first electric vibration need be considered ; this corresponds to the Rayleigh scattering. With coarser particles one must also take account of the first magnetic and the second electric vibrations. If an unpolarized beam of light is passed through a colloidal solution, the laterally scattered light is completely or partially plane polarized, but never elliptically polarized ; this seems to be borne out by the consensus of ex- perimental results. For gold solutions with particles (spherical) up to about 100 fifi in diameter, the light scattered laterally gives only the Rayleigh beams, the maximum polarization (almost 100 per cent) occurring at 90°. As the particles in- crease in size, the amount of unpolarized light in the plane at 90 to the incident direction increases very rapidly and the lines of maximum polarization move towards a larger angle than 90°, until for particles of 160 to 180 fifi diameter, they lie between 1 io° and 120 to the incident direction. As shown also by the Rayleigh formula, for constant concentration the 8* 1 16 PHYSICAL PROPERTIES OF COLLOIDAL SOL UTIONS scattered radiation of very fine turbidities is proportional to the volume of the very fine particles. In coarser sols, the scattered light grows slowly with increasing size of particle and finally reaches a maximum, which depends on the wave-length ; with gold particles, the maximum scattering is given by particles with diameters between 1/4 and 1/3 of the wave-length in the dispersion medium. Mie finds that results do not justify the assumption that the particles are perfectly conducting spheres. The scattered light from gold particles is generally much stronger than would be expected from perfectly conducting Spheres of the same size. In addition, with the finest subdivision of the gold, the scattered light shows a very distinct maximum in the greenish-yellow rather than in the blue-violet. The absorption of colloidal gold solutions depends on two pro- perties of metallic gold, the ability to absorb light and to re- flect light. Solutions in which the diffuse reflection is small compared with the proper absorption show the absorption maximum of the gold particles which lies in the green ; by transmitted light they are ruby-red. Solutions which show strong diffuse reflection appear by transmitted light blue, be- cause gold reflects chiefly the reddish-yellow light. Steubing, a pupil of Mie, 1 was the first to measure quan- titatively the intensity of the scattered light, as well as that of the transmitted light. Working with various gold sols, he found that as a general thing, only a small portion of light was lost by. scattering, the greater part of the light cut out being destructively absorbed in the metal. This result bears out the views expressed by Mie 29 and Pockels 25 that the ex- planation of the colours by resonance is not possible. In addition to finding the absorption maxima for different sols, Steubing measured the polarization of the scattered light; he found it to be partially plane polarized, the direction of the maximum polarization being at 90° to the incident beam and amounting to about 90 per cent of the total light in that direction. Contrary to the results of others he found that certain gold sols, blue by transmitted light, contained ex- tremely fine particles. Gans and Happel 30 extended Garnett's and Mie's theo- OPTICAL PROPERTIES OF COLLOIDAL SOLUTIONS 117 retical work so as to make the theory applicable to concentrated solutions and also to sols containing particles not small compared with the wave-length of the light. They deduced formulae for the refractive index of a colloidal solution and the absorption per unit length (not to be confused with the absorp- tion coefficient). They applied their formula to two special cases, (1) an infinitely dilute solution containing particles of various sizes, and (2) solutions containing infinitely small particles but of varying concentrations. Later Gans 31 extended Mie's work to apply to ellipsoidal particles, and found that the absorption curves moved forward to the larger wave-lengths as the particles departed from the spherical form. He con- cludes that the fine particles in Steubing's blue solutions were probably ellipsoidal. In a still later paper, 32 the same author gives the curves of absorption of silver sols consisting of ellipsoidal particles, from numbers calculated by Muller. 24 Supposing that the particles are ellipsoids of revolution with the ratio of the axes A : B, a variation in the value of A : B gives surprising variety in the form of the theoretical absorp- tion curve. Lampa 33 attacked the same problem of determining the absorption and refraction coefficients of an ideal colloidal solu- tion from an independent point of view. He began with Hasenorhl's calculations of the changes suffered by a plane polarized electromagnetic wave traversing a medium — an ideal gas — composed of uniformly distributed spheres with dielectric constant, permeability, and conductivity different from those of the supporting medium. His expressions for the optical constants of a dilute colloidal solution are shown to be identical with the analogous expressions given by Mie, and Gans and Happel. Experimenting on a red colloidal gold solution con- taining "Oil grm. of gold per 100 c.c, he found that the observed absorption curves were similar to the calculated curves but not coincident with them (see also Rolla 84 ). Lampa 36 and Robitschek 36 have shown by ingenious ex- periments that the red gold solutions (transmitted light) con- sist of finer particles than the blue solutions. By centrifuging a sample of blue solution, Lampa showed that the transparency u8 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS towards the red increases as the centrifuging proceeds, and that, therefore, since the larger particles are expelled from the solution first, the red solution contains the smaller particles. Robitschek found in the centrifuge tube a gradation from red transparency at the top of the tube to blue transparency at the bottom after a sample had been centrifuged for some time. Zsigmondy's conclusions regarding the colours of gold solutions are summed up as follows : — "The colour of colloidal gold solutions in transmitted light may be red, violet, or blue, and occasionally yellowish- brown, or brown. The ultramicrons of red solutions are green ; those of blue solutions are yellow to reddish-brown ; violet solutions contain both. We have therefore to do with green, yellow, or brown ultramicrons. . . . " Both green and brown ultramicrons may have all possible dimensions from the amicroscopic to 120 (iji and over. As a general thing, however, the large particles are yellow or brown, while the very fine subdivisions are green. At present there is no explanation for the fact that very small particles are sometimes brown. Nevertheless the following may be the key to the situation. According to Mie's theory, particles of gold having a diameter of 40 ji/j, and under must be green. The assumption is thereby made that the shape is spherical, and the particle a compact mass of metallic gold. Any divergence from the theory may mean that the conditions are not fulfilled. In other words, when the very small particles are brown, either the shape is not spherical or the entire space occupied by ultramicrons is not filled with metallic gold. The first assumption does not seem to be entirely necessary. It may also be said that the divergence from the theory is due to allotropic modifications of gold. The assumption is quite unnecessary, for the explanation of the colour, and in certain cases leads to contradictions. " With regard to the brown colour of very small particles, a large number of experimental facts point to the assumption that the ultramicrons are not composed of massive gold. For instance, whenever the green particles become flocculent, or approach very close to one another, the colour changes to OPTICAL PROPERTIES OF COLLOIDAL SOLUTIONS 119 brown, even when the aggregate is still amicroscopic. It would seem therefore that small brown particles are in reality conglomerates of the green. Green ultramicrons, on the other hand, are composed of compact gold, and are the result of the normal growth of amicroscopic particles, or better, perhaps, they are tiny crystals. " The assumption that the particles are spherical in form is made solely for the purposes of calculation, and a number of facts would seem to discredit the hypothesis. The very great independence of the colour on the diameter makes it seem plausible, that ultramicrons in red hydrosols are not necessarily spherical when the size is 40 fi>p and under " (see also Bancroft 38 ). In his work on the proof of the continuity of physical properties and molecular solutions, Svedberg 39 has performed two series of experiments on the optical properties of colloidal solutions: (1) colorimetric, and (2) spectrophotometric. In the first series he determines the limit of the visibility of the colour produced by various solutions of gold containing particles of different sizes. It is often found in comparing ■ the colour-intensity of colloidal and molecular solutions of the same substance that the colloidal solution is much more strongly coloured than the corresponding molecular solution (of the same concentration ?). Svedberg shows that, with de- creasing size of particles (i.e. increasing dispersion grade), from a certain size down to the molecular size the colour- intensity continually decreases ; in some cases he found that, with decreasing size of particles, the colour-intensity finally approaches very rapidly that of the corresponding molecular system. In his rather less satisfactory spectrophotometrical obser- vations he measured the absorption of the principal mercury lines due to columns of colloidal and molecular solutions respec- tively. From measurements on six substances — gold, selen- ium, indigo, aniline blue, indophenol.and azobenzol — he shows that, as regards light absorption, there is no real difference between colloidal solutions made up of observable discrete particles and the corresponding molecular solutions. i2o PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS In an exhaustive treatment of the colours of various colloidal solutions in relation to the size of the particles, Wo. Ostwald 2 enunciates the following law: "With increasing dispersion grade (i.e. decreasing size of particles) the absorption band of any colloidal solution moves to the shorter wave-lengths". He shows that in every case observed the absorption of a colloidal solution of very high dispersion grade approximates to the absorption of the corresponding molecular solutions. II. Double Refraction Induced in Colloids. Double refraction may be induced in various solutions in the following ways : — (i) by the action of an electrostatic field (Kerr phenomenon), (2) by mechanical action, such as stirring, (3) by the action of a magnetic field. The first method has been the object of much research since its discovery by Kerr 40 (see De Metz 41 ). The Kerr phenomenon is shown by true molecular solutions and, there- fore, may be taken as an effect produced in the molecules themselves and not on molecular complexes. Voigt ascribes the effect to the influence of the electric field on the frequency of the electrons in the liquids. In addition to this, according to Leiser, the field may produce orientation and deformation of the molecule. The production of double refraction by mechanical means is possible only with liquids which possess a certain hetero- geneity, i.e. with dispersoids of one form or another. In the case of colloidal solutions of the ferromagnetic metals uniform magnetic fields produce double refraction. According to Cotton and Mouton, 42 this phenomenon is due to an orientation of the particles and increases in amount as the size of the particles increases (See Havelock 43 ). BIBLIOGRAPHY. 1 Steubing : "Ann. der Phys." 26, 1908, pp. 329-71. 2 Wo. Ostwald : "Koll. Chem. Beih." 2, 1910-11, p. 409. 3 Preston : "Theory of Light," 2nd ed., § 282. i Wood : " Physical Optics," 1st ed., Chap. XIV, p. 351. 5 l^ichols, E. L. : "Phys. Rev." 26, 1908, pp. 497-511. OPTICAL PROPERTIES OF COLLOIDAL SOLUTIONS 121 6 Brucke : "Pogg. Ann." 88, 1852, p. 363. 'Tyndall: "Proc. Roy. Soc. Lon." 17, 1868, p. 223; "Phil. Mag." (4), 37, P- 388. 8 Rayleigh : "Phil. Mag." (4), 41, 1871, p. 107 and p. 447. 9 Rayleigh : "Phil. Mag." (5), 47, 1899, p. 375. 10 Arago, Preston : "Theory of Light," 2nd ed, § 255. 11 Babinet: "C.R." 11, 1840, p. 618. 12 Brewster: "Brit. Assoc. Rep." 2, 1842, p. 13. 13 Linder and Picton : "Jour. Chem. Soc. Lon." Vols. 61, 67, 71, and 87. 14 Spring: "Bull, de l'Acad. Roy. de Belgique (Sci.)," 1899, pp. 300-15 ; "Rec. Trav. Chim. Pays-Bas," II, 4, 1900, p. 339. 15 Lobry de Bruyn : "Rec. Trav. Chim. Pays-Bas," II, 4, 1900, p. 251. 16 Faraday: "Phil. Mag." (4), 14, 1857, pp. 402-3. 17 Rayleigh: "Phil. Mag." (4), 41, 1871, p. 107. 18 Preston : "Theory of Light," 2nd ed., § 165. 19 Ehrenhaft: " Phys. Zeit." 5, 1904, p. 387. 20 Bock: "Ann. der Phys." 68, 1899, p. 674. 21 Dimmer: "Akad. Wiss. Wien. Sitz. Ber." 117, 2«, 1908, pp. 913-24. 22 J- J. Thomson : " Recent Researches,'' p. 449. 23 Threlfall and Thomson : "Phil. Mag." (5), 38, 1894, p. 446 and p. 455. 24 Miiller : "Ann. der Phys." 24, 1907, p. I. 26 Pockels : "Phys. Zeit." 5, 1904, p. 152 and p. 460 (Ehrenhaft, p. 387). 26 Christiansen : "Ann. der Phys." Nov. 1884 (Wood, "Phys. Optics," 1st ed., p. 92). 27 Garnett : "Phil. Trans." (A), 203, 1904, pp. 385 and 205 ; 1906, p. 237. 28 Spence : "Phys. Rev." 26, 1908, pp. 521-23, and 28, 1909, pp. 233-63. 29 Mie : " Koll. Zeit." 1907, p. 129 ; "Ann. der Phys." 25, 1908, p. 337. 30 Gans and Happel : "Ann. der Phys." 4, 29, 1909, pp. 277-300. 31 Gans : "Ann. der Phys." 5, 37, 1912, pp. 881-900. 32 Gans: "Phys. Zeit." 13, 1912, pp. 1185-86. 33 Lampa: "Akad. Wiss. Wien. Sitz. Ber." 118, ia, 1909, pp. 867-83. 34 Rolla: "Accad. Lincei. Atti." 19, 1910, pp. 141-146. 35 Lampa: "Akad. Wiss. Wien. Sitz. Ber." 119, ia, 1910, p. 1565. 36 Robitschek : "Wien. Anz." 1912, pp. 241-42. 37 Zsigmondy (Spear) : " Chemistry of Colloids " (Wiley, New York, 191 7), pp. 94-95. 88 Bancroft : "Colour of Colloids," "J. of Phys. Chem." Vols. 23 and 24. 39 Svedberg : " Die Existenz der Molekule ". 40 Kerr: "Phil. Mag." 5, 26, 1888, p. 321. 41 De Metz : "La double Refraction accidentelle dans les liquides. Collection Scientifique," Gauthier-Villars, Paris, 1906. 42 Cotton and Mouton : " Les ultramicroscopes," etc. 43 Havelock: "Proc. Roy. Soc. Lon." A, 80, 1907, p. 28 ; "Phys. Rev." 5, 28, Feb. 1909, p. 136. 44 King: "Nature," 95, 1915, p. 701 ; "Proc. Roy. Soc." A, 88, 1913, 45 Martin: "Jour. Phys. Chem.," 24, 192Q. CHAPTER VI. MEASUREMENT OF THE SIZES OF ULTRAMICROSCOPIC PARTICLES. ALTHOUGH there is no doubt that the ultramicroscope en- ables one to see particles much below the former microscopic limit, still there is no very rigid method by which one can measure exactly the size of the particles involved. However, there are several methods by which the approximate sizes may be determined. Particles below the limit of visibility of the ordinary microscope have been called by Siedentopf 1 ultramicrons ; if the ultramicrons are visible in the ultramicroscope, they are named submicrons ; if not visible even in the ultramicroscope, amicrons. Table XVI shows the limiting sizes of the particles classed under the various heads. TABLE XVI.— LOWER LIMITS OF DIAMETERS OF SMALL PARTICLES. 2 Visible in ordinary microscope. •25 fifi or 2 - 5 x io _B cm. Ultramicroscopic particles. 1 | Submicrons. Amicrons. 1 1 Electric arc Strongest illumination sunlight All below a diameter of 15 mi or i*o nn or i5xio- 7 cm. roxio-'cm. roxio -7 cm. It has been remarked already that no direct determina- tion of the size can be made by measurement of the dia- meter of the particles ; i.e. the ultramicroscope betrays merely the presence of the particles with practically no evidence of the dimensions or shape of the individual particles. 3 One is then forced to get at the size indirectly by determining the 122 SIZES OF ULTRAMICROSCOPIC PARTICLES 123 number of particles in a given volume and, from the known total amount of dispersed material in a given volume of the solution, to determine the mass and size of each particle. Two methods of finding the number of particles per unit volume of solution have been used by Zsigmondy 4 : — 1. The measurement of the average distance between neighbouring particles in a given sample of the solution ; 2. A direct count of the number of particles in a deter- mined volume. In both of these methods the small sample viewed under the microscope must be very dilute ; it is gener- ally necessary to dilute a given colloid to some hundreds of times its original volume in order either to get the particles far enough apart for reliable measurement, or to render the number of particles few enough to be conveniently counted. Method (1) : If r equals the mean distance in cms. between the particles and if we consider them to be small spheres, then a, the radius of each sphere, is given by d where A = the weight of the particles in unit volume of the sample of the liquid viewed, and d = the density of the particles in the sol. Of course, in the measurement of A any dilution of the original solution must be taken into account. The values of r may be measured by means of a micrometer eye-piece or by viewing in the solution a graduated scale, such as the scale scratched on the slide of a haemocytometer. Method (2) : Zsigmondy fixed the volume in which the number of particles was counted by means of an eye-piece micrometer and the slit S (see Fig. 4, p. 42) which bounds the illuminating pencil. "By means of the eye-piece micro- meter a part of the cone of rays dd, Fig. 1 3, may be sharply defined from side to side, whereby the length and breadth of the volume chosen may be known. The depth of the illum- inated volume thus defined may be easily determined with the eye-piece micrometer by a quarter rotation of the slit S." 5 In similar observations by the author, 6 the volume of 124 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS liquid viewed was determined by the use of a Zeiss haemocyto- meter slide (Fig. 14). At the centre of a circular piece of glass, A, an area of 1 sq. mm. is divided into small squares of 1/20 mm. side by means of fine lines ruled with a diamond point. The plate B surrounds A so as to leave an annular Fig. 13. trough about the central disk. The upper surface of B is exactly o - i mm. above that of A, so that when the cover glass C is placed on B a layer o*i mm. thi<& exists between A and C. The surfaces of A, B, and C are, of course, ground perfectly plane. When a drop of a sol is placed on A and A B Fig. 14. covered with C, a volume of 0*00025 cu. mm. can be dis- cerned through the microscope. By raising or lowering the objective very slightly, it is possible to bring all the particles in a layer 01 mm. thick into view, and so for sufficiently dilute solutions the number of particles per cu. mm. can be very approximately determined. The following is a sample SIZES OF ULTRAMICROSCOPIC PARTICLES 125 of such a determination, typical as regards the method and the magnitude of the quantities involved : — A silver solution (after Bredig) containing 6-8 mgms. of metal per 100 c.c. was diluted with distilled water to one hundred times its original volume. A drop of the dilute liquid showed on the average the presence of 300 particles per volume o - i cu. mm. Therefore in the original solution per c.c. there were 3 x10 s particles weighing 6-8 x io~ 6 grm. If the specific gravity of the silver particles be taken as I0'5, the mean volume of the particles in solution is 2-2 x 10 ~ '* c.c. Assuming that the particles are in the form of small spheres, the mean radius being a, ^ira 3 = 22 x IO -16 , .-. a= 17 x io -5 There are elements of uncertainty in both of the above methods. Under the best circumstances the observations require considerable time, during all of which the Brownian movement will cause particles to move into and out of the field of view ; such a difficulty can be overcome only by a large number of observations on each sample. It is not known definitely whether or not merely diluting the sample may cause a change in the size of the particles. The ordinary method of finding the total amount of disperse substance per unit volume is by evaporating the solution and weighing the residue; in this, one assumes that the substance is all confined to the submicrons, while in reality there are probably always present amicrons and some of the material in the state of molecular solution. A more exact determination involves the separation of the disperse phase by means of a collodion filter and analysis of the dry residue and filtrate separately. An additional source of difficulty is in the choice of the density of the material suspended. Experiments such as those of Rose 7 and Cholodny 8 on gold and silver colloids show that there is not much error in taking the density equal to that of the solid for the metal sols ; for such solutions as mastic in water, the density reckoned from the dried residue would be only an approximation. Method (3) : If the particles involved are just about the 126 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS limit of the ordinary microscopic size (l~5 x iO~ 5 cm. in diameter) the methods given by Perrin 9 may sometimes be used to advantage, or the size may be determined in accordance with Stokes' law by the rate of settling of the particles in the liquid. The latter gives the velocity of fall, v, of a particle of radius a through a liquid -of viscosity 17 from the formula F F, the force acting on the particle, is in this case that due to gravity, .