摘要:

DISCUSSIONS OF THE FARADAY SOCPETY No. 18, 1954 COAGULATION AND FLOCCULATION THE FARADAY SOCIETY Agents for the Society’s Publications : The Aberdeen University Press Ltd. 6 Upper Kirkgate AberdeenThe Fai-aday Society reserves the copyright of all Communications published in the '' Discussions '' PUBLISHED . . . 1955 PRINTED IN GREAT BRITAIN AT THE UNIVERSITY PRESS ABERDEENA GENERAL DISCUSSION ON COAGULATIQN AND FLOCCULATION A GENERAL DISCUSSION on Coagulation and Flocculation was held in the Depart- ment of Chemistry, Shefield University (by kind perinission of the Vice-Chancellor), on the 15th, 16th and 17th September, 1954. The President, Prof. R. G. W. Norrish, Sc.D., F.R.I.C., F.R.S., was in the Chair and about 250 members and visitors were present. Among the distinguished overseas members and visitors welcomed by the President were the following :- Dr.P. C. Blokker (Holland), Dr. H. L. Booij (Holland), Academician B. V. Derjaguin (U.S.S.R.), Dr. D. G. Dervichian (France), Dr. E. Ellenbogen (U.S.A.), Prof. P. J. Flory (U.S.A.), Dr. G. H. Jonker (Holland), Mr. Khabarin (Soviet Embassy), Mr. H. B. Klevens (U.S.A.), Mr. H. Koelmans (Holland), Dr. S. Lifson (Israel), Dr. E. Matijevic (Yugoslavia), Dr. J. L. van der Minne (Holland), Dr. M. Mirnik (Yugoslavia), Mr. J. Mosse (France), Mr. K. J. Nieuwenhuis (Holland), Dr. and Madame Owdin (France), Prof. and Mrs. Overbeek (Holland), Mr. Th. A. J. Payens (Holland), Prof. P. S. Prokhorov (U.S.S.R.), Dr. H. Reerink (Holland), Dr. R. Rietema (Holland), Dr. M. J. Sparnaay (Holland), Dr.M. van den Temple (Holland), Prof. B. TeBak (Yugoslavia), Prof. H. Thiele (Germany), Mr. J. J. Voorn (Holland), Mr. A. J. de Vries (Holland), Dr. M. van der Waarden (Holland), Dr. D. H. Yaalon (Israel).A GENERAL DISCUSSION ON COAGULATIQN AND FLOCCULATION A GENERAL DISCUSSION on Coagulation and Flocculation was held in the Depart- ment of Chemistry, Shefield University (by kind perinission of the Vice-Chancellor), on the 15th, 16th and 17th September, 1954. The President, Prof. R. G. W. Norrish, Sc.D., F.R.I.C., F.R.S., was in the Chair and about 250 members and visitors were present. Among the distinguished overseas members and visitors welcomed by the President were the following :- Dr. P. C. Blokker (Holland), Dr. H. L. Booij (Holland), Academician B.V. Derjaguin (U.S.S.R.), Dr. D. G. Dervichian (France), Dr. E. Ellenbogen (U.S.A.), Prof. P. J. Flory (U.S.A.), Dr. G. H. Jonker (Holland), Mr. Khabarin (Soviet Embassy), Mr. H. B. Klevens (U.S.A.), Mr. H. Koelmans (Holland), Dr. S. Lifson (Israel), Dr. E. Matijevic (Yugoslavia), Dr. J. L. van der Minne (Holland), Dr. M. Mirnik (Yugoslavia), Mr. J. Mosse (France), Mr. K. J. Nieuwenhuis (Holland), Dr. and Madame Owdin (France), Prof. and Mrs. Overbeek (Holland), Mr. Th. A. J. Payens (Holland), Prof. P. S. Prokhorov (U.S.S.R.), Dr. H. Reerink (Holland), Dr. R. Rietema (Holland), Dr. M. J. Sparnaay (Holland), Dr. M. van den Temple (Holland), Prof. B. TeBak (Yugoslavia), Prof. H. Thiele (Germany), Mr. J. J. Voorn (Holland), Mr. A. J. de Vries (Holland), Dr.M. van der Waarden (Holland), Dr. D. H. Yaalon (Israel).CONTENTS General Introduction. By J. Th. G. Overbeek . PAGE 9 i . CLASSICAL COAGULATION- London-van der Waals Attraction between Macroscopic Objects. By J. Th. 6. Overbeek and M. J. Sparnaay. . Investigations of the Forces of Interaction of Surfaces in Different Media and their Application to the Problem of Colloid Stability. By B. V. Derjaguin, A. S. Titijevskaia, I. I. Abricossova and A. D. Malkina . The Effects of Humidity Deficit on Coagulation Processes and the Coalescence of Liquid Drops. By P. S. Psokhorov . Stability and Electrophoretic Deposition of Suspensions in Non- . Aqueous Media. By H. Koelmans and J. Th. G. Overbeelc. Coagulation as a Controlling Process of the Transition from Homo- geneous to Heterogeneous Electrolytic Systems.By Bo2o TeZak in collaboration with E. Matijevik, K. F. Schulz, J. Kratohvil, M. Mirnik and V. B. Vouk . The Rate of Coagulation as a Measure of the Stability of Silver Iodide Sols. By H. Reerink and J. Th. G. Overbeek . A Theory of the Heterocoagulation, Interaction and Adhesion of Dissimilar Particles in Solutions of Electrolytes. By B. V. Derjaguin . Kinetics of the Coagulation of Emulsions. By A. S. C. Lawrence and 0. S. Mills . The Coagulation of Non-Spherical Particles. By F. Booth . The Precipitation of Barium Sulphate from Aqueous Solutions. By W. G. Cobbett and C. M. French . The Swelling of Montmorillonite. By K. Norrish . Flocculation of Kaolinite due to the Attraction of Oppositely Charged Crystal Faces.By R. K. Schofield and H. R. Samson. . Sedimentation Thixotropy and Laminar Coagulation : Separate Forms of Bulk Phase and Surface Coagulation. By N. F. Yermolenko . 5 12 24 41 52 63 74 85 98 1 04 I13 120 135 1456 CONTENTS PAQE Coagulation and Thixotropic Structures. By P. Rehbinder . . . 151 The Stability of lnsoIubie Mctal Salt Sols in Aqueous Media. By A. Packter and R. Matalon . . 161 Flocculation and Recrystallization in Freshly Prepared Silver Rromidc Sols. By G. H. Jonker and H. R. Kruyt . . 170 GENERAL DIscussioN.-Dr. E. J. W. Verwey, Prof. J. Th. G. Overbeelc, Prof. B. Derjaguin, Dr. R. S. Bradley, Prof. I. Abricossova, Mr. H. B. Klevens, Mrs. I. Abricossova, Dr. D. 6. Dervichian, Dr. S. Levine, Mr. J. E. Adamson, Dr. A. K. Holliday, Dr. C. G. Sumner, Dr.R. H. Cousens, Dr. G. H. Elton, Mr. W. G. Picknett, Mr. C . G. A. Hill, Dr. J. N. Phillips, Prof. B. Teiak, Dr. A. Packter, Dr. G. H. Jonker, Dr. H. Reerink, Dr. M. Mirnik, Dr. K. Durham, Mr. F. Booth, Dr. A. S. C. Lawrence, Mr. 0. S . Mills, Dr. M. van den Tempel, Dr. L. Cohen, Mr. R. J. Cole, Dr. H. Koelmans, Dr. W. H. Banks, Dr. S. Lifson, Dr. H. Yaalon, Dr. M. van der Waarden, Prof. P. Rehbinder, Dr. P. Meares . 180 I J. COACERVATION lntroduetory Paper. By A. S. C . Lawrence . . 229 A Comparative Study of the Flocculation and Coacervation of Different Systems. By D. 6. Dervichian . . 231 Soap + Water + Amphiphile Systems. By A. J. Hyde, D. M. Langbridge and A. S. C. Lawrence . . 239 The Surface Potentials of Long Chain Sulphates and their Relation to Dispersion Stability.By B. A. Pethica and A. V. Few . . . 258 The Surface and Interfacial Viscosity of Soap Solutions. By B. C. Rlakey and A. S. C. Lawrence . . 268 Protein-Fluoroacid Interaction. Bovine Serum Albumin-per fluor o- Octanoic Acid. By M. B. Klevens and E. Ellenbogen , . 277 The Fractionation of Gelatin by Coacervation. By 6. Stainsby. . 288 Ordered Coagulation and Gel Formation. By Heinrich Thiele . . 294 GENERAL DIscussIoN.-Mr. H. B. Klevens, Dr. A. S. C. Lawrence, Dr. D. 6. Dervichian, Prof. J. Th. G. Overbeek, Dr. B. A. Pethica, Dr. P. A. Winsor, Dr. H. L. Booij, Dr. J. N. Phillips, Dr. A. V. Few, Dr. C. G. Sumner, Dr. P. C. Blokker, Mr. K. Durham, Mr. M. Camp, Dr. W. W. Emerson, Dr. G. Stainsby, Dr. P. Johnson, Dr. E. Ellenbogen, Dr. R. P. Brand, Dr.S. Lifson, Prof. €3. Teiak, Mr. K. J. Nieuwenhuis . . 302CONTENTS 7 PA06 III. BIOLOGICAL SYSTEMS Flocculation of Aggregates of Antigen and Antibody : Introductory Paper. By J. R. Marrack . The Diphtheria Antigen-Antibody Flocculation System. By C . G. Pope A Light Scattering Study of Diphtheria Toxin-Antitoxin Interaction. By P. Johnson and R. H. Ottewill . Virus 4 Red Cell Interactions. By B. P. Marmion . The Flocculation Time of Antigen-Antibody Reactions. By G . R. E. Naylor and M. E. Adair . Antigen-Antibody Precipitation in Gels. Non-Specific Effect on the Displacement of the Zone. By Jacques Oudin . Application of Diffusion Analysis in Immunology. By C . L. Oaklcy . The Interaction of Zinc Ions with Human Plasma Globulin. By N. H. Martin and D. J. Perkins . GENERAL DiscussIoN.-Dr. G . C. Easty, Dr. A. J. Hyde, Dr. R. H. Ottewill, Prof. J. R. Marrack, Dr. D. G. Dervichian, Dr. J. Oudin, Dr. P. Johnson, Dr. G. R. E. Naylor, Prof. B. Teiak, Dr. B. A. Pethica, Dr. Rosa Augustin, Prof. C . L. Oakley, Dr. J. N. Phillips, Prof. N. H. Martin, Prof. N. F. Maclagan 315 323 327 338 345 351 358 361 364 Author Index. . . 372

ISSN:0366-9033    

DOI:10.1039/DF9541800001

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

CQAGULATION AND FLOCCULATION GENERAL INTRODUCTION BY J. TH. G. OVERBEEK van’t Hoff Laboratory, University of Utrec ht Received 15th September, 1954 If colloids are defined as dispersed systems with particle sizes ranging between atomic dimensions and microscopic visibility, the fundamental problem of colloid science is : What determines the degree of dispersion? This problem has obviously two aspects. One aspect is concerned with the size and shape of the individual particles, the other aspect with the question whether the particles are free and independent or whether they are united in large aggregates. Using the terminology of the phase rule somewhat loosely, the question is : What deter- mines whether a colloidal system is a one-phase liquid, a sol, a one-phase solid, a gel, or whether by coagulation, flocculation or coacervation it separates into two macroscopically distinct phases ? This problem cannot be treated without considering the existence of two types of colloids, the irreversible, hydrophobic type, for which the gold sol is the classical example and the reversible, hydrophilic type exemplified by proteins, soaps and the like.With hydrophobic systems the dispersed state is never a state of true equilibrium. It is only the presence of energy barriers that prevents the dispersed particles from coagulating and forming a stable precipitate. For these systems stability of the dispersions and loss of stability by coagulation therefore have a very pronounced kinetic aspect. With hydrophilic systems, however, both the dispersed and the flocculated or coacervated states may be true equilibria and these equilibria are often more important than the kinetics leading to them.A common point in the study of both types of systems is that our ultimate interest is not in the directly observable kinetics or equilibrium states, but in the mutual interactions of the particles and those between particles and dispersion medium, allowing us to explain the observable properties. Interactions occurring very generally are electrical forces connected with the charge of the particles and leading as a rule to a repulsion between them. Indeed, the connections between colloid stability and electrical phenomena are so close, that in the General Discussion on the Electrical Double Layer 1 that the Faraday Society had intended to hold in September 1939 most of the subjects that will be discussed in the present meeting have been treated already and in a number of cases even by the same authors.Personally I feel that notwithstanding the dissimilarity in the titles the present Discussion is a natural continuation of that on the Electrical Double Layer of 1939. The period of 15 years between the two events has served to elaborate many of the ideas already present around 1940 and to improve the quantitative aspects of the theories and to design special experiments to tcst the theories. In fact, the last 20 years might be considered as the period in which the study of colloids has evolved from an art into an exact and quantitative science. Unfortunately work has been hampered by the war and its aftermath and especially the lack of contact between different groups of investigators has been a serious drawback.We should therefore feel all the more grateful to the 910 GENERAL INTRODUCTION Organizing Committee of the present General Discussion on Coagulation and Flocculation, not only for having it organized at this moment but especially for having given it a. very international character. I hope that nobody will feel his own work passed by, if I make special mention of the importance of the Russian contributions to this Discussion. I just mentioned forces of electrical origin as very important. Their existence seems to be well established. The principles on which they have to be treated are clear. However, the quantitative side of the treatment in cases with high charge densities still leaves much to be desired and adequate experimental data are still lacking in all but the most simple cases.Other generally occurring forces are of the dispersion or London-van der Waals type. They will in most cases cause attraction and promote coagulation. Although they have been incorporated into present theories of colloid stability, together with electrical forces, their actual role is still open to discussion. Quanti- tative data are scarce and even conflicting. It is hoped that this Discussion, if it does not solve the conflict, will at least stimulate further research in this field. In several papers presented at this meeting a third type of force is mentioned, viz. the repulsive action of adsorbed layers or solvation layers not connected with electric charges.It would be of value if these ideas could be cast into a more quantitative form. Finally it is evident that flocculations between antigens and antibodies, as mentioned in part I11 of this Discussion are based upon very specific, presumably short range interactions. It will be one of our tasks to consider how far the more general, non-specific interactions mentioned above are also important in biological sy s tems. In part 11 on Coacervation, we shall meet cases where consideration of forces alone, though important, is insufficient. Cases of true phase equilibria can only be understood by combining forces or energy with entropy. I have been asked to give an introduction to the first part of this Discussion, which will be devoted to classical coagulation, that is to the stability of hydro- phobic suspensions and emulsions and to closely related subjects.From the remarks made above it will be clear what I consider the main lines of investigation in this field. They are : kinetics of coagulation and especially the modification of the kinetics by interactions between particles. Still more fundamental are investigations on the forces of interaction themselves. Keeping these principles in mind, the contributions to part I can be grouped in a very natural way. Two papers, one by Derjaguin and one by Sparnaay and myself aim at a direct determination of the force between suitable objects. Although the ideal, the determination of a complete curve of interaction between two “ particles ” separ- ated by an electrolyte solution is still far away, experiments such as those of Derjaguin and Malkina hold considerable promise and show the feasibility of this type of approach.Norrish in his study on the swelling of clays also obtains rather direct informa- tion on forces between clay particles. One of the advantages of direct determination of forces with macroscopic objects over derivation of particulars of interaction from flocculation kinetics is that the larger surfaces used in these investigations are more homogeneous and better defined in their electrical and other properties. How bad the in- homogeneity of the surfaces of small particles can be is well illustrated by Schofield and Samson’s contribution on the flocculation of kaolinite, which is caused by the mutual attraction of negative and positive regions that coexist on the same particle.Rehbinder also points to the heterogeneity along the surface of the particles as a prerequisite of thixotropy and gel formation. Kinetics of coagulation will also receive due attention. All the contributions in this field are still based upon Smoluchowski’s admirable analysis 2 of 1916.J. TH. G . OVERBEEK 11 It is probably fitting to introduce in this Discussion the distinction between initial rate of coagulation and complete coagulation kinetics. The initial rate is only concerned with the formation of binary particles from single ones, whereas the complete kinetics have to include multiple particles as well. Lawrence and Mills point out the advantage of using emulsions, because primary as well as multiple particles are truly spherical.The present author believes, however, that spherical multiple particles are only obtained if coagulation is followed by coalescence and thus in point of fact one studies a succession of two essentially different kinetics.3 The other papers on kinetics are all concerned with the initial rate of co- agulation. Booth extends Smoluchowski’s method to non-spherical particles. Derjaguin calculates the rate of flocculation for pairs of dissimilar particles. Reerink and myself have determined initial rates of coagulation In different electrolyte solutions and used these data to obtain information on forces between particles in the form of surface potentials and van der Waals’ constants.Quite often the colloid chemist, in studying coagulation, takes the size of the primary particles as given. In this Discussion, however, we shall hear many contributions on sols in statu nascendi. The subject would seem difficult com- bining as it does the processes of crystal nucleation and crystal growth with actual coagulation. But being the first step in any preparation of a sol and starting with well-defined pure solutions, it has attracted many investigators. TeBak‘s contributions belong to this field, so do those of French and Cobbett, ofPackter and Matalon, and of Jonker and Kruyt. TeEak‘s work should also be mentioned in another respect. His ideas on the theoretical background of stability and flocculation deviate markedly from those of most of the other contributors.He considers present theories of colloid stability as “ somewhat too speculative and unable to embrace many important experimental findings ”. As an alternative he proposes an empirical relation be- tween Bjerrum’s distance and the flocculation value. Now it is immediately con- ceded that the quantitative agreement between the present rather coarse and schematized theories and experiments is never very good and that notably one of the weak points in the theory of electrical interaction is the inadequate treat- ment of short-range interactions between particles and counterions (Stern 4 theory). In my opinion the question should be put in the following way: Is the partial agreement that exists good enough to make further refinement of the theory and related experiments promising, or should we deduce from the lack of agreement that present theories are on the wrong track ? And if so, what is the right track and how do we know it is? The first part of our programme is typical hydrophobic, in that it is concerned nearly exclusively with aqueous solutions as dispersion media. It may be good that in a paper by Koelmans and myself non-aqueous solvents are considered and that even in completely non-polar solvents repulsion by Coulomb forces is often found to be the stabilizing mechanism. I hope that these remarks, none of which are very new or original, may be of some use as a framework to guide our discussions. 1 Trans. Faraday Soc., 1940,36, 1-322, 711-732, 2 Smoluchowski, Physik. Z., 1916, 17, 557, 585 ; Z. physik. Chem., 1917,92, 129. 3 see van den Tempel, Thesis (Delft, 1953) ; Rec. trau. chim., 1953,72,419 433 442. 4 Stern, Z. Elektrochem., 1924, 30, 508.