-. F==|7r^(/3 - Pl )g, where p and p x are the densities of the particles and the liquid medium respectively. From these equations we have 9 r,v Method (4) : As indicated under the preceding method, Stokes' law cannot be applied directly to particles so small that the gravitational settling is masked by the Brownian movement. The author 10 has recently suggested a method by which artificial settling may be produced by subjecting the colloidal particles to a vertical electric field. Experiments on the mass of colloid have not been found to give consistent results, but it ought to be possible to work with single par- ticles in water, as Millikan did with drops in air. When a vertical electrical field is applied, which gives a motion to the particle greatly in excess of either the gravitational or Brownian movement, the particle is dragged up or down through the liquid ; under such conditions, the comparatively insignificant gravitational force will be added to the electrical force for downward motion and subtracted for upward motion. If V = limiting velocity due to electrical field, and v — „ „ gravitation, Xe + mg = 6irrja (V + v), Xe — mg = 6ir7)a (V - v). Subtracting these, we have — 2-mg = 1 2-K'qav. SIZES OF ULTRAMICR0SC0P1C PARTICLES 127 From which by inserting the expression for m a 9 yv ~ 2 ' (p ~ P X )S ' By means of the ultramicroscope, a single particle may be watched in its motion with or without an electrical field acting. In practice, using the ultramicroscope, we have several different motions to take into account : (1) drift of liquid (d) as a whole (convection currents) ; (2) endosmosis (s) on the liquid as a whole, an effect which changes direction with a change in the direction of the electric field ; (3) velocity of particle due to electric field (V) ; and (4) velocity of particle due to gravitation (v). The observed velocity in one direction will be (with vertical field on so as to move particle vertically down) V+v±d±s = D. When the field is reversed the velocity will be V - v ±d±s = U. Since d may be observed directly when there is no field on, we have B' = D + d=V + v±s, U' = U + d = V - v ± s, the sign of s being retained the same in the two cases, since it will change in direction with V. Subtracting these equations, we have D' - U' = 2 v, from which by observation we obtain the velocity " v " of a particle due to gravitation — the " v " which is to be inserted in the above equation in order to obtain the value of the radius. In actual practice, by carefully preventing evapora- tion of the liquid, d may be made extremely small. The other methods n suggested for the determination of the radii of the particles are really of only theoretical im- portance. The radii may be deduced from various formulae, such as that for the Brownian movement, which were developed for the mathematical expression of some physical property of the colloid and which involve the radii only incidentally. 128 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS In one set of formulae of this type we may class together those which rest fundamentally on an application of Stokes' law to the equilibrium state set up in the colloidal solution, viz. : (i) the formulae for the Brownian movement (p. 73), (2) that expressing Perrin's law of the distribution of the particles at different heights in the liquid (p. 81), and (3) the expression for the diffusion coefficient of the particles. The latter is a result of the work of Sutherland, 12 Einstein, 13 Smoluchowski, 14 Cunningham, 15 and Millikan; 16 the diffusion constant, 8, is given by the expression PT * + A - Rl « N 6TTT)a where / is the mean path of the molecules of the solvent, and A is a constant of value approximately 0-815. As far as the measurement of the radius of the particle is concerned, all these methods involve work out of all proportion to their exactness and applicability. Other suggested formulae have to do with the optical pro- perties enumerated in a previous chapter; for example, (1) the absorption of light by a given solution, and (2) Rayleigh's law of the scattering of light by an atmosphere of fine particles (p. 105). These phenomena involve measurements which are too indefinite to be applied to the determination of the radii of the particles. As noted in Table XVI, the smaJlest particles visible in the ultramicroscope have a diameter of about 1 x io~ r cm. ; the most exhaustive work on this point is that of Zsigmondy and Siedentopf in determining the sizes of the particles in their various gold solutions. They found that even after they had deprived their solutions of all their ultramicroscopically visible particles, the solutions had still a faint opalescence and gave chemical reactions unique to the substance in solution. These facts point to the presence of amicrons and possibly molecules of gold in the solutions. On the other hand, the kinetic theory gives the following values for the sizes of the molecules named : — THE SIZES OF ULTRAMICROSCOPIC PARTICLES 129 hydrogen = cri x I0~ 7 cm., methyl alcohol = o - S x io~ 7 cm., chloroform = o - 8 x io"'cm. In view of the small gap which exists between the largest molecule and the smallest visible submicron, it is interesting to recall the determinations of the molecular weights of some typical colloids by the methods of the depression of the freezing-point and the measurement of the diffusion coefficient. As is well known, if A = the experimentally determined depression of the freezing-point which 1 00 grms. of the solvent suffers through the addition of p grms. of the substance, K = molecular depression of the solvent, and M = molecular weight of substance to be determined, A _ p_ K ~ M M = pK These determinations give the following results for the substances indicated : — Malto-dextrine . . . . . 965 Gum-arabic Glycogen Ferric hydrate Tungstic acid . Egg albumen . Starch . Albumose Tannin . i,8oo 1,625 . 6,000 i,75o 1 4,000 25,000 2,400 643-3 7oo The diffusion method rests on a determination of the rate at which the colloid diffuses into pure water. If we have a solution in a trough with parallel sides and 1 sq. cm. cross- section and the solution at one plane perpendicular to the- column of liquid is (n + |) normal and that at a second plane,. 1 cm. from the former and parallel to it, is (n - £) normal, then the difference in osmotic pressure at the two planes is equal to> the osmotic pressure of a normal solution, = RT per sq. cm. at 0° C. 9 i 3 o PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS This pressure tends to drive the dissolved molecules in the direction of the lower concentration, and acts on all dissolved molecules between the two planes perpendicular to the liquid, i.e. on — — grm.-molecules. If the force necessary to drive iooo I grm.-molecule of the dissolved substance with a velocity of I cm. per sec. is P kilograms — this force is known as the coefficient of friction of the substance — the velocity v is given by RT. iooo i ooo P . n cm. per sec. The quantity of dissolved substance passing the plane of lower concentration in I sec. is found from the number of mole- cules lying between that plane and a parallel plane v cms. distant. The number of milligram-molecules in the volume v c.cs. is v x n = K, •K- RT K is called the diffusion coefficient. The friction coefficients of substances of non-conducting solutions are found from the diffusion coefficient. According to a calculation made by Euler the friction of a grm.-mole- cule is approximately proportional to the square root of the molecular weight of the dissolved substance. If we apply this method to calculate the molecular weight of the four colloids examined by Graham, we have : — Gum-arabic ..... = 1,750 Tannic acid ... = 2,730 Egg albumen ..... = 7,420 Caramel ...... = 13,200 These determinations offer strong evidence of the continu- ous gradation in the sizes of the particles of the disperse phase of various solutions, from the size of ordinary molecules to that of the particles of coarse suspensions. THE SIZES OF ULTRAMICROSCOPIC PARTICLES 131 BIBLIOGRAPHY. 1 Zsigmondy : "Zur Erkenntnis der Kolloide," Chap. V; Translation (Alexander), Chap. VI. 3 Zsigmondy: "Erkenntnis," Chap. VI ; Alexander, Chap. VII. 3 Siedentopf : "Jour. Roy. Mic. Soc." 1903, p. 573. 1 Zsigmondy : "Erkenntnis," Chap. VI, 3 ; Alexander, Chap. VII, 3. 5 Zsigmondy : Alexander, p. 119. 6 Burton : "Phil. Mag." (6), 11, 1906, p. 425. 'Rose: vide Wilh. Ostwald, "Lehr. d. allg. Ch." 2 Aufl. 1, 1903, P- i°93- 8 Cholodny : " Koll. Zeit." 2, 19, Ref. and 340, 1907. 9 Perrin: "Bull. Soc. Fr. Phys." 3, 1909, p. 155. 10 Burton: "Proc. Roy. Soc. Lon.," 95 A, 1919, pp. 480-83. 11 Henri, V.: "Trans. Faraday Soc." 9, 1 and 2, 1913, p. 34; "Koll. Zeit." 12, 191 3, pp. 246-50. 12 Sutherland: "Phil. Mag." (6), 9, 1905, p. 781. 13 Einstein: "Ann. der Phys." 19, 1906, p. 289. 14 Smoluchowski : "Ann. der Phys." 21, 1906, p. 756 ; "Bull. Int. Acad. Crac," 1906, p. 211. 16 Cunningham: "Proc. Roy. Soc. Lon." 83 A, 1910, p. 357. 16 Millikan : "Phys. Zeit." 11, 1910, pp. 1097-1109J "Science," N.S. 32, 1910, pp. 436-48. CHAPTER VII. MOTIONS OF PARTICLES IN AN ELECTRIC FIELD. i. Cationic and anionic solutions. — The investigation of this property of the so-called colloidal solutions dates from the work of Linder and Picton. 1 Prior to that, experiments on the motion of the particles of ordinary suspensions under an elec- tric field had been carried out by various workers, and briefly the results obtained were as follows 2 : — In suspension in water, the particles of starch, platinum black, finely divided gold, copper, iron, graphite, quartz, feld- spar, amber, sulphur, shellac, silk, cotton, lycopodium, paper, porcelain, earth, and asbestos, move towards the positive pole. When the above materials are suspended in a similar man- ner in turpentine oil, they all move towards the negative pole, with the sole exception of sulphur, which moves in the same direction in turpentine as in water. Fine gas bubbles of hydrogen, oxygen, air, ethylene, carbon dioxide, and small liquid globules of turpentine and carbon bisulphide, when in water, all move toward the positive pole. 20 Turpentine globules and small gas bubbles in ethyl alcohol move to the positive pole. Quartz particles and air bubbles in carbon bisulphide move to the negative pole. These results led Wiedemann to make the statement that " in water all bodies appear, through contact, to become nega- tively charged, while, through rubbing against different bodies, the water becomes positively charged ". When Linder and Picton tested similar properties of the particles in chemically prepared solutions, they found that such a generalization was inexact. They give the following results : — 132 MOTIONS OF PARTICLES IN AN ELECTRIC FIELD 133 Suspensions of aniline blue, arsenic sulphide, indigo, iodine, shellac, silicic acid, starch and sulphur in water, and of bromine in alcohol, show attraction to the positive electrode. The following materials suspended in water move in the opposite direction : Ferric hydrate, haemoglobin, Hoffman's violet, Magdala red, methyl violet and rosaniline hydro- chloride. As a conclusion to their work Linder and Picton make the significant statement that experiment seems to show that, if the solution is basic or tends to break up so as to leave a free base active, the motion is to the negative pole, i.e. the particle is positively charged ; if the solution is acidic, motion is to the positive pole, and consequently the particles are negatively charged. Taking into consideration the recent results of many workers, we may divide colloidal solutions and suspensions into two classes, anionic and cationic, according as the par- ticles in solution move to the anode, i.e. are negatively charged, or to the cathode, i.e. are positively charged. Solutions in water : — Anionic. Cationic. 1. The sulphides of arsenic, 1. The hydrates of iron, chro- antimony, and cadmium. mium, aluminium, cop- 2. Solutions of platinum, sil- per, zirconium, cerium, ver, gold, and mercury. and thorium. 3. Vanadium pentoxide. 2. Bredig solutions of bis- 4. Stannic acid and silicic muth, lead, iron, copper. acid. 5. Aniline blue, indigo, molyb- 3. Hoffmann violet, Mag- dena blue, soluble Prus- dala red, methyl violet, sian blue, eosin, fuchsin. rosaniline hydrochloride, 6. Iodine, sulphur, selenium, Bismarck brown, methy- shellac, resin. lene blue. 7. Starch, mastic, caramel, 4. Albumen, haemoglobin lecithin, chloroform. agar. 8. Silver halides. 5 Titanic acid. 9. Various oil emulsions. 134 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS The charges on particles of starch, gelatine, agar, and silicic acid are very small and difficult to observe. Bredig solutions 3 of lead, tin, and zinc in ethyl alcohol are all cationic, while bromine in the same solvent is anionic. Methyl alcohol gives Bredig solutions with lead, bismuth, iron, copper, tin, and zinc which are cationic. The writer has also prepared anionic solutions of platinum, silver, and gold in ethyl malonate by Bredig's method. According to Thornton, 4 diatoms, unicellular algae, and vegetable micro-organisms in general are positively charged (cationic solutions) and amcebe and animal micro-organisms in general are negatively charged (anionic solutions) (see also Schneckenberg 6 ). Some organic colloids, such as globulin, and some in- organic, such as silicic acid, are anionic in alkaline solution and cationic in acid solution. 2. Theory of cataphoresis. — The study of the electrical motion of particles in suspension follows the work of Reuss, Faraday, Wiedemann, and Quincke on the phenomenon of electrical osmosis. When the anode and cathode compart- ments of a conductivity tube are separated by a diaphragm of porous earthenware,, the electrolyte will pass through this wall towards the cathode until an equilibrium pressure is at- tained. Similar effects were found by Quincke 6 by using capillary tubes instead of the earthenware diaphragm. The liquid was varied and the influence of the surface of the capil- lary was tested by lining the glass tube with other substances, e.g. sulphur ; oil of turpentine flowed toward the anode through a glass tube, but toward the cathode when the glass capillary was lined with sulphur. The interstices between the particles, suspended in a liquid and. set in motion by an electric field, may be looked upon as, in effect, a series of movable capillary walls ; that is, the liquid is stationary while the walls them- selves (the particles) move in the field. The theory of this motion of finely divided particles in sus- pension in liquids was long since propounded by Helmholtz 7 and later amplified by Lamb. 8 Without assuming, for the moment, anything with regard to the cause of the formation of MOTIONS OF PARTICLES IN AN ELECTRIC FIELD 135 the colloidal solutions, we may apply the same theoretical con- siderations to the movements of these particles. The fundamental assumption is that when a particle sus- pended in a liquid becomes charged, there exists about it a double electric layer ; when the particle is negatively charged, there is a layer of negative electricity on the surface of the solid particle, while in the liquid immediately surrounding it there is a corresponding layer of positive electricity. "On the whole the algebraic sum of the two equals zero, and the centre of gravity of the complete system, solid particle and surrounding positively charged fluid layer taken together, can- not be moved by the electric forces which arise from the potential fall in the liquid through which the current passes. However, the electric force will tend to bring about a displace- ment, relatively to each other, of the positively charged fluid layer and the negatively charged particle, whereby the fluid layer follows the flow of positive electricity while the particle moves in the opposite direction. If the liquid were a perfect insulator the new position would still be a condition of equili- brium. Since, however, through the displacement of the layers the equilibrium of the galvanic tension between the solid particle and the liquid is disturbed, and on account of the conductivity of the liquid always seeks to restore itself, the original state of electrical distribution will tend to be con- tinually reproduced and so new displacements of the particle with respect to the surrounding liquid will continually occur." 9 This theory was put forward by Helmholtz in the course of his mathematical development of the explanation (suggested by Quincke) of the electrical transport of conducting liquids through the walls of porous vessels or along capillary tubes ; Quincke assumed that there existed a contact difference of potential between the fluid and its solid boundaries. Through- out his treatment of the phenomenon, Helmholtz considers that there is no slipping of the fluid over the surface of the solids with which it is in contact. On this point Lamb disagrees with Helmholtz, holding that the solid offers a very great, but not an infinite, resistance to the sliding of the fluid over it, and that, while the effect of this slipping would be entirely insensible 136 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS in such experiments as those of Poiseuille, it leads to ap- preciable results in the present case in consequence of the re- latively enormous electrical forces acting on the superficial film of the liquid and dragging the fluid, as it were, by the skin through the tube. The practical difference between the views taken by Helmholtz and Lamb respectively may be shown in a simple case. Using the numerical results found by Wiede- mann, Helmholtz infers that for a certain solution of copper sulphate in contact with the material of a porous clay vessel, the contact difference of potential E between the solution and the solid wall is given by E where D is the electromotive force of a Daniell's cell. The variation introduced by Lamb would change this equation into E / D-aT 177 • ■ • • CD where d = the distance between the plates of an air con- denser equivalent to that virtually formed by the opposed surfaces of solid and liquid, and / is a linear magnitude, measuring the "facility of slipping" and equal to ??//3, 17 being coefficient of viscosity of the liquid and /3 the coefficient of sliding friction of the fluid in contact with the wall of the tube. Lamb gives reasons for supposing that / and d are of the same order of magnitude (that of 1 ~ 8 cm.). Of course, if / = d, Helmholtz's formula remains unchanged, and it is very prob- able that the ratio - differs very little from unity. d Lamb deduces the following expression for the velocity (v) of a charged particle through a liquid under an electric force, when the motion has become steady : — Xe = 47r« 2 ,r\.v—. . . . (2) where X = gradient of electric potential in the liquid, e = charge on the particle, a = radius of the particle, and 7] and / as above. MOTIONS OF PARTICLES IN AN ELECTRIC FIELD 137 We may look upon the particle with the double electric layer as a small condenser of two concentric spheres whose distance apart (d, the same as before) is small compared with a. The capacity of such a condenser would then be given by a 2 C - jK ... . . (3) where K = specific inductive capacity of the liquid. If V indicates the contact difference of potential between the solid and the liquid, we have (since Q = CV), e = a' • ■ (4) Substituting this value of e in equation (2) and transposing we get v - 3 ' 4tt t]v ■ • (5) all electrical measurements being made in electrostatic units. This equation, which is similar to one given by Perrin, 10 will enable us to find values of V . — for any solid and liquid, if for known values of X, we can observe the corresponding values of v. We may deduce immediately from this formula that the mobility of a particle of given constitution, in a given liquid medium, is independent of the radius, and that the product rjv for a given solution must be constant. 3. Method of measuring the velocities of particles (in cms. per sec. for field of potential gradient equal to one volt per cm.). — Two methods have been used for measuring the velocity of colloidal particles: (1) the U-tube method due to Nernst, Whetham and Hardy, 11 and (2) the ultramicroscopic observation of the velocity of single particles in an electric field. Probably the first is the more reliable method of the two. The limbs of the U-tube used by the writer 12 were each about 12 cms. long and about 1-5 cms. in diameter (Fig. 15); they were graduated in mms. throughout their length. Into the bottom of the U-tube is sealed a fine delivery tube provided 138 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS w with a tap (T) and a funnel (F) ; this tube is bent round so as to run up behind the limbs and to bring the funnel to the same height as the top of the U-tube. The colloidal solution to be tried is poured into the funnel so as to fill the funnel and small tube to the tap, which is closed ; water having a specific conductivity equal to that of the colloid is then poured into the U-tube so as to fill it to a height of about 3 cms. The whole tube is then placed in a large glass water bath so as to be almost submerged ; this water should be kept at a constant temperature during the course of any experiment. At the end of a few minutes the tap (T) is opened very slightly and the colloidal solution allowed to force the water gently up the limbs of the tube to any required height. If care- fully manipulated the surface of separation between the clear water and the solution is very distinct and will remain so for hours. Two electrodes of coiled platinized plati- num foil are supported at a convenient level in the two limbs of the tube and the clear water allowed to rise well above them. The electrodes are attached to the terminals of a set of storage , cells of con- stant voltage, and when the current is completed the surface of separation in one limb will at once begin to rise gradually while that in the other will sink. In practice, the connexions may be made through a reversing key and the voltage, usually fixed at about no volts, may be left on one way for ten minutes and then reversed for twenty minutes. The velocity is reckoned from the displacement of the surfaces during this final twenty minutes ; one-half the sum of the displacements in the two tubes is taken as the distance travelled by a particle in the given time. A typical set of observations is given in Table XVII. Fig. 15. MOTIONS OF PARTICLES IN AN ELECTRIC FIELD 139 TABLE XVII. Voltage— Height of Colloidal Surface. Observed Time. Sign of Krght Temp. Velocity in cm. Electrode. Left. Right. sec. "'37 + 118 11° C. 54 mms. 55 mms. 11-47 + 118 61 „ 50 » Current off 11-48 - 118 11° C. 61 „ 50 „ 11-58 - 118 55 >i 56 „ 96 X I0- 6 I2"c8 - 118 n°C. 5° .. 62 „ Electrodes at 15 mms. in each limb. It will be seen from the table that there has been an apparent settling of the colloid in the tube while the current was running. This is quite usual but, as the reckoning is made, it could not affect the rate, since this slight lowering of the surface is uniform in both limbs, so that while it is added to the velocity in one limb it is subtracted from the velocity in the other. In order to find the value of the electric force in the tube, it is, of course, necessary to know the effective distance between the electrodes A and B. To do this the tube is filled with, say, a "Oi normal potassium chloride solution, placed in the water bath, and the resistances are taken with the electrodes placed at the successive centimetre marks down the tube. In this way, for the particular tube used for the above results, it was found that the resistance of the curved part of the tube from 90 in L to 90 in R was 8 - 8 times the resistance of each cm. length of the single limbs. So that when, as in the case cited in Table XVII, the electrodes were placed at 1 *5 in each tube, the effective distance between the electrodes was 23 "8 cms., and therefore the strength of the electric field was 118 238 4/9 volts per cm. Thus the absolute value of the mobility of the silver particles in water at a temperature of ii° C. would be 19-6 x io -5 cms. per sec. per volt per cm. In order to obtain dependable results, great care must be taken to have the. temperature of the colloidal solution and the supernatant liquid quite uniform before the tap T is first Ho PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS opened, and throughout the whole of the observation the whole tube should be kept in a water bath. A method similar to the above was used by Coehn 13 and by Galecki u in similar measurements. Whitney and Blake, 15 and Schmaus, 16 measured the velo- cities of colloidal particles by immersing the electrodes in the colloidal solution itself. This method has two disturbing elements ; in the first place, the products of electrolysis pro- duced at the electrodes affect immediately the solution itself and, in the second place, there occurs at the electrodes a charging and discharging of the particles which causes anomalous motions in the neighbourhood of the electrodes ir . The first workers to use the ultramicroscope for velocity measurements were Cotton and Mouton. 18 Electrodes were introduced, a few mms. apart, into the sample of solution con- tained in the microscopic slide, a difference of potential of a few volts applied, and the time required by a single particle to cross the field of view noted. They found that as long as they viewed only the particles in the middle of the layer, the results were concordant, but as the particles in view were situated nearer and nearer to the bottom or to the top of the cavity, the motion of the charged particles first ceased and then was reversed. The distance from the glass walls to the layer at which reversal took place was 25 fi. Cotton and Mouton found that this reversal took place both with negatively and with positively charged particles. Near the walls of the chamber one would expect the liquid to move toward the cathode and sweep the particles along with it ; it is difficult to explain, however, the reversal of the motion in the case of the positively charged particles. In working with oil emulsions by this method, Ellis 19 introduced corrections for this disturbing feature by observing the apparent velocity at given depths and calculating the probable value of the velocity of the particles relatively to the liquid. In addition to the action of endosmose there are inherent in this method the same difficulties as described above in the Whitney and Blake method ; viz. the disturbances due to the electrodes being introduced directly in contact with the colloid itself. MOTIONS OF PARTICLES IN AN ELECTRIC FIELD 141 It was suggested by Ellis that endosmose affects the re- sults in the U-tube method, but in the author's experiments tubes of various sizes have been used at different times and all gave concordant results. Recent work by McTaggart 20 on the measurement of similar velocities for air bubbles in various liquid media shows that there is no such effect for tubes with diameters of the order of one or two cms. ; further, such an effect would be extremely small for the small currents used in such experiments. 4. Limitation of the U-tube method. — It has been suggested by the author 26 that the apparent settling noted just under Table XVII might be explained by the action of gravity on the colloidal particles. The particles when left to themselves will not show any settling on account of the Brownian movement ; it is well known that bodies falling in a fluid under gravitation will be accelerated until they reach a fixed limiting velocity at which they fall — the velocity involved in the formula for Stokes' law. Now, on account of the random nature of the Brownian movement, the particle is knocked hither and thither before it has time to attain a limiting velocity in the direction of the gravitational force. However, in the mobility experiment, since the particles are given comparatively large motions in a vertical direction by the electrical field, they do attain limiting velocities up or down and then the resultant force on each particle will be given by the algebraic sum of the electrical and gravitational forces. Such action would explain the settling apparent in Table XVII and calculations of the size of the particle from this view agree very well with observations of the size by other methods. Recent, as yet unpublished, work by Ross, under the direction of the author, has not supported this explanation of the settling but has brought to light limitations to the use of the U-tube method of determining mobility. It was found (1) that this settling effect was not constant for a given sample of colloid but that it increased with the voltage applied, i.e. the faster the particles were made to move in the electric field, the greater the settling effect, and (2) that, if the electric field is U2 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS left on in one direction for a sufficiently long time, the ascending column of colloid moves up more and more slowly and finally actually alters its direction, showing that the particles in this part of the column change the sign of their charge. In these mobility experiments it is always apparent that the upward advancing surface is always the sharpest, and there are often indications of local coagulation at this surface. It has recently been pointed out by Keller 27 in his work on the electrical charge on dye particles that when a particle moves into the neighbourhood of an electrode, it moves into a region more acidic or more basic and that consequently its charge may undergo change in size and, also, even in sign. This work suggests then that the mobilities should always be observed over short intervals of time and with small movement of surfaces in the tubes. 5. Experimental values of the .mobilities of particles. — In Table XVIII are collected the experimental determina- tions of the mobilities of particles in suspension ; the results are expressed in cms. per sec. per volt per cm. The pre- fixed sign indicates the kind of charge possessed by the particles. In the third column of the table are given the values of the potential difference between the particle and the medium, as calculated from the formula, p. 137 (/ = d). The corre- sponding values obtained by Quincke 6 and Tereschin 28 for the potential difference between glass and water in endosmose experiments were respectively "053 and '047 volt; Schmolu- chowski 29 points out that this means that glass particles in water (at 18° C.) would move in an electric field of one volt per cm. with the velocity of 34 x io -5 cms. per second — a value in close agreement with many of the mobilities in the table. This agreement is more than a coincidence and suggests that a common cause must account for the charging of the particles in the various cases. On the other hand, at the bottom of the table are inserted the values of the corresponding mobilities of typical electro- lytic ions in dilute solutions. Keeping in mind that Stokes' law (see Cunningham 30 and Millikan 31 ) does not hold in its MOTIONS OF PARTICLES IN AN ELECTRIC FIELD 143 TABLE XVIII.— MOBILITIES OF THE DISPERSE PHASE IN VARIOUS AQUEOUS SOLUTIONS. Mobility in cms. P.D. in volts be- Disperse phase. per sec. per volt tween the disperse Author. per cm. x 10- 5 . phase and medium. Suspensions. Lycopodium -25-0 -■035 Quincke ° Quartz -30-0 -•042 Whitney and Blake 15 Air bubbles -40-0 - '056 McTaggart 20 Suspensoids. Arsenious sulphide -22-0 -•031 Linder and Picton l Prussian blue -40-0 -■056 Whitney and Blake I6 Prussian blue -41 "5 -•058 Burton 21 Gold (chem. prep.) -40*0 -•056 Whitney and Blake 1B Gold (chem. prep.) -7-1 to 57-4 Galecki" Gold (chem. prep. and Bfedig) -26'0 -•036 Rolla 22 Gold (Bredig) -21'6 -•030 Burton 12 Platinum -30-0 - '042 Whitney and Blake 15 Platinum (Bredig) -24-0 -■034 Rolla 22 Platinum (Bredig) -20-3 -•028 Burton 12 Platinum (Bredig) - 20 to 40 S vedberg M Silver (Bredig) -32-0 to 38 Cotton and Mouton 18 Silver (Bredig) -20'O -•028 Svedberg 23 Mercury (Bredig) -25-0 -'°35 Burton 12 Silver (Bredig) -23-6 -•033 !» Bismuth (Bredig) IfO •015 tl Lead (Bredig) I2"0 •017 »! Iron (Bredig) ig'o •027 »» Ferric hydroxide 30-0 •042 Whitney and Blake 16 Ferric hydroxide 52 - 5 - °73 Burton 21 HA Globulin - ig - 8 to 22 -g - "031 Hardy 2 * HC1 Globulin - g - o to 11 '5 -•015 it NaOH Globulin 77 o-io i) H 2 S0 4 Globulin -18-5 -•026 n H 3 P0 4 Globulin -23-0 -•032 VI Emulsions. Hydrocarbon oil -43-0 -•060 Lewis 25 Spec, acid-free oil -37"2 -•052 Ellis 19 Acid-free oil -32-4 -•045 m Liquid paraffin -29-3 - -041 n Cylinder oil -27*0 -■038 it Water-soluble oil -48-0 -•067 >i Aniline, fresh dist. -31-1 -•043 1* Chloroform - lO'O — - 0I4 >> Gummigutt -i8-i -•025 »j Mastixharz -177 - -024 »» Electrolytic ions. Organic Comp.'s (high mol. wt.) 20 "O Hydrogen (+) 329-0 Hydroxide ( - ) 180 - Chlorine (-) 68-o ordinary form when the radii of the particles approach the length of the mean free path of the molecules of the medium, 144 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS we may consider that there is a possibility of complete con- tinuity in this phenomenon of motion in an electric field as we go from suspensions of large particles through the region of ordinary colloidal solutions to true solutions. As we shall see later, the mobility possessed by such par- ticles is greatly affected by the introduction of extremely small traces of electrolytes and, consequently, one gets some variety in the values of the mobility, obtained when the specific conductivity changes. For example, copper solutions, the specific conductivity of which varied from 3'i x io -6 to 8 - 2 x'io~ 6 , gave mobilities varying from 33-0 x io -5 to 23-4 x io -6 cms. per sec. per volt per cm. It is impossible^ therefore, to assign a definite number as the transport number of a particular colloidal particle. We have already noted that the mobility of a particle of given constitution in a given liquid medium is inde- pendent of the size of the particle. Hardy 32 prepared a series of similar sols of globulin containing particles of different sizes, but found that the velocities with which they moved in a given electric field were always the same. If particles of different sizes do exist in the electrically pre- pared solutions, the size would probably depend on the violence of the sparking during the preparation of the solution. Three silver solutions were prepared by the writer by using varying currents and voltages for producing the spark, all other conditions being the same except the time of sparking. As shown in Table XIX, the differences in the mobilities, which were all determined at 1 1° C, are all within the limits of error in the experiment. TABLE XIX.— SILVER SOLUTIONS. No. Voltage. Current. Time of sparking. Mobility in — - sec. volt per cm. I 2 3 80 volts. 60 ,, 4° .. 8"5 amperes. T5 6-5 10 mins. 20 „ 3° ,. - 197 X IO- - ig - 6 X IO- 6 - ig - 3 x io- 6 MOTIONS OF PARTICLES IN AN ELECTRIC FIELD 145 Since there is no a priori reason for assuming that all the particles are of a uniform size, these results would confirm Lamb's theory. 6. Effect of viscosity of solution. — The writer has carried out a series of experiments on the validity of the formula given on page 137 in so far as r\v = constant, as long as one deals with the same material in the particle, the same liquid medium, and constant potential gradient. TABLE XX.— SILVER COLLOIDAL SOLUTIONS. No. Temperature Centigrade. Mobility (r). Viscosity of water at given temperature Product t\v. I 2 3 4 5 6 3° 9-9° ii° 21° 31° 4°-5° I5 - I X IO- 5 18-6 x 10 - 5 ig'6 x 10 -° 25-5 x 10 - D 30-1 x 10 - 6 37*2 x 10- 6 •016214 •013300 •OI2822 •oogg22 •007972 •006577 24 - 5 X IO- 7 247 x 10- 7 25 - I x 10- 7 25 - x 10 -' 24-0 XIO-' 24 - 5 x 10 - 7 In Table XX are given the mobility determinations for silver colloidal solution in water over a range of temperatures from 3° C. to 40'5° C. In performing these experiments the water bath in which the velocity tube was always supported was heated and the water constantly stirred ; the temperature was maintained constant at any one time by the use of an ordinary thermostat. The sensibly constant value of r)v is in good accord with the requirements of the velocity formula. These experiments also indicate the primary importance of taking account of the temperature in this work ; a neglect of the influence of changing temperature in any form of apparatus for measuring these velocities leads to bewildering results. 17 7. The effect of the medium. — Linder and Picton 1 first sug- gested some interaction between the liquid medium and the particles: "Experiment seems to show that if a solution is; basic or tends to break up so as to leave a free base active, the motion is to the negative pole. If the solution is acidic, or tends to break up so as to leave a free H ion active, motion is to the positive pole." 10 146 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS On account of the inadequacy of a purely physical explana- tion of the cause of the charge possessed by colloidal particles, Hardy 24 was led to account for the phenomena from a chem- ical point of view. In the samples of globulin tabulated on p. 143, acid globulin gives cationic solutions, while basic globulin gives anionic solutions. A consideration of the classification of the Bredig metallic hydrosols and alcosols, given on p. 133, sheds light on the influence of the medium. In the results given on Table XVIII one is struck with the fact that the particles of the electro- positive oxidizable metals are all positively charged, while the electro-negative non-oxidizable metals give negatively charged particles. When we recall that iron in such solutions appears to form the hydrate, and that the particles bear' a charge of the same sign as the particles in chemically pre- pared colloidal solutions of ferric hydrate, one is justified in suspecting that in the cases of iron, bismuth, lead, and copper the process of manufacture of these electrically pre- pared solutions involves the production of a certain amount of the hydrate of the metal. Such an hypothesis at once suggests an analogous action on the part of gold, silver, plati- num, and mercury, viz. an interaction between the metal and hydrogen — a view to which the already known existence of a hydride of platinum would lend some colour. This explanation was first offered by Hardy 33 : " Consider the hydrosol of a metal such as platinum. The colloid par- ticles are negatively charged, they are anionic in character, and the charge is due to a reaction between the metal and the water at the moment of formation of the hydrosol whereby the hydride PtH is formed which ionizes in the sense PtH ^ Pt' + H\ The chief number of the ions Pt' are in the form of masses so large as to have the properties of matter in mass, they are not of molecular dimensions and they form an internaL phase. Ionization is a phenomenon of the surface of these masses only. It confers on the particle its electrical charge, and it is in this case the ' incomplete chemical combination ' which Lord MOTIONS OF PARTICLES IN AN ELECTRIC FIELD 147 Rayleigh regards as the source of contact differences of poten- tial to which I referred in an earlier paper. In reactions, there- fore, an electropositive colloid is a weak alkali, e.g. hydrosol of ferric hydroxide, and an electronegative colloid a weak acid, e.g. silica." The suggestions given by these results for the hydrosols are strengthened by the observations on colloidal solutions in the alcohols, which we may call, after Graham, alcosols. Pure methyl alcohol and pure ethyl alcohol were used in the prepara- tion instead of water. Although repeated trials were made with the metals gold, silver, and platinum, the writer has never succeeded in getting them to remain suspended in either of these alcohols. On the other hand, the metals lead, tin, and zinc form solutions in both of the alcohols, while with methyl alcohol solutions were also obtained with bismuth, iron, and copper. In all these solutions the particles moved to the negative electrode in an electric field, i.e. they are positively charged. Viewing these results in the light of the chemical nature of the alcohols, the former suggestion as to the interaction between the liquid medium and the metals is strengthened. Although these alcohols have a neutral reaction, they act like weak bases in combining with acids to form salts, or, in other words, they have an easily replaceable OH group. The easily oxidizable metals would thus be able to form at least a surface coat of hydrate, while the metals gold, platinum, and silver, the existence of which in a colloidal state depends on a replaceable hydrogen in the liquid, cannot form in the alcohols. A still further test of this hypothesis is afforded when one uses as the liquid medium a substance which has a replaceable H and not an OH. Anhydrous acids might be used, but there is great difficulty in keeping them free from water and, as is well known, electrolytes containing acids have extremely strong power of coagulating solutions. Ethyl malonate (Spence 3i ) is a liquid which fulfils the condition of having a replaceable H. When platinum, gold, and silver were sparked underneath this liquid, very stable colloidal solutions were obtained ; those of 148 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS the first two metals named are apparently as stable as the cor- responding hydrosols, while the gold solution coagulates at the end of a month or so. These particles were all found to bear a negative charge, similar to those of platinum, silver, and gold in hydrosols. When the other metals, bismuth, lead, zinc, and iron were used, a colloidal solution in ethyl malonate could not be obtained. On sparking with silver electrodes in pure anhydrous ether, (C 2 H 5 ) 2 0, a colloidal solution was obtained, the particles of which possess a negative charge as shown by a slight motion under the influence of an electric field. Lead electrodes did not give a colloidal solution in ether. In the accompanying table are given the values of the potential differences between the particles and the medium for the solutions in the alcohols and ethyl malonate in comparison with the hydrosols. TABLE XXI— VALUES OF V IN VOLTS. In ethyl In ethyl In methyl Metals. K — 80. malonate alcohol alcohol K = io-6. K = 25-8. K = 33. Platinum . -•031 -■054 _ Gold. -•033 -•033 — . — Silver -•036 -040 — — Lead + •018 — + •023 + •044 Bismuth . + •017 ' — — + •022 This table shows a surprisingly close agreement among the differences of potential between the particles and the liquids. Taking into account the wide differences between the specific inductive capacity, say, for water and ethyl malonate, we can deduce that the charge of electricity on the particle of a given metal must be much greater in water than in ethyl malonate ; in other words, the interaction between the particle and the solvent seems to be dependent on what may be defined as the ionizing power of the liquid. It is further interesting to note that these values for the differences of potential between the particles and the liquids are of the same order as the value found by Perrin for the difference of potential between chromium chloride MOTIONS OF PARTICLES IN AN ELECTRIC FIELD 149 diaphragm and slightly acidulated water ("025 volt), and also agrees in the same way with Helmholtz's values for the differ- ence of potential between very dilute aqueous solutions and the walls of glass tubes in which they were contained, if the correc- tions are made by introducing the value for the specific induc- tive capacity of water. 8. Theoretical considerations. — There is practically unan- imity in the opinion that these particles in colloidal solutions are enclosed by a double electric layer, the electricity of one sign on the surface of the particle being in equilibrium with an equal amount of electricity in the layer of liquid immedi- ately surrounding the particle. It is a matter of doubt how this double layer is formed. Following the opinion given by Quincke regarding suspensions of microscopic particles in liquids, many writers have been content to view the phenomena as an effect ex- pressed by the term "contact electrification"; the particles become charged by the rubbing of the moving particles of the liquid itself against the suspended particles. The recent work of Perrin 10 has produced results which throw considerable light on the phenomena of electrification by contact between liquids and solids. By measurements of the electric osmose of 'liquids through diaphragms of various materials he is led to these two laws : — (1) Electric osmose is only appreciable with ionizing liquids ; or, in other words, ionizing liquids are the only ones which give strong electrification by contact. (2) In the absence of polyvalent radicals, all non-metallic substances become positive in liquids which are acidic, and negative in liquids which are basic. In explaining these results he suggests the hypothesis that a positive electrification of a wall bathed by an acidic liquid is formed by H ions situated in the stationary liquid layer immediately contiguous to the wall. Opposed to it at a small distance there will be a corresponding excess of nega- tive ions forming another layer. When the wall assumes a negative charge it is on account of similar action of the OH ions. It is found that H and OH ions move much more iSo PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS quickly than other ions ; if then we explain this high velocity by assuming that they are smaller than other ions, we should expect them to penetrate nearer to the boundary of the liquid and so muster at the limiting layer of a liquid an excess of electric charges of one sign. Although the analogies between this phenomenon of electric osmose and that of the coagulation of colloidal solutions undoubtedly help in explaining the latter, the formation of these solutions can hardly be credited, to merely physical diffusion of the H and OH ions. As we have seen from the sign of charges borne by particles in solution, it is those which appear to depend on a replaceable H which are negative, while those depending on a replaceable OH are positive. The two views are given thus by Noyes 36 : — " In regard to the cause and character of the electrification two assumptions deserve consideration ; one, that it is simply an example of contact electricity, the colloid particle assuming a charge of one sign and the surrounding water one of the other. This correlates the phenomena of migration with that of electric endosmose. It does not, however, give an obvious explanation of the facts that the basic colloidal particles be- come positively charged and the acidic and neutral ones negatively charged. The other assumption accounts for these facts. According to it the phenomenon is simply one of ionization. Thus each aggregate of ferric hydroxide molecules may dissociate into one or more ordinary hydroxyl ions and a residual positively charged colloidal particle, and each aggre- gate of silicic or stannic acid molecules into one or more hydrogen ions and a residual negatively charged colloidal particle. . . . To explain the behaviour of neutral substances like gold or quartz by this hypothesis, it is necessary to supplement it by the assumption that in these cases it is the water or other electrolyte combined with or absorbed by the colloidal particles which undergoes ionization. It seems not improbable that there may be truth in each of these hypotheses, contact electrification occurring in the case of the coarse sus- pensions and ionization in the case of those which approximate more nearly to colloidal solutions." MOTIONS OF PARTICLES IN AN ELECTRIC FIELD 151 Comparing the results given for the signs of the charges borne by the particles in different solutions, we have the following : — (1) Water (H + . OH") can form two classes of colloids, the particles of which are respectively positively and negatively charged. (2) Replacing the mobile H + by the groups C 2 H 6 and CH 3 , to form the alcohols, seems to destroy the power of forming solutions with negatively charged particles. (3) Ethyl malonate CH 2 (COOC 2 H 6 ) 2 , which has the mobile H, readily forms those solutions containing the negatively charged particles and those only. It is evident that the formation of the solution depends on the chemical nature of the solvent. This leads to the follow- ing theory of the constitution of the solution : — (1) In the case of gold, silver, and platinum in water or ethyl malonate, we have an incomplete chemical combination with the liquid : thus for platinum and water we have the equation «Pt + H + . OH " = (Pt„H +) + OH. In analogy with Nernst's hypothesis of the solution pressure of metals in contact with an electrolyte, we may look upon the platinum-hydrogen aggregate as dissociating slightly so as to form an atmosphere of positively charged hydrogen ions about the negatively charged colloidal particle. (2) With the other metals in water or the alcohols, we have a corresponding formation of the hydroxide, thus «.Pb + H + .OH"= (Pb„.OH-) + H. By slight dissociation of the aggregate (Pb„ . OH) we obtain a positively charged colloidal particle surrounded by a layer of OH " ions in the liquid. 