ISSN:0366-9033    

DOI:10.1039/DF9541800009

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

I. CLASSICAL COAGULATION LONDON-VAN DER WAALS ATTRACTION BETWEEN MACROSCOPIC OBJECTS BY J. TH. G. OVERBEEK AND M. J. SPARNAAY van’t Hoff Laboratory, Sterrenbos 19, Utrecht, Netherlands Philips Research Laboratories, Eindhoven Received 24th June, 1954 In the first part of this paper a description is given of an apparatus with which attractive forces between two flat glass plates have been measured. One of the glass plates was attached to a spring. The bending of this spring was directly proportional to the force between the gIass plates and could be followed with an accuracy of 10-30 A with the aid of an electrical capacity method. The distances between the glass plates were measured by means of Newton interference colours. A discussion of the errors is given. The force- distance relation found, an inverse third-power law, followed the London-Hamaker theory but the force constant was found to be about 40 times larger than predicted by their theory.In the second part an extension of London’s harmonic oscillator is discussed, leading to deviations from additivity of London-van der Waals forces which might be helpful in the understanding of our experimental results. Two groups of atoms a large distance apart instead of two atoms are considered, and a weak interaction is assumed between atoms of each group. It then appears that the polarizability is no longer the determining quantity in the force between the atoms such as given by London, but that large deviations from additivity can occur in the attractive force, whereas the poIarizability remains prac- tically unaffected.PART 1. EXPERIMENTAL 1.1. INTRODUCTION The role ascribed to London-van der Waals forces in the stability of colloids 1 and in the formation of aggregates between particles, and especially the long-range character of these forces made an independent proof of their existence very desir- able. We investigated therefore the forces between optical flat glass (or quartz) plates in air. Preliminary publications 2, 3 , 4 of the results have appeared. The attraction between two (electrically neutral) paraIlel flat plates is given by an expression derived by de Boer 5 and Hamaker 6 from London’s 7 theory on the attraction between two atoms : F i s the force, d the distance between the plates, 0 is the area. The force constant A was predicted to be of the order of 10-12 erg.It is easily seen that, to check this expression, taking for instance 0 = 2 cm2, forces of the order of 1 dyne have to be measured with a distance d of about -$p between the plates. This condition proved to be a nearly insurmountable diffi- culty, probably because of dust particles and an irregularly shaped gel-layer present on the glass plates. The force F was measured by the bending of a spring to which one of the plates was attached. The distance d was estimated with the aid of Newton interference colours. The results obtained confirmed the exponent 3 in expression (1) for the dependence of the force upon the distance but the force-constant A was about 40 times larger than that predicted. 12J . TH. G. OVERBEEK AND M.J. SPARNAAY 13 1.2. THE VALUE OF THE FORCE-CONSTANT The value A = 10-12 erg was obtained from the following relations : A = r2g2h h = $hva2. (3) Relation (2) is introduced in the theory of de Boer and Hamaker ; q is the number of atoms per cm3 involved. h is the energy constant in London's theory in which the two atoms are represented by three-dimensional harmonic oscillators with a characteristic frequency v and a polarizability 01. h is Planck's constant. In the case of glass or quartz the main contribution to A is expected from oxygen, the polarizability for silicon being 40 times less than for oxygen.8 Margenaug inserting hv = 1.37 eV = 2.05 x 10-11 erg and a = 1-57 x 10-24 cm3 found A = 39.8 x 10-60 erg cm6. As q is about 5 x 1022 this leads to A = 10-12 erg.Expression (1) is derived on the basis of additivity, i.e. the attraction between two atoms is considered to be independent of the presence of a third atom. It is doubtful whether this procedure is allowed for glass or quartz. The oxygen atoms here do not have the same individuality as free atoms. In part 2 of this paper a certain type of deviation from additivity is considered theoretically. 1.3 THE APPARATUS. The essential parts of the apparatus used are schematically shown in fig. 1. A1 and A2 are the glass plates, their optically flat surfaces facing each other. A1 is attached to a spring F of known resilience with the aid of frame B and holder D, both made of brass, A2 rests on the pins T on top of three boxes K. These boxes were fixed to three micrometer movements regulating roughly the position of A2 towards A1.These micrometer screws are not shown in the figure. The fine adjustment of A2 with Fig. 1.-Essential parts of the apparatus. respect to A1 was obtained by changing the pressure in the boxes by means of a pump P. Changing the pressure in the three boxes simultaneously by 1 atmosphere resulted in a dis- placement of the glass plate A2 of 4p. The pressures were measured by the manometers M with an accuracy of 1 mm mercury. If the distance between the glass plates was small enough the lower plate pulled the upper plate down over a certain distance. This distance was measured by means of the decrease of the capacity of the condenser formed by the two silvered microscope cover- glasses 6 1 and C2, C1 being fixed to the holder D with insulating wax.C2 was immovably fixed to the massive brass body E. The other brass body G carried both E and the fixed end of the spring F. The parts shown in fig. 1 were mounted in a cylindrical box with flat top and bottom, that could be evacuated to 10-6 mm. The top plate carried two glass windows for observa- tion. Leads to the condenser-plates C1 and C2, transmission to the micrometer screws and conductance to the pressure boxes K, were all vacuum-tight sealed through the cylinder wall or bottom. The evacuation was necessary to decrease the viscous resistance of the air between the glass plates (see 1.6). The equilibrium condition for the system is (fig. 2) : fi is the force-constant of the spring, b is the distance between the pIates in absence of attrac- tive forces, dis the actual distance.(b - d) is thus the displacement of the upper glass plate and also that of the lower condenser plate.14 LONDON-VAN DER WAALS ATTRACTION By manipulating the micrometer screws and the pressure in the pressure-boxes, b can be changed. Due to the steepness of the attractive force stable equilibrium can only be obtained if d is larger than In fig. 2 where A = 10-11 ergs, 0 = 1 cm2 and j3 = 1.5 x 105 dynelcm dmin is near to 5700 A. Four values of 6 are given as an illustration, b = 5000 a, 7500 A, 10,000 A and 12,500 A respectively. The dotted curves indicated with Is, 2s, 3s and 4s are the results of the addition of the attractive force-curve and the straight lines 1, 2, 3, 4 representing the force of the spring.The units on the abscissa vary with proportional variation of A 0 and p, the rest of the figure being unaltered. FIG. 2.-Force against distance in the system used, A = 10-11 erg; j3 = 1.5 x 105 dynelcm. Relatively stiff springs have to be used and this limits the displacements (6 - d ) of the upper glass plates to less than lOOA. Consequently the condenser plates C1 and Cz have to be very close together. If their distance is 4 x 10-3 cm a displacement of 10 A changes the capacity by about 5 x 10-4 pF. This change could just be observed with a heterodyne set-up consisting of two oscillating circuits, one with a crystal stabilized frequency of 1500 kc, the other containing the condenser C12 in parallel with a precision condenser. The beat frequency between the two circuits was compared with a 1024 period tuning fork and could be reproduced within one beat per second corresponding to a variation in the capacity of 5 X 10-4 pF.The precision of the whole procedure, however, de- pended largely on the quality of the condenser C12. The preparation of this condenser was one of the most delicate operations involved in the measurements. The relation between the distance d and the interference colours is given in table 1.10 TABLE 1 .-RELATION BETWEEN INTERFERENCE COLOUR AND DISTANCE BETWEEN PLATES first order second order third order d(A) colour 0 black 1000 grey 1300 white 1400 straw yellow 1650 bright yeIlow 2200 orange yellow 2750 red d(A) colour 2850 violet 2950 indigo 3350 blue 4125 green 4300 green yellow 4750 orange 550 dark violet d(A) colour 5750 indigo 6300 green blue 6687 bright green 7150 green yellow 7500 rose 7650 carmine 8100 violet 8250 violet grey It appeared after long experience that colours of the first order could be observed such that the distance d could be determined with a precision of 15 %, colours of the second order up to 3 %, then a decrease followed, the precision at d = 15,000 A being about 5 %.J .TH. G. OVERBEEK AND M. J . SPARNAAY 15 In measuring large distances (higher orders than the third one give alternating green and red bands) it was necessary to count the number of orders passed through upon increasing the distance from that at a colour of known order. This could be checked by the mano- meters M giving the position of the pins on top of the pressure boxes K and thus giving the position of the lower glass plate A2.Vice-versa the method could be used to check the rate of displacement per atmosphere of the pins previously determined under a micro- scope. There are no interference colours at distances smaller than lOOOA, but the distance can be measured with the aid of the light reflected from the gap between the glass plates. If its intensity is I, then, according to Lord Rayleigh :11 I 1 6 ~ ~ 6 % 10 h(1 - e2)' -E- 10 is the intensity of the incident light ; e, a numerical factor, is 0.2 ; X is the wavelength, M 5 x lO-5cm. 1.4 CLEANING AND MOUNTING OF THE GLASS AND QUARTZ PLATES. The plates used were slightly wedge-shaped in order to make the different reflection images more easily separable. The unevennesses on the optical flat surfaces were smaller than 400A which is probably the limit obtainable.12 The area of the plates mainly used was 4 cm2, their density at 15" C was d1s = 2.556, their refractive index nd = 1.5209.Later on glass plates with area 1 cm2, d1s = 2.55, nd = 1.515 and quartz plates (d1s = 2.66 ; nd (ord.) = 1.544. and nd (extra-ord.) = 1.539) with an area of 1.7 cm2 were obtained. The radius of curvature of the big glass plates was 300-500 metres, that of the smaller plates was too large to be measurable. The glass plates were first cleaned with chamois-leather dipped in 3 % H202 and after- wards with alcohol. Then the plates, the plate A1 being fixed in the frame By were quickly but carefully brought together in such a way that interference colours became visible.If this could not be done very easily, dust particles were still present between the plates and cleaning was repeated. The two plates with interference colours still visible were then mounted in the apparatus. The brass body G (see fig. 1) with spring F, holder D and condenser C1,2 could be raised about 4 cm. The two glass plates were laid down on the three pins T. Part G was then carefully lowered until the upper glass plate A1 was attached to the spring F by two pins on the frame B sliding into loosely fitting holes in D. The connection was made sufficiently solid by pouring molten wax between B and D. The whole system was then closed, evacuated to the desired pressure of about 0.01 nim (see (1.7)) and only then the plates were separated by lowering the lower plate A2.It required considerable experience to fix the plates into their proper places and to avoid them attracting so strongly that relative movements became too difficult. In these circumstances frictional movements between the plates can have a very bad influence upon the quality of the surfaces.14 However, if the distance is too large and the attraction not strong enough, the plates may lose contact before the apparatus is evacuated and this almost certainly brings dust-particles between the plates and spoils the measurement. The viscosity of the air makes the manipulation more easy by providing an " air-cushion " between the plates that disappears only slowly. It has never been possible to get the plates moving completely freely at a distance smaller than 7000A or perhaps l0,OOOA.The obstacles apparently present could occas- ionally be crushed if a force was exerted sufficiently large to obtain a distance smaller than ddn (see eqn. (5)). The smallest distance thus obtained was about 200 A. These obstacles probably were silica gel particles. Their influence increased after exposure to a wet atmosphere in agreement with the hygroscopic properties of glass, and decreased after rubbing the surfaces with chamois-leather provided with some finest quality polishing rouge. This is in agreement with general ideas on poilshing glass, the role of polishing rouge being the removal of gel-layers formed by water on the uneven surface .lo 1.5 CALIBRATION OF THE SPRING AND CONDENSER.The condenser C12 was calibrated before and after each series of measurements in terms of force on the spring F by putting small weights on the upper glass plate AT, and observing the capacity. As the sensitivity of the condenser was not always constant,16 LONDON-VAN DER WAALS ATTRACTION frequent rechecking during measurements was desirable. This was done in the following way. When the glass plates were mounted and the apparatus evacuated, the glass plate A2 was tilted using the micrometer screws such that it just touched the other plate Al. Then the pressure in the three boxes K was uniformly varied. This resulted in a uniform displacement over a known distance of A2 and thus of A1 and the lower condenser plate C1. The corresponding change of the capacity was measured.In this way the relation between capacity and distance was obtained. It could be compared to the relation between capacity and force by means of the force constant /3 of the spring F. Three different springs were used with P I = 1.5 x 105 dyne/cm, p2 = 8 x 105 dyne/cm, /33 = 15 x 105 dyne/cm. 1.6 MEASUREMENT AND EVALUATION. The glass plates were brought into a parallel position with the aid of a white light-source. This gave two images upon reflecting against the two optical flat surfaces facing each others These two images were brought to coincidence while the plates might still be separated by 0- 1 mm. Then the distance was carefully decreased until interference-colours became visible. This procedure required some experience. Once interference-colours were visible the plates could be brought into the desired position and measurements made.Two measurements of the capacity were needed at least, one at a large distance doo such that attractions were practically absent and one at the distance where the attractive force was to be measured. A convenient value for doo was 4p. A measurement was repeated many times upon increasing and decreasing the distance. An (arbitrarily chosen) example is given in table 2. One scale-division on the precision-condenser corresponds with a bending of 40 A of the spring with /3 = 1.5 x 105 dyne/cm. The average force F is found to be 0.7 dyne. In general more than one colour was visible at distances of the order of lp, either due to the curvature or to a deviation from parallel position.Each colour was seen over an area 0, belonging to an approximately constant distance d,. The attractive force Fc for each distance was supposed to be given by (1). For the whole surface the force becomes d, = dc + &is a distance such that 22 * - OC - 0. Two criticisms can be made concerning dc d,3 this interpretation : first, the force-distance law was not yet known : second, the summation should be replaced by an integral. However, after many experiments were carried out, the use of the force-distance law with an exponent near to 3 was justified, and replacement by an integral would hardly increase the precision, much larger sources of error originating from elsewhere. Table 3 gives an illustration of eqn. (7). The same experiment is chosen as in table 2.Table 3 is representative in that one term Oc/d,3 predominates in most cases. Terms smaller than 0.1 of the largest term were generally neglected. TABLE 2.-REPEATED MEASUREMENTS OF TABLE 3.-EVALUATION OF TOTAL AREA W E FORCE OF ATTRACTION AT A DIS- AND AVERAGE DJSTANCE IN AN EXPERI- TANCE BETWEEN THE PLATES OF 13,000 W MENT (see table 3) scale-divisions force (dynes) 18.5 1.1 1 10 0 6 0 15 0.90 20 1 -20 17.5 1-05 11 0.66 14 084 oc in cm2 dc in A 0.5 11,000 0.39 2 13,500 0.82 1 15,000 0.30 d, = 13,OOOA 0, = 3.5 cm2 Using the force as given in table 2, average distance and total area resulting from table 3 and taking an exponent 3, A becomes 0.8 X 10-11 erg.J . TH. G . OVERBEEK AND M. J . SPARNAAY 17 1.7 THE INFLUENCE OF THE VISCOSITY OF THE AIR. Reynolds 16 gave an expression for the relation between the velocity dd/dt = - 4 under the influence of a force F of a flat circular plate (radius c) towards a second plate at a distance din a parallel position in a medium with viscosity 71 : Taking for the viscosity of the air '1 = 1.8 x 10-6 poise, assuming c to be 1 cm and assuming the van der Waals force (1) to be the driving force, it is found that for d = 5000 A the velocity is only 0.6 Alsec.It goes asymptotically to zero if the equilibrium position is approached. Furthermore, if a measurement is started with a large distance b M d (see eqn. (4)) which must be decreased, d the actual distance between the plates, stays considerably behind, say 20008,. It then requires 10-20 minutes before b = d which is still not enough.These long periods were very undesirable because they allowed all kinds of mechanical and thermal disturbances to occur. Consequently the viscosity of the air was decreased by means of a decrease of the air-pressure P in the apparatus. As the mean free path of N2 and 0 2 molecules is about 600 8, at 1 atm the viscosity does not de- crease until the pressure has become 600/d = PO atm. Below this pressure (i.e. the Knudsen region) the viscosity is an approximately linear function of the pressure. It was found necessary to leave some air in the apparatus to damp vibrations of glass plate Ax. Eqn. (8) has to be extended with an inertia term in order to get insight into the magnitude and character of the vibrations. This leads to (9) I?Z is the mass of the vibrating glass plate A1 together with frame B, holder D and condenser- plate C1: mu2 = m;i + mozq 3- Bq = 0.is the force-constant of the spring F. The attractive force was neglected in (9). It would make the vibrations only slightly less harmonic (see fig. 2). E,quation (9) is the expression for a damped oscillator. Upon solving it appears that critical damping takes place at Inserting m = 20 (which gives o = 6.3 if /3 = 8 x 105 dynelcm is taken), d h = 5000 A, c = 1 cm one finds 7 = 6.25 x 10-12 poise. This corresponds to P = 036 X 10-2 mm. If dw b = lp, then P = 1.4 x 10-2mm. If dw b = 2p, then P = 5.2 X 10-2 mm. Under these conditions the time in which an oscillator is damped down to 2 % of its original value is calculated to be of the order of 8 sec. This means that even deviations from equili- brium of for instance 500A occasionally occurring are not too harmful.It was preferred to take the pressure slightly less than that derived from (10) because the glass plate A1 could then be seen " dancing " around its equilibrium-value indicating that it was moving freely. Due to their harmonic character the vibrations, although having an unfavourable influence upon the precision, permitted a reasonable estimate of the equilibrium-distance. 1.8. POSSIBLE ELECTROSTATIC EFFECTS. In order to prevent electrostatic charges on the glass plates a radio-active -preparation was always present. The attraction never decreased even after waiting a week and re- suming the measurements. Neither did it decrease after ionization of the air in the cylinder- box (P = 10-2 mm) or after evaporation of a silver-layer of 200 8, thickness upon the plates.The distance between the evaporating silver-droplet and the glass plates was only 12 cm whereas Tolansky 17 recommends 30 cm. Therefore the silver-layer was rather poor and prevented the plates coming closer than 1.2 p. The amount of moisture had no influence upon the attraction. Lastly the strong dependence of the force measured upon the distance shows that an electrostatic inter- pretation must be ruled out Homogeneously distributed electric charges on the glass plates would result in a force not depending upon the distance at all. 1.9. DISCUSSION OF THE ERRORS. As far as can be seen the main errors involved were due to : B = 2mw (10) (a) obstacles between the plates, (6) vibrations of the glass-plate fixed to the spring, (c) unexpected alterations of the condenser CI, 2.18 LONDON-VAN DER WAALS ATTRACTION (a) It is difficult to account quantitatively for the errors due to obstacles.They might play a role in any measurement. For instance in one case there was found a re- pulsion of 0 5 dyne at d = 15,000 & an attraction of 2.2 dyne at d = 7500 A and again a repulsion at d = 6500 A. This kind of irregular values, completely irreproducibk, was often found. Such a series of measurements was discarded. (b) Table 4 gives the influence of the vibrations as estimated after long experience. TABLE ~.-INFL~NCE OF VIBRATIONS ON THE PRECISION OF THE FORCE MEASUREMENTS precision at d precision at doo (in dynelorn21 (in dynelcmz) zoc 200 0.2 ,* 0.15 -f GOO0 0.5 -* 0.15 t 10,000 1.5 0.1 0.4 15,000 3 0.15 0.2 18,000 3.6 0.1 0.15 * precision determined by obstacles.At the large distance dao the vibrations were damped to a smaller extent than at the distance d where an attraction was measured. The area 0 in the second column is equal to 0, in eqn. (7) and is averaged over many measurements. (c) If no sudden change in the capacity was observed the difference before and after a series of measurements of the sensitivity was considered to be a linear function of the time. dm M 15,000 A. 1.10. RESULTS The results for the glass-plates mainly used are given in fig. 3. d in Angstrgm u n i t s FIG. 3.-Force against distance for glass plates with nd = 1.5209 ; d15 = 2.556. The straight line fitting the measurements corresponds to Fis the fop.ce/cm2; A = 3.8 X 10-11 erg; n = 3 & 03.18 Other results are given in table 5.These results are considered less reliable than those of fig. 3, but they still give the same order of magnitude for A. The force F i n row 1 and 3 was found upon tearing the plates apart. The rows 2, 4, 9 and 10 give forces measured with detectable obstacles between the plates. The force values in the rows 5, 6, 7 and 8 are highly inaccurate due to the small area of the plate A1 allowing for strong vibrations. The thickness of the silver-layer, row 13, was 200 A, thus making the quartz less transparent. This made the distance-value less accurate.J . TH. G. OVERBEEK AND M. J . SPARNAAY 19 The values found with the glass plates nd = 15209, dyj = 2556 were divided between those given in fig 3 and those given in row 2, table 5, the fist being values with the plates moving freely, the second being values with obstacles detected.This division is somewhat arbitrary and it might be that low values in fig. 3 are still due to obstacles. It is seen, however, that the exponent in (11) is near to the predicted one. A possible explanation for the large deviations from the predicted values for the constant A will be given in part 2. TABLE 5 no. material d (A) P (dynelcm2) A x 1011 (erg) 200 750 - 1.5 X 105 0-11-2.2 { ::sL 1.5209) varying between varying between dl5 = 2.556 2500 and 7000 0 6 and 50 0.1 1-3 0.0 1 5-1 -5 200 102-1 05 5,000 20 3.2 7,000 10-0-20-0 6.5-13.0 9,000 5.0-10*0 6.7-1 3.5 11,000 23-43 6.3-1 1.1 16,000 0.8-3.0 6.0-23 .O 3,000 20 1.1 25 3.0 13,000 17,000 0.2 1.9 0.7-20 3.0-8.0 } 4,000 :H { !{$; ;;: A2 12 13 quartz treated with silver 8,000 4.0-8.0 3.9-7'8 We are greatly indebted to Mrs.M. J. Vold for pointing out an error in our original table 1. The small systematic difference between the results published here and those given in our preliminary publications 1 9 2 ~ 3 are due to this error. PART 2. THEORETICAL 2.1. THE EXTENSION OF LONDON'S OSCILLATOR MODEL A possible explanation for the fact that the force constant A considerabfy exceeds the one predicted might be found in an extension of London's harmonic oscillator model.19 Two groups of n atoms each instead of two atoms will be considered, the atoms being represented as harmonic oscillators.A weak inter- action is supposed to exist between atoms of the same group. The distance R between the groups is large compared with the distances between the atoms of the same group. The Hamiltonian function of the whole system 20 is n n 2n 2n20 LONDON-VAN DER WAALS ATTRACTION 1 2m Gji = - ; Aii = &zw$ ; Aik (i+ k) represent the interactions between atonis of the same group; Bjk = - represent the interactions between atoms of different groups. All the Bjk will have the same value throughout the whole treatment. (e = electronic charge). (px)j, (py)i, (pz)i are the x-, y- and z-components of the momenta of the i-th oscillator, xi, yi, and zi the same for the co-ordinates. Generalized co-ordinates and momenta can be introduced upon transforming (12) with e2 2 ~ 3 2n 2n We write down only the equations for the z co-ordinates.For instance taking n = 2 the transformation becomes : $1 = &(Zl + Z2 f 23 -t- 241, 33 = 4(Z1 - 22 -k Z3 - Z4), s2 = &(z1 + ZZ - 23 - z4), 34 = i(zl - z2 - Z3 + z4), (14) and analogous equations for the momenta. The generalized co-ordinates will be of secondary interest for the calculation of the energy required and will not be considered further. The transformation means that matrix (A, B) formed by the Aii, Aik and Bik elements must be brought into diagonal form.21 The diagonal elements are the roots of det (A, B)=O. The transformed Hamiltonian function is the sum of the Hamiltonian functions of 212 unperturbed harmonic oscillators with identical masses but with different frequencies.The 2n energy values obtained can be expanded in inverse powers of the distance A, thus giving the interaction-energy between the two groups, distance R apart. Jehle 22 gave a wave-mechanical treatment of the problem. Our case (1) (see 2.2) will correspond with his and the same result concerning the energy will be obtained. As is done in London’s theory it will also be important in this case to compare the attrac- tion to the polarizability. The polarizability a,, of the groups can be found upon introduction of generalized co-ordinates and momenta of the Hamilton function. and calculating the corresponding frequencies. The frequencies found must be inserted in It will appear that in general the relation between polarizability and van der Waals’ constant is not of the simple type given in eqn.(3) for a single pair of atoms. 2.2. THREE CASES. It is evident that the procedure described above can be carried out for special cases (1) Aik = c, for all values of i and k given by (12). (2) Aik(i = k + 1 and k = i + 1, except when i, k = n or 2n) = c, ; all other Aik (3) The same as (2) but now the four elements Aik: i = 1, k = n ; i = n, k = 1 ; i = n + 1, k = 2 n ; i = 212, k = PI + 1 also have the value c,. The fist case means that the interaction between any two atoms of the same group is equally strong. This seems unlikely on geometrical grounds. The calculation is simple, however, and the final results give an upper limit for the deviation from additivity. The second case is based upon the picture of a string of atoms (to be taken in the z-direction) each having interactions with its nearest neighbours only.The picture underlying the third case differs from that in the second case in that the first and the last atom are considered as nearest neighbours. only. Three types of interaction are chosen : are zero.21 J. TH. G . OVERBEEK AND M. J . SPARNAAY 2.3 CALCULATION OF THE THREE- CASES It can be seen upon suitable addition and subtraction of rows 22 in det (1) that there are 2n-2 roots of det (1) = 0, a = - c,, one root a + (a - 1) cz - nb = 0 and one root CASE 1 a - (n - 1) c, + nb = 0. det (1) = a c z - - - C.2 CZ a I I \ I ! \ I I I 1 I e2 R3 b=-2B. -_- tic - i=n+l a . 2 and i = l . . * . n i + k = l . . . . . i+k=n+l . . . 2n a=Aji i = l . . . . . 2n i = l .. . . . n i = n + l . . . 2n i + k = l . . . . . n and i + k = n + l . . .2n Cz= - 2Aik - I - A L-.-,-.I L - v L 3 n n The latter two roots are of interest only since they are the only ones containing terms depending upon R. The potential energies of two harmonic oscilIators with frequencies w+ and w- can be deduced from : Just as London did, these frequencies are considered as frequencies of two quantum h mechanical harmonic oscillators with lowest eigen values &w+ and 4k.o- where fi = - 277' Expanding w+ and w- one finds for the interaction energy : e2 - 3(n - 1) % = = = - - - mwC2 If wg is low enough to allow for the classical limit, the attraction free energy becomes This can be found after transforming the partition function into a Gauss integral.23 Then the value of det (1) is required, not its roots.The classical limit might be important in physiology. det (1A) = a c z - - - cz The roots of det (1A) = 0 give the generalized fre- quencies of the n oscillators of one group. There are (n - 1) roots, and one root (a - cz) = 0 n 4- (0 - 1) c, = 0.22 LON D ON-V A N D B R W A A L S ATT R ACT I 0 N Inserting the corresponding frequencies into (1 6) the polarizability for case 1 becomes (21) 4c 2 a, = na,(l +(n - 1)--z- m2m04 -1- * ' .}' CASE 2 The matrix (A, B) for the second case can be easily constructed. Adding the 2nth row to the first, the (2n - 1)th to the second and so on, then subtracting the 2nth column from the first, the (2n - 1)th from the second and so on, its determinant value is the product of the determinants ( A + bU) and (A - bU).l a + b cZ+b b - - - - - - - - - b det ( A 9- bU)= cZ+b a + b c z + b - - - - - - - b \ \ \ I \ \ \ I I I I J \ \ \ 1 I \ \ \ 1 \ \ \ b I \ \ \ p \ \ \ 1 1 - b cZ+b a + b I), _ _ _ _ _ _ _ _ This is generally true for the type of matrices involved here. The matrices must be sym- metrical with respect to the main diagonal. Generally the transformation (22) 1 Zk(k = n + 1 I . . 2n) = - (Si + ti) d2 will give the desired separation as was kindly pointed out to us by Dr. Bouwkamp of the Philips Research Laboratories. The same procedure (adding and subtracting of rows and columns) will serve to simplify det ( A + bU) and det (A - bU). For n = 3 and n = 4 there are four roots containing b; for n = 5 and n = 6 there are six.From these the total attraction can be calculated in the same way as in case 1, and appears to be No calculations for other n-values were made. The polarizability can be found upon solving the determinant with diagonal elements a and elements c, immediately bordering them, all other elements being zero. The roots a, have been found by Coulson 24 to be P'n a, = 2cZ cos - r = l . . , 11. n 3 - 1 (24) The polarizability then becomes CASE 3 It can be proved that the determinant for this case has only two roots containing b. First add all the rows to the first. This gives a root (a - 2c2 - nb) = 0. Then add columns 2 . . . n to the first and subtract the sum of columns n + 1 . . . 2n. This gives (a - 2cz + nb) = 0. It is seen upon suitable subtraction of rows and columns, preferably such that only two elements b symmetrical to the main diagonal remain, that all terms containing b cancel in the further development of the determinant.One could ofJ. TH. G . OVERBEEK AND M. J . SPARNAAY 23 course as well have started with determinants (a + bU) and (a - bU). Considering the two roots containing 6 the attraction becomes : The determinant leading to the polarizability has also been treated by Coulson 24 and has roots (27) 2 T S as = 2czcos- s = 0 . . . . . n - 1. The polarizability becomes Although there is no direct proof case 3 will probably be the limit of case 2 for n = 03. 2.4. DISCUSSION It appears that in all cases treated the weak interactions between atoms in the same group give only second-order effects in the polarizability whereas the total interaction energy which is itself a second-order effect will be strongly affected.If, however, the interactions are so strong that the oscillators are always in phase, the two oscillators would behave as one oscillator with charge 2e. Addi- tivity is then restored on a new basis and a London-type expression applies again. Such an expression is found by Coulson and Davies 25 considering extended oscillators as a model for large chain molecules. A negative value of c, means that there is a tendency of the oscillators to be in phase, a positive value means a tendency to be in counterphase. If there is dipole-interaction only between atoms of one group, then Ro is the distance between the atoms involved. A reasonable value of cz is 26 - 0.1 mw2.Considering then a chain along the z-axis there is an increased attraction of about 50 %. If, however, a chain is taken along the x- or y-axis the attraction is decreased. In these cases there is a tendency of two neighbouring oscillators to be in counterphase as far as the z-direction is concerned, giving the largest contribution to the total attraction. If n < 10 there is in all these cases only an increase of a few % of the polarizability. London’s additivity theorem applies to the case of varying distance between all the atoms involved. This means that it is often misinterpreted in colloid chemistry where one is concerned with the case of two groups of atoms with a variable distance, the distance between the atoms in one group being constant. The models treated here are, of course, oversimplifications. The A &ems may depend upon the direction in space and they certainly will assume different values between different pairs of atoms instead of having either the value or zero as assumed in the models.One might think of a mixture of the cases treated here in a given physical situation. However, the models, although not giving a quantitative explanation of the strong forces experimentally found, may serve to demonstrate the possibility of a strongly increased van der Waals inter- action between groups of atoms combined with a normal value of the polarizability.24 FORCES OF INTERACTION OF SURFACES 1 Verwey and Overbeek, Theory of the stability of Zyophobic colloids Plsevier, 2 Overbeek and Sparnaay, Proc. K. Akacl. Wetensch., B, 1951,54,387, 3 Overbeek and Sparnaay, J. Colloid Ski., 1952, 7, 343. 4 Sparnaay, Thesis (Utrecht, 1952). 5 de Boer, Trans. Faraday SOC., 1936, 32, 21. 6 Hamaker, Physica,1937,4,1058. 7 London, 2. Physik, 1930, 63,245 ; 2. physik. Chem., 1931,11,222. Eisenschitz and 8 Stevels, Progress in the theory of the physicalproperties of glass (Elsevier, Amsterdam, 9 Margenau, Rev. Mod. Physics, 1939, 11, 1. Amsterdam, 1948). London, 2. Physik, 1930, 60, 491. 1948), p. 94. Fajans and Kreidl, J. Amer. Ceram. SOC., 1948, 31, 105. 10 Van Heel, Inleiding in de optica (Nijhoff, s’-Gravenhage, 3rd edn., 1950), p. 86. 11 Lord Rayleigh, Proc. Roy. SOC. A, 1936, 156, 343. 12 Mayer, Physik dunner Schichten, Wissenschaftliche Verlagsgesellschaft (Stuttgart. 13 Tolansky, Multiple beam interferometry (Clarendon Press, Oxford, 1948), p. 24. 14 Bowden and Tabor, The friction and lubrication of solids (Clarendon Press, Oxford, 15 Grebenschikov, Keramika i Stekle, 1936,7, 36 ; Sotsialisticheskaya Reconstruktsuya Bowden and Tabor, The friction and lubrication of solids 1950). 1950), p. 168. i Nauka, 1935, 2, 22. (Clarendon Press, Oxford, 1950), p. 302. 16 Reynolds, Phil Trans., 1885, 177, 157. 17 Tolansky, Multiple beam interferometry (Clarendon Press, Oxford, 1948), p. 25. 18 Weatherburn, A first course in mathematical statistics (Cambridge University Press, 19 London, Z. physik. Chem. B, 1931,11,222. 20 Margenau, Rev. Mod. Physics, 1939, 11, 1. 21 Born and Jordan, Elementare Quantenmechanik (Springer, Berlin, 1930), especially 22 Jehle, J. Chem. Physics, 1950, 18, 1150. 23 Eidinoff and Aston, J. Chem. Physics, 1935, 3, 379. 24 Coulson, Proc. Roy. SOC. A, 1938,164, 393. 25 Coulson and Davies, Trans. Faraday SOC., 1952, 48, 777. Davies, Trans. Faraday 26 London, 2. physik. Chem., B, 1931, 11,250. Cambridge, 1947) (“ t-test ”). chapters I1 and 111. SOC., 1952,48, 790.