9. Calculation of charge on colloidal particles. — The exact calculation of the value of the charge on a colloidal particle has not been satisfactorily carried out, but it is of interest to enumerate the methods which have been suggested. (1) Approximations to the value of this charge have been suggested by the use of formulae 4 and 5 (p. 137), viz. : — 152 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS * = v -ir Kandv .» S>_ s. . ~-e l/UQCITY (CMS itlO'V Fig. i6. the pure copper solution was first taken, gradually increasing quantities of the chosen electrolytic solution were then added to fresh samples of the stock copper solution, and the corre- sponding mobility measured each time. The measurement of one mobility was usually completed within one hour of the addition of the electrolyte. In order to illustrate the relation between the number of molecules of the various electrolytes added per c.c. of the copper colloidal solution and the resulting mobility of the copper particles, all of the results are brought together in Table XXIX and illustrated in the curves in Fig. 17. Column II gives the normality, in respect of the electrolyte, COAGULATION OF COLLOIDS 167 TABLE XXIX.— RELATION BETWEEN THE NUMBER OF NEGATIVE IONS ADDED PER C.C. TO THE COPPER COLLOIDAL SOLU- TIONS AND THE RESULTING MOBILITIES OF THE PARTICLES. Numbers propor- Solution. Normality : grm.-mols. per c.c. tional to the number of ions per c.c. : Grm.- ions per c.c. Mobility at 18° C. KC1 1 4- 24 -g X IO -6 2 17*0 X IO -6 17*0 X IO -6 + 257 X IO -6 3 38-0 X IO -6 38-0 x io -6 + 26-2 x io -6 4 74 - o x io _0 74 "O X IO -6 + 22-8 X IO -0 5 154-0 x IO -B 154-0 x io _s + 187 x io-" K 2 S0 4 1 + 25-4 X IO -5 2 7*7 x io -6 77 X IO _s + 25-3 X IO _B 3 ig-2 x io -0 ig-2 x icr" 4- 24-0 x io - " 4 38-4 X IO -0 38-4 x io-" 4- 21-8 X IO -0 5 g6 - o x io -6 g6-o x io -8 + 14-4 X IO -D 6 153 'O X IO -6 153-0 X IO -6 4- o-o x io -5 A1 S (S0 4 ) S 1 4- 23-4 x io -6 2 4 - 6 x icr" 13-8 X 10-" 4- 21-5 x io -D 3 g-2 x io -6 27-6 X IO -6 4- ig-2 x io -0 4 i8'3 x io -6 54 - g x io -0 4- 18-5 x io - ' K s P0 4 1 4- 25-4 x io -5 2 3-6 x io _s 3-6 X IO - " 4-21-5 X IO -6 3 7 - 2 X IO -0 7 -2 X IO - " 4- 16-8 x io-° 4 14-4 x io -6 14-4 X IO -6 4- 3'4 X io-" 5 21 - 6 x io -6 2f6 X I0 _G - 4-8 X IO -0 6 32-8 x io -6 32-8 X IO _e - 7 - g x io -6 K 6 (FeCy 6 ) 2 1 4- 30-4 X I0~ 6 2 3-55 x io- B 7-1 X IO -8 4- 14-0 X IO -0 3 7-15 X IO -6 14-3 X IO - " 4- 3-8 x io-° 4 107 x io -6 21-4 X IO -6 4- i-o X I0 _D 5 14-3 x io -6 28-6 X IO -6 - 1*5 x io -5 6 21 "4 x io -B 42-8 x io -0 - g-i x io -5 of the mixture of the colloid and the electrolyte, i.e. the number of grm.-molecules of the salt per c.c. of the mixture. According to the accepted dissociation theory we may look upon the salts in these extremely dilute solutions as being completely ionized, and so the normality as denned above will be directly proportional to the number of ionized mole- cules of the particular salt per c.c. However, if we are to compare the efficiency of various ions in discharging the colloidal particles, we must deduce numbers directly propor- tional to the number of such ions per cubic centimetre. For example, taking the above definition of normality, we may 168 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS look upon a 3 x i o -6 normal solution of potassium phosphate as containing the same number of molecules as the number of molecules of potassium ferricyanide in a 3 x io -6 normal solution of potassium ferricyanide. But the latter solution will contain twice the number of FeCy 6 ions, that the former contains of P0 4 ions. Consequently, in Column III are written the numbers directly proportional to the number of acid radical ions present per cubic centimetre; of course, IfiO v ffzi to* \ 140 V N \ K.C 1. \ \ ifn - \ t \ \ inn \ \ y ^ 80 \ \ \ °\ fin \ \ i \ \ 40 «v, u r e.C. v z /i/ z (sc \ \ \ Q \ \ \ \ , so K> h r^ <, tl u \ \ J %»» ff ^ \ \ 5 20 \r» 30 Fig. 17. yelocily x 10'' those numbers opposite aluminium sulphate and potassium ferricyanide are the only ones which will differ in the two columns. In the last column are 'copied the various mobilities in cms. per sec. per volt per cm. The curves in Fig. 17 are drawn with the mobilities as abscissae and the numbers proportional to the number of ions per c.c. as ordinates. The very marked overlapping of the curves for potassium phosphate and potassium ferricyanide at COAGULATION OF COLLOIDS 169 once suggests the fact that the two ions P0 4 and FeCy, have the same power of reducing the mobility of the copper particle ancj, therefore, of producing the coagulation of the copper. Although the experiments on aluminium sulphate were not carried out as far as those on potassium sulphate, never- theless the corresponding curves show a remarkable coincidence in the region common to the two. These latter two curves have an additional importance in that they show that the action of the S0 4 ion is practically independent of the metal ion. Since aluminium is trivalent and potassium monovalent, if the metal ions exerted any marked influence on the copper particle, we should expect these two curves to be very far apart. Again, comparing the five curves, one has the very strongest evidence of the great differences in the powers of monovalent, divalent, and trivalent acid ions to reduce the mobility of the positively charged copper and, consequently, to produce coagulation. Examination of the curves will show that the mobility results indicate that the ratios of the powers of various acid ions to reduce the mobility of the copper par- ticles are not very far removed from the observed ratios of the powers of the same ions to produce coagulation. 3. Action of electrolytes in electro-endosmose. — The intimate connexion, already pointed out, between the motion of the colloidal particle in an electric field and the phenomenon of electro-endosmose has led to the examination of the effect of electrolytic solutions containing ions of different valencies on the latter phenomenon. Extensive researches on this point have been carried out by Perrin, 27 Elissa/of, 28 and Briggs. 29 Perrin measured the rate of flow of a given liquid through a porous diaphragm when a potential fall of about 10 volts per cm. was maintained across the diaphragm. The various diaphragms were made in the form of cylinders about 1 -5 sq. cm. cross-section and from 10 to 12 cms. long by packing the material in a glass tube. The liquid was drawn by the current towards one or other of the electrodes, depending on the com- position of the liquid, but independent of the insoluble material of which the diaphragm was made ; the substances used for !7o PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS the porous diaphragm were the following: aluminium oxide, naphthalene, chromium chloride, silver chloride, barium sul- phate, boric acid, sulphur, salol, carborundum, gelatine, cellu- lose, silex, zinc sulphide, calcium carbonate, powdered glass, barium carbonate, and manganese trioxide. He found that only ionizing liquids (those with a high dielectric constant) gave appreciable electro-osmosis, and that of these liquids a medium feebly acid gave a positive charge to the walls of the diaphragm (i.e. the liquid moved toward the positive electrode), while in a medium feebly alkaline the walls became negatively charged, the liquid positively charged. He tried the effect of adding various electrolytes to each liquid medium and found that the charge given to the walls was usually diminished and then reversed in sign. Particularly strong effects were shown by the strong acids and bases, and by solutions of salts with polyvalent ions. "The electric potential of any wall whatever in aqueous solution is always raised by the addition to the solution of a monovalent acid; it is always lowered by the addition of a monovalent base. " Having given a liquid which gives to a wall an electrifica- tion of a certain sign, the addition to this liquid of a polyvalent ion of the opposite sign diminishes greatly the electrification of the wall and sometimes even reverses the sign, the electrifica- tion then obtained being, however, generally much below that given by the ions H+ and OH - . Further, the influence of divalent ions is generally very much less than the influence of trivalent ions, which are in turn much weaker than tetravalent ions." The latter statement is a generalization from experiments on the diaphragms mentioned above with the following electrolytic solutions : lanthanum, barium, calcium, and cobalt nitrates, magnesium chloride, manganese sulphate, acid potas- sium carbonate, potassium ferro- and ferri-cyanides, acid potassium phosphate, oxalic and citric acids. Although Perrin's results do not permit us to give definite numbers to show the ratios of the discharging powers of monovalent, divalent, trivalent, and tetravalent ions, they COAGULATION OF COLLOIDS 171 point to an action analogous to that in the coagulation of col- loidal particles. In a manner exactly parallel to the latter phenomena, the positive ions in salt solutions do not seem to affect a positively charged wall, while a negatively charged wall is not affected by the negative ions in solution. Perrin develops this parallel action exhaustively in his article (see Briggs, Bennett, and Pierson 29 ). Recently Elissafof 28 examined similar effects of salts on the electro-osmosis shown in capillary tubes of glass and quartz, placed in strong electric fields. Pure water moves in a capillary tube to the negative electrode ; the addition of elec- trolyte to the water lessens this motion and often reverses it. In this action the kations are the powerful agents, the effect varying rapidly with the valency of the kation but being inde- pendent of the valency of the anion. Inorganic salts of the light metals act according to a valency law, analogous to the Schulze-Linder-Picton law for the coagulation of colloids. In agreement with recent work by Freundlich and his co-workers on, coagulation, Elissafof found that the kations of acids, heavy metal salts, and salts of light metals with organic basic ions gave abnormally large effects. Experiments by McTaggart 30 on the charge possessed by bubbles of gases in liquid media give similar results for the action of ions of different valencies. By varying the com- position of the aqueous medium, air bubbles can be made to move either to the anode or the cathode. Bubbles possessing a given charge have their motion decreased and then reversed by adding small quantities of electrolytes ; analogous valency phenomena are present in this case also. The ion bearing a charge opposite to that of the bubble is the potent discharging factor of the added salt; the action depends entirely on the valency of this ion, and is apparently quite independent of the valency of the other ion. In view of the parallelism between these electro-endosmose effects and the coagulative powers of various ions, there can be very little doubt that we are dealing with very closely re- lated phenomena. 4. Ultramicroscopic observation of electrolytic action. — 172 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS Recent direct observation with the ultramicroscope leaves no doubt that the addition of electrolytes to a colloidal solution causes the condensation of small particles into larger ones which easily settle. As we have already noted, early observers of Jhe Brownian movement — Jevons, Gouy, Spring — found that cessation of this motion and consequent coagulation resulted from the addition of electrolytes to suspensoids. The ultramicroscope in the hands of Zsigmondy, Cotton and Mouton, Maltezos, and others, showed that, on the addition of the electrolyte, the particles in the sol increased in size. Cotton and Mouton 31 describe thus the effect of adding small traces of aluminium sulphate to Bredig silver sols: "When one examines with the ultramicroscope the flakes con- stituting the coagulum, one distinguishes a large number of brilliant points crowded closely together, and the idea which suggests itself to the mind is that these flakes are formed of the colloidal particles themselves, which have been brought to- gether to form a coherent mass. ... If one allows a small quantity of aluminium sulphate to diffuse slowly into a sample of the sol (Bredig silver sol) in the ultramicroscope, one sees that the aspect of the sol is changed little by little. Instead of the isolated points of light absolutely independent, there will be seen groups, composed at first of only two or three points which are evidently bound together. If one waits some time, the number of such groups goes on increasing while at the same time larger groups resembling strings of beads come into evidence. ... It should be emphasized that, at least in this case, the particles are not stuck together and do not touch one another. If they were touching, one should not be able to dis- tinguish one from the other once coagulation has set in. Not only are they separated by microscopic distances, but they possess, at least at first, a certain independence. In the groups formed by a small number of grains, the Brownian motions which still persist are not identical for the different grains. It is undoubtedly this structure which leads to the spongy flakes of which the coagulum is usually composed." A new phenomenon has been brought to light by the experi- ments of Mayer, Schaeffer, and Terroine, 32 who worked with COAGULATION OF COLLOIDS 173 sols of gold, silver, platinum, arsenious sulphide, and ferric hydroxide. They find that the addition of traces of alkali has the effect of increasing the size of the colloidal grains if the colloid is positive, and of decreasing the size if the col- loid is negative. The addition of traces of acids produces the reverse effect. This suggests that the reason alkalis have a stabilizing effect on such sols as platinum is that the grade of dispersion is made higher by the alkali (see C. Henry, 38 and Chassevant and Posternak 34 ). The results of recent work on this point may be sum- marized as follows (Reissig, 35 Wiegner, 36 Galecki, 37 Oden and Ohlon 38 ):— (a) A very slight electrolytic content causes no apparent lessening in the number of the particles. (b) In a sample of colloid to which small quantities of electrolyte have been added, the number of its sub-microns may increase slightly at the expense of its amicrons, although there may be no indication of colour change in the sample (e.g. gold sol). (c) The electrolytic coagulation of colloids which contain particles of various sizes progresses by the condensation of small particles on those of a larger size and not by the coales- cence of particles of equal size. The larger ultra-microns act as condensation nuclei for the smaller particles. (d) The colour changes of sols (e.g. gold) which accom- pany the addition of electrolytes run parallel to ultramicroscopic changes, in that the size of the particles increases and their number decreases as more and more electrolyte is added. 5. Changes in physical properties due to electrolytes. — Apart from the microscopic observation of the individual par- ticles and the motion of those particles in an electric field, the physical properties by which the coagulative action of salts has been most often traced are (1) the colour, (2) the viscosity of the solution. (1) Colour changes. — These changes indicate that there is a gradual increase in the size of the individual particles in the solution in the early stages of coagulation. Distinct varia- tions in the colour of samples of gold and silver solutions 174 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS have been observed by many workers. In the case of gold sols, as first surmised, by Faraday, 2 and later proved by Zsigmondy, 39 Gutbier and Resenscheck, 4l ^ # by the addition of coagulating reagents the colour goes through the following series of changes: red, purple-red, red-violet, blue-violet, and deep blue, the Tyndall phenomenon becomes more and more evident, the solution becomes turbid, and finally the disperse phase separates in the form of powder, flakes, or gels. Carey Lea, 41 and Von Meyer and Lottermoser 42 have traced similar changes for silver solutions from dark brown, through brownish- red and brownish-violet, and then to a deep green. 43 As a usual thing other solutions become simply muddy or cloudy without any distinct colour change. (2) Viscosity changes during coagulation. — As noted by Freundlich, 44 although we know very little of the theory of the viscosity changes produced in a medium by dissolving sub- stances which give even molecular disperse (true) solutions, still " as long as we use viscosity for comparative experiments alone — for comparing different qualities and different sols — it is of the greatest value. . . . We can detect (easily) very slight changes in solutions by measuring viscosity." In the main, three different methods of measuring the viscosity of colloids have been used: (1) velocity of flow through capillary tubes (e.g. Ostwald viscosimeter), (2) loga- rithmic decrement of an oscillating disk, (3) torque on concen- tric cylinders (e.g. Couette's apparatus 45 ). These three methods do not in general give rigidly concordant results on account of the variations in the distribution of the shears in the liquid layers (see Garrett, 4 ' Hardy 47 ). Various writers have pointed out the many complexities present in colloidal solu- tions which will affect the value of the viscosity : the promi- nence of different elements affecting the viscosity will depend on which of the above methods is used for the determination. These various contributing circumstances may be enumerated as follows : the internal friction of each of the several phases, the surface friction of the internal surfaces, the surface tension of the internal surfaces, the density of the electrical charge at the internal surfaces, the shape of the particles, the nature of COAGULATION OF COLLOIDS 175 the surface of the particle as to the absorption layer, and probably the degree of dispersion. Einstein 48 first developed a theoretical formula for the viscosity (17^ of a suspension of rigid spheres in any liquid, in terms of the viscosity (■>?) of the pure liquid and the ratio (/} of the volume of the matter suspended to the volume of the medium, viz. — Vl = ,(1 + k.f), where k is a constant. The value of the constant k has been calculated by many workers to be from i - o to 475 (see Einstein, 48 Hatschek 49 ) and experimentally tested by others (Bancelin, 60 Harrison, 51 Freundlich and Ishasaka 62 ) for suspen- sions of rather large particles. The values for k found experi- mentally vary over a large range even for the larger particles, while in the case of small particles in suspension (Oden, 53 Woudstra 54 ) the linear law expressed in the above equation is departed from. However, a rigid experimental test is almost out of the question, first on account of the fact that the formula is developed for the case of smooth spheres in suspension, and secondly from the necessity of obtaining exactly the volume of the disperse phase, not merely the weight. In any case, the above formula will apply only to solutions containing particles which are not deformable, and which amount to considerably less than 50 per cent of the total volume of the system. Hatschek 45 has deduced a completely different formula for the variation in the viscosity of the emul- soids. However, entirely apart from theoretical considerations as to the laws governing the changes, such alterations in the vis : cosity will always indicate some corresponding change in the sols. Woudstra 64 has tried the effect of adding electrolytes to solutions of silver, ferric hydroxide, and chromium hydrox- ide ; he found an ultimate slight increase in the viscosity due to additions of electrolytes even in quantities insufficient to cause any measurable variation in the viscosity of pure water when added to it. There is in his work the suggestion of the stronger action of the ions of higher valencies. Freundlich and Ishasaka 52 have made unique use of viscosity changes 176 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS in measuring' the rate of coagulation of aluminium hydroxide sols, and here again the valency of the active ion is impor- tant. Although there has been an immense amount of work done on the viscosity changes of such sols as blood and rubber solutions, no very settled conclusions have as yet been arrived at. The whole question of the interrelation of viscosity, mobilities of ions and particles, and electrical conductivity, bristles with unsolved difficulties (see Hardy, 47 McBain, 65 Ostwald 66 and Pauli "). 6. Ions entrained by the coagulum. — When the phenomena of coagulation was first studied from a chemical point of view, analysis of the coagulum (precipitate) showed that the latter al- ways absorbed,* during the process of coagulation, a portion of the electrolyte instrumental in producing the change. Crum, 8 as early as 1854, found that in the coagulation of suspended aluminium hydroxide, the coagulum always contained small quantities of the acid or salt necessary for the coagulation. In their exhaustive study of colloidal solutions, as represented by metallic sulphides, Linder and Picton 10 found, in the case of the coagulation of arsenious sulphide particles ( - ve), by the addition of barium chloride, that the coagulum carried down a distinct amount of the metal ( + ve ion) but none of the acid radicle. That this portion entrained was intimately bound up with the coagulum was demonstrated by the fact that by digest- ing the coagulum noted above with other metallic solutions, e.g. ammonium chloride, the entrained metal ■ ions (barium) could be replaced entirely in the course of a few days by other metals, e.g. ammonium. This same work was confirmed and extended by Whitney and Ober, 68 who showed, in addition, that the amounts of the metals calcium, barium, strontium, and potas- sium entrained by the coagulum from the same amount of a given colloid were exactly proportional to the equivalent weights of these metals (electrochemical equivalents). Whit- ney and Ober were able to assign to the coagulum the formula * Van Bemmelen suggests the use of adsorption for the surface phenomenon and absorption for the volume phenomenon. COAGULATION OF COLLOIDS 177 Ba . 90 (As 2 S 3 ), which tends to substantiate the claim that we are here dealing with complex chemical combinations. Spring 59 studied the action of electrolytes by observing the diffusion of the electrolytes from a strong solution, e.g. copper sulphate, into a supernatant layer of the suspensoid, e.g. mastic sol ; the layer of copper sulphate at the surface of contact was robbed of its. copper while the liquid at this level showed the presence of sulphuric acid. Similar results were also found with various metallic chlorides ; Spring as- cribes this phenomenon to hydrolysis of the salts in solution and absorption of the metal ions by the colloidal par- ticles. Duclaux's 60 explanation of the absorption of the ions of the precipitating electrolyte is that the latter are merely sub- stituted for other ions — his so-called active part of the col- loidal unit already entangled in the colloidal particle while it is still in the state of suspension. For instance, in the produc- tion of colloidal copper ferrocyanide by the interaction of potassium ferrocyanide and copper chloride, the colloidal particle retains proportions of the potassium varying between the limits indicated by the formulae (FeCy^Cu^K^g and (FeCy 6 )Cu r94 K . l2 , which may also be written thus (FeCy 6 )Cu 2 +KFeCy 6 )K 4 and(FeCy e )Cu 2 + i/30(FeCy,)K 4 . In the case of the coagulation of this negative colloid by the metal ion, e.g. hydrogen, barium, aluminium, etc., "instead of the so-called entrainment by coagulation, the action will consist in the substitution of the hydrogen, etc., ions for a corresponding number of potassium ions". In the light of his results, Duclaux regards the colloidal particle as a product of purely chemical reaction. On the other hand, the similarities between the absorption phenomena of colloidal solutions and the absorption effects of various solids, e.g. charcoal, lead one to suspect the existence of some specific absorptive power possessed by the surface of solids. This relationship has been developed by the follow- ing series of experiments. I. The absorption of liquids, colloids, and gases by 12 178 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS insoluble powders as carried out by Thoulet, 61 Schmidt, 82 Davis, 63 McBain, 64 Van Bemmelen, 65 Nils Carli, 66 and others. 2, The absorption of electrolytes by the gels 'of coagulated colloids, as carried out first by Crum 3 and Warrington, 67 and recently by Van Bemmelen and his pupils, 66 Godlewski, 68 and others. 3. Recent work by Freundlich and his co-workers on the absorption by the colloidal particles during the process of coagulation. Van Bemmelen differentiates between the phenomenon exhibited by porous bodies, charcoal, powdered glass, etc., — a distinctly surface effect which he calls adsorption — and the more intimate union producing a homogeneous solution of one substance in another — a distinctly volume effect which he calls absorption. As far as the experiments on the ions en- trained either by the dried gels of sols when shaken in solu- tions of salts, or by the particles during coagulation, there is a probability that both adsorption and absorption intervene — a circumstance which would add to the complexity of the problem. The work by Freundlich and his co-workers pushes further the researches of Linder and Picton, Spring, Whitney and Ober, and Duclaux. As a connecting link between this work and that of Van Bemmelen we may quote the experiments of Frion 69 on the action of barium sulphate precipitate in en- training magnesium and lanthanum ions during precipitation from solutions in which those ions are present. He found that the amount of these ions carried down by the barium sulphate precipitate depended on the acidity or basicity of the solution, the concentration of the entrained ion in the solution, and the valency of the entrained ion. The lanthanum ions (trivalent) were absorbed ten times as strongly as the mag- nesium ions (divalent). In their extensive investigations of the adsorption of negative ions (cations) by barium sulphate precipitate, Weiser and Sherrick ro find little evidence to support the Schulze law, but they note that there is a tendency for ions of higher valency to be adsorbed more strongly than those of a lower valency ; COAGULATION OF COLLOIDS 179 from the arrangement of the adsorbed ions in order of in- creasing adsorbability they conclude that there are two factors which determine the adsorption of ions by a given disperse phase : the specific nature of the adsorbed ion and the valency of the ion. Dissimilar ions of the same valency may exhibit great differences in adsorption, while ions of same valency which are closely related chemically may be expected to show the same adsorption. The significant fact added to our knowledge by the work of Whitney and Ober 68 was that the ions of electrolytic solutions were absorbed by a given quantity of a certain colloid in amount exactly proportional to the electrochemical equivalent weights of these ions ; i.e. the amounts of calcium, strontium, barium, and potassium respectively were roughly proportional to K4°)> i(%7'7)> i( I 37'4) anc > 39" 1 - Freundlich and Schucht T1 have shown that the same law holds for other colloids — a fact which points to coagulation taking place when a certain charge of the opposite sign is brought up to the colloidal particle. Further, according to Freundlich ("Kap. Chem.," p. 354), for a given colloid, ions of differing valency are absorbed equally strongly in equimolecular concentrations of the ions jn solution. Consequently, if in order to produce coagulation of a given colloid, a number of ions sufficient to supply a given charge must be brought up to each particle, solutions of monovalent, divalent, and trivalent ions necessary and sufficient to produce coagulation will have to be in de- creasing order of strength. In addition the strengths necessary must be determined by a consideration of the absorption of the colloidal particles for ions of electrolytes. Freundlich adopted the variation of Henry's law, 72 which expresses the absorption of various solids, to express the absorption process of colloids and tested the result experi- mentally. We shall present it here in its simplest form. If the molecular condition of the solute in the solvents is the same, Henry's law for the distribution of a body between two immiscible solvents is C a = /3.Q where C a and C b are the concentrations of the body in the i8o PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS two solvents a and b, and /3 is a constant. If, however, the molecular weight of the solute in the solvent b is n times that in the solvent a, the equation takes the form C.-/8.CA Adapting this equation to the absorption by colloids Freund- lich writes it i y = a . C», where y = amount of given substance absorbed by unit mass of the disperse phase, C = concentration of the absorbed substance in the sol, and a,n = constants for a given colloid. 1 i i —f x\ > w Concent? It> SoR- Fig. 18. Various workers have applied this formula to the absorp- tion by charcoal and other solids of various electrolytes and dye solutions: the values of i/» (Freundlich, " Kap. Chem.," pp. 1 50-51) lie between o-i 1 and 0-50. Freundlich has proved the truth of the formula for various colloids (e.g. Freundlich and Schucht, with mercury sulphide). He finds i/« to lie be- tween 0-14 and 0-20 for the various colloids studied. Paine 20 found for Bredig colloidal copper i/« to be o - i6. Putting in the values of i/» such as those recorded, we have the resulting curve of the form illustrated in Fig. 18, from which we see that, for very small concentrations, the percentage of COAGULATION OF COLLOIDS _ 181 salt absorbed is very large, whereas for increasing concentra- tions the curve becomes asymptotic to a line parallel to the axis of concentrations. If this curve represents the absorp- tion by a given colloid of all electrolytes, irrespective of the valency of the ions, then at small concentrations of mono- valent, divalent, and trivalent absorbable ions, the number of ions absorbed by the colloid may be such that, for the mono- valent type there is absolutely no coagulative action, whereas for the divalent, or trivalent type, there may be sufficient to cause more or less rapid coagulation. For example: " Freund- lich found that for a hydrosol of arsenious sulphide containing I '86 grms. per litre, C093 milligram-molecules of aluminium nitrate (or the equivalent of cerium sulphate) were required per litre for coagulation. The amount of the ions absorbed per grm. of arsenious sulphide is given as about o - o87 milliequi- valents, or o - i62 milliequivalents for one litre of the above solution, i.e. 0*054 milligram-molecules in the case of a trivalent ion. This would mean that about 50 or 60 per cent of the tri- valent ions (present in the electrolyte necessary for coagulation was absorbed by the colloid in its coagulation, as compared) with a small fraction of 1 per cent (of the amount necessary for coagulation) of the monovalent ions." If, in addition, as the work of Whitney and Ober, Freundlich, and others seems to indicate, electrochemically equivalent quantities of various ions must be absorbed in order to produce coagulation, we see from the absorption curves that the concentrations of ions of different valencies necessary to produce coagulation may easily differ in accordance with the Linder-Picton-Schulze law. If y x represents the number of monovalent ions necessary to produce coagulation in a given sample of colloid, that quantity will be absorbed from the electrolytic solution in which these ions have a concentra- tion Cj ; the quantity of divalent or trivalent ions necessary for the same coagulative result will be given respectively by _y 2 = 1/2^ and_y 3 = 1 \zy-ti which correspond to the absorption from solutions of concentrations C 2 and C 3 respectively. A simple inspection of the absorption curve will show that there exists a wide range of values to the ratios Cj : C 2 : C 3 . 1 82 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS Freundlich has found exceptional agreement with this theoretical result in the case of salts of the light metals, while the salts of heavy metals and those with complex organic radicles seem to be absorbed in abnormally large quantities by colloids. Freundlich's conclusion is that "it follows necessarily that the coagulative power of a given salt depends greatly both on the valency and on the absorption coefficient, because with different (ionic) values, either of valency or absorp- tion, very different concentrations are necessary in the solution in order that the equivalent quantity of the (active) ion shall be absorbed ". Considerable discussion has taken place among physio- logical chemists as to the action of electrolytes on protein solutions. As first pointed out by Hardy in his work on globulin, such compounds in acid solution bear a charge of one sign while in alkali solutions the sign of the charge is reversed : the point where the charge was zero was known as the iso- electric point. At first the view was put forward that the protein micelle absorbed the acid or alkali ions which gave the charge to the whole. The phenomenon of coagulation by electrolytes, according to this view, was looked upon as an adsorption phenomenon, and it was thought that both ions of a neutral salt take part in this action simultaneously and in opposite senses ; so that the total result is the algebraic sum of the opposite action of the oppositely charged ions of the neutral salt. Following out this idea, both anions and cations have been arranged in series of gradually increasing or de- creasing adsorptive powers (see Bancroft 73 ). According to recent work by Loeb, 74 the preceding point of view is entirely wrong, and he makes out a very good case for explanation of the phenomena resulting from the addition of neutral salts on the basis of classical chemical action. For example, Loeb shows that gelatine in solution is in a critical state when the hydrogen ion concentration is a certain definite amount, viz. pH = 47, which he calls the isoelectric point. At this point the gelatine is non-ionized and does not show cataphoresis. On the more acid side of this point, the gelatine forms a COAGULATION OF COLLOIDS 183 compound in which the gelatine fills the r61e of a positive (metal) radical in combination with such negatively charged radicals as chlorine or hydroxyl ; when ionized the gelatine ion is positively charged. On the more basic side of the isoelectric point, the gelatine acts the part of a negative (acid) radical in combination with such positively charged radicals as hydrogen or sodium, and, when ionized, the gelatine ion in this case is negatively charged. Loeb maintains that the whole action is in agreement with ordinary chemical reactions and that when a neutral salt is added to either of these solu- tions the gelatine units in solution react with only one ion of the neutral salt ; on his view, it is useless to try to balance up adsorptive effects of anions and cations in a way attempted by the colloidal chemists. McBain 75 classifies these protein solutions with soaps and dyes, such as congo red, under a class which he has called colloidal electrolytes. These he defines as " salts in which one of the ions has been replaced by a heavily charged, heavily hydrated ionic micelle (particle) which exhibits equivalent conductivity which is not only comparable with that of a true ion but may even amount to several times that of the simple ions from which it has been derived. This ionic micelle is a typical but very highly charged colloidal particle of very great conductivity." In a sense this is in line with Loeb's ideas, if the latter's protein ion is replaced by the ionic micelle suggested by McBaia 7. Critical review of the present attitude to electrolytic coagulation. — In the light of the experimental results quoted above, the Schulze-Linder-Picton law cannot be upheld in its simple form to which Whetham's explanation was applied. The coincidence, nevertheless, is remarkable enough to convince one that there is fundamentally some truth in the Whetham view. Greater weight, however, must be given to Freundlich's ideas as to the absorption of ions of different valency from solutions of different concentrations. The Freundlich view has been attacked recently by Wo. Ostwald 12 because it assumes that in equimolar solutions of salts of different i8 4 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS valencies there is equally strong absorption by the colloidal particle in question. Referring to the adsorption formula i y = aC» where y = amount of given ion adsorbed by unit mass of the disperse phase, and C = concentration of adsorbed substance in the sol, a and n should be constants for a given colloid. Ostwald quotes the following table to illustrate the variations which really occur in the values of a and n — variations which tend to invalidate Freundlich's fundamental assumption. TABLE XXX. Variations in Adsorption Constants a and n. Colloid. Coagulant. Ratio of Extreme values of n. Ratio of Extreme values of a. Arsenious sulphide Mercury sulphide Aluminium hydroxide Organic salts >» »» Inorganic salts i :7 i : i 1 = 3-8 1 : 2-3 1 :2-s 1 : 2-5 1 : 7-4 1 : 6-2 In the course of testing, the various theories of coagulative power have led to almost numberless experiments in which attempts have been made to arrange both the positive ions and negative ions in series showing their coagulative powers in order of intensity. Some of these experimental results are arranged in Table XXXI. This table indicates vividly the futility of attempt- ing to get order out of such a mass of conflicting results. Furthermore, reference to Tables XXII to XXIV will show that even selecting only the chlorides (or the nitrates or the sulphates) of various metals and experimenting on the same colloidal solution (arsenious sulphide), different experi- menters are not led to the same order for the coagulative power of metal ions. In addition, the same experimenter does not obtain the same series order for metal ions when he uses various sets of salts, e.g. chlorides, nitrates and sulphates. As pointed out by Weiser and Middjeton, 22 the adsorption COAGULATION OF COLLOIDS 185 TABLE XXXI. Series Showing Relative Coagulating Power of Ions. Sol. Authority. Order of Decreasing Coagulative Power. C O •a Fe'">Pb>Hg>Mg>Ba> Sr > Co > Ca > Zn > Fe" > Cd >Ni>H>NH 4 >K>Na. Al>Zn>Ni> Mn>Ca>Fe"> Mg>H>NH 4 >Na>K. Ce = In = Al > U0 2 = Sr = Ca> Be = Zn= Ba>Mg> H>K> Na>Li. Fe'" = Al = Cr > Ba = Cd > Sr = Ca>H>Cs>Rb>K>Na> Li. Ba = Sr > Ca = Al > Mg = Cs = Mn = Cu>U0 2 >Rb>K>Ni = Cd = Zn > Na > NH ( > Li >H. Al = Pb > Ba = U0 2 > Ag > K = Na. Al > Ba = Sr = Ca > H > Cs > Rb >K>Na>Li. Th= U0 2 >Cu = Zn>Ca>Mg> Li>K = Na>NH 4 . CO C u bo rt J3 U _£> U > rt bo a a a "t3 ■3 rt It '0 < Albumin (alkaline). Albumin (alkaline). Albumin (acid). Hydrous ferric oxide. Hydrous ferric oxide. Hydrous ferric oxide. Barium sulphate precipitate. Powdered charcoal. Hofmeister 80 (adsorption). Bancroft 79 (adsorption). Pauli 81 (coagulation). Freundlich 77 . Weiser and Middle- ton 22 (coagulation). Weiser and Middle- ton 2a (adsorption). Weiser and Sherrick 70 (adsorp- tion). Osaka 82 (adsorption). Sulphocyanate > I > C10 3 > NO s > CI > Acetate > Citrate > P0 4 > S0 4 > Tartrate. Sulphocyanate = I > C10 s > NO s > CI > Acetate > P0 4 > S0 4 > Tartrate. Sulphocyanate > I > Br > N0 3 > CI > Acetate. Chromate > S0 4 > OH > Formate >Cl>N0 3 >Br>I. Chromate > Tartrate > S0 4 > Citrate > Oxalate > IO s > P0 4 . P0 4 > Citrate > Tartrate > Oxalate > S0 4 > I0 3 > Chromate. Ferrocyanide > NO, > N0 2 > C10 3 > Permanganate ~> Ferricyanide > CI > Br > CN > Sulphocyanate >I S0 4 >Cl>Br>No s >I. 1 86 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS of ions by a coagulating colloid is a complex operation ; at least two adsorbing media are concerned in the process, viz. : (a) the electrically charged particles during the process of neutralization, and {b) the electrically neutral particles or coagulating masses during the process of agglomeration and settling. These authors show that the order of adsorption of ions in the coagulum does not in general agree with the order of coagulating powers of these same ions. The following remarks of Ostwald 12 are probably justified, although they do not advance the question any more nearly to a solution : " The principal error of the current theory of coagulation by electrolytes is the over-emphasis which has been laid on the role of the valency of ions dominating coagulation. The valency is not at all the determining factor in the coagulation of suspensoids. We find not only great variation in the single classes of ions, but sometimes divalent ions are more powerful than trivalent and some monovalent more powerful than some divalent. Instead of the discontinuous variable valency, there must be provided for a successful theory a continuous variable which will account for the difference formerly ascribed to valency alone. Instead of the valency only, there must be introduced a physico- chemical constant of a higher order. . . . Further, it seems to the author that in the future theory of coagulation it is of equal importance to consider the second ion added, the influence of which has been neglected up to the present. On account of bearing a charge similar to the colloidal particle, this ion possesses a peptising effect, and only a theory which takes this into account can hope to succeed in foretelling results. The peptising effect should be considered as im- portant as the coagulating power has been considered up to the present." Similar ideas have often been insisted upon by Bancroft, 73 and seem to get strong experimental support from a recent paper by Burton and Bishop, 23 the conclusions of which are given earlier in this chapter. By contrasting the action of univalent and trivalent ions as the colloidal solution is diluted, one is driven to the conclusion- that one is dealing with COAGULATION OF COLLOIDS 187 two widely differing phenomena. That is, the essential mechanism by which univalent ions cause coagulation must be quite different from that by which trivalent ions produce this result. Or, from another point of view, there are possibly several elements entering into the process of coagulation. One set of these elements are particularly accentuated when one deals with univalent ions ; another set is predominant in the use of trivalent ions. For example, on account of the very large amount of electrolyte added for the univalent ion compared with the amount added for the trivalent ion, the electrical conductivity in the former case is very considerably higher than in the latter case. Now, if electrical conductivity is for any reason a potent factor in causing coagulation — a circumstance that may very well be — the influence of this factor might easily dominate the action with univalent ions, but be of quite secondary importance in the case of trivalent ions. Combined with such an effect, there might be an influence of valency quite in the way that Whetham pictures it (or of adsorption, as Freundlich pictures it), which might be the dominant feature with the trivalent ion, but of secondary importance with the univalent ion. Such considerations would justify one in enunciating the following principles of coagulation : — (z) There are, at least, two properties of the system made up of the colloidal solution, plus electrolyte, which have influence in determining the coagulating power of any ion. (ii) These two influences are such that they tend to counteract one another to a certain extent. (iii ) These influences are such that one of them dominates the action of univalent ions, while the other dominates the action of trivalent ions. In the action of divalent ions, the two influences seem to be somewhat equalized. There are many possibilities to suggest for these influences. In addition to electrical conductivity and valency cited above, we must remember that in all this work the influence of the ion bearing the same charge as the colloidal particle has almost always been ignored. This has often been commented on (see Bancroft, Ostwald). It does seem unscientific to 188 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS ignore completely - the ion charged similarly to the colloidal particle ; one would suspect that it would oppose the action of the other ion. Now, in dealing with the coagulating power of a univalent ion, one always has present in the solution in equimolar concentration another ion of equal or greater valency, while in testing a trivalent ion, there is present in equimolar concentration another ion which is nearly always of less valency than the ion tested. A proper appreciation of the concomitant action of these other ions charged similarly to the colloidal particle may throw a flood of light on the whole process of coagulation by electrolytes. In particular, this other ion may have a peptising effect, or its presence in solution may exert a definite effect on the adsorption of ions by the colloidal particle. An exhaustive series of experi- ments with a carefully selected list of electrolytes, introduc- ing as many combinations of valency as possible, would undoubtedly be of use, provided a colloid of constant concen- tration were used throughout. II. Coagulation by Mixing Positive and Negative Colloids. Linder and Picton 10 were the first to point out the classifica- tion of colloids into the two classes, cationic and anionic, accord- ing as the particles migrated in an electric field to the negative or to the positive electrode. They also were the first to note that, under certain conditions, a colloid bearing a charge of one sign added to one bearing a charge of the opposite sign brings about precipitation of the two colloids — a phenomenon confirmed by Lottermoser. 