ISSN:0366-9033    

DOI:10.1039/DF9541800012

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

24 FORCES OF INTERACTION OF SURFACES INVESTIGATIONS OF THE FORCES OF INTERACTION OF SURFACES IN DIFFERENT MEDIA AND THEIR APPLICATION TO THE PROBLEM OF COLLOID STABILITY BY B. V. DERJAGUIN, A. S. TI~VSKALA ($2), I. I. ABRXCOSSOVA ($3) AND A. D. MALIUNA ($4) Academy of Sciences of U.S.S.R., Institute of Physical Chemistry, Laboratory of Surface Phenomena Received 3rd August, 1954 The symmetric case of two-sided (or free) films of dilute soap solutions formed between two bubbles pressed together is investigated. Equilibrium thicknesses of these films have been measured as a function of capillary pressure inside the bubbles counterbalanced by the film’s “ disjointing action ”. In this case, in contrast to that of wetting films, molecular forces may only counteract and diminish the effect of the repulsion of ionic atmospheres which creates the equilibrium disjoining action.The results obtained clearly demonstrate the existence of an equilibrium disjoining action arising from ionic atmosphere overlapping and are in quantitative accordanceDERJAGUIN, TITIJEVSKAIA, ABRICOSSOVA AND MALKINA 25 with the corresponding theory, under the condition of introducing the important cor- rection for the thickness (about 40 A) of polymolecular hydrate layers. To prove the existence and the gap-width dependence of the molecular attraction between two macroscopic bodies a new type of microbalance has been constructed. This microbalance owing to the use of a certain kind of negative feed-back coupling is especially suited for measurements of weak forces of extraordinarily great gradient in space that would destroy the stability of equilibrium position of any ordinary high- sensitivity balance.With its aid, direct measurements of molecular attraction between plane and spherical quartz and glass surfaces were conducted by Abricossova and myself, at first in air and (lately) in vacuo. After extreme care had been taken to remove all traces of surface electric charges and organic impurities, we succeeded to obtain quite reproducible results. The force values are the same when measured in air and in vacuo and are proportional to the radius of curvature of the spherical surface in accordance with the formula for molecuilar interaction of macrobodies deduced by me 20 years ago. The measwed force values are about 1-2 orders smaller than the values that result from the London-Hamaker formula.Some years ago we obtained as Prof. Overbeek and Dr. Sparnaay still do, results about one order of magnitude higher than those calculated by the London-Namaker formula and of very bad reproducibility. This unexpectedly large discrepancy seems to be caused by surface charges and points to the exceptional difficulty in removing them. The last part of this report describes a new method using crossed fibres permitting the “ modelling ” of colloid particles interaction by means of experiments with macrobodies in a much more quantitative and precise manner and with much fewer scattering of results than in Buzag’s method. As a criterion, the general formula for surface interaction given by the author 20 years ago, but taking the shape factor into account precisely is used.This formula also explains the cause of the very great scatter of results in Buzag’s experiments and the much smaller one is ours. 0 1. It seems clear that any theory of colloid stability and coagulation must be based on the consideration of interaction forces which arise when dispersed particles are brought close together. If the mutual approach of the surfaces give rise to repulsion forces which become strong enough at small distances, coagulation is evidently impossible. Inasmuch as aerodisperse systems coagulate in all cases, it is evident that the repulsion forces of this kind are associated with the properties of the thin layers of the liquid dispersion medium which separates the particles at the moment of their approach.Costichev 1 was the first to assume the existence of such repulsion forces in thin liquid films. Hardy2 developed the same idea and attempted to sub- stantiate it by direct experiments on two plane surfaces separated by a liquid layer. The results of his experiments, however, were not confirmed.3 The first proof of the existence of a steady “disjoining pressure’’ of thin liquid layers was due to the experiments of the present author and his co-workers.4-6 Elton made an attempt to attribute the results of these experiments to the effect of “ electroviscosity ”.7 The groundlessness of Elton’s argument and the errors involved in his reasoning were, however, elucidated in detail by Kussakow and the present author.* The experimental relation 4 of the disjoining pressure isotherms to the electro- lyte concentration supplied a basis for calculating the repulsion forces in thin films due to the interaction of the electric double layers 9 situated at the interfaces be- tween the film and the adjacent phases.The latter paper was the first to develop a method for calculating both the energy and the forces of this interaction. This method was subsequently also applied to strongly charged surfaces.10-13 An attempt to calculate the interaction of similarly charged surfaces in electrolyte solutions was also made by Levine,l4 and Corkhill and Rosenheed.15 Levine’s statistical derivation of the expression for the energy of interaction of particles, using Debye and Huckel’s method of charging ions, involves an error which, in particular, leads at long distances to attraction instead of repulsion26 FORCES OF INTERACTION OF SURFACES forces.The present author was the first to detect this error 16 and show a way to correct it.* Simultaneously a proof of the correct expression for the energy of interaction showed thermodynamically the erroneousness of the results of Levine and of those of Corkhill and Roscnheed.11 These results and methods of calculation were subsequently applied to the interpretation of a number of surface phenomena as well as of some of the pro- perties of colloids, in the first place their stability. The author at fist developed a theory of the stability and coagulation of weakly charged sols and derived a criterion of their coagulation which generalized and revised Eilers and Korff’s rule.18 In 1941 the author, in collaboration with Landau, developed a theory of the stability and ‘‘ concentrational ” coagulation of strongly charged sols 13 (based on the non-simplified equations of Gouy-Chapman), which enabled the Hardy- Schultze and Ostwald’s rules to be substantiated and quantitatively revised.? Calculation of the repulsion forces in films were used by Langmuir 19 to refine the determination of surface tension by the capillary method : the present author showed the error of Langmuir’s correction consisting in simple subtraction of the wetting film thickness from the capillary radius and gave an exact formula.20 An exact method of allowing for the effect of polymolecular adsorption layers on capillary condensation was simultaneously developed.20 Zocher and co-workers 11 used the calculations of the ionic repulsion forces to interpret the interference colours in Schiller layers and their sensitivity to the electrolyte concentration.The application of such calculations to the data of Kussakow and the present author on the thickness of wetting films in equilibrium with the corresponding capillary pressure 5 9 21 showed that only a part of the disjoining pressure has an electrostatic origin. The rest is due to the molecular interaction of the film with the substrate. The existence of non-electrostatic effects also follows from the investigations of the disjoining pressure in the wetting films of hydrocarbons.6 It is evident, however, that the application of the results of the theoretical and experimental investigations of the interaction forces between plane surfaces to the interaction of colloid particles requires that the shape of the latter should be taken into account.The possibility of a rigorous, general and simple method $ of such recalculation *see, e.g. Der-iaguin, Trans Faraday Soc., 1940, 36, 209, the second passage, An analogous reasoning was subsequently developed in extended and more elaborated form by Verwey and Overbeek 17 (1948). ?This shows the fallacy of the critical remark made by Verwey and Overbeek in their paper17 published in 1948 containing a derivation of the same Hardy-Schulze equation made with no reference to our paper : 13 “ The work of Derjaguin, mentioned earlier. on the interaction of two flat double layers, for instance, is based on these simple equations.From what has been said about this approximate theory of the double layer it follows that it cannot give any satisfactory results ”. This remark, based on ignoring the work of Landau and the present author of 1941 is repeated on p. 188 of the same book, in the chapter dealing with the history of the question, where the authors moreover mention my alleged disregard of the van der Waals forces. The latter remark is also wholly incorrect inasmuch as the van der Waals forces have been taken into account by the present author in the theory of the stability of strongly charged sols in the same paper quoted above.13 For weakly charged sols these forces have already been taken into account in the derivation of the Eilers-Korff rule in the addendum to the paper presented to the discussion on the double layer (Trans.Far‘aday SOC., 1940, 36, 730). All these incorrect statements in the historical review of the question have unfortunately remained uncorrected in the subsequent publications by Verwey and Overbeek, 3 The method of direct calculation of the electrostatic interaction developed by Levine 23 for spherical particles has yielded a number of valuable results for some special cases, but requires extremely laborious and cumbersome calculations which hamper the derivation of the more general relations.DERJAGUIN, TITIJEVSKAIA, ABRTCOSSOVA AND MALKINA 27 or transition is presented by the following previously derived 22 formula : N- G J* R(h)dh, (1) h where N is the force of interaction of two particles ; h is the minimum width of the interspace, G is the form factor which only depends on the radii of curvature and orientation of the normal sections of both surfaces at the point of their closest approach; R(h) is the force of interaction per unit area for plane surfaces of the same nature situated in the same medium at a distance h apart.Formula (1) is valid provided the distance, ha, at which the interaction of these planes may be neglected, is small compared to the radii of curvature of the particles. Eqn. (1) should be considered as the fundamental equation in the similarity theory of surface forces, which enables the interaction of colloid particles to be rigorously and quantitatively investigated on macro-models as, e.g., in the method of crossed filaments (see 3 4).For a sphere and a plane we have G = 2rrr; (2) for two spheres of radius r, and for two filaments 22 of radii PI and r2 meeting at an angle w, G = nr; 3 2. An investigation of the equilibrium disjoining pressure of a wetting film bounded by dissimilar phases may constitute a model method of studying the phenomena taking part in the processes of essentially heterogeneous coagulation and adhesion, such as flotation. In such cases, moreover, part of the disjoining pressure may be due to the preponderance of the van der Waals attraction of the film molecules to the substrate over their mutual attraction. A particular interest, both as a check on the theory and for its application to the questions of the stability of foams, is presented by the investigation of the disjoining pressure isotherms for the free films formed between gas bubbles pressed together. EXPERIMENTAL AND RESULTS For this purpose an all-quartz apparatus was used which is shown diagrammatically in fig.1. The apparatus consists of a cylindrical vessel A filled with the liquid under in- vestigation, with a bulb D sealed in the vessel. At the top of the bulb an orifice 2 mm diam. is made for blowing out the lower bubble. A hemispherical bulb C. with an orifice in the bottom for blowing out the upper bubble, has a plane top wall, i.e. a window for observing the free film whose thickness h is to be measured. The pressure excess PI (over the atmo- spheric pressure) is applied through the four-way joint F which connects the bulb C with the tube I3 leading to bulb D and with the U-tube manometer E.The mouth of the latter is immersed in the liquid in vessel A, and the manometer is filled with the solution under investigation. The pressure is then exerted through the joint F and the bubbles formed are brought together (fig. 2) with the aid of a micro-manipulator. The thickness h of the free film is measured by microscopic observation after steady interference patterns have been set up in the film of uniform thickness. The measurements were made by illuminating the film through a vertical illuminator from a monochromator, either by the method described before 4 or using a microphotometric head appended to the microscope which enables the reflection coefficient to be measured for the incident light reflected from the film 25.Simultaneously measurement is made of the depression dh of the liquid level in the left-hand tube of the siphon pressure-gauge, reckoned from the position corresponding to the moment when the pressure in the hemisphere C is atmospheric, while the liquid level in A coincides with the future position of the fiIm between the two bubbles. The position28 FORCES OF INTERACTION OF SURFACES of this level (see fig. 1) can be controlled by previously focusing a " test "-film in the micro- scope and reading the level at the moment when the free liquid surface in the vessel (varied by an auxiliary siphon or otherwise) reaches the object plane of the microscope situated between bubble holders C and D.It may be readily shown that dh is a measure of the disjoining pressure P. Let the height of the " zero " level of the liquid in the left-hand tube of the pressure gauge, corre- sponding to the level in A just mentioned, be denoted by ho. After additionally pouring a quantity of the liquid into the vessel A, sufficient to raise its level to a height enabling not only the lower but also the umer bubble to be formed (see fig. I ) , the leviiof the liquid in the left-hand branch of the pressure-gauge rises to a height hl. After applying the pres- sure through the four-way joint, this level falls to a height h. FIG. 1 .---Scheme of apparatus for measurements of the disjoining pressure of free films as a function of their thicknesses. S FIG. la. A II FIG.2.-The optical set-up for measurements of film thicknesses. By the disjoining pressure P of a free fiIm we mean the excess of the pressure PI exerted by the film in a state of equilibrium on the bounding interfaces over the pressure Po, in the adjacent volume of the liquid which has formed the am. Since, for a plane film surface, we have P1 = pg(h1 - h) and PO = pg(h1 - ho), where p is the liquid density and g the acceleration of gravity, we may write In this case the disjoining pressure evidently equals the capillary pressure in the bubbles and balances the latter. Fig. 3 shows the results of the measurements obtained for aqueous solutions of un- decylic acid of various concentrations. In acidified (10-3 N HCI) solutions of undecylic acid the free films possess a stability of limited duration : gradually thinning, they collapse as soon as a thickness of 50-70mp is reached.* This does not occur in 10-3 N KCI solutions.Hence it may be concluded that stable films in undecylic acid solutions are only obtained when the corresponding soap is formed. * The same apparatus was used to investigate the kinetics of thinning and the lifetime T of the free films of some aqueous solutions.24 7 proved to be a decreasing function of the capillary pressure P in the bubbles and an increasing function of the film diameter d, (7 M a 3- bd, or even T = d). P = P1 - Po = pg(h0 - h) dgdh. (4)DERJAGUIN, TITIJEVSKAIA, ABRICOSSOVA AND MALKINA 29 Fig. 4 shows the results of measurements obtained for the steady * thicknesses (using a photometric head appended to the microscope) and pressures of the free films of sodium oleate aqueous solutions with addition of NaCl in various concentrations.The results obtained may be naturally attributed primarily to the interaction of the diffuse ionic layers formed at the filrnlgas bubble interfaces, which is evidenced by the decrease in the film thickness with increasing electrolyte concentration. I h 150 5 0 ______. -_ 500 1000 ISOQ 2 0 0 0 0' PL I FIG. 3.The isotherms of the equation of state (h against P relations) of the free films of aqueous solutions of undecylic acid. FIG. 4.-The dyna P- cm2 isotherms of the equation of state (h against P relation) of aqueous solutions of sodium oleate. the free films of DISCUSSION To interpret the data obtained we may use the equation (5) 1 du du Kh - - s o dF&)(l - k W ) - J! d(l - &)(l - kW)' * Complete equilibrium is reached within 10-30 min.30 FORCES OF INTERACTION OF SURFACES where K = lid is the reciprocal of the thickness of the ionic atmosphere; y, the concentration of NaCl in moles cm-3 ; R, the gas constant ; T, the absolute 1 temperature; P, the disjoining pressure of the free film, z = -- - F, the faraday ; $0, the potential of the filmlair interface.Eqn. (5) is a’ gene& ization of eqn. (24) given elsewlhere.13 It only differs from the latter by the presence of a second term on the right-hand side. Using the values of P and h measured and calculating d from the known electrolyte concentration by the Debye-Hiickel-Gouy formula, the values of z and $0 may be found by formula (5) with the aid of tables of Jacobi’s elliptical functions m(U, k).The surface charge cr is connected with the parameter z by the formula, or Table 1 shows the observed values of P and h as well as those of $0 in mV calculated by formula (5) for aqueous solutions of undecylic acid at various con- centrations. In the calculations d = 1 / ~ was taken equal to 10-5 cm, assuming arbitrarily that the conductivity of the distillate measured was due to the presence of KCl in a concentration of 10-5 N. TABLE 1.-POTENTIAL OF THE FILM GAS INTERFACE C (& (I%) % concentration P (dynes cm-2) 0~00002 770 1100 51 840 950 51 930 850 51 1280 800 58 0*00003 580 1430 51 750 1300 55 1380 1050 66 2020 700 67 0*00006 560 795 1860 0*0001 660 1080 1470 1860 0.0006 580 690 1040 21 10 1500 1400 1000 1500 1350 1200 1050 1500 1500 1450 1050 51 59 75 56 68 74 77 52 58 71 82 Taking into account the insufficient accuracy (f 10 mp) in the measurements of the film thicknesses (without any microphotometric head appended to the microscope) and the uncertainty as to the actual thickness of the diffuse ionic double layer, attention is only called to the order of magnitude of the calculated values of $0 and to their general trend as a function of the film thickness h.ItDERJAGUIN, TITIJEVSKAIA, ABRICOSSOVA AND MALKXNA 31 will be seen that $0 assumes different values which increase as h decreases. This agrees with the theory of interaction of double layers if we assume the adsorption origin of the surface charge. We therefore may assume that, for a given P, the thickness of a free film depends upon the nature and concentration of the electrolyte and upon the potential or the charge of the liquidlair interface.In a number of cases the decrease in the thickness of free films stabilized by soaps, due to the effect of the dissolved electrolytes, results in the collapse of the films. This rule, however, is not a general one, being inapplicable, e.g., to sodium oleate solutions, Similarly to these calculations, an attempt was made to apply formula ( 5 ) to sodium oleate solutions containing various concentrations of NaCl. In this case the measurements were more accurate owing to the use of a microphoto- metric head on the microscope. A significant disagreement was observed at high values of y (7 >0*01 N).According as y increases, h tends to a limiting value of ca. 120A which, within the range of P used, is independent of P within the limits of experimental error. This is incompatible with formula (5). For such concentrations of NaCl this formula gives values of h below 160A for any values of z, even for z = 0 which corresponds to $0 = co. For a wetting film, the thickness of the steady film of the solution, which remains at high NaCl concentrations, could be attributed to the effect of the van der Waals forces exerted upon the film by the substrate. For a free film this possibility is excluded; on the other hand,.the mutual attraction of the film molecules always tends to decrease the thickness of the film and produce its collapse (which in fact is always effected within a fraction of a second for pure liquids) but cannot produce the opposite effect, viz., the ‘‘ disjoining ” action.Moreover, for a free film there is no solid wall which could somewhat retard the setting-up of the steady thickness of a wetting film throughout its area (the possibility of readily obtaining quite steady wetting films of such kind has, however, been achieved in the experiments of Kussakov and the present auth0r).4~8 Finally, it should be mentioned that the equilibrium of free films is observed in soap solu- tions when the soap concentrations are below the critical concentration of micelle formation, viz., at 10-3-10-4 N. All this leads to the assumption that the limiting thickness of a free film, 12 = 120& is due to the “physical” hydration of the adsorption monolayers, i.e.corresponds to the presence of two contiguous polymolecular layers of the aqueous NaCl solution which are built up on the sodium oleate adsorption mono- layers owing to some energy or entropy effect equivalent to the forces of the corresponding range. It should be noted that with 0.1 N NaCl a thicker unsteady free film is at first formed. As soon as it has thinned down to about 400 mp, there appear individual dark spots (on monochromatic illumination) at some points over the film area. These spots increase in number and area until they assume the form of round patches whose thickness is exactly equal to the limiting one. Their coalescence produces the ultimate steady film. This seems to point to the fact that the free film thicknesses of from 120 to about 400A are highly unstable and that the stable hydrate layers of the solution mentioned above are separated from the rest of the volume of the liquid by a sharp interface; a similar conclusion, which also agrees with Fmmkin’s theory of incomplete wetting,25 was previously arrived at by the author for other cases (wetting films) on the basis of measurements of the viscosity of polymolecular films by the “blow-off” method as well as measurements of polymolecular adsorption of the vapours of liquids incompletely wetting the adsorbent surface near their saturation point and transition to the bulk liquid phase.27 Such an abrupt transition from a hydrate (or, in general solvate) layer to the bulk of the liquid, similar to a phase transition, points in its turn to the32 FORCES OF INTERACTION OF SURFACES probability of the existence of structural peculiarities in hydrate layers-peculiarities which, on transition to the bulk liquid phase, can only disappear abruptly, and not gradually or continuously.The hypothesis of a sharp hydrate layerlbulk phase interface enables a definite (fictitious) charge, o, to be formally attributed to that interface. Ascribing arbitrary values to G we may theoretically calculate the values of h, by the formula (5) with the aid of the relation (5’). In that case all points in fig. 4 prove to fall, within the limits of experimental error, on the corresponding theoretical curves drawn as solid lines for c of the order of 160c.g.s. units, irrespective of both P and the NaCl concentration,” with the exception of the points corresponding to the lO-4N NaCl solution, The data referring to this concentration fit the theoretical curve, provided d is taken as corresponding to the ionic strength of the 2.3 x 10-4 N solution, which may be accounted for by the effect of hydrolysis of the sodium oleate present in a concentration of 10-3 N.It should be noted that our value (w 120A) obtained for the limiting thickness of the free film of sodium oleate solutions is close to both the thickness of the “ black spot’’ on the films of sodium oleate aqueous solutions, according to Johonnot’s28 measurements. The thicknesses of the films of the external aqueous phase as obtained by Kremnev 29 for extremely concentrated and highly disperse foam-like emulsions stabilized by sodium oleate are also in accord with our results.In Kremnev’s experiments when the volume of the external water- phase exceeded its minimum possible value the excess gradually separated out on standing of the emulsion. Hence it may be seen that the mechanism of the stability of such limiting emulsions is associated with the stability of the free films observed by the author and also seems to be due to hydration and electro- static repulsion. At lower electrolyte concentrations the electrostatic repulsion forces produce the thickening of the free films, which must also increase the stability of the foams formed by these films. Conversely, the addition of an electrolyte cannot only reduce, but sometimes even completely destroy the stability of free films, as has been observed by the author on addition of 10-2 N and 10-1 N KC1 to undecylic acid aqueous solutions.In the case of free films we thus may distinguish stability cases similar to these of hydrophobic and hydrophilic sols.? A still lower stability, of a merely kinetic nature, is possessed by the free films formed (in a quartz vessel) by aqueous solutions of alcohols and fatty acids (the latter in the presence of HC1, i.e. under conditions in which the formation of soaps is eliminated). After their formation, these films gradually decrease in thickness, the latter being a defmite function of time, and, reaching (within 10-50 sec) some critical thickness of the order of 500A suddenly collapse. The electrolytes accelerate this process.In our experiments made in the apparatus described above the lifetime $ r of a film for a given film area and a given capillary pressure P proved * The accuracy of the measurements is insufficient to consider this constancy of u an experimental fact. On the contrary, taking suitable different values of u for different values of y, the curves may be made to fit the experiments points still better. The constancy of cr may, however, be deduced assuming the dielectric constant of the solvate layer to be much smaller than that of the bulk phase of the solution and assuming the constancy of the charge at film air interfaces. t We leave out the effect of the elasticity of adsorption Iayers on the stability of free films-a factor which is of utmost importance for the stability of free films of protein solutions.3 As is well known, Hardy 30 was the first to study the lifetime of bubbles under a free liquid surface. Comprehensive investigations of the effect of the concentration of solu- tions of surface-active substances, including semicolloids, on the life of their films are due to Rehbinder 31 and later Talmud,32 and Trapenikov.40DERJAGUIN, TITIJEVSKAIA, ABRICOSSOVA AND MALKINA 33 to be strictly reproducible and clearly showed its physical meaning : the life of a film is determined by the kinetics of its thinning to the critical thickness at which there occurs the transition to an unstable state. 