43 This phase of the behaviour of colloids has been very com- pletely investigated more recently by Niesser and Friedemann 83 and Biltz. 84 The latter has shown that, as in the case of coagulation by electrolytes, the immediate precipitating action depends greatly on the manner in which the two colloids are mixed, i.e. whether slowly drop by drop, or rapidly with shak- ing. For colloids mixed together quickly and treated uni- formly, Biltz enunciated the following laws : — COAGULATION OF COLLOIDS 18$ 1. If to a given colloid one of opposite sign be added in small proportion, there is no precipitating action. 2. As the quantities of the second colloid added at once are increased the coagulative action becomes more and more noticeable, until a proportion is reached which causes immediate coagulation. 3. As this amount is still further increased coagulation ceases to appear ; that is, there is an optimum of precipitating action shown for certain proportions, and if in any case these favourable proportions are exceeded on either side, no pre- cipitating action takes place at all. 4. With the exception of a sol of selenium, which may have some anomalous chemical action, mixing two sols of the same sign produces no precipitation at any stage. Billiter 85 showed that, when two colloids of opposite sign were mixed, with one in excess, the direction of migration of the whole was always the same as that of the colloid in excess. The whole of this mutual coagulative action points un- doubtedly to the electrical nature of coagulation. It is believed that the particles in excess in a mixture of two oppositely charged colloids are attracted and absorbed by the other particles to such an extent that there results a larger unit, the charge of which is the same in sign as that of the absorbed particles. At the time of maximum precipitating action, the numbers of each kind of particle are just sufficient to produce uncharged masses which coalesce by surface ten- sion and fall to the bottom (compare Bancroft 73 ). One would conclude from such action that the proportion of the two colloids in the precipitate would approximate to a constant quantity, which is in accordance with experimental results ; in fact, many reactions formerly believed to be purely chemical are really of the above nature, as, for example, tannin and gelatine, tannin and basic colours, basic and acid colours, etc. In general, the charges on the particles of emulsoids are much less apparent than in the case of suspensoids, and the phenomena resulting from mixing emulsoids are of much greater complexity. Allied to this is the action of various 190 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS colloids and salts on suspensions of bacteria, which has been investigated particularly by Niesser and Friedemann, 83 Bechhold, 86 and Buxton and his co-workers. 87 III. Protective Action of Certain Colloidal Solutions (Schutzkolloide). Many organic colloids (emulsoids) when added, in compara- tively minute quantities, to suspensoids have the power of preventing the coagulation of the suspensoid particles. The consensus of opinion seems to be that, on account of the sur- face tension relations between the medium, the suspensoid particle, and the emulsoid substance, the latter surrounds the suspensoid particle with a thin coating which prevents the coalescence of the particles, either by preventing the cause which brings about coagulation (the discharge of the particles), or merely by offering a material obstacle to the coalescence. Many examples of this protective action have been furnished by various workers. Quantitative determinations of the protective action of organic colloids have been worked out thoroughly by Zsigmondy 88 and others in relation to gold sols and by Miiller and Artmann 89 in relation to arsenious, antimony, and cadmium sulphides. The results for gold solu- tions are expressed by what Zsigmondy has called the gold- value of the given organic colloid. This gold-value is denned as follows : " The gold-value of a given protecting colloid (Schutzkolloid) is the number of milligrams of the colloid re- quired to protect 10 c.cs. of a stable gold solution, containing from - 0053 to o - oos8 per cent of gold, from the precipitating action of I c.c. of a 10 per cent solution of sodium chloride". Gelatine has much the lowest gold-value, the substances in an ascending series of gold-values being gelatine, casein, egg-albumen, and gum-arabic, all of which have strong pro- tective action. Dextrin and various kinds of soluble starch also act as protectors but to a lesser extent than the above- named substances. Since the discovery of the protective action of these sub- stances it has been found that many so-called colloidal solu- tions owe their very existence as colloids to the presence of COAGULATION OF COLLOIDS 191 some protecting substance in small concentration. Reference to the classification in Table III (Ie) and Table IV (Class 5) will show to what a great extent this phenomenon plays a part. Undoubtedly the action of protective colloids is of first importance in many practical applications of colloidal study. The fluids of the body, so extensively colloidal in their nature, may alter greatly in their action as their content of protecting colloids varies. Again, in agriculture, the humus of the soil is probably a protecting colloid and as such will have a far- reaching effect in retaining the richness of the surface layers. IV. Action of Various Radiations on Sols. The intimate connexion between coagulation and the charge possessed by the particles is shown by the action of /3 rays of radium on typical solutions. The 7 rays, which are probably of the nature of X-rays, have been found to have no effect on the sols ; the a (positively charged) rays of radium have not sufficient penetrating power to affect the particles in any considerable volume of the solution. The /3 rays have sufficient penetrating power to traverse a layer of a solution some centimetres thick, and, as they possess a negative charge, they should exert a discharging effect on any positively charged particles and thereby hasten coagulation, while any effect on negatively charged particles should be that of increasing the charges and thus stabilizing the solution. Hardy 90 tried the effect of /3 rays on sols of purified globulin dissolved in (a) acetic acid, and (J>) sodium hydroxide ; as already noted, the globulin particles in solution (a) are catiohic, i.e. positively charged, while those in (b) are anionic, i.e. negatively charged. The effect of the ft rays was to bring sample (a) to the state of a jelly in three minutes, whereas the particles in solution (b) were rendered more mobile in an electric field, i.e. showed an increase in charge. Henri and Mayer 91 found that exposing a sample of a sol to radium bromide had no effect in the cases of the pure sols of silver and ferric hydroxide, but that when an electrolyte, e.g. sodium nitrate, was added to the sols in 192 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS quantity much too small to produce coagulation, the silver sample remained uncoagulated while the ferric hydroxide was coagulated, when both were again exposed to the /3 rays from radium. A sample of haemoglobin was coagulated by the /3 rays in seven hours. Dreyer and Hanssen 92 exposed samples of albumen to the influence of ultraviolet light and found that coagulation set in. Careful experiments carried on under the writer's direc- tion on the influence of strong ultraviolet light on a so.l of copper in methyl alcohol (positively charged particles) gave no coagulation of the particles. Spring 17 tried the discharging effect of X-rays and that of the brush discharge from a Holtz machine and of the dis- charge of an induction coil on samples of mastic, silica, Bredig solutions of gold, silver, and platinum, but obtained a negative result in every case. Later 93 he tested the transparency of such sols for X-rays but found no abnormal absorption by the solutions. BIBLIOGRAPHY. 1 Scheerer: "Pogg. Ann." (2), 82, 1851, p. 419. 2 Faraday : "Phil. Mag." (4), 14, 1857, p. 401 and p. 512. 3 Crum: "Ann. Chem. Pharm." 89, 1854, p. 156. 4 Graham: "Phil. Trans." 1861, p. 163; " Proc. Roy. Soc. Lon." 13, P- 335- s Jevons : "Trans. Mane. Phil. Soc." 1870, p. 78. 6 Gouy : "Jour, de Phys." 7, 1888, p. 561 ; "C.R." 109, 1889, p. 102. 7 Stingl and Morawski : "Jour. f. prak. Chem." 20, 1879, P- 7°- 8 Hardy: "Jour, of Physiol." 33, 1905, p. 258. 9 Schulze, H. : "Jour. f. prak. Chem." (2), 25, 1882, p. 431 ; 27, 1883, p. 320; 32, 1884, p. 390. 10 Linder and Picton : "Jour. Chem. Soc. Lon." vols. 61 "67, 71, and 87. 11 Freundlich: "Zs. f. Phys. Chem." vols. 73, 79, 80, 83, 85, 86; " Kolloidchem. Beith." 1915, 1916. 12 Wo. Ostwald : "Zeit. Kolloidchemie," 26, 1920, pp. 28 and 69. 13 Whetham : " Theory of Solution," p. 396. 14 Oden: "Der Kolloide Swefel," 1912, p. 156. Bancroft: "Second Coll. Chem. Rep,. Brit. Assoc," 1919, p. 8. 16 Freundlich: " Kapillarchemie," 1909, p. 367. 16 Mines : "Kolloid Chem. Beih." Ill, 5-6, 1911-12, p. 191. 17 Spring: "Rec. Trav. Chim. Pays-Bas" (2), 4, 1900, p. 204. 18 Freundlich : " Kapillarchemie," p. 348. COAGULATION OF COLLOIDS 193 10 Hober and Gordon : " Hofmeister's Beitr. z. chem. Physiol." 5, 1904, p. 432. 20 Paine : "Camb. Phil. Soc. Proc." 16, V, 191 1, p. 430. 21 Galecki : "Zs. f. anorg. Chem." 74, 19 12, p. 179. 22 Weiser and Middleton : "J. of Phys. Chem." 24, 1920, p. 30. 23 Burton and Bishop : "J. of Phys. Chem." (in print). 24 Burton: "Phil. Mag." (6), 12, 1906, -p. 472 ; 17, 1909, p. 583. 25 Billiter : "Ann. der Phys." u, 1903, p. 903. 26 Whitney and Blake : "Jour. Amer. Chem. Soc." 26, io, 1904, p. 1339. 27 Perrin : "Jour. Chim. Phys." 2, 1904, p. 607 ; 3, 1905, p. 50. 28 Elissafof : "Zs. f. Phys. Chem." 79, 1912, p, 385. 20 Briggs, Bennett, arid Pierson : "J. of Phys. Chem." 22, 19 18, p. 256. 30 McTaggart: "Phil. Mag." (6), 27, 1914, p. 297 ; 28, 1914, p. 367. 31 Cotton et Mouton : "Les Ultramicroscopes, etc." p. 124. 32 Mayer, Schaeffer, and Terroine : "C.R." 145, 1907, p. 918. 33 Henry, C. ; "C.R." 145, 1907, p. 141 5. 34 Chassevant and Posternak : "Chem. News," 88, 1903, p. 38. 35 Reissig : "Ann. der Phys." (4) 27, 1908, p. 186. 36 Wiegner : " Koll. Zeit." 8, 191 1, p. 227. 3 J Galecki : "Zs. f. anorg. Chem." 74, 1912, p. 174. 38 Oddn and Ohlon : "Zs. f. Phys. Chem." 82, 1913, pp. 78-85. 39 Zsigmomdy : " Zur Erkenntnis d. Koll." chap. XI. ; (Alexander), chap. XII. 40 Gutbier and Resenscheck : "Zs. f. anorg. Chem." 39, 1904, p. 112. 41 Carey Lea : "Amer. Jour, of Sci." 37, 1889, p. 476. 42 Von Meyer and Lottermoser : "Jour. f. prak. Chem." (2), 56, 1897,. p. 241. 43 Lottermoser: "Phys. Zeit." I, 1899, pp. 148-49. 44 Freundlich : "Trans. Faraday Soc." 9, 1 and 2, 19 13, p. 34. 46 Hatschek : "Trans. Faraday Soc." 9, 1 and 2, 1913. 46 Garrett: " Inaug. Dissert. Heidelberg," 1903. 47 Hardy: "Jour, of Physiol." 33, 1905, p. 281 et seq. 48 Einstein: "Ann. der Phys." 19, 1906, p. 289. 49 Hatschek: "Koll. Zeit." 7, 1910, p. 301; 8, 1911, p. 34; 11, 1912, p. 280. 50 Bancelin: "Koll. Zeit." 9, 191 1, p. 154. 61 Harrison : "Jour. Soc. Dyers and Col." 27 Apr. 191 1. 62 Freundlich and Ishasaka : "Trans. Faraday Soc." 9, 1 and 2, 1913, p. 66; see also Kawamura, "Jour. Coll. Sci. Imp. Univ. Tokyo," 25,, 8, 1908. 53 Ode'n : "Zs. f. Phys. Chem." 80, 19 12, p. 709. 54 Woudstra: "Zs. f. Phys. Chem." 63, 1908, p. 619. 65 McBain : "Trans. Faraday Soc." 9, 1 and 2, 1913, p. 34 (disc). 56 Ostwald : "Trans. Faraday Soc." 9, 1 and 2, 1913. 87 Pauli : "Trans. Faraday Soc." 9, 1 and 2, 191 3. 68 Whitney and Ober : "Jour. Amer. Chem. Soc." 23, 1901, p. 842. 13 194 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS 89 Spring: "Rec. Trav. Chim. Pays-Bas" (2), 4, 1900, pp. 215-17. 60 Duclaux: "Jour. Chim. Phys." V, 1, 2, and 3, p. 29; VII, 1909, pp. 405-46; "C.R." 154, 1912, p. 1426. 61 Thoulet: "C.R." ioo, 1885, p. 1002. 62 Schmidt : "Zs. f. Phys. Chem." 15, 1895, P- 5 6 - ' 63 Davis: "Jour. Chem. Soc. Lon." 91 (2), 1907, p. 1666. 64 McBain: "Phil. Mag." (6), 18, 1909, p. 916. 65 Van Bemmelen : "Die Absorption"; "Zs. f. anorg. Chem." 23, 1900, p. in, and p. 321, etc. 66 Nils Carli : "Zs. f. Phys. Chem." 85, 1913, p. 263. 67 Warrington : "Jour. f. prak. Chem." 104, 1868, p. 316. 68 Godlewski: "Bull. Acad. Sci. Cracovie," A, 1913, p. 335. 69 >Frion : "Jour. Chim. Phys." 7, 1909, pp. m-16. 70 Weisser and Sherrick : "J. of Phys. Chem." 23, 1919, p. 208. 71 Freundlich and Schucht : "Zs. f. Phys. Chem." 85, 1913, p. 641 ; {vide "Zs. f. Phys. Chem." 73, 1910, p. 385). 72 Procter: "Brit. Assn. Rep." (Dublin), 1908, p. 201. 73 Bancroft : "Second Coll. Chem. Report, Brit. Assoc." 1919, p. 2. 74 Loeb : "J. of General Physiology," vols. 1 and 2, 1919. 75 McBain : "Third Coll. Chem. Report, Brit. Assoc." 1920, p. 2. 76 Pappada: " Zeit. Kolloid Chem." 6, 191 1, p. 83. 77 Freundlich: " Kapillarchemie," 1909, p. 352. 78 Pappada : " Gazz. Chem. Ital." 42, I, 1912, p. 263. . 79 Bancroft: "J. of Phys. Chem." 19, 1915, p. 349. 80 Hofmeister: "Pfluger's Archiv." 24, 1887, p. 247. 81 Pauli : " Hofmeister's Beitrage z. Chem. Physiol." 5, 1904, p. 27. 82 Osaka : "Mem. Coll. Sci. Kyoto, Imp. Univ." I, 191 5, p. 267. 83 Niesser and Friedemann : " Miinchn. Med. Wochenschr." 1903, No. 1 1. 84 Biltz : "Ber. d. d. Chem. Ges." 37, 1904, p. 1095. 85 Billiter: "Ber. Wien. Akad. Wiss." 113, 1904, p. 1 1 59 ; 51, No. 11, 1904. 86 Bechhold: "Zs. f. Phys. Chem." 48, 1904, p. 385. 87 Buxton and others: "Zs. f. Phys. Chem." 57, 1907, pp. 47, 64, 76; 60, 1908, pp. 469, 489- 88 Zsigmondy : ' ' Erk. d. Koll." p. 66 ; (Alexander), p. 80. 89 Miiller and Artmann : " Oster. Chem. Ztg." 7, 1904, p. 149. 90 Hardy : "Jour, of Physiol." 29, 1903, p. 29 ; " Camb. Phil. Soc. Proc." 12, III, 1903, p. 201. 91 Henri and Mayer: "C.R." 138, 1904, p. 521 ; "C.R. Soc. de Biol." 57, 1904, P- 33- 92 Dreyer and Hanssen : "C.R." 145, 1907, p. 234. 93 Spring: "Rec. Trav. Chim. Pays-Bas" (2), 6, 1902, p. 460. 3i Kruyt and van der Spek : "Proc. K. Ac. Wet. Amst." 17, 1915, p. 1158 ; Kruyt: "Koll. Zeit." 22, 1918, p. 81 ; (and Jac. van der Spek) "Koll. Zeit." 25, 1919, p. 1 ; (and van Arkel) "Rec. Trav. Chim. COAGULATION OF COLLOIDS 195 d. Pays-Bas,'' 39, 1920, p. 656; also 39, 1920, p. 609; 40, 1921, p. 249; 40, 192 1, p. 169. 95 Mukerjee : "J. Amer. Chem. Soc." 37, 1915, p. 2024 ; (and Sen) " Lon. Chem. Soc. Jour. Trans.'' 115, 191 9, p. 462; "Lon. Chem. Soc. Jour. Trans." 117 and 118, 1920, p. 350. 96 Burton and Mclnnes : to appear in "Jour. Phys. Chem." 1921. Additional papers on coagulation by electrolytes : — Barus: "Sill. Amer. Jour. Sci." (3), 37, 1889, p. 122; "Bull. U.S. Geol. Survey," No. 36, 1886, p. 508. Billiter: "Zs. f. Phys. Chem." 45, 1903, p. 307; "Zs. f. Elektroch." 14, 1908, p. 624. Bodlander: "Jahrb. f. Mineral." II, 1893, p. 147. Freundlich : "Zs. f. Phys. Chem." 44, 1903, p. 129. Freundlich and Schucht : "Zs. f. Phys. Chem." 80, 1912, p. 564. Ishasaka : "Zs. f. Phys. Chem." 83, 1913, p. 97. Kimura : "Mem. Coll. Sci. and Engr. Kyoto, Imp. Univ." V, 6, 1913, pp. 175 and 201. Lottermoser and von Meyer: "Jour. f. prak. Chem." (2), 57, 1898, p. 540. Pappada: " Gazz. Chim. Ital." 42 (1), 1912, p. 263; " Beibl." 37, 1913, p. 36. Prost: "Bull. Acad, de Sci. Brux." (3), 14, 1887, p. 312. Rebiere : "C.R." 154, i9i2, T p. 1540. Schlosing: "C.R." 70, 1870, p. 1345. Winnsinger : " Bull. Soc. Chim. Paris," 49, 1888, p. 452. Woudstra : " Zs. f. Phys. Chem." 61, 1908, p. 607. 13 CHAPTER IX. THEORY OF THE STABILITY OF COLLOIDS. Several attempts have been made to give a general theory of the colloidal state, applicable to all classes of sols. The problems of special interest, from a theoretical point of view, may be classified into three main divisions : — 1. What is the process by which the disperse phase is pro- duced in the solution ? 2. What are the forces which ensure the stability of such a state? 3. What is the nature of the coagulation of sols by the addition of electrolytes, or, in a few instances, of non- electrolytes ? Naturally these questions must ultimately be treated as a whole, but in each of the theories which have been proposed stress has been laid particularly on one or other of these points. In what follows, these questions will be considered chiefly in relation to dispersoids, but the bearing of the phen- omena on emulsoids will also be noted briefly. I. The Production of the Disperse Phase. It has already been shown that the methods of preparation of dispersoids fall naturally into two classes : (a) condensation methods, in which the particles grow from molecular sizes to the colloidal size, and (&) dispersion methods, whereby large complexes of the colloidal material are broken up into the small colloidal particles. This subdivision suggests that the stable colloidal particle is, in every instance, an equilibrium state between two opposing sets of forces : viz. those tending to bring about the coalescence of small particles to form 196 THEORY OF THE STABILITY OF COLLOIDS' 197 larger ones and those tending to cause the dispersion of the colloidal substance throughout the medium. After the work of Linder and Picton, 1 Lobry de Bruyn, 2 Zsigmondy and Siedentopf, 3 and Svedberg * on the transition from coarse suspensions to ordinary molecular solutions, there can be little doubt that colloidal solutions do exist which con- tain particles of any size from that visible in the microscope to that of molecules. This view has induced workers to search after the laws which regulate the various forces at work in fixing, under any given conditions, the size of the particles. Donnan 5 has offered a suggestion as to these laws. He assumes that the colloidal substance disintegrates in the liquid medium up to a certain grade of dispersion because the cohesive forces between the liquid and the solid are greater than the adhesive forces between the molecules of the solid. When the particles become so small that the liquid layer about them be- comes thinner than the range of molecular attraction of the liquid, the forces of attraction due to the liquid will decrease and when they are just equivalent to the mutual attraction of the particles of the solid, the size remains constant. When the colloidal particles are produced by a condensation method, they will grow to the same limiting size fixed by the same limiting con- ditions. However, such a simple explanation of the phenomena will hardly account for the existence of colloidal solutions of such a wide range of concentrations and dispersity as we find between the extreme limits of Linder and Picton's arsenious sulphide solutions or Zsigmondy's gold sols. Garnett 6 probably first states, in this regard, the bearing of the process of crystallization on the production of colloidal solutions. "When a homogeneous liquid separates into two states, say, a liquid and crystals, the new state (phase) appears first as minute droplets which, represent an unstable state and which changes to the stable crystalline state in a longer or shorter time, according to the relative magnitude of the force of crystallization and the force due to surface tension. Sub- stances which do not readily crystallize, whose molecules there- fore have feeble polarity, permit the unstable emulsion state to 198 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS become subpermanent, and this is the state known as colloidal solution/' 7 Von Wiemarn 8 has developed similar ideas to account for all colloidal solutions. The two sets of forces are presented thus : " In agreement with the present view of crystallographers, a crystal presents a completely uniform system of points about which the molecules execute their harmonic motion ; this is the so-called space-lattice. It is not hard to imagine that a free crystal surface in contact with the surrounding liquid medium, in which the crystal forms, must disturb, to a certain extent, the uniformity of these points and the motion of the molecules at this surface of separation. The layer at the crystal surface will approach in its properties the internal layers of a highly compressed liquid, just as at the surface of a liquid the transition layer will resemble in its properties the internal layers of a highly compressed gas. It would be a great mistake to assume that the conditions at the crystal- liquid surface of separation are the same as in an ordinary liquid. They approach one another but are not the same. " Two factors play an important rdle in the production and properties of the free surface of the crystal, viz. : — " A. The influence of vectorial molecular forces on the molecules constituting the free crystal surface, and " B. Molecular kinetic processes coming into play at the free crystal surface. " The factor A gives rise to the capillary pressure which is added to the external pressure on the crystal face and which is magnified as the grade of the dispersion increases (i.e. as the size of the crystals decrease}. Therefore, in general, this factor A causes the dispersed body to depart from the liquid state (i.e. increases the size of the particles), and this tendency is the stronger the greater the grade of the dispersion of the crystal- lizing body because, for most substances, the melting-point is raised by an increase of pressure. Only in a few cases, e.g. ice, the factor A causes the dispersed substance to approach the liquid state, for the melting-points of such substances as ice are lowered by increase of pressure. " The factor B tends to cause all bodies, without exception, THEORY OF THE STABILITY OF COLLOIDS 199 to approach the liquid state, because it lessens the regularity of the orientation of the molecules at the surface layers. Thus we see that in only a few cases will the factors A and B exert influences in the same sense. For the great majority of sub- stances these two influences are diametrically opposed. Ex- periment shows us that the factor B works more energetically than A, because disperse crystalline bodies are more soluble, more fusible, more transitory, and have stronger reacting power, the higher the grade of dispersion — an effect which in- creases more and more as the liquid state is reached. "It is not hard to confirm that the factors A and B struggle with one another for mastery, although the factor B comes out victor. The factor A acts more and more energetically the greater the surface tension, while the factor B, on the other hand, increases with the increase of the activity of the dis- persion medium in relation to the disperse phase. ... In this way we see that the physico-chemical properties are functions of the grade of the dispersion." Following out this line of thought, Von Weimarn shows that the production of a colloidal solution in any given case will depend on the relative potency of these two factors under the given conditions of the reaction. He maintains that any substance whatever can be produced in the colloidal state pro- vided the proper conditions of solubility, concentration, etc., are discovered. In confirmation of this thesis, Von Weimarn has produced over two hundred substances 9 in the colloidal state, many of them, e.g. ice, not having been previously so produced. Furthermore, he maintains that the initial stage in the evolution of any colloidal solution is the formation of small crystals ; a statement which he holds to be true even for gelatine and agar-agar. 10 A corollary of this proposition is that there is no amorphous state of a substance in the sense of it being entirely non-crystalline ; for example, a so-called amorphous powder or a gel is merely an aggregation of small crystals held together in small masses by the effects of surface tension (see Frankenheim n ). More particularly, according to Von Weimarn, in any so- called chemical reaction, when the rate of precipitation is low, 2oo PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS there is produced a distinctly crystalline deposit ; when this rate is high, one gets a higher degree of dispersion — a sol, a flocculent precipitate, or a jelly, as the case may be ; when two very concentrated solutions of substances which, by their inter- action produce a very insoluble precipitate, are mixed, a jelly always results. Even the most definitely so-called crystalloidal bodies may be obtained in the colloidal or gelatinized states if produced in solutions in which they are very insoluble. An ordinary precipitate, such as barium sulphate, is at first formed by the combination of the ions in very minute crystal elements , which are sufficiently soluble in water rapidly to unite to form crystals, which gradually increase in size by absorbing the smaller crystal elements. It is well known in ordinary ana- lytical work that such precipitates will pass at first through any filter, but gradually become filterable by the effects of time and warmth. If, however, their insolubility is sufficiently in- creased by a large excess of a common ion, or by effecting the combination in a medium, such as methyl alcohol, in which the sulphates are extremely insoluble, the molecules cannot coalesce in the form of large crystals but remain in spherical masses and a colloidal sol results. 