6 3. In a theory of colloid coagulation and stability, besides the electrostatic repulsion forces, the molecular attraction between the disperse particles as a function of the distance between their surfaces must be correctly allowed for.Until recently this problem was solved on the basis of theoretical calculations of the dispersion interaction (usually after London), summing these interactions over all the molecules of both the particles and the intervening medium. The grounds underlying this method of calculation, however, are questionable, the method being based on the experimentally non-verified law of decay of molec- ular interaction at comparatively long distances at which the electromagnetic retardation 33 should interfere ; moreover, this method is based on the assumption of a strict additivity of the dispersion interactions, which is unquestionably inexact for condensed systems.EXPERIMENTAL AND RESULTS This imparts considerable interest to direct measurement of the attraction of macro- scopic bodies separated by a narrow gap as a function of its width. Using the similarity relation (1) this would also enable the corresponding forces to be calculated for particles of colloidal dimensions. A task of this kind has been fulfilled by the present author in collaboration with Abricossova by a method specially devised and applied 34 to direct measurements of the resultant F' of molecular attraction between the plane surface of a plate P resting on one arm of the balance beam (see fig. 5) and a convex surface of a kns Q * placed at a small distance H over the plate, FIG. 5.-The set-up of the microbalance with negative feed-back coupling for the measure- ments of the resulting molecular attraction between two bodies as a function of their gap-width.These measurements necessitate a high sensitivity of the balance, i.e. a low value of dN/dx, where N is the reaction of the balance arising when the end of the beam acquires a displacement x ; however, in the field of molecular attraction F possessing a high gradient dF/dx - > dN/dx the beam will be in an unstable equilibrium and will stick to the lens, Q. * The use of another plane surface would increase F. It would, however, complicate the measurements, requiring that the surfaces should be strictly parallel, enhancing the effect of the viscosity of air in the gap, increasing the frequency of intervention of the dust particles which hinder the mutual approach of the surfaces, and hampering accurate measurements of the gap-width. B34 FORCES OF INTERACTION OF SURFACES This difficulty was overcome by using a kind of negative feed-back coupling." The balance beam 35 mm long, weighing 0-1 g, was supplied with a 20-turn coil rigidly attached to the beam.The coil was situated in the field of a permanent magnet, MM (fig. 6). The agate edge C (fig. 5), of the beam rested on an agate fulcrum bearing a, the fulcrum coinciding with the centre of gravity of the beam. One arm of the latter bore 8 glass plate. The rough balancing was effected by shifting a glass filament rider weighing 10-30mg by means of a special driving gear. The negative feed-back coupling was produced by the current passing through the coil R from a photoelectric actuating device (photoelectric relay) which " tracked " the deflection of the beam, with a current yield up to 100 Alradian.The current was led to the coil through Wollaston wires 6 p in diameter. FIG. 6.-The feed back coupling of the molecular forces balance. The photoelectric relay diagram is illustrated in fig. 5 and 6. Condenser K was used to illuminate a linear typographical grating Pi with a beam from source L'. After passing a lens 0 1 the light beam was focused on a mirror S attached to the balance beam. By means of the lens 0 1 a mirror S, and another lens 0 2 with the same focal length (7-5 cm), the real image of the first grating Pi was obtained in the plane of another grating P2 possess- ing the same spacing (60 lines per cm).After passing through the second grating the light reached the caesium cathode of a vacuum photoelectric cell which governed the grid of an amplifying valve. The anode current partially compensated by a dry voltaic battery was directed to the balance coil. When the balance beam occupied a certain zero position the anode current i was equal to zero. The defiection of the balance beam through a very small angle a, affected the amount of light admitted to the photoelectric cell by the second grating, producing a current i = tea, where K is a constant depending exclusively upon the actuating device and the amplifier. The passage of the current i in a requisite direction through the balance coil effected the negative feed-back coupling as a resuIt of which the balance beam was subject to a torque : M = ni = n ~ a = la, where ra and I are constants, n depending exclusively upon the number and shape of the turns in the coil and the magnetic field intensity. The convex surface of the lens resting on a support with a fine lifting gear could be slowly approached to the plate so that the distance W between the plane and convex surfaces slowly decreased until the attraction force F became measurable.This produced a deflection of the balance beam through a (very small) angle at which the moment Fu where Y is the arm of the force, was balanced by the feed-back coupling moment M. F was calculated from the formula : n was determined by measuring the current change Ai produced (in the absence of the force F) by a displacement Ay of the glass filament rider used for the rough balancing of the balance beam.The current i was measured by a microammeter of the 0.1 class, which enabled the force F to be determined to within 10-7 g. The sensitivity may be increased st21 further either by using a mirror galvanometer, or by shunting the balance coil, or by decreasing the number of its turns which propor- tionally reduces n. It is essential that, apart from raising the sensitivity of a balance, F = nilr. * The use of negative feed-back coupling is also expedient in the case of an ordinary beam balance,35 the period of oscillations being shortened and the sensitivity raised,DERJAGUIN, TITIJEVSKAIA, ABRICOSSOVA AND MALKINA 35 feed-back coupling sharply decreases the period of its oscillations, in our case down to 10-3 sec.This may, however, entail auto-oscillations of an enormous amplitude. In the measurement of molecular forces these were absent owing to the damping effect of the narrow air-gap. When the measurements are made in vacuo, these oscillations may be eliminated by ensuring a phase advance at the amplifier output with the aid of a phase shifter. The fine adjustment of the gap width (to within O-Olp) was effected by micrometric shifting of the grating& such as to produce a deflection of the balance beam with the mirror after which the light flux falling upon the photoelectric cell, remained unaltered (“ optical tracking device ”). The minimum gap thickness was calculated from the diameters dm of Newton’s rings which were measured under a microscope either with an ordinary eye- piece micrometric scale or with a micrometer screw, the gap being illuminated by a cinema lamp through a constant-deflection monochromator and a vertical illuminator. The ordinal number m of a ring equals 2Hm/A, where Hm is the air-gap width at the given ring and A is the wavelength of the illuminating light.Continuous variation of the wavelength produced by rotation of the monochromator prism enables m to be calculated from the formula : where An (d;) is the change in dm = const which corresponds to a change in A of AA ; A,,,(P$) is the change in d?ECOnSt corresponding to the transition from the mth to the (m f A m)th ring. Having determined m, we may obtain H from the formula : H = i ( m - 4RA --), where R is the radius of curvature of the spherical surface.FIG. 7.-The energy of “ molecular ” attraction per cm2 of two bodies as a function of their gap-width, logarithmic plot. The balance rested on five slabs with rubber plates sandwiched between them. The whole was supported by a gypsum scale isolated from the building foundation and dug directly in the ground. To minimize the effect of vibrations the optical part of the actuating device system was further improved : the light beam reflected by the mirror of the balance beam was then reflected by a mirror rigidly attached to the supporting platform. This made the photoelectric current independent of the joint vibrations of the balance beam and platform but directly dependent on H. The optimum value of the feed-back coupling coefficient I and of the radius of curvature of the lens (3-10 cm), as well as the sensitivity actually attainable (10-7 g) depended on the effect of vibrations and viscosity of the air gap upon the balance beam.36 FORCES OF INTERACTION OF SURFACES The removal of electric charges from the surfaces is of utmost importance for measuring their molecular interaction proper.For this purpose radio-active substances or a quartz lamp were used. The removal of charges from the surfaces when brought close together 3 2.6 2.6 2.4 2.2 2 1.8 1.6 I. 4 1.2 I 0.8 0.6 0.4 0.2 I H i n microns FIG. 7a.-The energy of molecular attraction of two quartz surfaces per cm2 as a function of their gap-width. proved impossible. The correspunding results are given for benzylcellulose/ glass (curve I) and glasslglass (curve 11) in fig.7, where the logarithms of H and U = F/2vR are plotted as ab- scissae and ordinates, respectively, U being, according to formulae (1) and (2), the energy of attraction of two parallel plates per sq. cm. The removal of charges from the surfaces separated by wide gaps (5 mm and upwards) reduces the observed interaction forces by three or more orders of magnitude. The results obtained for fused quartz surfaces are shown in the same figure (fig. 7, curve 111) and in fig. 7a. There are reasons to believe that curve I11 in fig. 7 and the curve in fig. 7a represent the molecular attrac- tion between the surfaces and that the electrostatic component, if present, is very insignificant. DISCUSSION The experimental data lead to the following conclusions : (i) The energy of attraction of two quartz plates H = 1.5 x 10-5 cm apart amounts to 10-5 ergs cm-2 or somewhat less.(ii) “he observed value of the interaction energy shows the inadequacy for gaps exceeding 10-5 cm of the theoretical estimates of molecular attraction of surfaces resulting from simple summation of the London interactions for all pairs of molecules. If we assume that the dispersion forces in solids are also additive as in gases (which is clearly inexact) and calculate the constant A for quartz by the formula F = AR/3H2, where F is the measured force of interaction between a sphere of radius R and a plane plate, and H is the minimum width of the gap between them, then it follows from our experiments that A < 5 x 10-14 ergs instead of the theoretical estimate 17,36 A m 1 - 2 x 10-12 ergs.(iii) A still greater deviation from our experimental values of molecular attraction is exhibited by the results of Overbeek and Sparnaay 36 which correspond to a value of A m 2 x 10-11 ergs. This value exceeds that obtained from our measurements 400-fold evidently because Overbeek and Sparnaay took no effective means to remove the electrostatic effects in their measurements. (iv) Our results agree with the theory of Casimir and Polder 33 which takes into account the electromagnetic retardation by reason of which molec- ular forces decay at sufficiently long distances not following London’s law as (r-7) but faster (as r-8). This circumstance may weaken the molecular attraction of surfaces at gaps wider than lO-5cm and thus account for the reported results.The sharp decrease of the electrostatic forces with increasing H (fig. 7, curves I and 11) seems to be due to non-uniform distribution of the charges over the surface, it being possible that charges of either sign form a mosaic. It shouldDERJAGUIN, TITIJEVSKAIA, ABRICOSSOVA AND MALKINA 37 be noted that the results obtained in the measurements of Overbeek and Sparnaay 36 are probably of the same nature and origin. No feed-back coupling, however, being used in that investigation,36 the sensitivity, accuracy and reproducibility of the measurements are some orders below ours. This would have prevented the authors from observing any forces, had they taken measures, similar to ours, to remove the surface charges.Thus, they seem to show that the van der Waals forces may only appreciably accelerate the coagulation of aerosols beyond the estimate given by Smoluchowski’s theory provided that the radius of the particles is considerably smaller than 10-5 cm-the distance which is already sufficient for the forces to vary one power higher than by London’s law. The result obtained is still more important for the stability theory of lyophobic sols. The validity of the H-3 law will make the force of attraction between sufficiently large convex particles vary as about H-3 when the distances H are larger than some values Ho. In the cases in which the electrolyte concentration which produces coagulation is so low (as, e.g., for polyvalent counter-ions) that the diffuse layer thickness is sure to exceed Ho, the law of the 6th power of the counterion charge as a measure of its coagulating power derived by Landau and the author 13 should be replaced by the 8th power law.Such definition of the applicability limits of the 6th and 8th power laws results from the fact that the form of the criterion of stability of strongly charged sols, as follows from the derivation of this criterion given by Landau and the present author,l3 is determined by the behaviour of the attraction forces at the distances between the particle surfaces which correspond to the energy barrier between the particles at the moment of its disappearance. According to the computations given above 13 this distance is close to the thickness of the diffuse ionic layer.8 4. From formula (1) it follows that in studying the phenomena of aggregation of colloid particles for larger models it is necessary to use very smooth macro- scopic bodies of a regular shape. Failing this, the curvature of their surfaces near the contact zone cannot be estimated and the results obtained cannot be given an exact quantitative interpretation. This disadvantage is inherent in Buzagh’s well-known investigations on the adhesion of particles to plane surfaces, and also accounts for the marked scatter in his results. Malkina and the present author have therefore devised the method of Ma- ments crossed 37 at right-angles * with a view to developing a rigorous method of modelling the interaction of colloid particles on such macroscopic surfaces 39 as enables formula (1) to be used to calculate the energy of interaction in ergs cm-3 of plane surfaces.The results obtained are important. EXPERIMENTAL AND RESULTS A quartz beaker A is filled with the electrolyte solution in which two quartz filaments are immersed : filament a, 25-4Op in diameter, is placed vertically, its thicker end being clamped rigidly ; filament b, 80-12Op in diameter, is held in a horizontal position, the two filaments thus being at right-angles. Filament b is supported by a specially designed stand whose principal part constitutes a frictionless torsional suspension support. A metal cube N with a perforation and a stop screw for a quartz rod is held in the stand by two crossed thin steel plates (fig. 8). Such a system of bracing simultaneously eliminates all the three translational degrees of freedom and two rotationaI ones, leaving only one degree of freedom, viz., rotation * It should be noted that, independently of ‘our investigation, Buzagh’s method was considerably improved, though in a different direction, by Fuchs in an investigation 38 in which, in particular, he observed and studied the slow adhesion kinetics in aqueous and non-aqueous media.However, in his investigation, too, no direct measurements of ad- hesion forces for particles of a definite surface curvature were made, so that no vaIues of the specific energy of adhesion could be obtained.38 FORCES OF INTERACTION OF SURFACES about a vertical axis passing through the centre of the stand. A string passing over a brass pulley 0 connects the arm C with a weight P.To minimize the friction of the pulley, the latter has numerous drilled perforations and is mounted on two steel centres. When the arm C is deflected in one direction, the elasticity of the bracing produces an opposite torque. According as water is added from reservoir E or sucked out from vessel D through a tube, the weight P is slowly lifted or lowered, respectively, producing deflections of filament b. The addition of water is regulated by microtap K. The arm of the latter is pointed at the end, the point being projected on a graduated scale. This enables the rate of admission of water to D to be regulated and made constant to within 0.1" of tap rotation. Filament b, when set in motion on decanting water from D through the lower tube with tap K, touches filament a and deflects it through a strictly definite distance from the position of equilibrium.After a definite time of contact controlled to within 0.1 sec has elapsed, filament b is deflected in the opposite direction by lifting the weight P in vessel D (by adding water from the upper reservoir). The adhesion force acting between the quartz surfaces deflects filament a from the equilibrium position as it follows the motion of filament b. FIG. &--The i experimental set-up for the measurements of the interactions of two fibres. This arrangement enables the force tending to detach one rilament from the other to be varied very slowly and gradually. The deflections of filament a from its position of equili- brium are observed with the aid of a reading microscope M.capable of both horizontal and vertical adjustment and fitted with an eyepiece micrometric scale and a vernier by means of which the linear deflection of the filament is read. The quartz beaker containing the electrolyte solution and the filaments is kept at a temperature maintained constant to within 0.01" by a thermos tat. To determine the force of interaction of the quartz filaments in dynes by direct reading on the eyepiece micrometer scale, the latter must be calibrated to read in units of force. For this purpose the elastic pro- perties of the deflected filament a were estimated by the method of comparing two vibration periods: TO for a free pendulum and TI for a coupled one. A metal sphere of a known mass M (which may be con- sidered concentrated in one point, the centre of the sphere), was suspended on a bifilar hair as shown in fig.9, so as to form a pendulum with a constant plane of oscillations . Being deflected from the equilibrium position in the oscillation plane, the sphere, under the action of gravity, performs for small deflections, simple harmonic motion with a period TO = 27rd(M/Ko) where M is the mass of the pendulum and KO is the restoring force per unit linear deflection. FIG. 9.-The d ~ m e of the ~easurements of the rigidity of quartz fibres.DERJAGUIN, TITIJEVSKAIA, ABRICOSSOVA AND MALKINA 39 When the pendulum is couplcd, as shown in the right-hand part of fig. 9, with the quartz filament whose elastic properties are to be determined, the period Twill differ from that of the free pendulum TO and will be given by Ti = 2dM/(Ko + K), where Kis the restoring force per unit linear deflection of Hament a which depends upon the rigidity of the latter.*- 120 240 360 4-0 600 I time in m i n FIG. 10.-The adhesion kinetics of two quartz fibres in the 0.01 N aqueous solution Of MgS04 in relation to temperature. t 2 0 40 6 0 SO I00 time i n mtn FIG. 1 1 . T h e adhesion kinetics of two quartz fibres in aqueous solutions of MgSO,, at 20" for different concentrations. On simple mathematical transformations we obtain Having determined K and the value of one division of the eyepiece scale in centimetres (by means of an object scale) we obtain the value of the scale division in dynes. After40 FORCES OF INTERACTION OF SURFACES measuring the adhesion force, the data were recalculated for plane surfaces using the following formula which results from eqn.(1) and (3) : where U(h) is the " energy of adhesion ". The initial measurements were made exclusively on freshly drawn quartz filaments in various aqueous solutions. First it was ascertained that adhesion in pure water cannot be detected, being much less than 0.1 ergs cm2. Measurable adhesion requires two necessary (but not sufficient) conditions : intro- duction of an electrolyte and protracted stationary mutual contact of the filaments in the solution. As an example, curves are given in fig. 10 and 11 in which the energy of adhesion U is plotted against the time of contact T for aqueous solutions of MgS04 at different temperatures for a concentration of 0.01 N (fig.10) and for different concentrations at 20" (fig. 11). DISCUSSION It should be emphasized that the results obtained cannot be attributed to contamination of either the filament surfaces or solution because interruption and renewal of the contact resulted in the disappearance of adhesion, whilst subsequent stationary contact gave the same adhesion kinetics. It seems hard to account for this phenomenon in any other way than by assuming that the layer of the liquid which separates the filaments during their '' contact " is gradually thinned, which results in the appearance and gradual increase of the van der Waals forces. The latter are overcome in tearing the filaments asunder and are registered as adhesion forces. It should be noted that adhesion kinetics of this kind has also been observed for surfaces of different nature and shape, e.g., for metal surfaces,38 in other media, e.g., non-aqueous.A strong temperature effect and small influence of the contact pressure upon the adhesion kinetics are characteristic of the results obtained. The method devised thus enables not only the intensity but also the kinetics of interaction of surfaces to be observed, which may be used as a characteristic of the lyophilic nature of surfaces. It will also be noted that in order to interpret the observed adhesion kinetics in terms of the viscous resistance of the inter- vening liquid we should have to endow the latter with a viscosity 108 times as high as its bulk value. The effect therefore cannot also be accounted for by electroviscosity .1 Costichev, Soil Science (Russ.) Moscow, 1940, 116. 2 Hardy, Phil. Trans. A, 1931, 230, 1. 3 Bowden and Bastow, Nature, 1935,135,828. 4 Derjaguin and Kussakov, Bull. Acad. Sci. U.R.S.S., Classe mathem. naturell. d r . 5 Derjaguin, Kussakov and Lebedeva, C.R. Acad. Sci. U.R.S.S., 1939, 23, N7, 668. 6 Kussakov and Titijevskaja, C.R. Acad Sci. U.R.S.S., 1940, 28, 333. 7 Elton, Proc. Roy. Soc. A, 1948,194,259,275. 8 Derjaguin and Kussakov, J. Physic. Chem. (Russ.), 1952, 26, 1536. 9 Derjaguin, Bull. Acad. Sci. U.R.S.S., Classe mathem. natur. skr. chim. (Riiss.), 1937, 5, 1153 ; Acta physicochim., 1939, 10, 333 ; see also Trans. Faraday Soc., 1940, 36, 203; 1940, 36, 730. chim. (Russ.), 1937, N5, 1119; Actaphysicochim., 1939, 10, 25 ; 1939, 10, 153. 10 Frumkin and Gorodetzkaja, Acta physicochim., 1938,9, 327. 11 Bergmann, Low-Beer and Zocher, 2. physik. Chem. A, 1938,181,301. 12 Langmuir, J. Chem. Physics, 1938, 6, 873. 13 Derjaguin and Landau, Acta physicochim., 1941, 14, 633 ; J. Expt. Theor. Physics 14 Levine, Proc. Roy. Soc. A, 1939,170,145, 165 ; Trans. Faraday Soc., 1939,35, 1125. 15 Corkill and Rosenhead. Proc. Roy. SOC. A , 1939, 172, 410. 16 Derjaguin, Trans. Faraduy Soc., 1940, 36, 203. 17Verwey and Overbeek, Theory of the Stability of Lyophobic Colloids (New York, (Russ.), 1941, 11, 802, reprint in J. Expt. Theor. Physics (Russ.), 1945, 15, 662. Amsterdam, 1948), p. 32.DERJAGUIN, TITIJEVSKAIA, ABRICOSSOVA AHD MALKINA 41 20 Derjaguin, Acta physicochim., 1940,12,181. 18 Eilers and Korff, Trans. Faraday SOC., 1940, 36, 229. 19 Langmuir, Science, 1938,88,430. 21 Schofield, Trans. Faraday SOC., 1946, 42B, 219. 22 Derjaguin, Kolloid-Z., 1934, 69, 155. 23 Levine, Proc. Roy. SOC. A, 1933, 170, 145, 165. 24 Derjaguin and Titijevskaja, Colloid J. (Russ.), 1953, 15, 416. 25 Wells, Ann. Physique, 1921, 16, 69. 26 Frumkin, Acta physicochim.,l938, 9, 363. 27Derjaguin, Trans. Confer. Colloid Chem. (ed. b y Acad. Sci. Ukrain S.S.R., Kiev, 28 Johonnot, Phil. Mag., 1899, [5], 47, 501. 29 Kremnev and Soskin, Colloid J. (Russ.), 1947, 9, 269 ; Kremnev and Kagan, Colloid J. (Russ.), 1948, 10,436. 30 Hardy, J. Chem. SOC., 1925, 127, 1. 31 Rehbinder and Wenstrom, Kolloid-Z., 1930, 53, 145 ; J. Physic. Chem. (Russ.), 1931, 2, 754. Rehbinder and Trapemikov, J. Physic Chem. (Russ.), 1938, 12, 573. 32Talmud and Sukhovolskaja, J. Physic. Chem. (Russ.), 1931,2,31 ; Z.physik. Chem. A, 1931, 154, 277. Talmud and Bresler, J. Physic. Chem. (Russ.), 1933, 4, 796. 33 Casimir and Polder, Physic. Rev., 1948, 73, 360. 34 Derjaguin and Abricossova, J. Expt. Theor. Physics (Russ.), 1951, 21, 495 ; C. R. 35 Derjaguin, C.R. Acad. Sci. U.R.S.S., 1948, 61, 275. 36 Overbeek and Sparnaay, J. Colloid Sci., 1952, 7, 343 ; Kolloid-Z., 1954, 136,46. 37 Tonilinson, Phil. Mag., 1928, 6, 695 ; 1930, 10, 541. 38 Fuchs, Klichnikov and Tziganova, C.R. Acad. Sci. U.R.S.S., 1949, 65, 307. 39 Derjaguin and Malkina, Colloid J. (Russ.), 1950, 12, 431 ; see Colloid Science, 40 Trapeznikov, J. Physic. Chem., 1940, 17, 820. 1952), p. 26. Karassev and Derjaguin, Colloid J. (Russ.), 1953, 15, 365. Acacl. Sci. U.R.S.S., 1953, 90, 1055. ed. Kruyt (Amsterdam, 1952), vol. 1.