12 In this way some years ago, Paal 13 obtained in colloidal form the chlorides of sodium and potassium by the double decomposition of their organic compounds in organic media in which the chlorides were sufficiently insoluble. In the cases of the dispersion methods of preparation, Von Weimarn treats the electrically prepared metal sols as, in reality, the result of the condensation of small crystals from the vapours of the metals, and the colloids produced by re-solution of a precipitate, e.g. peptization, merely as samples of changes in the solubility of the precipitate due to the stabilizing ion. The theory put forward by Von Weimarn dispenses with the view suggested by Schulze, 14 Carey Lea, 16 and others that in colloidal solutions we have allotropic forms of the various substances involved ; the allotropy is merely in the massing of the individual minute crystals (see Scherrer 32 ). In addition to the forces outlined by the above theory, we must take account of the effect of the charge on the particles, THEORY OF THE STABILITY OF COLLOIDS 201 especially in the case of most suspensoids. In view of the work of Hardy on the globulins alone, one cannot neglect the effect of the electrical charges at any stage of the process. It may be that Von Weimarn includes them tacitly in the forces under factor A ; nevertheless, in the equilibrium state of the colloid, the charge on the particles is important enough to de- mand special attention. The problem of accounting for the charge possessed by colloidal particles has led to the suggestion of various theories as to the production of the colloidal particle. There can be no doubt that this charge is due primarily to some chemical combination followed by a partial dissociation of a portion of the colloidal unit. It is quite possible that these chemical actions may vary greatly in the nature and still bring about similar final results. Two or three examples of this may suffice. Duclaux 16 and Jordis 17 have shown pretty conclusively that, with such colloids as ferric hydrate, copper ferrocyanide, etc., produced by double decomposition, the particles constitut- ing the disperse phase consist in the main of the chemical com- pound named, but that this compound always retains a certain amount of one of the primary reacting substances, which in some way gives the charge to the particle. Conversely, Duclaux accounts for peptization by saying that this process adds to the precipitate to be redispersed the ions Which produce the charge on the particles. In line with Duclaux's suggestion is Hardy's discovery that the charge possessed by globulin particles depended on whether the medium was acidic or basic. As another instance of some chemical action, the writer 18 (p. 151) has given evidence to show that the charge pos- sessed by the metallic particles of the Bredig electrically pre- pared solutions is due to a chemical reaction between the medium and the metal followed by dissociation. II. The Cause or the Stability of Colloidal Solutions. Practically every one who has attempted to account for the stability of colloidal solutions assumes that they are two-phase systems. The distinctions raised are as to the relations of 202 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS the two phases : (i) the purely physical theory looks upon the sols merely as suspensions of fine particles, each one of which is self-contained ; (2) Quincke's theory assumes that the system of particles in the liquid medium constitutes a foam- like structure, the surrounding liquid being a true solution of a very slight amount of the disperse phase in the pure sol- vent, while the walls of the structure are solutions of a small quantity of the liquid in the solid. The latter is practically the view of Van Bemmelen as given by the adsorption compounds. In any case, the forces which determine the sta- bility of the sol, i.e. which keep the disperse phase from preci- pitating in response to gravity, are in the main : (1) surface tension, (2) electrical repulsions, and (3) the Brownian move- ments ; to these Duclaux has added the force due to osmotic pressure. 19 Up to the present, attempts to account for the stability of both suspensoids and emulsoids by the same theory have been so unsuccessful that we are driven to divide them as suggested by Woudstra 20 : " When we picture to ourselves the sols as structures of two phases with very great areas of contact, there are two possibilities : the surface of contact of the two phases is continuous or it is not. In the first case we might imagine the sol as a honeycomb scaffolding of water dissolved in the colloid, surrounded by an aqueous solution of the colloidal material. In the second case, the sol consists of a number of discrete particles of the colloid which, under certain influences, are able to defy gravity and remain divided in the water which forms the medium. ... To the first group belong gelatine, albumen, egg-albumen, silicic acid, etc., i.e. emulsoids in general ; to the second group (suspensoids), metal sols, sulphide sols, hydroxide sols, etc." As has already been pointed out, these two groups differ in two particulars which have an exceedingly important bearing on their stability. First, those of the emulsoid group move little, if any, in an electric field, i.e. the particles show little if any charge, and, secondly, probably as a result of this lack of charge, these colloids are much less sensitive to added electrolytes than are the suspensoids. Follow- ing Quincke, then, we may assume that the all-important THEOR Y OF THE STABILITY OF COLLOIDS 203 factor in the stability of emulsoids is the surface tension be- tween the two continuous phases of the sol. On the other hand, we have in the case of the suspensoids, in addition to surface tension, the electrical forces due to the charge. The potential energy due to surface tension, T, possessed by an area, A, is T x A, and, since the coalescence of particles will reduce the total surface area, in order to have the surface energy due to this cause a minimum, small particles will tend to coalesce into larger ones. At the same time, if each particle bears a definite change, the coales- cence of such particles will bring about an increase in the potential energy due to the charge. Equilibrium will result when these two effects just counterbalance. That is, the total potential energy of the particles will be the sum of all such quantities as : — T x A + £E . V, [or T x A + ^E a /C, or Tx A + £CV 2 ] where T represents the surface tension between the particle and the liquid, V the potential difference between the particle and the liquid, and A, C, and E respectively the area, capacity, and the charge of each particle. In the case of spherical, conduct- ing particles bearing charges of a certain definite size and sur- rounded by an outer layer of ions of an opposite charge, the capacity of a single particle will be (p. 137) C = K . r 2 ld, where r is the radius of the solid core of the particle, d is the average distance between the surface of the core and the outer layer, and K is the dielectric constant ot the medium. The coalescence of two such particles reduces the capacity of the two and therefore increases the potential energy due to the charges on the particles. We may say then that the charges on the separate particles keep them separated while the forces of surface tension, if left to themselves, would cause coalescence and consequent coagu- lation. As seen from the three forms of the equation for the potential energy above, anything which lessens the value of 204 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS V, when C is unchanged,, will decrease the potential energy and consequently weaken the force opposed to surface tension. When possible this will take place and consequently the sol will tend to coagulate when V is decreased. So far there is fair agreement in the views of various workers ; a great deal of discussion has taken place on the question as to how the particles really become charged. On account of the similarities between colloidal and electro-endos- mose experiments, the early workers accounted for the mobil- ity of the particles in an electric field by saying that there is a contact difference of potential between the particle and the liquid. In view of our lack of knowledge of what contact difference of potential really means, such a statement is hardly an explanation of how the charging comes about. Particles were known to become either positively or negatively charged, and examination of various results led Coehn 21 to formulate the following empirical law : " A substance of higher dielectric constant charges itself positively when it comes in contact with a substance of smaller dielectric constant". Later Heydweiler 22 showed that this law did not hold in the cases of metals and liquids. Since the work of Perrin 23 there is no doubt that the pro- cess is due to electrolytic ions. Early workers (e.g. Bredig 24 ) adopted the principle enunciated by Nernst, 25 viz. that every ion possessed a specific solution pressure in any given liquid, and conceived the complete colloidal unit to consist of a solid core charged by the loss of certain positive or negative ions which form an outer layer about this core : this is the double layer proposed by Quincke 26 and Helmholtz. 27 The principal differences expressed in the views of later writers have been merely regarding the nature of this dissocation. Billiter 28 suggested that the colloidal particle, e.g. silver, dissolves in accordance with Nernst's law, but only in the form of positive ions ; consequently the core left is negatively charged. Thus an electrical double layer is formed on the surface of the colloidal particle, the outer layer positive, the inner layer negative. The writer, on the other hand, has submitted evidence to show that the dissociation in the cases of the THEORY OF THE STABILITY OF COLLOIDS 205 Bredig metal sols is really that of a layer of hydroxide or hydride on the surface of the metal particles. Duclaux 16 believes that the charge always arises from the dissociation of a portion of extraneous substance retained by the particles from the reacting media ; for example, he has shown that in the colloidal particles of ferric hydroxide, there is always re- tained a small trace of ferric chloride, which was used in the production of the sol. He pictures the colloidal particle thus : an inner solid core of ferric oxide, surrounded by a layer of ferric chloride; this latter layer dissociates, in the Nernst manner, leaving an excess of positive iron ions on the solid core, and, as an outer layer, an atmosphere of negative chloride ions. As a conclusion, in the present state of our knowledge of these solutions, we may make the statement that the exist- ence of the colloidal particle is fundamentally due to an equili- brium maintained between the forces of surface tension and the repulsion due to the electrical charges. In a stable colloid, settling to the bottom of the vessel in obedience to gravity is prevented, in the case of sufficiently small particles, by the molecular shocks which give rise to the Brownian movement. III. The Nature of the Coagulation of Suspensoids. From these experimental data we see that the dominating factor in bringing about coagulation of the dispersoids is un- doubtedly the neutralization of the charge possessed by the particle. This may conceivably be done by so altering the properties of the liquid medium itself that the dissociation producing the electric double layer is lessened ; this would bring about at least a partial recombination of the two charged layers. However, in most cases the experimental results point to an absorption by the particle of ions bearing a charge opposite to that of the particle (see Paine 29 ). Billiter 28 supposed that the mobility of a colloidal particle in an electric field was due to the fact that, under the influence of the electric field, ions diffuse off the outside of the double layer into the surrounding medium and leave the colloidal unit with a net charge similar to that on the core itself. This 206 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS colloidal particle then moves similarly to an ion. Billiter's further assumption that this net charge is much below the charge on an ion and that coagulation represents a condensation of these particles about an ion, does not seem to be in agreement with the general experimental results. Nevertheless, we may con- sider, after Billiter, that any outer layer is a constantly chang- ing system of ions ; when a foreign electrolyte is added, there is an increase in the concentration of ions about the particle and, on account of some absorption effect, which may be due to surface concentration or merely strong electrical attraction, a certain number of ions of charge opposite to that on the core are drawn on to the core itself and thus produce the discharg- ing effect. Freundlich at one time suggested that the surfaces of colloidal particles act as semipermeable membranes with respect to ions, and that, in the case of a negatively charged particle, the migration velocity of positive ions is accelerated on passing the outer layer, while the velocity of negative ions is reduced ; and conversely for positively charged particles. The influence on coagulation of shaking the mixture, quick addition of the electrolyte, etc., and the existence of the initial, apparently quiescent period during coagulation, lends colour to the view, as expressed in Whetham's theory, 30 that the discharge of the particles and consequent coalescence, depends on a charge of a certain size being brought up to the particle. It is sometimes objected that such a theory cannot be applied to explain peptization. However, there is no reason why the converse effect may not take place when the stabilizing ions are added to the moist coagulum to be peptized. An analogous phenomenon has been recorded by the writer: exceedingly small doses of aluminium sulphate added to a Bredig silver sol produces coagulation ; if to a series of similar samples of the sol increasingly large amounts of the sulphate are added, it is found that the coagulative power of the salt goes through a maximum, and that large doses pro- duce a fairly stable sol, in which, however, the particles are found to have changed from negatively charged to positively charged, presumably from the adsorbed aluminium ions. THEORY OF THE STABILITY OF COLLOIDS 207 Granted that the particles are necessarily discharged before coagulation sets in, the question as to how the coalescence occurs still remains. Three active agencies are at work before the discharge has taken place, viz. surface tension, Brownian movement, and electrical repulsions. The first will always tend to cause decrease in the total surface by coalescence, the Brownian movement will continually tend to bring the par- ticles into collision, but the electrical forces will always tend to prevent the particles approaching one another very closely. Anyone who has watched the movement of the particles either in liquids or gases will be struck by the fact that collisions do not appear to take place ; two or three particles may approach one another, rotate about a common centre for a few moments, and then break away. One is driven to the conclusion that they are held apart by considerable forces, while they are always knocked helter-skelter by the molecular shocks. Once the electrical repulsion is materially reduced, the surface tension forces come into play to cause coalescence.* BIBLIOGRAPHY. 1 Linder and Picton : "Jour. Chem. Soc. Lon.'' vols. 61, 67, 71, and 87. 2 Lobry de Bruyn : "Rec. Trav. Chim. Pays-Bas" (2), 4, 1900, pp. 236 and 251. 3 Zsigmondy : " Zur Erkenntnis der Kolloide ". 4 Svedberg : " Die Existenz der Molekiile ". 6 Donnan: "Phil. Mag." (6), 1, 1901, p. 647; "Zs. f. Phys. Chem." 37 1901, p. 735 ; 46, 1903, p. 197. " Garnett : "Phil. Trans." 205 A, 1906, p. 237. 7 Hardy: "Jour, of Physiol." 33, 1905, p. 254. 8 von Weimarn : "Grundziige der Dispersoidchemie " (Steinkopff, Dres den), 191 1. 9 von Weimarn: "Koll. Chem. Beih." 19 12 ; vide Wo. Ostwald, "Die neuere Entwicklung der Kolloidchemie ". 10 von Weimarn: "Jour. Chem. Soc. Lon." A, 2, 1910, p. 1046. *One often observes in papers that the effects of surface tension and of electrical charge are confused ; it is often said loosely that the electrical charge lessens the surface tension. As shown by many experiments, 81 an electrical charge does not affect the surface tension per se. Moreover, the dimensions of the mechanical tension on the surface of a charged body, due to the charge, are quite different from those of surface tension. Of course, in general, an electric charge will act so as to oppose the effect of the surface tension. 208 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS 11 Frankenheim : "Pogg. Ann.'' hi, i860, pp. 1-60. 12 Procter: "Brit. Assn. Rep." (Dublin), 1908, p. 201. 13 Paal and Zahn : "Chem. Ber." 42, 1909, pp. 277 and 291. 14 Schulze : "Jour. f. prak. Chem." (2), 25, 1882, p. 431. 15 Carey Lea : " Sill. Amer.'Jour. Sci." (3), 41, 1891, p. 482. 16 Duclaux : "Jour. Chim. Phys." V, pts. 1, 2, and 3, p. 29. 17 Jordis: "Koll. Zeit." 2, 190,8, p. 361, and 3, 1908, pp. 13, 153. 18 Burton : "Phil. Mag." (6), 11, 1906, p. 425. 19 Duclaux: "Jour. Chim. Phys." 7, 1909, p. 405 ; 10, 1912, p. 528 (cum Langevin); "C.R." 154, 1912, p. 1426. 20 Woudstra:'"Zs. f. Phys. Chem." 61, 1908, p. 607. 21 Coehn : "Ann. der Phys." 64, 1898, p. 217. 22 Heydweiller: "Ann. der Phys." 66, 1898, p. 535. 23 Perrin : "Jour. Chim. Phys." 2, 1904, p. 607 ; 3, 1905, p. 50. 24 Bredig : " Anorganische Fermente". 25 Nernst: "Zs. f. Phys. Chem." 9, 1892, p. 139. 26 Quincke: "Pogg. Ann." 113, 1861, p. 513. 27 Helmholtz: "Memoirs Lon. Phys. Soc." 1888. 28 Billiter: "Wien Sitzungsber." 112, 1903, p. 1105. 29 Paine ; "Camb. Phil. Soc. Proc." 16, 1912, p. 430. 30 Whetham : " Theory of Solution," p. 396. 31 Burton and Wiegand : " Phil. Mag." (6), 23, 1912, p. 150. 32 Scherrer: "Ges. Wiss. Gott. Nachr." 191 8, p. 96; "Chem. Zentibl." h IQI 9, P- 32 2 - CHAPTER X. PRACTICAL APPLICATIONS OF THE STUDY OF COLLOIDAL SOLUTIONS. THE practical applications of colloidal solutions are so wide- spread that entire volumes might be devoted to such questions as their relation to manufacturing processes, their occurrence and economic value in nature, and their importance in the physiology of the human body. We shall have to content ourselves with merely suggesting the outlines of this phase of the subject. Processes essentially colloidal in their nature have been employed for many years prior to the development of the theoretical interest in colloidal solutions as such^ Instances of this may be found in the manufacture of soaps, rubber, and paper, and in such processes as the extraction of sugar from beet-root. 1 Probably in no field has the theoretical treatment of colloidal solutions received wider application than in dyeing and the related industry of tanning. Modern accounts of the process of dyeing take into consideration the colloidal state for two reasons : (i) the textile fibres to be dyed are colloidal in their nature, and (2) many of the dye solutions are true colloidal solutions. Michaelis, 2 Freundlich and Neumann, 3 and Biltz and Pfenning 4 have separated the dyes into three classes with regard to their colloidal nature: viz. (1) those in which nearly all the sub- stance exists as visible ultramicrons and which may easily be subjected to dialysis, (2) those in which the substance exists as a mixture of submicrons, amicrons, and possibly molecules and which may be dialysed but only at a very slow rate, and (3) those which contain no visible ultramicrons but which show fluorescence and diffuse readily through parchment paper. 