ISSN:0366-9033    

DOI:10.1039/DF9541800024

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

DERJAGUIN, TITIJEVSKAIA, ABRICOSSOVA AHD MALKINA 41 THE EFFECTS OF HUMIDITY DEFICIT ON COAGULATION PROCESSES AND THE COALESCENCE OF LIQUID DROPS BY P. S. PROKHOROV U.S.S.R. Academy of Sciences, Moscow Received 23rd August, 1954 The mechanism of elementary processes of drop coalescence under static and dynamic conditions is considered. It is experimentally demonstrated that the coalescence of two drops, brought into contact, is prevented by the presence of an air-vapour gap between them. The saturation of the atmosphere surrounding the drops with the vapour of the same liquid is favourable for their coalescence. It is shown by theoretical treatment that the principal reason for the failure of drops to coalesce is a surplus pressure arising in the air-vapour gap between the drops due to suction of air into the gap from the exterior by the vapours of the liquid diffusing from the gap.Experiments under dynamic conditions were carried out in order to elucidate the effect of humidity deficit on the efficiency of drop collision. From the results obtained it follows that in considering the growth of water drops due to coagulation the dependence of the efficiency of drop collision on humidity deficit of the surrounding atmosphere should be taken into account. It has been found that the 100 % efficiency of drop collision is realizable only under conditions of zero humidity deficit or in Dresence of supersaturation of the surrounding atmosphere with water vapours. The mechanism of the collision of suspended particles is one of the most vital problems in the physics of aero-dispersion systems.In the final analysis all processes of the coagulation of natural and artificial fogs are reduced to this42 COALESCENCE OF LIQUID DROPS problem. In spite of the apparent simplicity of the process (the collision and coalescence of particles), it is actually extremely complex and subtle in nature. It is generally assumed that in aerosol coagulation efficiency is equal to unity, i.e. each collision results in cohesion, or, in the case of liquid particles, in coales- cence. The attempts to prove this thesis directly are, however, far from numerous,I and they were carried out but with a small number of aerosol particles. In spite of the evidence of these investigations there is a phenomenon which gives rise to doubt as to the validity of the contention that collisions are 100 % efficient in all cases.This is the failure of colliding liquid drops to coalesce. It is well known that when drops of a liquid fall on the surface of the same liquid they can float for several minutes before coalescing with the bulk of the liquid? The related phenomenon of the elastic rebounding of colliding drops has been described and investigated by a number of authors.3 However, no satisfactory explanation of these paradoxical phenomena has been given as yet. Some of the explanations which reduce the effect to the mechanical rigidity of the “ quasi-crystalline ” surface of the layer of the liquid 4 are at variance with modern ideas in respect to the properties of surface layers of liquids, besides, they contain no serious proof whatsoever that it is possible for liquid surfaces not to coalesce after the removal of the layer of air between them.Other hypotheses based on the viscosity of the air which retards its being squeezed out 5 do not explain the dependence of the effect on the nature of the liquid. Benedick’s6 attempt to reduce the effect to the action of adsorption layers leaves the causes of the phenomenon entirely without explanation. FIG. la.-Apparatus for FIG. lB.-Apparatus for observing the in- bringing drops into con- terference pattern for drops in contact at tact. various levels of vapour saturations. To get at the true cause why coalescence does not occur measurements 7 were made of the thickness and profile of the gap between two drops before “ contact ” occurred.The drops were forced out of two capillary tubes a and a1 (fig. la). It was unexpectedly found that under such conditions the drops may not merge for an indefinitely long period of time during which the profile of the air gap remains completely unchanged. This allows the gap to be measured. The width of the gap was measured at various points by means of direct observation under a microscope M (fig. lb) and by microphotography of the interference bands, the gap being illuminated through the vertical illuminator v by monochromatic light from the monochromator u and the light source S. To preclude ambiguity in the determination of the gap width due to ignorance of the orders of the interference bands we used a previously described 7 method of varying the wavelength of the light.In order to bring the drops into contact and to compensate for evaporation so that the contact area would remain constant the two capillaries were connected with one another and with the tube N (fig. la), in which the level of the liquid was regulated by micrometrically lowering a glass rod n partially immersed in the liquid. As is easily deduced from Laplace’s firstFIG. 2.-Microphoto of the interference pattern for drops of hexane in contact. [To face page 43.P. S. PROKHOROV 43 law, the intercommunication between the capillaries guaranteed a plane area of contact between the drops which simplified observation of the bands of equal thickness in reflected light. The drops were protected from air currents, and an atmosphere with a fixed content of vapour of the same liquid was maintained by means of the glass tube m which was connected with a device allowing a continuous current of air to be passed through at will.By mixing an air current devoid of foreign vapour (path a, fi,. lb) with a current containing vapour of the liquid from which the drops were formed (path b) it was possible to create the atmosphere desired about the drops. The resulting vapour content was determined from the readings of the thermometers Ra and Rb. Fig. 2 is a micro- photograph of the interference pattern for drops of hexane. Below it the profile of the gap along AA1 is shown, as computed from the microphotograph (see above). It is apparent from the figure that the gap does not possess the symmetry of a figure of revolution unlike the profile of a wetting film between a bubble and a solid surface 8 or a free film between two bubbles ; 9 this perhaps results from the circumstance that the air gap is stationary owing to dynamic rather than static equilibrium (see below).The presence of two points of minimum thick- ness a1 and a2 at the ends of the crescent interference line and comparatively wide “ gates ” connecting the central maximum thickness h with the surrounding volume of air is characteristic. The asymmetry of the pattern increases with the contact area of the drops but its character remains the same for all liquids in all the cases studied. The fact that the air gap remains stable for an unlimited period of time is $re- futable proof that other causes exist in addition to the viscosity of the air which prevent the latter from being squeezed out of the gap and maintain a pressure in the gap larger than that of the surrounding atmosphere.Using Laplace’s first law of capillarity the surplus pressure, AP‘, is found to equal AP’ =2u/r, where a is the surface tension of the drops, and r is their radius (the curvature of the ‘‘ flattened ” surface areas of the drops has been neglected in comparison with the curvature of the remaining surface). The true mechanism of the phenomenon became apparent from the observation that in an atmosphere saturated with the vapour of the liquid it was impossible to keep the drops from coalescing. The presumption was made that the surplus pressure AP’ expressing the deviation from the laws of hydrostatics was related to the diffusion of the vapours in the gap between the drops.To study the pressure which develops when vapours diffuse through a narrow slot the following model experi- ments were carried out. A chamber (fig. 3) was used formed by a niche in a plate nl, covered by a plate nz. Dust particles present (or especially introduced) between the two plates guaranteed a gap of some width H which could be varied. Some of the liquid under investigation was poured into the chamber. The surplus pressure in the chamber was measured by the manometer M. By means of the stopcock k the pressure in the chamber at the commencement of the experiment was evened out with the external pressure. However, when the stopcock FIG. 3.-Chamber for model experiments on diffusion through a narrow slot.was shut the manometer never failed to register a pressure differential which in a few minutes reached a constant value AP. (The same value was attained if a greater pressure was initially created in the chamber.) The theoretical treatment of this phenomenon is different for two extreme cases : where A and A1 are the mean fke paths of air and the vapour molecules. Tt is (1) hh B H, and (2) WI < H,44 COALESCENCE OF LIQUID DROPS known that in case (1) the motion of molecules of each kind in the gap is inde- pendent of the other, hence the partial pressure of the air inside and outside the chamber is the same. The full surplus pressure in the chamber is therefore equal to the " humidity " deficit : where p is the pressure of the saturated vapour of the liquid inside the chamber, PO is the vapour pressure in the surrounding atmosphere (zero in our experiments).In case (2) which corresponds to our experiments the motion of molecules of each kind is not independent of the other, and in the first approximation Pascal's hydrostatic law mly be used. According to that law the difference in the partial pressures of the air i s approximately equal and opposite to the difference AP. The surplus pressure AP inside the chamber is evidently due to diffusion of air into the chamber, the loss of vapour due to diffusion in the opposite direction being compensated by evaporation from the liquid. A quasi-equilibrium value of AP is established when the flow of air into the chamber by diffusion is balanced by its outflow (together with some of the vapour) under the influence of the hydrostatic pressure difference AP.Equating the two currents and neglecting radial variations of the pressure gradients in the gap, we obtain AC HJAP A p = P - P o , D12-'H= - 1 1271 cl, where 0 1 2 is the diffusion coefficient for the air+vapour mixture, cl the concentra- tion of air molecules, AC, the concentration difference. Hence we obtain where PO is the atmospheric pressure. In the case of ethyl alcohol the value of 0 1 2 is known, so that in one of the experiments (at H = 2.8 x 10-4 cm) it was possible to compute the theoretical value found to be AP = 1160 dyneslcm2, which is close to the measured value AP = 1020 dyneslcm2, thus confirming the theory.A strict quantitative application of the theory to computation of the width and profile of the air gap between the drops clearly entails great mathematical difficulties which are connected with both the complicated configuration (see above) of the air gap and with the circumstance that the radial flow of the air effects the surfaces of the drops by internal friction,* which alters the boundary condition, making it easier for the air to escape and thus decreasing AP. It can be shown, however, that the order of magnitude of the pressure AP rougly computed from (1) is quite sufficient to balance the capillary pressure AP' = 20/r (see above), which explains the fact that the drops do not coalesce. Indeed, the experimental value of H = 0.78,~ gives AP = 16,100 dynes/cm2, i.e.a value 40 times greater than 0'; thus the order of magnitude of the forces acting according to the diffusion theory is sufficient to explain the effect. The fact that the actual pressure AP is less than the theoretical value must be attributed in the main to radial currents in the surface layers of the drops (see above). It follows from the theory described that as the vapour pressure PO about the drops increases, AP should decrease, and hence if equilibrium is to be preserved, the gap must be narrowed. In order to check this conclusion the width of the gap between the drops was measured at its narrowest points at different values of the humidity of the air current flowing past the drops which was achieved by adding dry air to the air flow (see fig.lb). The data obtained are given in table 1. * Using a microscope, by means of the motion of smalI particles of soot suspended in the liquid we could observe the radial currents in the dsurface layers forming the boundary of the gap between the drops.P . S. PROKHOROV 45 It follows further from the theory that the repulsive forces between the drops should increase with the vapour pressure of the liquid at saturation. This is confirmed by the measurements of the gap h at its narrowest points a1 and a2, given in table 2 (for the temperature 20" C). Thus we see that the principal reason for the failure of drops to coalesce during lengthy contact under static conditions is a surplus pressure arising in the air-vapour gap between the drops due to the suction of air into the gap from the exterior by the vapours of the liquid diffusing out of the gap.TABLE 1 hexane vapour content after mixing, % * 0.0 19.5 47.1 74.7 100.0 gap width in p 0.36 10.38 0.29 0.24 0.22 t The vapour content in the air current passed through path b was considered equal lo 100 % although complete saturation was not attained there. TABLE 2 71 % 62e2 5ze2 5,0e3 'Ee?? 'k? hex. hexane 10% 18% 29% 38% tt:f 50% pentane ether liquid oct. oct. oct. OCt. oct. mean value of h in p 0.5 0-48 0.42 0-40 0.39 0.28 0.24 0.70 0.78 I - - - 420.2 443.4 vapour pressure, in 120.0 - I mm Hg Experiments on the collision of drops under dynamic conditions were carried out at a relative humidity of 20 %, 75 % and 100 %. With the procedure em- ployed two drops could be placed on a strictly vertical axis at a fixed distance from each other.A drop about 1 mm in diameter, forced out of the upper capillary (fig. 4), when falling collides with a drop of the same size projecting out FIG. 4.-Apparatus for drop collision under dynamic conditions of the lower capillary. By displacing the lower drop employing a co-ordinate table we were able to alter the angle at which the colliding drops met. Measure- ments were made of the horizontal displacement x of the lower drop at which the46 COALESCENCE OF LIQUID DROPS efficiency of the drop collision became less than unity. This displacement was a function of the difference z between the elevations of both drop centres prior to the fall of the upper drop. By the coalescence zone of colliding drops we mean the area limited by the surface of the revolution of the curve x = x(z).Table 3 shows experimental data characterizing the effect of humidity deficit on the efficiency of drop collision. It should be noted that all collisions in which the drops meet in the direction of the central line are efficient except those taking place at low velocities and a relative humidity of 20 % and 75 %. relative height Z of fall humidity of the drop, % mm 20 0.0 0.2 0.4 0.7 2.1 4.0 75 0.0 0.2 0.3 0.4 0.5 1.3 1.8 2.0 2.4 3.6 4.0 100 0 4 0.2 0.4 0.6 0.8 1.0 1.2 1.6 1-8 2.0 3.0 3.8 4.0 TABLE 3 [width X OF coalescence zone - 0.193 0.175 0.150 0*040 I - 0.250 0.255 0.235 0.180 0.180 0.120 0.90 0.075 0.070 - - - - 0.535 0.445 0.430 0.420 0.340 0.270 0.230 0.210 0.200 - remarks The drops are in non- coalescent contact coalescence The drops are in non- coalescent contact coalescence The drops coalesce in con tact coalescence I2 coalescence It can be easily seen from table 3 that at equal velocities in the absence of a humidity deficit, the coalescence zone of colliding drops is larger than at a relative humidity of 75 %, and by far larger than at a relative humidity of 20 %.From the results obtained for the collision of water drops at various values of the humidity deficit, it follows that the forces able to preclude the coalescence of drops under static conditions play a similar, though not so decisive, part during drop collisions.1%13 In the course of investigating the dependence of coagulation phenomena of water fogs on the humidity deficit, we also discovered an effect of a humidity deficit on the growth of fog particles as a result of coalescence arising from collisions.This was possible since the procedure used excluded condensation processes.P. S. PROKHOROV 47 Unlike other investigators, as a model for cloud processes we used a con- tinuous intransient aerosole flow rising in a vertical tube, and watched for the formation of drops of such size which fall out by gravity at a given flow value. To create aerosol vapours formed over the water surface in the flask T (see fig. 5) are carried away by the current of air which is preliminarily cleaned of con- densation nuclei by means of a no. 4 sintered glass filter @I and a filter of hygro- scopic cotton @z. The air+vapou current a and the air current b which has a lower temperature enter into the mixing zone A.Supersaturation results, and when condensation centres are introduced through canal c a water fog is formed which is transferred to the thermostated vertical tube B. The flow velocity was measured using the rheometers Ql, Q2 and Q 3 . F ~ G . 5.-Apparatus for the modelling of water fog behaviour in a rising air current. The tube B has a wider part P. The angle a (fig. 5) at the dilation is about 30°, the length of the cylindrical part of the dilation is 8 cm. This gives reason to suppose that in the dilation the current flows in the same manner as in the tube, i.e. according to the Poiseuille law. The flow velocity decreases proportion- ally to the increase in the cross-section of the tube (ug = 25~10, and the velocity distribution through the cross-section remains parabolic.Large drops, entering the dilation, remain there due to the decrease in velocity, while smaller ones slip through, and regaining their former velocity owing to the narrowing of the tube to the original dimension, enter the special cuvette K shown in more detail in fig. 6. The body of the cuvette M is metal, cylindrical in shape and has a glass extension H. The metallic part of the cuvette is furnished with hollow partitions connected in series to allow the flow of water at a given temperature from the thermostat U. Because of this, the air-vapour current in the tube B, in passing through this zone, could rapidly acquire a temperature which was a few degrees higher or lower than the original temperature (below the metallic part of the cuvette).The variation of temperature was recorded by a thermocouple. To avoid turbulence, the plates were given a wedge-like " streamlined " shape. The air-vapour current in the tube B and the cuvette B was laminar (Re = 140 for a flow velocity of 21.2 cmlsec, and Re = 260 for 39.3 cmlsec). The cuvette48 COALESCENCE OF LIQUID DROPS K has two glass windows rn and n in the sides (fig. 5) at right angles to each other. One of them served for lighting, and the other for the observation of fog particles through a microscope. The light from the electric arc E passes through the I-1 FIG. 6.-The design of the cuvette of the model condensers L1 and L2, the-parallel slot H, the glass thermo-filter SP and is focused by the lens L3 on to the central part of the cuvette.This enabled us to conduct observations along the lines of an ultramicroscope. The interior of the cuvette was painted black. The drops which separated from the flow were formed by the coalescence of original drops in a zone with a height h = 5 cm, lying between the level of the windows m and n and the point where the tube narrowed. The increase in the velocity after the narrowing of the flow precluded the falling of drops which coalesced after this narrowing. To determine the direction of the move- ment of the drops a rotating disc D was used which had a series of slot-like openings along the perimeter placed in pairs in the order : wide slot-narrow slot-space-wide slot-narrow slot-space, etc.that in a stream which has passed the dilation and observation point the concentration of THEORY OF THE PROCEDURE.-sUPPOSe drops with radii from r to r + Ar is equal to n(r)dr. The number of coalescences of drops with radii rl and r2 in a unit volume and unit time is ~1~~12n(rl)n(~2>drldrz, where €12 is the probability of collision of drops with radii rl and r2, and 012 is the efficiency of the collisions which may depend on the humidity deficit AE. The number of drops with radii p > rc formed by coalescence in a unit of volume within a unit of time is (2) N ~ J = 1 J n(rl)Yl(r2)€12o12dridr2, where r, is the radius of a drop just beginning to separate from the current. The boundary of the area of integration is given by r13 + r23 > re3. (3) Replacing r2 by another variable p whose dependence on rl and r2 is expressed by p = (r13 + r$)* we obtain, instead of (2) : where Yomh = (rc3 - rimax)* is the minimum radius of a drop which, after coalescing with a drop of maximum radius romax, will be able to fall in the current.Here rmax = 2*~0ma (rmax is the radius of the drop formed as a result of the coalescence of two drops with radii equal to romax). NO = z12rmm dp J For a concrete case eqn. (4) will read P2 rc ro min r12 ro max n ( r ~ p 3 - p 1 ~ ---€12dr1, where a12 is the average efficiency of collision for the drops being considered. From the equation obtained it follows first of all that if the collision efficiency, ~ ~ 1 2 , changes, the number N(rc) of drops separating out increases proportionately.P.S. PROKHOROV 49 In our case, however, superheating the air current At may affect N(rc) not only by means of the factor &2, but also due to the fact that in an unsaturated atmosphere evaporating drops may decrease their radii to such an extent that those collisions which, in the absence of evaporation, led to the formation of drops which were able to fall in the given current, will now produce drops unable to fall to the level of the observation zone. Obviously, the decrease in the number of observed falling drops will, on the average, be the same as if the critical radius rc of the falling drops in eqn. (4) increased by the value Arc ; in the first approxima- tion Arc is equal to the average decrease in the radius of those drops (lying in a rather narrow interval) which rise in the current before coalescence but after co- alescence fall down the tube.All the other values in the right-hand part of eqn. (4), including YO mh, Yoma, n(rl), €12, are considered constant. If the value Arc is small in comparison with the interval of integration rmax - re, then it is evident that the respective changes in the value of the integral in the right-hand part of eqn. (4) will also be small and cannot explain the significant (several-fold) decrease in N(rc) which was observed by us (see below). In order, however, that the radii of the class of drops of interest to us should actually lie in a sufficiently narrow interval (i.e. that romiJr0max should be a little less than unity), it is necessary that rc should not be too close to r o d .On the other hand, however, rc should not be close to rma. An optimum value for rc is one lying approximately half-way between the values of rOmm and 2*roma. Supposing Stokes' law to be approximately correct for our case, we obtain where Ro and R1 are the radii of the widened and straight parts of the tube. We selected a value of the relation RoIR1 = 1-12 which lies within the required limits, between 1 and 2% (= 1-26), In order to determine the value of Ar it is necessary to calculate the change in the drop dimensions due to condensation of evaporation in the current while passing through the 5 cm zone between the heating zone and the top of the chamber. For this purpose the theory of drop growth in a rising current (11) may be used in which the following equation was obtained : * V02 - g - [c(h) - co(h)]dh = const.= - 2 ' Here v1 is the velocity of rise of a drop with a radius r1 at height h ; vo is the velocity of rise of the drop directly after leaving the heating zone ; g is the acceleration of gravity; D is the diffusion coefficient for water vapour; r ) is the viscosity; c = the density of the water vapour at height h ; co = their density at saturation; h = the height above the heating zone. The difference ACO = c(h) - co(h) can be calculated for h = 0 if one knows the temperature change At occurring after the current passes through the heating zone. For h > 0, 1 Ac I < I co 1 due to drop evaporation (or condensation). As- suming, therefore, in (6) that Ac = ACO for all values of h, we obtain a good approximation for the possible variation of the velocity Av , and, consequently, for the radius Ar.We find where 2112 - 4 0 -_ vo2 - - g - Acoh, 2 9 7 (7) *The form of the equation is slightly modified, to apply to the problem under investigation.50 COALESCENCE OF LIQUID DROPS After calculating 01 from (7) we can then find rl, using Stokes' law, Fig. 7 shows values of rl calculated in the manner described, for various values of At, with ul = 39.3 cm/sec and u2 = 21-2 cm/sec, and h assumed to be equal to 5 cm (straight line BB1).* 70 "ii e I L- I B C €3 A c, 4, - , . , , . "i , * . . -4. -3 -2 -9 o r 2 3 4 Yt0c FIG. 7. The same figure (curve CC1) shows the results of similar calculations of the change of the dimensions of a drop of double volume with a radius P;nax = 2*romax The straight line AA1 gives the values of the radius rc at which the drops separate out of the current in the cuvette.It is evident that Ar represents about 5 % of r1 when u1 = 39.3 cmlsec, and about 7 % when u2 = 21 -2 cm/sec which is small even in comparison with (rmm - rc). Hence it follows that the effect of evaporation on the number of drops separating out is small. From fig. 7 it is also directly evident that a drop of double volume, even with the current superheated 3" to 4" C, cannot reduce its radius below re, i.e. its fall cannot be stopped. Conversely, drops with radii rOma even with the current cooled down by 4" C during their full rise cannot grow to r = rc, i.e. to falling dimensions. RESULTS OF MEAsuREmms.-Experiments on the collision of water drops in an air-vapour current with various values of humidity deficit were carried out at a flow velocity u = 21-2 cmlsec for one series of experiments and 3993 cm for another.Those values of flow velocity enabled us to calculate by means of eqn. (7a) the maximum radii of rising drops equal to the minimum radii of falling drops. At u = 21-2 cm/sec, r = 4-3 x 10-4 cm, and at u = 39.3 cmlsec, r = 5-8 X 10-4 cm (the corrected value is 6-5 x 10-4 cm). * It can be easily shown that deviations from Stoke's law for drops which are able to fall in such a current only increase the validity of the estimates and conclusions which follow.P. S. PROKHOROV 51 The results are shown in fig. 8 where the difference of temperature At between the cuvette and the tube widening is plotted along the horizontal axis, and the number of drops falling within 5 min, along the vertical axis.As is seen from the curve (fig. S), the lower the degree of saturation the lower the efficiency of drop collision.% 10 The graphs clearly indicate that lacking a humidity deficit the efficiency of drop collision a12 reaches a maximum, presumably equal to 100 %. 1 1 I L -4 -3 -2 -7 0 1 2 3 a t " C The asymmetry of the curve relative to the vertical axis, i.e. the lesser influence of the cooling of the current than of an equal superheating may be attributed primarily to the fact that part of the saturation produced is erased by vapour condensation on the walls of the cooling coil. There is, however, reason to suppose that even the elimination of vapour condensation would not do away with the asymmetry of the graphs, and that the effect itself is asymmetric in nature, as the collision efficiency cannot increase above 100 %, and the probability of collision (with the drops meeting in the capture cross-section) increases too insignificantly to change the situation materially. 1 Fux, Acta physicochim., 1935, 3, 819. 2 Mahajan, Phil. Mag., 1929,7,247 ; 1930,10,383 ; Nature, 1930,126,761 ; 2. Physik, 3 Rayleigh, Proc. Roy. Soc., 1879, 5, 28. Aganin, Zhur. geophysiki, 1935, 5, 408 ; 1932, 79, 389; 1933, 81, 605. Izvestiya Akademii Nauk S.S.S.R., seriya geographii and geophysiki, 1940, 3, 305 ; Gorbachev and Nikiforova, Kolloid-Z., 1935, 73, 14 ; Gorbachev and Mustel, Kolloid-Z., 1935, 73, 21. 4 Hazlehursta and Neville, J. Physic. Chem., 1937, 41, 1205. 5 Kaiser, Ann. Phys. Chim., 1894,59, 66. 6Benedicks, Nature, 1944, 153, 80. 7 Deryagin and Prokhorov, D.A.N., T. liv, no. 6, 1946. 8 Deryagin and Kusakov, Izvestiya Akademii Nauk S.S.S.R., seriya Ichimii, 1937, no. 5 , 9 Deryagin, Priroda, 1943, no. 2, 23. 10 Prokhorov and Yashin, Kolloid. Zhurn., 1948, 10, 2. 11 Prokhorov, Sbornik. Noviye idei v oblasti izucheniya aerozolei, izdanie Akademi 12 Prokhorov and Zeonov, Kolloid. Zhur., 1952, 24, 7. 13 Prokhorov, Deryagin and Zeonov, D.A.N., T81, no. 4, 1951. 1119. Nauk S.S.S.R., 1949.