209 14 210 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS The action of the dyes of these various classes is determined by the extent of their colloidal properties. Many writers have given a colloidal theory of the whole process of dyeing ; the relation of the electrical charge possessed by the particle of the dye to the action has been particularly emphasized by Gee and Harrison, 5 and by Feilmann, 6 while the function of mordants as a phase of colloidal behaviour is suggested by Krafft 7 and others. " Wood 8 unifies the various conflicting theories of the process of dyeing by pointing out that this process is really dual in its nature, the two stages in the process being (i) absorption of the dye by the fibre tissue, and (2) the fixation of the dye in the fibre. The first stage is, in general, an example of the absorption phenomena of colloids as detailed by Van Bemmelen, whereas the fixation may be purely chemical in some cases or, in others, merely a precipitation of a colloid by salts. The evolution of the photographic plate 9 serves as a strik- ing example of the use of gelatine and similar colloids in arts and industries. In the everyday operations involved in baking, distilling, and dairying, colloidal solutions are always occur- ring, and many of the reactions are regulated by the laws of these solutions. It is probable that no one substance is of more interest from its colloidal nature than common clay. In the' manufactures of cement and porcelain, in the purification of effluent waters, and' in the treatment of various soils, the colloidal properties of clay are of the first importance. Clay is defined as the mineral part of the soil and con- sists mainly of rock material divided into particles less than o - 002 mm. in diameter (Russell 10 ) ; pure clay consists of " com- plex silicates containing much iron and alumina," while clay as it is used in the manufactures and as it exists in fertile soils will be mixed with varying proportions of calcium carbonate and phosphate, organic matter, soil water containing carbon dioxide in solution, and residues of plants. The setting of cement is now thought to be due to the slow coagulation of the hydroxides of silicon, aluminium, and iron and the action of the absorbed carbon dioxide in forming after a APPLICATIONS OF COLLOIDAL SOLUTIONS 211 time hardened calcium carbonate. The admixture of gravel to form concrete provides nuclei about which the coagulation takes place. The plasticity of the clay, so important in porce- lain manufacture, is explained by the fact that the clay in the air-dried state contains substances which dissolve in water in the colloidal state. In common with many other col- loids, clay in suspension has great absorptive power, not only for various ions in solution but also for many other substances both in the crystalloidal and colloidal states. In the coagu- lation of clay solutions, the coagulum will carry down the various absorbed substances. Since clays absorb and retain substances such as " oils, fats, concentrated soap solutions, starch dextrine, maltose, glycerine, plant and animal albumin, casein, inorganic dyes such as Prussian blue and Turnbull's blue, all coal-tar dyes . . ., animal colouring matters such as carmine, the colouring matter of the blood, the yellowish-brown colouring matter of urine, faecal matter, further, all bad odours, and certain hydrocarbons — they are suitable for clearing, decolorizing, and purifying the effluent waters of factories and works, which contain substances in the colloidal state, and many colouring matters, those of the carbohydrate industries, starch and dextrine, dyeing, tanning, soap-boiling ) paper and sugar works, breweries and distilleries, and finally town sewage ". u Such a coagulation is of daily occurrence in the formation of deltas at river mouths ; on meeting the salt water of the ocean the silt of the river water is coagu- lated quickly. The greatest economic importance of clay is as an essential element of a good agricultural soil ; its importance is not so much on account of its chemical composition as it is due to the colloidal nature of the clay. " It is a mistake to suppose that the medium on which the soil organisms live and which is in contact with the plant roots, is the inert mineral matter that forms the bulk of the soil. Instead the medium is the colloidal complex of organic and inorganic compounds, usually more or less saturated with water, that envelops the mineral particles ; it is therefore analogous to the plate of nutrient jelly, used by bacteriologists, while the mineral particles serve mainly to 14* 212 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS support the medium and control the supply of air and water and, to some extent, the temperature." 12 The great absorptive power of these surface colloids in the soil suffices to retain near the surface practically the whole of any food added to the soil ; this results in time in the development of a rich humus at the surface. Whatever the view taken of the necessary com- position of the soil colloids, 13 there is unanimity in ascribing to the colloids the essential actions of a good soil : for example, the formation of compound fine particles in the humus, the absorption of soluble manures, the retention of water, the ascent of water from great depths (Linde u ), the swelling of the soils when wet and the contraction when dry, are probably all essentially colloidal phenomena. The extensive interest developed recently in colloidal solu- tions has had important bearing on the study of physiology. Advances have been marked in two directions : (i) the increased power of observation afforded by the ultramicroscope, and (2) the extended study of the body fluids as colloids. Under the first heading, we may draw attention to the new bacteria first identified by the use of the ultramicroscope, such as those relating to yellow fever, foot and mouth disease, certain forms of cholera, and tobacco disease ; again, Raehlmann's ultramicro- scopic study 15 of blood and urine has confirmed our know- ledge of these fluids under various conditions, e.g. he identi- fied particles of albumen in the urine of nephritic patients. In the second place, studies of such problems as the change in the viscosity of the body fluids under changing circumstances, 16 the influence of salts on the properties and action of the blood, 17 and the laws regulating the permeability of cell walls for salts and colloids in the human body, are bound to advance both our knowledge of the action of the normal body and our power of treatment of abnormal conditions. In all these phases of the practical applications of the work on colloidal solutions we see what a vast unexplored region is still before us. In spite of the immense amount of work that has been done during the last twenty years, it is quite apparent that, both from a theoretical and a practical point of view, there still is APPLICATIONS OF COLLOIDAL SOLUTIONS 213 need for much additional research before one would be able to suggest, with any degree of satisfaction, a general theory of the colloidal state. We may very well conclude with the words used by the pioneer worker Zsigmondy, 18 in closing his first account of the early work on colloidal solutions : — " From the foregoing outline no general theory of colloids can be given, for the study of colloids has become a great and extensive science, in the development of which many must assist ; only when the voluminous material supplied by much physico-chemical research has been properly systematized, will the theory of colloidal solutions be raised from mere considera- tion of the similarities in special cases to the standing of an exact science." BIBLIOGRAPHY. 1 Rohland : " Colloidal and Crystalloidal State of Matter," 191 1. English Trans. (Britland and Potts), Van Nostrand. 2 Michaelis : "Deutsche Med. Wochenschr." 1904, No. 42 ; "Virchow's Archiv." 179, 1905, p. 195 ; Zsigmondy, "Erkenntnis d. K." p. 158. 3 Freundlich and Neumann : " Koll. Zeit." 3, 1908, p. 80. 1 Biltz and Pfenning : "Gedankboek aan van Bemmelen," 1910, p. 108. s Gee and Harrison : "Trans. Faraday Soc. Lon." 1910. 6 Feilmann : "Jour. Soc. Dyers and Col." 25, 1909, p. 158. 7 Krafft: "Chem. Ber." 32, 1899, p. 1608. 8 Wood : " Chemistry of Dyeing" (Gurney and Jackson), London, 191 3. 9 Luppo-Cramer : Many papers scattered through "Zeit. Chem. Koll." 10 Russell: "Soil Conditions and Plant Growth" (Longmans, Green & Co.), London, 1913. 11 Rohland : "Coll. and Cryst. State," p. 18. 12 Russell: " Soil Conditions, etc.," p. 110. 13 Russell : "Soil Conditions, etc.," pp. 74-77- 14 Linde : "Jour. Phys. Chem." 16, 1912, pp. 759 and (Bates) 766; (Dupre) "Trans. Roy. Soc. Canada," (3), 7, III, 1913, pp. 105 and 123; (3), 8, III, 1914, p. 133. 1B Raehlmann: " Berl. Klin. Wochenschr." 1904, No. 8; " Deutsch. Med. Wochenschr." 1904, No. 29. 16 Pauli : "Trans. Faraday Soc." 9, 1 and 2, 191 3. 17 Mines: "Koll. Chem. Beiheft." Ill, 5-6, 1911-1912, p. 191 ; "Jour, of Physiol." 40, 1910, p. 327. 8 Zsigmondy: " Erkenntnis," p. 183. SUBJECT INDEX. Numbers refer to pages. Aberrations, optical, 29. Absorption of salts, 169, 176 et seq. — optical, 2, 29, 96, 99, 105. Alcosol, 9, 147. Amicron, 122. Animalcule, 1, 51. Anionic sols., 133, 146. Antipoint, 33. Aperture, 30, 36. — numerical, 29, 30, 37, 38. Arc, electric, ig, 122. Artificial atmospheres, 99. Atomic charge, 92, 93. Benzol, sol, 9. . Brownian movement, animalcules, 51. causes of, 60 et seq. cessation of, 63. cinematograph and, 57, 64. definition, 2, 51 et seq. — — electrolytes and, 55. evaporation and, 52. in gasses, 8g. in sols, 45, 155, 207. velocities, 54, 59, 179. Bubbles, gas, 132, 141, 171. Cataphoresis, 65, 134. — theory of, 134. Cationic sols, 133, 146. Cedar oil, 31, 37. Cement hardening, 5, 210. Centrifuging, 117. Charge on colloidal particles, 151. Chemical constitution of sols, 12. Clarckia Pulchella, 51. Classification of sols, n et seq. Clay, 5, 210. Coagulation, 4, 8, 83, 205. — power of electrolytes in, 155 et seq. — rate of, 164, 206. Coagulum, 21. Colloids, 2, 7. — : anhydrophilous, n, 24. — hydrophilous, 11, 24. — irreversible, n, 21, 24, 25. — lyophile, 11. — lyophobe, 11. — reversible, 11, 21, 22, 24, 25. — stable, ir. Colloids, unstable, n. Colour of solutions, 96, 116, 173. Concentration and absorption, 180. Condensation method of preparation, 13, 14, 196. Condenser, immersion, 38. Conductivity, electrical, 22. Contact difference of potential, 137, 143, 148. Crystallisation and sols, 197. Crystalloid, 2, 7. Definition of colloidal solution, 1. Deltas, 211. Density of particles, 82. — optica], 105. Depression of the freezing-point, 129. Dialysis, 8. Diatoms, 134. Diffraction, 29, 31, 33, 35, 36. Diffusion of light, 2. — of liquids, 2, 7, 73, 177. — of particles, 73, iag. Disperse phase, 9, 10, 11. Dispersion, chemical, 14, ig. — grade of, 173. — mechanical, 14, 18. — medium, 9, n. — method of preparation, 13, 14, ig6. — optical, 30. Dispersoid, g, 10, n. Distribution of particles, 4, 80. , Double decomposition, 14, 16, 177. — electric layer, 135, I4g. — refraction, 120. Dyeing, 5, 2og. Electrical charge on particles, 4, 12, 22, 53, 65, 137, 151. Electrochemical equivalent, 176, 179. Electrokinetic effect, 163. Electrolytes, 4, 12, 22, 142, 155 et seq. Ellipsoidal particles, 117. Emulsion, 10 (Oil), 140. Emulsoid, 11, 22, 23, 23, igo. Endosmose, 140, 156, i6g, 204. Ethyl malonate, 11, 139. Flocculation, 65. Fraunhofer lines, 37. 215 2i6 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS Galvanotropism, 5. Glass, cobalt, 98. — gold ruby, 39. — manufacture of, 5. — metal, 107, iog, in. Glycersol, 9. Gold value, igo. H/EMOCYTOMETER, I24. Henry's law, 179. Hydrogel, 20. Hydrolysis, 14, 16, 102. Hydrosol, 9. Illumination, axial, central stop, 2S, 47- — dark background, 2, 3, 32, 40, 43, 45- — oblique, 32, 41, 43, 46. — orthogonal, 40. Index of refraction of particles, 48. Infusoria, 53, 61. Inorganic sols, 12. Ion, coagulating, 169. — . entrained, 23, 24, 156, 176. — stabilizing 21, 24. Ionizing power of liquids, 148. Isoelectric point, 156, 164. Kerr phenomenon, 120. Kinetic theory of matter, 2, 4, 61, 6g 94. Limit of magnification, 29. — of resolution, 29, 32, 35, 37. Limitations of the ultramicroscope, 47. Limiting concentration of sols, 87. Lippmann phenomenon, 156. Magnetic field and colloidal particles, 66. Microscope, 28. Microstructure, amorphous, granular, spicular, 112, 113. Mixing oppositely charged particles, 188. Mobility of particles, 132 et seq., 205. — measurements of, 142. Molecular constants, 92. — motions, 66, 6g. Molecules, 8, 48, 52. — visibility of, 32. Monobromonaphthaline, 37. Mutual actions of particles, 63. Object glass,' 29. Objectives, achromatic, 30. — apochromatic, 30. — diamond, 29. — immersion, 29, 31, 37, 38. Cnagrariae Oenothera, 51. Optical properties of sols, 96 et seq. Organic sols (organosol), 12, 19. Osmosis, 3, 73, 81. — electric, 134, 149, 156, 171. Oxidation methods of preparation, 14, 15- Peptisation, 14, 20, 21, 24, 206. Physiology and colloids, 212 Polarisation of scattered light, 96, ioo, "5- Pollen, movement of, 51. Porcelain, 211. Potential difference between phases, 148. Preparation of colloidal solutions, 12 et seq. Protecting colloids (Schutzkolloide), 25. Pulverisation, electrical, 14, 18. Purification of effluent waters, 210. Radiations, effect on sols, 191. Radium, 192. Reduction methods of preparation, 13, 14. Reflection, selective, 97. Resolving power, 33, 35*. Reversal of direction of migration, 163. Rotation, Brownian movement of, 55, 79- Scattering of light, 96, 100, 105. Schutzkolloide, 5, 12, 14, 17, 23, 25, 190. Size of particles, 10, 12, 52, 66, 83, 118. Sky, blue colour of the, 2, 99. Sol, 5, 14, 23, 212. Sols (substance of disperse phase), albumen, 7, 12; alumina, 7, 20; arsenious sulphide, 3, 87, 101, 106 ; Bredig metal, ig, 21, 134; cara- mel, 7; Carey Lea's silver, 26; casein, 17 ; Cassius' purple, 25 ; cochineal, 56 ; copper, 166 ; copper ferro-cyanide, 21, 177 ; dextrine, 7, 17 ; dyes, 12 ; egg albumen, 17, 23 ; ferric hydroxide, 23 ; gamboge, 55, 64, 78; gelatine, 8, 17, 21, 25; globulin, 22, 24; gold, 1, 13, 25, 3g, 103, 118; gold ruby glass, 9; gum-arabic, 7, 17 ; gum-tragacanth, 7; lysalbin acid, 17; mastic, 18, 56, 82 ; Mohlau's indigo, 26 ; molyb- danic acid, ig; oxides,- 12; Paal's gold, 26 ; protalbin acid, 17 ; rub- ber, 64 ; silicic acid, 7, 16, 24, 106 ; silver, 13, 114; silver chromate, 14 ; silver iodide, 25, 26 ; soaps, 12 ; stannic acid, 25 ; starch, 17 ; sulphides, 12, 16, 17, 23 ; sulphur, 15 ; tannin, 7, 8 ; thorium hydrox- ide, 16 ; urea, 64, 80 ; water glass 17- Stability of sols, 23, 53, 196. SUBJECT INDEX 217 Stokes' law, 73, 83, 89, 126. Snbmicrons, 122. Sugar, 78, 209. Surface tension, 5, 66, 156, 207. Suspensions, 3, 10, 12. Suspensoid, 12, 24. Tanning, 5, 209. Temperature and mobility, 145. Total reflection in illumination, 43. Turbid media, 99. Tyndall phenomena, 2, 3, 100, 174. Ultramicrons, amicrons, submicrons, 118, 122, 125, 173. Ultramicroscope, 13, 28 et seq., 38. — Brownian movement under, 3. — cardioid, 45. — history of, 32 et seq. Ultramicroscope, observation of action of electrolytes, 171. — paraboloid, 46. — slit, 2, 41. Ultraviolet light, 192. Velocity of Brownian movement, 75. — of particles in an electric field, 132 et seq. — U-tube method of measurement, 137. limitation of, 141. — with ultramicroscope, 140. Viscosimeter, Couette's apparatus, 174. — oscillating disc, 174. — Ostwald's 174. Viscosity, 54, 74, 78, 145, 174 et seq. — and temperature, 77, 145. Washing of precipitates, 20. NAME INDEX. Numbers refer to pages. Abb£, 29, 30, 31, 33, 35, 36, 45, 46, 47, 49. Airy, 33. Alexander, 49. Amici, 31. Arago, 100, I2i. Artmann, 190, 194. BABINET, 100, 121. Bache, 56, 62, 66, 94, 95. Bancelin, 175, 193. Bancroft, 87, 95,119, 121, 182, 185, 186, 187, 189, 194. Barus, 194. Bary, 11, 27. Bechhold, 165, 190, 194. Beck, 48. Begeman, 92, 95. Bennet, 171. Berzelius, ig, 25, 27. Billiter, n, 27, 163, 188, 189, 193, 194, ig5, 20 1, 205, 206, 207. Biltz, 16, 27, 194, 20 9. 2I 3- Bishop, 86, 95, 154, 162, 186, 193. Blake, 140, 143, 154, 163, 193. Bliss, 64, 65, 67, 94. Bock, 106, 121. Bodazewski, 89, 95. Bodlander, 195. Boltwood, 92. Boltzmann, 70, 90, 95. Boussinesq, 68. Bredig, 18, 27, 67, 87, 94, 113, 125, 134, 146, 162, 163, 164, 172, 201, 204 205, 206, 207. Brewster, 30, 31, 100, 121. Briggs, 169, 171, 193. Brown, 1, 6, 51, 52, 53, 60, 62, 66, 94. Briicke, 99, 101, 121. Burton, 49, 86, 95, 118, 131, 152, 153, 154, 162, 186, 193, 207. Buxton, 6, 165, igo, 194. Cantoni, 55, 62, 79, 94. Carbonelli, 63, 94. Carli, Nils, 178, 194.. Carnot, 80. Carpenter, 49. Chassevant, 172, 193. Chaudesaigues, 57, 60, 75, 76, 78, g2, g4 Cholodny, 125, 131. Christiansen, no, 121. Clausius, 68, 92. Coehn, 140, 154, 204, 307. Cotton (and Mouton), 6, 43, 44, 49, 66, 95, 120, 121, 140, 143, 154, 172, 193, Couette, 174. Crum, 155, 175, 178, 192. Cunningham, 128, 131, 142, 154. Dabrowski, 57, 60, 76, 85, 92. Dancer, 52, 94. Davis, 178, 194. de Broglie, gi, g2, 95. de BufTon, 51. de Lapparent, 63. Dellebare, 43. de Metz, 120, 121. Dewar, 92. Dimmer, 106, 121, 175. Donnan, 197, 207. Dreyer, 192, 194. Drude, 115. Duclaux, 22, 27, 177, 178, 194, 201, 202, 205, 207. Edmunds, 45, 46, 49. Ehrenhaft, 90, gT, g2, g5, 106, 108, 109, 121. Einstein, 5, 6, 68, 73, 76, 77, 78, 7g, 83, 89. 92, 94. i*8, 131, 175, 193. Eliot, George, 51. Ellis, 140, 141, 143, 154. Ellissafoff, 169, 171, 193. Englemann, 41, 49. Euler, 124. Exner, 53, 54, 56, 61, 62, 68, 75, 76, 77, 94. Faraday, i, 5, 6, 13, 18, 27, 38, 39, 40, 49, 102, 103, 121, 134, 155, 192. Feilman, 2ro, 213. Fery, 92. Fischer, 17, 27. Frankenheim, igg, 207. Fresnel, 36. Freundlich, 9, n, 27, 160, 161, 162, 171, 175. 178, 179 et seq., 187, ig2, 193, 194. 195. 206, 2og, 213. Friedemann, 165, 188, 194. 218 NAME INDEX 219 Frion, 178, 194. Fuchs, 66, 94. Galecki, 140, 143, 154, 162, 172, 193. Gans, 116, 117, i2i. Garnett, no, in, 112, 113, 121, 197, 207. Garrett, 174, ig3. Gee, 210, 213. Geiger, 92. Gleichen, 51. Godlewski, 178, 194. Gordon, J., 38, 48. Gordon, (and Hober), 162. Goring, 31, 49. Gouy, 54, 55, 61, 62, 63, 64, 66, 68, 6g, 79. 80, 94, 155, 172, 192. Graham, 2, 6, 7, 8, 11, 19, 20, 26, 147, 155. 192- Gray, Stephen, 51. Gutbier, 193. Hanssen, 192, 194. Happel, 116, 117, 121. Hardy, 11, 20, 21, 23, 27, 137 et seq., 143, 144, 146, 149, 154, 157, 163, 174. 175. I 9i. i92> 193. 194. 201. 207. Harrison, 175, 193. Harrison (and Gee), 210, 213. Hartnack, 31. Hasenohrl, 117. Hatschek, 175, 193. Havelock, 120, 121, Heimstadt, 45, 49. Helmholtz, 33, 36, 134, J35, 136, 152, 153. 154. 204, 207. Henri, 11, 27, 57, 58, 59, 60, 64, 65, 67, 75> 76, 94. 131. 179. 191, 194- Henry, C, 172, 193. Hertz, in. Heydweiler, 204, 207. Hober, 11, 27, 162, 193. Hofmeister, 185, 194. Hogg, 48. Hooke, 29, 31. Hyde, 43, 49. Ignatowski, 45, 47, 49. Ishasaka, 175, 193, 195. Jentzsch, 45, 47, 50. Jbvons, 52, 55, 64, 66, 67, 79, 94, 155, 163, 172, 192. Jordis, 201, 207. Karczag, 9, 26. Keller, 142, 154. Kelvin, 92. Kerr, J20, 121. Kimura, 195. Krafft, 8, 26, 210, 213. Kuspert, 17, 27. Lamb, 89, 95, 134, 136, 153. Lampa, 117, 121. Langevin, 5, 6, 68, 74, 83, 92, 94. Larmor, 94, 95. Lea, Carey, 26, 174, 193, 200, 207. Lecoq, 26, 27. Leeuwenhoek, 51. Lehmann, O., 89, 95. Leiser, 120. Leonardo da Vinci, 99. Lewis, 143, 152, 154. Linde, 212, 213. Linder (and Picton), 2, 6, 12, 17, 27, 101, 121, 125, 126, 132, 133, 143, 145 153. 159. 160, 176, 178, 185, 188 192, 197, 207. Lister, 31. Lobry de Bruyn, 17, 27, 101, 102, 121, 197, 207. Loeb, 182, 183, 194. Long, ig, 27. Lorentz, g2, 111. Lottermoser, 174, 188, 193, 195. Luppo-Cramer, 213. Maltezos, 55, 63, 64, 65, 66, 67, 68, 94, 172. Martin, 29. Maxwell, 68, 70, 80, 92, 108. Mayall, 45, 49. Mayer, 172, 191, 194. McBain, 175, 178, 183, 193, 194. McKeehan (and Zeleny), 89, 95. McTaggart, 141, 143, 154, 171, 193. Mensbrugghe, 68, 94. Meyer, 92. Michaelis, 209, 213. Middleton, 162, 184, 185, 193. Mie, 115, 116, 118, 121. Miller, 6. Millikan, 8g, 91, 92, 93, 95, 126, 128, 131, 142, 154. Mines, 161, 192, 213. Mohlau, 26. Morawski, 155, 192. Moreau, 92, 95. Morris-Airey, ig, 27. Mosotti, 88. Mouton. See Cotton. Miiller, A., 13, 20, 26, igo, 191. Miiller, 108, 117, 121. Nachet, 45, 49. Nageli, 69. Needham, 51. Nernst, 137, 204, 205, 207. Neumann, 11, 27, 209, 213. Nichols, 120. Niesser, 165, 188, 194. Nobert, 45. Noyes, 11, 27, 150, 154. 220 PHYSICAL PROPERTIES OF COLLOIDAL SOLUTIONS Ober (and Whitney), 176, 178, 179, 181. Oden, 161, 172, 175, 185, 192, 193. Ohlon (and Oden), 172, 193. Osaka, 185, 194. Ostwald, Wo., 6, g, 11, 12, 13, 17, 27, 120, 158, 174, 175, 183, 186, 187, 192. Paal, g, 26, 200, 207. Paine, 162, 180, 193, 205, 207. Pappada, 185, 194, 195. Pauli, 175, 185, ig3, ig4, 213. Pellat, 92. Pelletan, 4g. Perrin, 5, 6, 55, 57, 58, 60, 76, 7g et seq., 126, 128, 131, 137, 149, 154, 169, 170, 171, ig3, 204, 207. Pfenning, 2og, 213. Picton. See Linder. Planck, 92. Pockels, log, 121. Poiseuille, 136. Posternak, 172, 193. Poynting, 90, 95. Praznowski, 31. Preston, gg, 120, 121. Pritchard, 30, 49. Proctor, ig4, 207. Prost, 195. QUECKETT, 49. Quincke, 134, 135, 142, 143, 149, 153, 202, 204, 207. RAEHLMANN, 212, 213. Raffo, 15, 27. Rahe, 6. Ramsay, 55, 56, 64, 79, 94. Rayleigh, 33, 36, 47, 4g, 50, 92, 105, 106, 107, log, in, 121, 128, I4g. Reade, 32, 43, 45, 49. Rebiere, 195. Regener, 92, 95. Reissig, 172, 193. Resenschek, 174, 193. Reuss, 134. Riechart, 45, 49. Robertson, 29. Robin, 49. Robitschek, 117, 118, 121. Rohland, 6, 213. Rolla, 117, 121, 143, 154. Roscoe, 99. Rose, 125, 131. Ross, 32, 45. Russell, 210, 213. Rutherford, 92, 93, 95. Scarpa, 43, 49. Scha^ffer, 172, ig3. Scheerer, 15s, 192. Schlosing, 195. Schmauss, 140, 154. Schmidt, 178, 194. Schneckenberg, 134, 153. Schucht, 194, 195. Schultze, 53, 54. Schulze, 49, 87, 95, 159, 160, 185, 200, 207-, Seddig, 57, 77, 78, 94. Shadbolt, 45, 4g. Sherrick, 178, 185, 194. Siedentopf, 2, 3, 6, 40, 41, 45 et seq., 128, 131, 197. Smoluchowski, 5, 6, 59, 65, 68, 71, 72, 73. 74. 75. 77- 79. 8°. 83, 89, 90, 94, 128, 131, 142, 154. Spear, 27, 95. Spence, 113, 114, 121, 147, 154. Spencer, 37. Spiro, 157. Spring, 27, 55, 56, 64, 94, 101, 102, 121, 162, 172, 177, 178, 192, 194. Stephenson, 31, 45, 49. Steubing, 96, 116, 120. Stingl, 155, 192. Stokes, 73, 83, 89, 126, 141. Stoney, 38, 49. Sutherland, 128, 131. Svedberg 5, 12, 13, 16, 19, 27, 56, 57, 58, 59, 60, 65, 76, 77, 94, 119, 121, 143, 154, 197, Z07. Teague, 170. Tereschin, 142, 154. Terroin, 172. Thirion, 63, 94. Thomson, go, 92, gs, 106, 108, log, 121. Thornton, 134, 153. Thoulet, 178, ig4. Threlfall, 108, 121. Tolles, 31. Tolman, 188, 189. Townsend, 92. Tyndall, 2, 6, 99, 100, 101, 121, 174. Van Bemmelen, 5, 6, 176, 178, 194, 202, 213. Van der Waals, 92. Voigt, 120. Von Meyer, 174, 193. Von Weimarn, 9, n, 13, 27, 197, 199, 200, 207. Warrington, 178, 194. Weiser, 162, 184, 183, ig3, 194. Wells, 45, 49. Wenham, 6, 32, 43, 45, 46, 49. Whetham, 137, 160, 161, 163, 187, 192, 206, 207. Whitney, 140, 143, 154, 163, 176, 178, I7g, 180, 193. Wiedemann, 132, 134, 153 Wiegand, 207. NAME INDEX Wiegner, 172, 193. Wien, 108. Wiener, 53, 54, 56, 60 et seq., 68, 75, 76, 94. Wilson, H. A., 92. Winnsinger, 195. Wolff, 102. Wood, J. K., 210, 213. Wood, R. W., g8, 99, 120. Woodward, 43, 45, 49. Woudstra, 175, 193, 195, 202. Wright, Lewis, 48. Zahn (and Paal), 26, 207. Zeiss, 30, 37. Zeleny, 8g, 95. Zsigmondy, 2, 3, 6, 12, 13, 27, 40, 41, 48, 49. 55. 56, 60, 64, 68, 75, 79, 87, 94, 95, 118, 121, 123, 128, 131, 172, 190, 193. 194. 197. 2°7. 213- PRINTED IN GREAT BRITAIN BY THE UNIVERSITY PRESS, ABERDEEN D t^ pt. of Dairy Industry N» T. 8. Col. of Agr. at Cornell University. DATE DUE t CAYLORO PKINTC9IN U.S.A. QD 549.B?7T92T er8,,yUbrary 1 l!!?.i?.te', < : al Properties of colloidal sol 3 1924 002 981 904