ISSN:0366-9033    

DOI:10.1039/DF9541800041

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

STABILITY AND ELECTROPHORETIC DEPOSITION OF SUSPENSIONS IN NON-AQUEOUS MEDIA BY €3. KOELMANS AND J. TH. G. OVERBEEK Philips Research Laboratories, Eindhoven, Holland van’t Hoff Laboratory, University of Utrecht, Holland Received 21st June, 1954 The stability of suspensions in solvents of very low polarity is treated in part 1 of this paper. Theoretical considerations lead to the conclusion, that quite modest electric charges and [-potentials are sufficient to stabilize suspensions of coarse particles (> lp) whereas hardly any stabilization can be expected from adsorbed layers of non-ionized long-chain molecules. Experiments on the settling times of suspensions of a number of solids in xylene confirm that only ionized surface-active substances give rise to stability. Long-chain com- pounds that do not increase the conductance of the xylene, do not give rise to a sufficient [-potential of the particles and do not improve the stability very much.In part 2 the electro-deposition from suspensions in polar organic media is investigated. It is shown that the particles are accumulated near the electrode by the applied field, but that the formation of an adhering deposit is caused by flocculation introduced by the electrolyte formed by the electrode reaction. The combination of electric double-layer repulsion together with attraction of London-van der Waals nature allows a quantitative description 1 of the stability of aqueous colloidal systems. Changing from water to a non-aqueous solvent usually means a lowering of the dielectric constant E , bringing about a decrease in the dissociating power of the medium, thus limiting the formation of a sufficient charge on the particles.This does not seem to be a serious disadvantage for systems in liquids of medium E like the lower alcohols and acetone. Merely by grinding the solid phase together with the medium, stable suspensions may be prepared,2 which show electrokinesis and can be flocculated with electrolytes in a similar way to aqueous suspensions. The properties of these suspensions in relation to electrophoretic deposition will be discussed in part 2 of this paper. The same grinding technique applied to non- polar solvents results always in flocculated suspensions. This poor dispersion is often greatly improved when a surface-active stabilizer is added. In part 1 of this paper special attention is given to the factors governing the stability of suspensions in solvents of low polarity.1. THE STABILITY OF SUSPENSIONS IN NON-POLAR MEDIA Recently two different views on the problem have been published. Van der Minne and Hermanie 3 measured electrophoresis of suspensions in benzene and found a good correlation between stability and electrophoretic velocity with a critical c-potential of about 25 mV. They consequently attributed stability to the existence of an electric double layer. On the other hand, Mackor and van der Waals 4 explained the stabilization of carbon black in heptane by non-ionic chain-molecules as observed by van der Waarden,% 6 as caused by a repulsion of entropic nature, viz. steric hindrance of adsorbed chains.Before giving our own experiments we want to discuss these two concepts on the basis of the Verwey and Overbeek stability theory. 52H . KOELMANS A N D J . TH. G. OVERBEEK 53 ELECTRIC DOUBLE LAYER As ionic concentrations in xylene (for convenience we will refer to this liquid) are always low, ionic double layers are very diffuse. At an ionic concentration of 10-11 N, which is of the order of magnitude observed, the Debye length, 1 / ~ , in xylene is about 16 p. The capacity of a double layer is therefore very low, and only very little charge is needed to obtain appreciable surface potentials. In analyzing whether the corresponding free energy can provide the potential barrier of about 15 kT required for stability,7 we may, at the low ionic concentra- tions involved, roughly describe repulsion with the Coulomb law.where r is the radius of the particles considered as spheres and R the distance between their centres. In contrast to aqueous systems where, as a result of the screening effect of the counter ions, the decay is much steeper, the repulsive potential decays slowly (R-1) with distance. When the repulsion (eqn. (1)) is combined with the van dex Waals attraction according to Hamaker,s the curve for the particle interaction plotted against the distance shows a maximum, Vma. The height of the maximum is not very sensitive to the choice of the van der Waals constant a as a consequence of the slow decay of the repulsion. Table 1 gives values for Vmax calculated for a = 10-12 ergs, and expressed in units of kT at room temperature (4 x ‘10-14 ergs).VR = Fer2/R, (1) TABLE MAXIMAL REPULSION AS A FUNCTION OF PARTICLE SIZE AND SURFACE POTENTIAL t mV - - 25 13 35 26 1 50 62 4 75 152 11 - 100 286 20 1 150 662 54 4 - - It appears that in spite of the low free energy of the double layer, particles of I p and coarser can be stabilized by 5-potentials of the order of magnitude observed by van der Mime and Hermanie.3 T h i s must be ascribed to the fact that in the region where attraction gives no appreciable contribution the repulsion is still important. The low total repulsion which already threatens the stability of small particle systems (r < 10-6) in water, makes stabilization by electric charges for small particles in xylene completely impossible.STERIC HINDRANCE OF ADSORBED CHAINS Repulsion by steric hindrance of adsorbed chains is only present when the adsorbed chains of two neighbouring particles interact. This means that at a distance more than twice the stabilizer length only van der Waals’ attraction is present. The depth of the resulting minimum of energy at a distance of 40& for different values of r and a is given in table 2. TABLE 2.-vAN DER WAALS’ ATTRACTION BETWEEN SPHERES AT A DISTANCE OF 40A BETWEEN THE SURFACES a r = 10-4cm rEy,$Fz r=lO-scm 10-12 5 10.0 42.0 1.2 10-13 51.0 4 2 0.1 1044 5.1 0.4 0.0 154 STABILITY OF SUSPENSIONS As there is no reason to assume the van der Waals constant in xylene to be greatly different from that in water (a m 10-12) the figures of table 2 show that adsorbed chains cannot prevent flocculation, unless the stabilizer length is comparable with the particle size.Summarizing the results, we may distinguish the four cases of table 3. particle size 1 large 2 large 3 small 4 small TABLE 3 stabilizing mechanism stability ionic double layer stable steric hindrance flocc. steric hindrance stable ionic double layer flocc. EXPERIMENTAL Our experiments, having been performed with relatively coarse particles, only give evidence about points 1 and 2 of table 3. Particles of different substances were prepared by grinding combined with gravity fractionation so as to give an average size of 1 p. Substances used were Fe2O3, 4 2 0 3 , HgS, BaS04, CaC03, Si02 (quartz), Ti02 (rutile), C (graphite), Se (metal). Suspensions were prepared by mixing the powders with xylene, care being taken to avoid moisture and (undesired) surface-active substances.Stability was evaluated by measuring settling times in glass-stoppered graduated cylinders. At both ends of the stability scale there is some arbitrariness in noting the point of complete sedimentation. As in general great differences in stability werein- volved, the latter was not serious in our experiments. Electrophoresis was measured in the cylindrical microcell according to the technique described by van der Minne and Hermanie.3 In the adsorption experiments the concentrations of stabilizer before and after addition of the powder were determined by titration (lower fatty acids) or by spreading on a Langmuir trough. Conductivity down to 10-14 0-1 cm-1 was measured by a simple d.c.method using a Jones-type 12 cell with a constant of 00684 and a Philips d.c. electronic voltmeter G.M. 6010. STABILIZATION EXPERIMENTS Classification into ionic and non-ionic stabilizers.-The criterion whether the stabilizers used were of ionic or non-ionic nature in xylene, was based on conductivity measurements. It is seen from table 4 that there is rather a sharp distinction between stabilizers increasing TABLE 4.-sPECIFIC CONDUCTIVITY K OF IONIC AND NON-IONIC STABILIZERS IN XYLENE stabilizer conc. mmoles/l. K ohm-* cm-1 xylene no stabilizer < 10-14 non-ionic oleic acid 10 5.0 x 10-14 stearic acid 10 3.0 x 10-14 stearyl alcohol 10 1.0 x 10-14 ionic Cu oleate 10 4.7 x 10-10 Aerosol OT * 10 2-0 x 10-10 tri-iso-amyl-amm. picrate 10 2.4 x 10-10 Ca di-isopropyl salicyla te 10 3.0 X 10-10 Span 80 7 10 2.3 X 10-10 Span 40 7 10 6-1 X 10-10 * Aerosol OT = Na dioctylsulphosuccinate. 7 Span 80 and 40 = sorbitan mono-oleate and -palmitate respectively. The origin of the ions in xylene solutions of Span 40 and 80 is not wholly clear.As the conductivity decreased rather sharply after repeated recrystallization from methanol, it may be due to impurities in these commercial products.H . KOELMANS AND J . TH. G . OVERBEEK 55 the conductivity of the xylene to about 10-10 SZ-1 cm-1 and others that do not bring the conductivity much above 10-14 9-1 cm-1. It seems justified to consider the fist group as ionic and the second as non-ionic. Stabilization with non-ionic detergents.-A number of powders, viz., Fe203, A&@, 2402, C, Ti02, GaC03, BaS04, Se and HgS in xylene were stabilized with acids of varying chain length.The acids used were oleic, stearic, myristic, capric, caprylic, caproic and benzoic acid. In general, the effect of the acids on stability was small. The suspension, which settled in less than 1 min in the absence of acid, now settled in a few minutes to 1 h, whereas more complete dispersion of the powder resulted in settling times of a day and more. Exceptions to this behaviour were Fez03 and A1203 suspensions, where sedimentation times up to several hours were observed. Prolonged heating of the powders at 1200" C, however, greatly reduced the settling time, suggesting that the stronger stabilization in suspensions of unheated powders is due to chemical reaction.The latter is supported by the fact that the stability increased gradualIy during several hours after preparation of the suspensions. FIG. 1.-The settling time of Fez03 in xylene, stabilized with fatty acids, as a function of adsorption. CIS, c14, Cloy CS, c6 represent stearicy myristic, capric, caprylic and caproic acid. Fig. 1 gives the settling time in minutes as a function of adsorption for (unheated) Fez03 in xylene with fatty acids. The effect of oleic acid is greatest, a result which was also found in other suspensions. In agreement with the results of Rehbinder 9 the stabil- ization increases in the series of normal fatty acids. In contrast with the results with oleic acid, the higher normal fatty acids show a maximum stabilization. Analogous results were also found for A1203 in xylene.The stabilizing properties of fatty alcohols were still poorer than those of the cor- responding acids. Table 5 shows that the effect again becomes smaller with decreasing Iength of the stabilizer molecule. Stabilization with ionic detergents.-When an ionic stabilizer (cf. table 4) was added to Fe2O3, AI2O3, Bas04 and Si02 in xylene, the suspensions in genera1 did not settle56 STABILITY OF SUSPENSIONS completely in several days. The sedimentation times did not differ much from that of a stable suspension of the same powder in water or a suitable organic solvent of a higher dielectric constant than xylene. Complete stability could aIso be obtained in suspensions stabilized with fatty acids when 2 to 4 % of methanol was added to the suspension.Measurements showed that this addition increased the conductivity of the suspension by about a factor 104. The influence of the length and nature of the fatty acid then disappeared; all suspensions showed settling times of several days, which is in agreement with complete dispersion. TABLE 5.ATABILIZATION OF Fez03 IN XYLENF! WITH FATTY ALCOHOLS stabilizer conc. (mmoles/l.) blank - stearyl alcohol 10 myristyl alcohol 10 lauryl alcohol 10 capryl alcohol 10 settling time (mh) 0.5 20.0 10.0 6-0 4.0 ELECTROPHORESIS MEASUREMENTS The relationship between electrophoresis and stability.-The work of van der Minne and Hermanie shows that in order to avoid an overshadowing of electrophoresis (pro- portional to the field strength E) by electrostatic phenomena (proportional to E2) low field strength and perfect insulation are essential.The electrophoresis cell developed by these authors enabled us to measure electrophoresis in suspensions with a conductivity as low as 10-11 ohm-1 cm-1. The field applied never exceeded 100 V/cm. Comparison of table 6, colums 7 and 8, where the results are listed for suspensions stabilized with ionic detergents * shows, that in agreement with the measurements of van der Minne and Hermanie, a close relationship between stability and electrophoresis exists. As the thickness of the double layer in our suspensions was always larger than the particle size, [-potentials have been calculated from Hiickel’s equation 4 = 67qY/,. (2) TABLE THE CORRELATION BETWEEN STABILJTY AND ELECTROPHORESIS FOR SUSPENSIONS IN XYLEM Cu oleate oleic acid stearic acid caproic acid oleic acid stearic acid tri-iso-amyl- ammonium picrate Aerosol OT Span 80 Aerosol OT Span 40 oleic acid stearic acid 5 10 15 15 15 15 10 10 10 10 10 10 10 vol. % liquid added powder stabilizer mzz;,l.of polar 8 no 2.3 2.25 % CH30H 2*6t ,Y 2.6 2.6 2.75 % &H50H 2.65 Y Y 2.65 no 2.3 no 2.3 no 2.3 no 2.3 no 2.3 2.25 % CH30H 2.6 59 2.6 charge + + + 3- + + no + + + 3- + + sed. time, h > 24 > 24 > 24 > 24 15 2 0.03 > 24 > 24 3 24 5 > 24 > 24 Vel &ec per V/cm 0.110 0.145 0.165 0.150 0.08 0.05 no 0-143 0.126 0.147 0.07 1 0.103 0.1 10 c mV 53 62 70 65 31 20 no 68 60 71 33 43 48 t The +values in the cases where alcohol was added, were taken from literature.A critical c-potential of about 30 mV is found, in agreement with the results of table 1 for particles of 1 p . * As might be expected from their low conductivity, the suspensions stabilized with non-ionic detergents only showed electrostatic phenomena.H . KOELMANS A N D J . TH. G. OVERBEEK 57 The relationship between adsorption and stabjlity.-The adsorption isotherm of Aerosol OT on Fe2O3 in xylene is given in fig. 2. For each experimental point of the isotherm, stability and electrophoresis of the corresponding suspensions were determined. Owing to the low conductivity no electrophoresis could be measured at the lowest point of the curve. Fig. 2 shows that both stability and electrophoresis increase with increasing adsorption, and remain approximately constant when adsorption is maximal.Analogous 40- 1 1 15 20 equi 1. conc. (m mol s I .) 5 10 9 - Ads.rnolsxlOl S FIG, 2.-Adsorption isotherm of Aerosol OT on Fez03 in xylene. For each point of the curve, stability and electrophoretic mobility of the corresponding suspensions are given. S = stable ; F = flocculated. FIG. 3.-Adsorption isotherm of oleic acid on Fe2O3 in xylene + 3.75 % CH30H. For each point of the curve, stability and electrophoretic mobility of the corresponding suspensions are given. S = stable ; F = flocculated. experiments were carried out for a suspension of Fez03 in xylene containing 3.75 % of methanol, with oleic acid as a stabilizer. As the methanol itself greatly contributes to the conductivity, electrophoresis measurements in this case could be extended to low equilibrium concentrations of the stabilizer.Again (fig. 3) adsorption runs parallel with stability and electrophoresis. DISCUSSION In agreement with the results of table 3 the experiments with suspensions show that stability is only obtained when an electrical double layer is formed on the particles. The primary demands for an electric charge are adsorption and58 STABILITY OF SUSPENSIONS dissociation of the stabilizer. In the second place the polarity of the ions must differ enough to give preferential adsorption of one type of ion. This condition will in general be fulfilled when the stabilizer consists of a large organic and a small inorganic ion, the small polar ion being preferentially adsorbed by the polar surface.In confirmation of this view all suspensions of table 6, except the suspension with tri-iso-amyl ammonium picrate, where both ions are large, showed a positive charge. In agreement with the figures of table 2 suspensions of large particles with non-ionic detergents are never truly stable. The slight stabilization observed increases with increasing chain length. The longer chains evidently keep the particles farther separated and make the energy trough less deep. As it is difficult to free oleic acid from molecules of higher molecular weight the greater effect of this acid in comparison to the normal fatty acids may be due to impurities. The stronger stabilization with fatty acids in the case of reactive powders is easily explained by ionization of the soap formed.The maxima in the stability curves of fig. 1 might be due to a weak attraction between the aliphatic chains. This would lead to adsorption of a second layer of fatty acid molecules pointing with their polar heads to the medium, and to a slightly deeper minimum in the energy against distance curves. Support for this point of view is found in the work of Hirst and Lancaster,lo who found partial desorption of normal fatty acids from powders in benzene not much above room temperature, and further by the fact that the maxima in the stability curves disappeared when the suspensions were heated to 60" C. As we worked exclusively with rather coarse suspensions the predictions above for small particles cannot be verified from our experiments. The work of van der Waarden 11 shows that stability in this case can indeed be obtained with non-ionic stabilizers.In order to complete the experimental check of table 3 it would be necessary to show that ionic stabilizers (with a short chain) fail to make a small particle system stable. 2. ELECTROPHORETIC DEPOSITION Hamaker and Verwey L 2 consider the deposition of particles from a stable non-aqueous suspension by means of electrophoresis to be a close analogue to sedimentation. They assume that the accumulation of particles under influence of the applied electric field leads to sufficient pressure on the innermost layers of particles to overcome the double-layer repulsion and to lead to an adhering deposit. It is shown in the following sections that by the electrolysis accompanying electrophoresis, sufficient electrolyte may be formed at the electrode to cause flocculation of the particles.The critical time t* observed in electro-deposition, should therefore be interpreted as the time required to build up a critical electro- lyte concentration rather than a critical particle accumulation. THEORY Considering the deposition of a positively charged suspension in methanol, the cathode reaction might be where M+ is the cation of the electrolyte in the methanol. A fraction of the OH- ions generated at the cathode is transported away by the electric current. The net production of M+OH- at the cathode is thus tM equivalents for every faraday passing, tM being the transport number of the M ions. By diffusion, M+OH- is carried into the solution. By solving 4,s the diffusion equation 2 M+ + 2 CH30H + 2e + 2 M+OH- + C2H6 (dissolves), for the appropriate boundary conditions, the concentration of MI-OH- can be13. KOELMANS A N D J .TH. G . OVERBEEK 59 function of time and place. The concentration at the electrode to be calculated as a (Celectr) is found where cg = initial electrolyte concentration, Z = current in A, tM = transport number of M+, F = faraday, S = area of the electrode, D = diffusion constant of M+OH-, t = deposition time. The assumption of undisturbed diffusion, on which eqn. (4) is based, becomes incorrect when t is great. There is evidence in the literature 6 7 that in unstirred solutions the diffusion layer reaches to a depth of about 5 0 0 ~ . As the average displacement @)+ = (2Dt)P, ( D being about 10-5 cm2/sec for ordinary electro- lytes) this means that eqn.(4) can be used safely up to t w 100 sec. It is generally observed that a critical time t* has to elapse before the formation of an adhering deposit starts. Calculating the concentration at the electrode after the critical time with the aid of eqn. (4), values of the same order as the flocculation concentration are found. In a positively charged suspension of MgC03 in CH30H, t* was 20 sec for I = 1.55 x 10-3 A and S = 1-26 cm2. Taking tM = 0.5 and D = 10-5 cm2/sec, which are the values for KOH in methanol, we find eelectr = 10 mmoles/l. The flocculation value with KOH for a concentrated suspension is cflocc = 6.0 mmoles/l. Applying an analogous calculation to a negatively charged suspension of , 5 0 2 in acetone which is 10-5 M in LiCl gives celectr = 4.2 mmoles/l.and cflocc = 4 to 6 mmoles/l. The concentration built up by electrolysis is clearly of the same order as the flocculation concentration. A closer agreement cannot be expected because of the difficulty in determining the flocculation value under exactly the same con- ditions as prevail for the suspension near the electrode. The following simple relations between the critical time and the conditions of electro-deposition are expected from eqn. (4) where q and p are constants, Vis the voltage applied and k the specific conductance of the suspension. EXPERIMENTAL THE CRITICAL T~ME t *.-During electrophoresis the particles are accumulated at the electrode, but the deposit stays fluid as long as the double-layer repulsion between par- ticles prevents actual contact.Consequently the yield Y will not only bedependent upon the time of electrophoresis but also on the time elapsed between the end of the electrophoresis and the moment of weighing, during which the non-solidified part of the layer can flow off. Fig. 4 illustrates this for MgCO3 in methanol. If the deposit is weighed continuously during deposition as has been done by Biguenet and Mano,* the yield is proportional to the time of electrophoresis and no critical time is found. If weighing is postponed until the fluid part of the layer has flowed off, which we found to be the case after a waiting period of 15 min (tw = 15), a Y against t curve of the type sketched in fig. 5 is found. Below t*, no adherent deposit is found.At the critical time t*, practically the whole deposit turns rigid within a few seconds. tab = PI-2 == qv-2k-2,60 STABILITY OF SUSPENSIONS u 400 8( FIG. 4.-The weight of deposit as a function of the time be- tween stopping electrophoresis and weighing the deposit for a MgCO3 + CH3OH suspen- sion. V = 6 V ; Csusp= 8 %. l i t, sec FIG. 5.-The yield as a function of time of deposition at different waiting times (t,,,). FIG. 6.-The dependence of the critical time on the voltage applied in MgC03 3. CH30H suspensions.H. KOELMANS AND J . TH. G . OVERBEEK 61 FIG. 7.-The dependence of the critical time on the voltage applied in a SiO2 suspension in acetone (0.9 x 10-4 N LiCl). FIG. 8.The dependence of the critical time on conduc- tivity in a MgC03 I- CH3OH suspension. At each point the corresponding concentrations of added KI are given in mmoIes/l. V = 7.2 V; Csusp.= 7.4 %. FIG. 9.-The dependence of the critical time on conductivity in a Si02 + acetone suspension. At each point the corresponding concentrations of added LiCl are given in mmoIes/l. Y = 7.0 V; Cmsp. = 2 %.62 STAB I LIT Y 0 F S U S P E N S 1 0 N S VARIATION OF t* WITH APPLIED VOLTAGE.-The results for MgCO3 + CH30H (at three suspension concentrations) and Si02 + acetone are given in fig. 6 and 7. The influence of the suspension concentration in fig. 6 which is quite non-systematic is evidently due to small variations in the electrolyte content between the different concentrations. VARIATION OF t" WITH CONDUCTIVITY.-The measurements for MgCO3 f CH30H with KI as added electrolyte and Si02 + acetone with LiCl are given in fig.8 and 9. Apart from the curvature in the lower part of fig. 8, for which no explanation has been found, the measurements co&m the proportionality of t* with k-2. In the Si02 + acetone curve no point is present for zero electrolyte concentration. The conductivity of the pure suspension was so low that even at 40 V applied voltage no adherent deposits were obtained. The additions of electrolyte, although they changed the conductivity considerably, had only a small influence on the electrophoretic velocity. DISCUS SlCON Three different theories of electro-deposition have been advanced. In the first the electric field is supposed to overcome the repulsion between two particles.In the second, a cumulative influence is considered of several layers of particles pressing upon each other, causing the particles close to the electrode to adhere to it and to each other. The third theory postulated in this paper considers flocculation by electrolyte to be the final cause of formation of a deposit. The fact that a critical time exists seems to rule out the first theory. Both the accumulation theory 3 and the flocculation theory demand that the critical time is inversely proportional to the voltage, but the influence of other variables is expected to be different as shown in the following table. The experiments de- scribed are in agreement with the flocculation theory, except for the concentra- tion dependence shown in fig.6. The critical time varies, however, erratically with concentration and this variation is probably more due to accidental variations in the conductance than to the concentration. TABLE 7.-INFLUENCE OF DIFPERENT VARIABLES ON THE CRITICAL TIME electrophoretic suspension mobility conc. voltage conductance accumulative theory V-2 independent u' C-1 flocculation theory V-2 k-2 independent independent The local increase in electrolyte concentration near the electrodes lowers the local field by a factor which may easily amount to 10 or more. This would make the accumulation mechanism still less probable. It is, however, conceivable that in other systems the products of the electrode reaction are weakly or not at all ionized. In such cases a decrease of the local electrolyte concentration would follow, coupled with an increase in the local field, the flocculation mechanism would be ruled out in favour of the accumulation mechanism.An important factor in explaining why at t = t* practically the whole layer turns rigid in a few seconds may be the following. When as a result of the flocculation mechanism the particles in the electrode area touch, part of the medium is squeezed, thereby bringing the electrolyte concentration in the adjacent layer, which is already high, to the flocculation value, etc. Owing to convection this mechanism might fail at the circumference of the layer, thus explaining why at t > t* a small part of the layer still flows off. The part which flows off corresponds to a layer of about 60 p the gradual divergence in fig. 3 being caused by the increasing radius of the coated electrode (a cylinder of 1 mm diam.). The authors are indebted to Dr. E. J. W. Verwey, Director of the Philips Research Laboratories, for his permission to publish this paper; to Dr. J. L. van der Minne and Mr. P. H. J. Hermanie (Kon. Shell. Lab.) for their help in the construction and use of the electrophoresis cell, and to Mr. P. A. Boter for carrying out the adsorption measurements and most of the experiments on electrophoretic deposition.H. KOELMANS AND J . TH. ci. OVERBEBK, 63 PART 1 1 Verwey and Overbeek, Theory of the Stability of Lyophobic Colloids (Amsterdam, 2 de Boer, Hamaker and Verwey, Rec. trav. chim., 1939,58,662. 3 van der Minne and Hermanie, J. Colloid Sci., 1953, 8, 3 8 ; 1952, 7, 600. 4 Mackor and van der Waals, J. Colloid Sci., 1952,7, 535. 5 van der Waarden, J. Colloid Sci., 1950,5, 317. 6 van der Waarden, J. Colloid Sci., 1951, 6, 443. 'ref. (l), p. 171. 9 Rehbinder, Lagutkina and Wenstrom, 2. physik. Chem. A, 1930,146,63. 10 Hirst and Lancxster, Tram. Faraday SOC., 1951,47, 315. 11 ref. (5) and (6) ; cf. Mackor, J. CoZloid Sci., 1951, 6,492. 12 Jones and Bollinger, J. Amer. Chern. Sac., 1931,53,411. 1948). Colloid Science, vol. 1, ed. by Kruyt (Amsterdam, 1952). 8 Hamaker, Physica, 1937,4,1058. PART 2 1 Hamaker and Verwey, Tram. Faraday SOC., 1940,36,180. 2 Hamaker, Tram. Faradly SOC., 1940,36,279. 3 cf. also Hill, Lovering and Rees, Trans. Faraday Soc., 1947;43,407. 4 Rosebrugh and Miller, J. Physic. Chem., 1910, 14,816. 5 Thomson and Cayley, Quart. J. Math., 1857, 1, 316. 6 Nernst and Merriam, 2. physik, Chem., 1905,53,235. 7 Agar, Faraday SOC. Discussions, 1947,26. 8 Biguenet and Mano, Le Vide, 1947,2,291, 304.

ISSN:0366-9033    

DOI:10.1039/DF9541800052

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

H. KOELMANS AND J . TH. ci. OVERBEBK, 63 COAGULATION AS A CONTROLLING PROCESS OF THE TRANSITION FROM HOMOGENEOUS TO HETEROGENEOUS ELECTROLYTIC SYSTEMS BY Bo2o TE~AK in collaboration with E. :MATIJEW~, K. F. SCHULZ, J. ICRATOHVIL, M. MIRNIK ~m V. B. VoUK Laboratory of Physical Chemistry, Faculty of Science, University of Zagreb, Croatia, Yugoslavia Received 18th June, 1954 To emphasize the complex character of coagulation processes the discussion has been divided into three sections comprising : (i) constitutive factors, (ii) semi-constitutive factors, and (iii) colligative factors. The constitutive factors include the interactions of the constituents of the disperse phase with the constituents and components of the dis- persing medium, giving the potential-determining complkxes (ionogenic groups) on the boundary.To obtain an insight into the character of such interactions the various aggregation and dispersion curves of the precipitation systems were used (von Weimar’s precipitation curve, typical precipitation curve, general precipitation diagram). The semi-constitutive factors include the controlling interactions between potential- determining ions and counter-ions, poly-ions, etc. (phenomena which are expressed in the SchulzeHardy rule, the Burton-Bishop rule, the antagonistic effects of electrolytes, the dielectric constant effect of the dispersing medium, the protective action of lyophilic substances, etc.). Among colligative factors we have considered : (i) the data characterizing the macro- component (number and size of the core of the micelles), (ii) the surface density of the potential-determining complexes which conditions the distribution of the microcomponents in the layer, and (iii) the distribution of microcomponents in the solution in bulk (inter- lmicellar liquid), The free-energy changes resulting from the differences in distribution of the bearers of colligative properties in the layer and intermicellar liquid have been taken as one of the dominating factors for coagulation and peptization processes.64 COAGULATION AS A CONTROLLING PROCESS There is a large number of factors to be considered in every colloidal system, especially in those where the dynamical processes of coagulation or peptization take place.They are in part specific and mainly chemical in nature ; others may be treated more appropriately in general physical terms.Therefore, it seems reasonable to discuss the coagulation processes according to the specific and non- specific elements from which they may be composed. Following this line of approach we have tried to make a division between experimentally observable constitutive, semi-constitutive, and colligative properties. In this way it might be possible to correlate the results of Berzelius,l Gay-Lussac,Z Selmi,3 FaradayP Schulze,~ Linder and Picton,6 Zsigmondy,7 Hardy,8 Lottermoser,9 Whitney and Ober,10 von Weimarn,ll Freundlich,l2 Oden,l3 Haber,l4 and others, including the experimental and theoretical work on nucleation, crystal growth, adsorption, coagulation and precipitation studies of today. THE PRECIPITATION SYSTEMS First, it is necessary to collect the experimental data about the conditions and kinds of interaction between the constituents of the disperse phase and the components of the dispersing medium.In this respect all the data which are sig- nificant for the appearance or disappearance of a new phase in electrolyte solution may be taken as a convenient basis for considering the specific factors of colloidal stability. Besides the classical von Weimarn’s precipitation curves (precipitation against concentration of the precipitating components in equivalent ratio), it is also necessary to examine typical precipitation curves 15 (precipitation against concentration of one of the precipitating components, the concentration of the other component being constant), and general precipitation diagrams 16 (the concentration of one of the precipitating components against the concentration of the other component).If such curves could be obtained by various techniques and so allow a deeper insight into the relation of size and structure of the precipi- tates, it would be reasonable to expect that many complex and hitherto confusing problems might be solved. We have usually followed precipitate formation or peptization by measurement of the intensity of the scattered light (so-called tyndal- lograms), and in this way much information was obtained in a systematic way. Of special importance are the relations where (i) the ionic solubility, (ii) the complex solubility, (iii) the crystallinity, are connected with (i) the nucleation, (ii) the growth and (iii) the aggregation phenomena.For illustration we may consider systems where the substances have nearly the same ionic solubility, e.g. silver chloride and barium sulphate, or silver bromide and silver thiocyanide. The behaviour of these systems is very different, although there are also some similarities. The main differences are caused by factors con- trolling the formation of complexes and crystal units, the growth into primary particles or micelles, and their aggregation into crystalline aggregates or coagulates. Thus barium sulphate under usual conditions in water solution cannot be obtained as sol in statu nascendi. However, by changing the dispersing medium, e.g., by performing the precipitation in water + ethanol, it is possible to prepare relatively stable sols. It would lead us too far to cite all the possibilities which occur in practice, and therefore only one summarizing diagram for barium sulphate is given in fig.1. By comparing this diagram with typical precipitation curves of silver chloride,l7 many essential differences may be noted. In general, the specific interactions between the substance from which the core of the micelle is composed and the constituents or components of the dis- persing medium may be characterized by various precipitation maxima in the typical precipitation curve, or in the somewhat analogous occlusion and fractional pep- tization cuTve.18 A useful overall picture is obtained from the general precipita- tion diagram showing the limits for the formation of precipitate in a plot of the logarithm of concentration of one of the precipitating components against the other (fig. 2).It is easy to see that our typical precipitation curves are sectionsT E ~ A K , M A T I J E V I ~ , SCHULZ, KRATOHVIL, MIRNXK AND VOUK 65 N CONC.OF Na,SO, ,i N CONC. OF BaCI, FIG. 1.-Precipitation curves of barium sulphate in water and water 4- ethanol, obtained by reaction of barium chloride and sodium sulphate (BaS04, 0.002M). l-mh. tyndallograms. logCx-(N) (X'=CI; BCIY or CNS-) F~IG. 2.-General precipitation diagram for silver chloride, silver bromide, silver iodide and silver thiocyanide systems, C66 COAGULATION AS A CONTROLLING PROCESS through the precipitation region which reflect in more detail the precipitating processes.According to the position and the meaning we have to distinguish: (i) the concentration maximum found between the limits of the complex solubility region and the common-ion stability region, (ii) the crystallization maximum (between limits of common-ion stability region and the ionic solubility region), and (iii) the isoelectric maximum (the equivalency region for the activities of the potential- determining complexes). For systems where the precipitate shows crystalline character, instead of a concentration maximum, a different aggregation maximum is formed.19 It seems to us that many peculiar effects of the stabilization, sensi- tivity, reversibility, etc., encountered with coagulating and precipitating systems could be better understood, if the characteristic differences of the factors which condition the appearances of our maxima and minima of the "precipitation spectra " were taken into account.& NQskM. CQGC. OF Me NITRATE (AgbQiS.WO ON, WirrOO0040 M) LOG NORk COW.OF K (HBr : 0000 K4 N, AgNOa: FIG. 3.-Schematic presentation of typical precipitation and coagulation curves of silver bromide in statu nascendi. Upper part : the precipitation curve showing the positive and negative concentration maximum and the isoelectric maximum, AgBr 0.00001 M, 10-min tyndallogram ; lower part : the effect of coagulating ions on positive and negative silver bromide sol in statu nascendi (Schulze-Hardy rule), AgBr 0.0001 M, 10-min tyndallograms. Some of the limits, especially those which are indicated in the solubility against precipitation curve of the general precipitation diagram, are not sensitive to addi- tion of neutral electrolytes and poly-electrolytes, but they may be very sensitive to the presence of substances which are capable of influencing the formation of potential-determining complexes, which change the solubility relations.In this way it is possible to distinguish the crystallization effects from the coagulation effects.20 CHARACTERISTICS OF COAGULATION In a series of publications21 we have described all the classical coagulation effects with a series of colloidal systems under easily controllable experimental conditions ; evesy system was followed from " birth to death " (sols in statuTEEAK, M A T I J E V I ~ , SCHULZ, KRATOHVIL, MIRNIK AND VOUK 67 nascendi). Thus we observed typical phenomena of coagulation under repro- ducible standard circumstances which enabled us to focus attention on a number of factors which were hitherto ill-defined due to the sparse and scattered experi- mental data.In order to make the presentation of experimental data as short as possible we shall restrict ourselves to material already published ; the new results will be given only for the sake of completeness. Examples of empirical rules and dominant effects are mentioned under special sub-headings. I 1 0 - M i n u t e s Tyndallogram Ag I- I* N i No NO,< I X l d S N 1 oncentration ma x irnum Concentrat i m a x imu in lsoelectric maximum 2 4 6 8 6 4 2 0 FIG. 4.-Schematic presentation of a typical precipitation curve and of critical coagulation regions of coagulating ions for silver iodide sol in statu nascendi. Upper part: the 10-min tyndallogram for silver iodide sol (0.0001 M) showing the complex solubility region (- A and 4 A), the concentration maxima (- B and + B), the isoelectric maximum ( f D), and the common ion stability regions (- C and + C) ; lower part : the effect of concentration of the stabilizing ion on the coagulation values of univalent, divalent and trivalent dominating ions. The Schulze-Hardy rule The Schulze-Hardy rule and the connection between typical precipitation and coagulation curves for silver bromide system are given in fig.3. It has also been shown that the size of the dominating ion is one of the factors controlling the coagulation value.22 The stabilizing-ion efect The effect of the concentration of the stabilizing ion on the coagulation values of univalent, divalent, and trivalent dominating ions is shown in fig.4. The basic scheme is illustrated by a typical precipitation curve for silver iodide; the raagulation concentrations for various dominating ions are represented by shaded areas which are limited by curves connecting the corresponding coagulation values.68 COAGULATION AS A CONTROLLING PROCESS The Burton- Bishop rule We have discussed and explained the rule of Burton and Bishop as the result of a secondary effect of the change of the stabilizing ion concentration caused by adsorption.23 The efect of mixed electrolytes The various effects ranging from sensitization and additivity to superadditivity and antagonism have been exemplified by silver bromide and silver iodide sols in statu nascendi.24 The old results showing that the antagonism of the same pair of electrolytes is much higher for sols of higher charge has been repeated; for instance, for the pair lanthanum nitrate + potassium sulphate the coagulation value of lanthanum nitrate reached 1300 % for silver bromide and 10,000 % for silver iodide. For the pair thorium nitrate + potassium sulphate unusual trends were found with silver iodide, the thorium coagulation value exceeding 100,OOO % of the normal thorium nitrate coagulation value if potassium sulphate was present in a concentration equal to the coagulation value (fig.5). FIG. 5.-The effect of a mixture of thorium nitrate and potassium sulphate on the coagulation of negative silver iodide sol in statu nascendi (AgI, 0.0005 M).The coagulation value of thorium nitrate 00000098 N ; of potas- sium sulphate 0.154 N. % of the coagulation value K, SO, The eflect of dispersing medium In order to see whether the dielectric constant of the dispersing medium is alone responsible for the variation of the coagulation values, some experimental results with water + ethanol and water + acetone mixtures (fig. 6), as well as with water + dioxane mixtures and with solutions of glycine have been obtained and incorporated in the two summarizing plots (fig. 9 and 10). Fig. 7 shows the effects of these mixed media on complex solubility limit in the general precipita- tion diagram. The effect of mixed precipitates If the substance of the core of micelle is of composite nature, e.g.a mixed crystal, or if there is a possibility of formation of several potential-determining complexes with different distribution in the layer, there is a large number ofTEZAK, MATIJEVIC, SCHULZ, KRATOHVIL, MIRNIK AND VOUK 69 possibilities of changing the characteristics of the coagulation processes. Such experiments may be valuable in answering questions concerning the role of specific, semi-specific and non-specific factors in colloid systems, but owing to their com- plexities real progress could be expected only when a fairly large number of similar and dissimilar systems had been thoroughly and systematically investigated.24 FIG. 6.-Coagulation values of potassium nitrate, barium nitrate and lanthanum nitrate for negative silver bromide sols in statu nascendi (AgBr 0.0002 M) in water and different iso-dielectric water + ethanol and water + acetone mixtures in presence of various concentrations of the stabilizing ion (Br-).INTERPRETATION OF DATA It has been mentioned already that there is a large number of factors influencing the stability of colloidal systems. The first step towards explanation would be to bear in mind the morphology of such systems and to distinguish the nature of forces, which-although operating in separate parts-produce cumulative, complex effects characterizing the system as a whole. In fig. 8 a schematic presentation is given of the morphological elements of a colloidal system. We have to distinguish three regions : (i) the core, (ii) the layer and (iii) the interior of the solution (intermicellar liquid).Further, it seems to us that many difficulties encountered in our understanding are due to the failure to grasp the differences and mutual relationships between constitutive, semi- constitutive, and colligative properties of the components involved. In particular it seems convenient to look upon the layer as a special entity. Although the origin of the layer is closely connected with the constitutive properties of the substance composing the core of the micelle on the one hand, and the constituents and components of the solution on the other, a large number of characteristic70 COAGULATION A S A CONTROLLING PROCESS coagulation and peptization phenomena may be interpreted, qualitatively at least, as consequences of concentration.differences of colligative elements in the layer and the solution. The colligative elements have been mentioned in the early attempts to formulate a theory of coagulation. Duclaux 25 compared the osmotic pressure in the inter- micellar liquid with the osmotic pressure which is exerted by the micelles themselves, LOG C,- (MI FIG. 7.-Complex solubility curves of silver iodide in aqueous, ethanolic and acetone solutions of potassium iodide at 20". -- - - D i s p e r s i ng m ed ium 0 - _ _ _ I - =- Microcomp-nt --- Potential determining complex FIG. 8.-Schematic presentation of the morphological elements of a colloidal system : the core (macrocomponent), the layer and the intermicellar liquid. assuming that a ratio of these osmotic pressures would be decisive for the stability of the micelles.Similarly, Langmuir26 has constructed his theory of the forma- tion of tactoids, thixotropic gels, protein crystals and coacervates from con- siderations of osmotic pressures in the colloidal system as a whole. Our approach here is qualitative and somewhat different.TEZAK, MATIJEVI6, SCHULZ, KRATOHVIL, MIRNIK AND VOUK 71 The starting-point is the distribution of potential-determining complex groups on the wall of the micelles. The term ‘‘ potential-determining complex ” is used because it may be the result of specific interactions of the constituents of the two phases, causing the potential differences of the physical and chemical nature between the boundary layer and the interior of the solution.As a consequence, a layer many tens or hundreds of Angstroms in thickness may show a different concentration of the kinetic units responsible for osmotic pressure (microcom- ponents) than is the concentration in the intermicellar liquid. This is the reason for distinguishing the core of the micelles (macrocomponent), the layer-con- ditioned primarily by the surface density of the potential-determining complexes -and the intermicellar liquid. The number and size of the cores of micelles, the thickness of the layer, and the concentration of the microcomponents in the layer, should be compared with the concentration of the similar kinetic units in the volume elements of the same size in the bulk solution. The difference in the state of these two parts of the system may be expressed as the free energy leading to coagulation or peptization processes if the concentration in the layer is smaller or larger than the concentration in the bulk solution.Therefore, the stability conditions may be treated from the point of view: (i) of building or destroying the layer and (ii) of changing the concentration relationship of the microcomponents in the layer and in the intermicellar liquid. As items (i) are controlled by the processes of formation and activity of the potential-determining complex groups, they must be taken as specific for the system under consideration. On the contrary, items (ii), especially when the electrolytes are applied to lyophobic sols, show very frequently the common characteristics expressed in the cited empirical rules.The electrical behaviour has been much stressed in the theory of stability of colloidal systems. However, it seems that the treatment of the double layer as a homogeneous region of idealized electrical properties has not given either simple or experimentally justified results. This provides a reason for starting again from first principles. One of the first steps towards an explanation of the Schulze-Hardy rule was the statistical approach of Whetham 27 giving the coagulation values : cl: c2: c3: c4 = 1 : i / X : 11x2: 11x3, for univalent, divalent, trivalent, and tetravalent ions (for x = 40, and C1 = 0.1 they are in the ratio of 0.1 : 0.0025 : 0.00007 : 0.0000015 N, which agrees fairly well with coagulation values for silver iodide sol).Whetham’s picture may be developed further by including the elementary interaction between the ions fixed on the wall and the ions in the solution, with the assumption that the crilcal condition for coagulation is reached when the coulombic interaction between ions in the layer has attained a fixed frequency ratio to the similar processes in the bulk solution. As the main elementary process in such a system may be represented by Bjerrum’s relationship, dc = ztz-e2/2DkT, we have followed the coagulation values of various ions in different dielectric media by using the plot of critical distance against the logarithm of the coagulation value. Fig. 9 gives such a relationship for silver bromide in water + ethanol, water + dioxane and water + acetone, as well as in 1.0 and 2.0 M glycine solutions.The differences between various media of the same dielectric constant may be attributed to the complexing action of these media as shown in fig. 7. Fig. 10 shows also the linear relation- ship between the critical distance dc and the logarithm of the coagulation values for potassium, barium and lanthanum ions in media of different dielectric constants. As the logical next step towards an explanation of the complex effects of a mixture of electrolytes, it seems appropriate to use Ostwald’s concept of the cor- responding physical chemical states of the ions in a dispersing medium. Accord- ing to Ostwald 28 the coagulation should take place at approximately the same value of the activity coefficient of the dominating ion. If there were no specific72 COAGULATION AS A CONTROLLING PROCESS interactions, many phenomena could be described in this way.The specific adsorbability or the special dynamic structures of the ions in the layer and in solution may give a different picture. From this elementary interpretation of experimental material we may proceed to the consideration of electrokinetic phenomena. Although there are some doubts about the reliability of experimental values of zeta-potential, a large FIG. 9.-Plot of Bjerrum’s distance against the logarithm of coagulation values of potas- sium nitrate, barium nitrate, and lanthanum nitrate ; silver bromide sol in statu nascendi in water + glycine, water + ethanol, water + acetone and water + dioxane media. FIG. 10.-Plot of Bjerrum’s distance against the logarithm of the coagulation values of univalent, divalent, trivalent and tetravalent dominating ions ; negative silver bromide sol in statu nascendi in water, water + glycine, water 3.ethanol, water .+ acetone and water + dioxane. number of important data may be collected by careful comparison of the results of electrophoretic, endosmotic and streaming-potential determinations with those of adsorption, stability, electrode reactions and others9 We are here concerned with a number of different fields of experimental and theoretical, chemical, physical, and biological, pure and applied researches.TEZAK, M A T I J E V I ~ , SCHULZ, KRATOHVIL, MIRNIK AND VOUK 73 Therefore it is not surprising to find, in spite of the lack of convincing experiments, many theories.Some of them are comprehensive and elaborate, aiming to give not only the qualitative but also the quantitative aspects of the problem.30 It may be said that all theories of colloidal stability are somewhat too speculative and unable to embrace many important experimental findings. This is the reason that, for the time being, it seems much more appropriate to put the emphasis on a step-by-step development of principles, and clear-cut experimental checks of those parts of the theories which could be applied directly in limited and experimentally consistent regions. 1 Berzelius, Urbok i kemien (Stockholm, 1808-30) ; cited in Hatschek’s The Foundation 2 Gay-Lussac, Instruction sur l’essai des matizres d’argent par la uoie humide (Paris, 3 Sehi, Nuovi Ann.di Scienze Naturali di Bologna, 1845, 4 (2), 146. 4 Faraday, Phil. Mag., 1857, 14, 512. 5 Schulze, J. prakt. Chem., 1882, 25, 431. 6 Linder and Picton, J. Chem. SOC., 1895, 67,63. 7 Zsigmondy, Annalen, 1898, 301, 361. 8 Hardy, Proc. Roy. SOC. A, 1900, 66, 110. 9 Lottermoser, J. prakt. Chem., 1905, 72, 39. 10 Whitney and Ober, Z. physik. Chem., 1902,39,630. 11 Von Weimarn, Kolloid-Z., 1908, 2, 301 ; 3, 282 ; Grundzuge der Dispersoidchemie Die Allgemeinheit des Kolloidzustandes (Dresden and Leipzig, 12 Freundlich, 2. physik. Chem., 1910, 73, 385. Freundlich, Joachimson and Ettisch, 13 Oden, Arkiv Kemi, Min. Geol., 1920, 7, 26; Svensk Kem. Tidskr., 1932, 44, 65. 14 Haber, Ber., 1922,55, 1717. 35 Teiak, Z. physik. Chem. A, 1935,175,219. 16 Pinkus and Timmermans, Bull. SOC. chim. Belg., 1937, 46,46. 17 Teiak, Glas. Hem. DruJtva Kz. Yugosl., 1933, 4, 137; Kolloid-Z., 1934, 68, 60; 2. physik. Chem. A, 1942,191,270. 18 Teiak, Z. physik. Chem., 1936, A 175, 284 ; B 32,46, 52. 19Teiak, Arhiu. kem., 1947, 19, 9. 20 Tefak and Kratohvil, Arhiu kem., 1952, 24, 67. 21 Teiak, Matijevik and Schulz, J. Amer. Chem. SOC., 1951,73, 1602, 1605 ; J. Physic. 22Teiak, 2. physik. Chem. A, 1942, 191, 270; Teiak, et a!., J. Physic. Chem., 1953, 23 Teiak, Matijevi6 and Schulz, J. Physic. Chem., 195!, 55, 1567. 24 Teiak, Matijevi6, Schulz, Kratohvil, Wolf and Cernicki, J. Colloid Sci., suppl. 25 Duclaux, Kolloid-Z., 1910, 7, 73. 26 Langmuir, J. Chem. Physics, 1938,6, 873. 27 Whetham, Phil. Mag., 1899, 48, 474. 28 Ostwald, Kolloid-Z., 1935, 73, 301 ; 1941,94, 169. 29 Mirnik and Teiak, Trans. Faraday SOC., 1954,50, 65. 30 Derjaguin, Trans. Faraday SOC., 1940, 36, 203. Levine and Dube, Trans. Faraday SOC., 1940, 36, 215; J. Physic. Chem., 1942, 46, 239. Levine, J. Colloid Sci., 1951, 6, 1. Verwey and Overbeek, Theory of the Stability of Lyophobic Colloids (New York, 19481. Loeb, J. Colloid Sci., 1951, 6, 75. of Colloid Chemistry. 1832). (Dresden, 19 1 1). 1925); Chem. Rev., 1925,2,217. 2. physik. Chem. A, 1929, 141,249. ’ Chem., 1951,55, 1558, 1567; 1953, 57,301. 57, 301. vol. 1, 1954.

ISSN:0366-9033    

DOI:10.1039/DF9541800063

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

THE RATE OF COAGULATION AS A IYEASURE OF THE STABILITY OF SILVER IODIDE SOLS BY H. -RINK* AND J. TH. G. OVERBEER van’t Hoff Laboratory, University of Utrecht Received 25th June, 1954 The form of the energy barrier between two sol particles is calculated from the electrical repulsion and the van der Waals attraction. Flocculation is retarded by this barrier, and the retardation factor W of the slow coagulation as compared to the rapid coagulation of the same sol is connected to it. It follows from numerical computations for monodisperse sols with spherical particles : (a) the value of W is mainly determined by the height V, of the energy barrier ; (b) there is a nearly linear relationship between log W and log c,, c, being the con- Approximate equations are derived for the relation between W and Vm, and between W and the concentration and valency of the electrolyte, the van der Waals constant, the surface potential and the particle radius.Experiments were performed to test the theory. Various silver iodide sols were mixed with various electrolytes. By means of different sol and electrolyte concentrations a range of 104 in W was covered. The change in turbidity was used to measure the rate of coagulation, This method worked well with polyvalent gegenions while there were some complications with mono- valent ions. The theory is confirmed by our own experimental results and by work of other authors as far as the linear relationship between log W and log ce is concerned. For small par- ticles absolute values of the surface potential and the van der Waals constant as derived from the slow coagulation agree reasonably well with other estimates.With coarser sols the calculated value of the surface potential was definitely too low. centration of electrolyte. The stability of lyophobic colloids depends upon the energy of interaction between two approaching particles. According to Verwey and Overbeek 1 this energy is composed of a long range electrical repulsion and a long range van der Waals attraction. For a given colloid the attraction is assumed to be constant whib the repulsion changes with the electrolyte content of the system. With decreasing repulsion the stability decreases. When there is no repulsion every collision of two colloidal particles leads to coagulation (rapid coagulation).When the repulsive energy is not zero only a fraction 1/W of the collisions leads to coagulation (slow coagulation). With increasing repulsion the value of W increases. Therefore W can be used as a quantitative measure of the stability, and we will call W the stability factor. No lyophobic sol is absolutely stable against coagulation ; that is W is always finite. However Wmay be so large, e.g. W > 109 that a sol in this state does not change perceptibly in many years. A relation between the stability factor W and the energy of interaction can be derived from the theory of Verwey and Uverbeek. It is the purpose of this paper to test this relation and some of its implications. * Present address : Koninklijke/Shell Laboratory, Amsterdam. 74H . REERINK AND J .TH. G . OVERBEEK 75 I. THEORETICAL PART 1. INTERACTION OF COLLOIDAL PARTICLES. The energy of interaction has been calculated for the models of infinite plane particles and of spherical particles. In our experiments we used silver iodide sols with relatively small particles which from electronmicrographs 2 were shown to be nearly spherical. Therefore we chose the spherical model. (i) Structure of the double layer. As far as the stability is concerned the following model of the double layer will suffice.3 The particle surface acquires a surface charge by adsorption of potential determining ions. A layer of gegenions adheres to the surface forming an ionic condenser, the Stern layer.4 From here the diffuse part of the double layer extends into the solution.% 6 The repulsive energy depends upon the potential across the diffuse part of the double layer, $8 (Stern potential), and the concentration and valency of the gegenions in the solution.1 (ii) Interaction of spherical difuse double layers. The electrical energy of interaction between the overlapping double layers on two spherical particles of equal size V g , calculated according to Verwey and Overbeek, appears to be positive which means that the particles repel each other. An approximate ex- pression reads 7 (at 25" C in water as a solvent) : V T = 4.62 x 10-6 (ay2/u2) exp (- KHO) = 4.62 x 10-6 (ay2/v2) exp (- TU) = C exp (- TU), y = (ez/2 - l)/(& + l), z = ve$a/kT, v = valency of gegenions, K = (8~rnv*ez/~kT)* is the familiar expression in the theory of Debye and Huckel8 ; 1 / ~ is a measure of the thickness of the diffuse double layer.7 = KU, u = Ho/a, a = particle radius. HO = shortest distance between particle surfaces, An equation for the repulsion between two unequal spheres of radii a and b can be derived in the same way as (1.1). Vf= 2b/(a + b) x V $ = q T ; b > a, (1.2) (iii) Forces of attraction. The concept of long range van der Waals forces was first introduced in colloid chemistry by Kallmann and Willstatter,g and theoretically developed by de Boer 10 and Hamaker.11 In the stability theory of Venvey and Overbeek these forces play an importantrole. Sparnaay 12 succeeded in measuring directly forces of the predicted order of magnitude. An approximate expression for the attraction potential between two spheres for short distances (u < 1) is given by Hamaker (1.3) vy = - 2b/(u + b) x A/12U = - q A/12U = q VT, where A is the van der Waals constant.iv) Total energy of interaction. The total energy V is the sum of the repulsive and attractive potentials V(4 = VR (4 + VA (4 (1.4) Fig. 1 shows the influence of electrolyte concentration c, on V, calculated with complete expressions for attraction and repulsion and with the approximations (1.1) and (1.3). It appears that the approximate curves are much too low. The main cause for this is a failure of eqn. (1.3) in this region of u values. Notwithstanding this systematic error the approximate equations are still quite useful as will be pointed out in 0 4 (ii). 2. THE RATE OF COAGULATION. The kinetics of rapid coagulation of monodispersed sols have already been described in 1916 by von Smoluchowski,l3 who considered the process as a diffusion of the colloidal particles towards each other.It has been shown by Muller 14 that normal polydispersity has little influence on the results.76 RATE OF COAGULATION With regard to the slow coagulation von Smoluchowski assumed that the stability factor W remained constant during the whole process. Experiments show that this is by no means true : 15,16 the rate of coagulation decreases in the course of slow coagulations. "/kT 5- - 0. - _ I I I , 0 0. I 0.2 0 . 3 0.4 u FIG. 1 .-Energy of interaction as a function of particle distance for equal spheres. Drawn curves : exact calculations according to Verwey and Overbeek, and Hamaker. Dashed curves : approximated with (1.1) and (1.3) a = lO-Gcm, A = 10-12 erg, v = 1.z = 3. Curves I : ce = 59-5 mmole/l. Curves I1 : ce = 93 mmole/l. 4 '1 kT 3 C FIG, 2.-Energy of interaction and corresponding values of exp (Y/kT)/(u + 2)2. a = 10-6cm, A = 10-12 erg, v = 1, z = 3. Drawn curves : c2 = 75 mmole/l. Dashed curves : c, = 93 mmole/l. This is explained by the fact that, other conditions being equal, the repulsion between aggregates is larger than that between single particles. Since we want to characterize the stability of the original sol and not of the aggregates, the value of W must be extra- polated to zero time.H. REERINK AND J . TH. G . OVERBEEK 77 Considering the slow coagulation as a diffusion process in a potential field Fuchs 17 derived a relation between the energy of interaction V and the stability factor W.du exp (V/RT) ~ (u + 212 From potential curves of the type given in fig. 1 the value of W can be evaluated by graphical or numerical integration. In fig. 2 two potential curves and the corresponding values of exp (V/kT)/(u + 2)2 are given. It appears that the value of W is mainly deter- mined by the maximum V, in the potential curve, the width and shape of the exponential curves being about the same. From plots of log W against log c, a nearly linear relationship is found (see fig. 3). At high electrolyte concentrations the repulsion is zero and W = 1. The bend in the curves lies in the region where V,/kT = 1. 0 i I I I I I 1 I I -0.5 8 0 - 5 1 0 1.5 2.0 2-5 loglo c e FIG. 3.-Relation between stability factor and electrolyte concentration c, (mmole/l.) Curve I : a = 10-6 cm.A = 2 X 10-12 erg. v = 2, z = 6, Curve I1 : a = 10-6cm. z = 5, Curve 111: a = 5 x 10-6 cm. z = 5, A = 2 x 10-12 erg. A = 2 x 10-12 erg. v = 1, co = 1, 3. INFLUENCE OF POLYDISPEKSITY AND STERN POTENTIAL. It can be shown18 that polydispersity tends to stability curves which are slightly concave towards the axes. On the other hand the Stern potential $8 decreases somewhat with increasing electrolyte concentration, which effect tends to give convex curves. Both influences are difficult to estimate. Since they are opposite to each other and from experiments nearly straight curves are obtained we neglected both effects and used the theory for mono dispersed sols with constant $a. 4, DERIVATION OF APPROXIMATE RELATIONS.To avoid the laborious computations of the exact Verwey and Overbeek theory two approximate equations were derived. One has the form W = k exp V,, indicating that the stability factor W is determined by the maximum V, in the potential curve. The other starts from the approximate equations (1.1) and (1.3) and leads to a linear relationship between log Wand log c,. (i) The maximum in the potential curve. For V , > kT only the values of exp (V/kT)/(u+2)2 which lie in the neighbourhood of the maximum contribute to the integral in (2.1). In this region (u + 2) only changes a few per cent. Therefore we write (u, 3- 2) instead of (u + 2), where u, corresponds to the maximum V,. From (2.1) we obtain : 00 W = 2/(u, 4- 2)2 1 exp (V/RT) dii (4.1) 078 RATE OF COAGULATION Expanding V(u) in the neighbourhood of V,,, in a Taylor series gives V = V, + Vz(Au)2/2 + .. . (4.2) Using (4.2) and neglecting higher terms the exponential curve is replaced by a Gauss as V; = 0. curve with the same height and the same curvature in the maximum. - _- (vm'kT) exp [- pZ(Au)2] d(Au)f p = (- Vi/2kT)*. (4.3) (u, + 2)* rum Replacing the lower limit of integration by - co, which introduces only a negligible (4.4) In the appendix it will be shown that p(u, 3- 2)2 is practically constant. Thus W is determined by V,. With the help of eqn. (4.4), Wcan be evaluated from the potential curves without the tedious graphical integration of the exponential curves. In fig. 4 this procedure is com- pared to the complete calculation.It appears that eqn. (4.4) is rather a good approxima- tion, except evidently in the region where Vexact approaches the value 1. (ii) The lineuv relation between log Wand log Ce. derived (see appendix) : error, we obtain : W = 2&/p(urn + 2)2 x exp (VJRT) Starting with the approximate equations (1.1) and (1.3) the following relation can be log W = - (A/24 u,kT) log Ce - (A124 u,kT) log (SrNv2e2u2 10-6/ckT) + (3/2 - A/12umkT) log urn + Slog 96rkTIA - + log (2 - Turn) (urn + 214 = - kl log ce + k2 (4.5) In fig. 4 curves calculated from eqn. (4.5) are shown together with the exact curves and where kl and k2 are constants, and N is the Avogadro number. the approximation (4.4). 109,0W FIG. 4.-Relation between W and c, for different approximations. Left set of curves : a = 10-6 cm.A = 2 x 10-12 erg. z = 6. v = 2. Right set: u = 10-6 cm. A = 10-12erg. z = 3. v = 1. exact calculations. approxima tion (4.4). approximation (4.5). Drawn curves : Dashed curves : Interrupted curves : 0.5 0 0.5 I 1.5 ;? At first sight eqn. (4.5) appears to be a bad approximation. In the first place the curves lie much too low. This is readily explained, because the approximate energy curves lie much lower than the exact ones (see fig. 1). As the absolute values of the ap- proximatioils for the repulsive and attractive energies are both too large a nearly exact compensation of errors occurs for certain combinations of $& and A (for instance Q = 10-6, A = 3 x 10-13, z = 3, ZI = 1). Secondly, the curves are not straight. This is explained in the appendix.Nevertheless eqn. (4.5) is useful to calculate the slope of the stability curve. This slope is given by (see appendix) (at 25" C in water as a solvent) : '0% CG! (4.6) dlog - w- __ - 2.15 X 107ay2/v2 d log c,H . REERINK AND J . TH. G . OVERBEEK 79 If one point of the curve is obtained with the exact theory or with eqn. (4.4) the re- mainder can be calculated conveniently with (4.6). Table 1 shows that exact and approxi- mate slopes are in reasonable agreement. It may be remarked that according to both calculations the value of A has no influence on the slope of the stability curves. The slope is proportional to the radius of the particles and increases with increasing surface potential. TABLE 1.-cOMPARISON OF EXACT AND APPROXIMGTE SLOPE. dlog W a A 2 0 d log ce cm erg exact approximation (4.6) 10-6 10-12 3 1 - 6.6 - 8.6 10-6 2 x 10-12 3 1 - 6.6 - 8-6 10-6 2 x 10-12 5 1 - 14.0 - 15.3 10-6 2 x 10-12 6 2 - 4.9 - 44 5 x 10-6 2 x 10-12 5 1 - 72 - 76 5.EVALUATION OF STERN POTBNTIAL AND VAN DER WAALS CONSTANT FROM EXPERIMENTAL STABILITY CURVES. The slope of the stability curves immediately leads to y and to the Stern potential $8 with the help of eqn. (4.6) and (1.1). With $6 as determined in this way stability curves are constructed for a number of values of the van der Waals constant A. These curves are all parallel. The value of A belonging to the experimental curve can now be determined by interpolation. 6. APPENDIX. The linear relationship between log Wand log c, For two particles of equal size the total energy of interaction follows from (1.1) and (1.3) : V(u) = Cexp (- TU) - A/12u.(6.1) (6.2) (6.3) The maximum of V (u) is obtained when Cexp (- Turn) = ~ / 1 2 7 4 . Combination of (6.1) and (6.2) gives In practical cases the values of T U ~ lie in the neighbourhood of 1 and u, changes only Eqn. (6.3) shows that for V, = 0 the value of TU, exactly equals 1 and by differen- Vm = A / 1 2 ~ , X (117 Um - 1). very slowly with T. tiating eqn. (6.2) it is found that which is zero for TUm = 1. consider TU, w 1 and u, as a constant. As the flocculation conditions are always close to the case where V, = 0, we may We thus may write From (4.4), (6.3) and (6.5) we obtain IITUm - 1 = - In TUm. (6.5) log W = - (A/12urnkT) log T - (A/12~,&2') log + log 2n* - logp (Urn + 2)' (6.6) (6.7) And from (4.3) and (6.1), p2 = - c / 2 k T = A/24kT X (2 - TUm)/Ui.Combination of (6.6) and ( 6 . 9 , with the help of the delinitions in ( l . l ) , leads to : log W = - (A/24u,kT) log Ce - (A/24umkT) log (8dWe2a2 lO-6/ckT) + (312 - A/12~,kT) log + *log 96~kT/A - 4 log (2 - TUm) (u, 4- 2)'s (6.8) where Ce is expressed in mmoles/l., and N is the Avogadro number.80 RATE OF COAGULATION Since on changing ce the changes in (2 - 7um) and u, are small compared to the changes Therefore, (6.9) in ce all terms in (6.8) except the first one may be considered to be constant. log W = - kl log ~e + k2, see eqn. (4.5). It is clear that eqn. (6.5)-(6.9) only hold in a relatively small region of walues. Application of (6.8), outside this region and taking the non-constancy of u, into account will result in curved stability curves (see fig.4). The slope k1 still contains u,. This may be eliminated by calculating u, from eqn. (6.2) using the condition that TU, = 1. This leads to urn = AeJl2C. (6.10) Inserting this value into eqn. (6.8) the slope of the stability curve is found to be (at 25" C and using water as a solvent) dlog WJd log Ce = - C12elt.T = - 2.15 X 107 L Z Y ~ / V ~ . (6.1 1) 11. EXPERIMENTAL TEST OF THE THEORY The theory has been tested by specially designed experiments on silver iodide sols and by using data already present in the literature. 7. PREPARATION AND CHARACTERIZATION OF AgI-SOLS. here to the bare outlines. Details of our experiments on AgI will be reported elsewhere. We will restrict ourselves In order to test the influence of particle size, five sols were used.Sol A was prepared by mixing dilute solutions of AgN03 and KI, followed by electro- dialysis and electrodecantation using the methods described by de Bruyn and Troelstra.19 Sol B consisted of the fine particles of sol A, that did not settle after centrifuging during 3 hours at about 2000g. Sol C consisted of the coarse particles of sol A obtained by careful sedimentation. Sol D was obtained from sol A by ageing at 95" during 50 hours. Sol E was prepared following Troelstra 20 by pouring a solution of AgI in concentrated All the sols used were brought to pI = 4 with KI. Particle sizes were determined by sedimentation, turbidity measurements (using Rayleigh's law) or from electronmicrographs. Although none of these methods gives very accurate results, table 2 shows a reasonable agreement between different methods.KI into water under vigorous stirring. TABLE 2.-PARTICLE RADIUS IN A OF DIFFERENT AgI SOLS SolA solB so1 C sol D sol E 250 550 - 1560 I 2000 rate of sedimentation (minimum value) electronmicroscope (number average) - - - - turbidity (weight average) 520 205 520 650 - 8. DETERMINATION OF RATE OF COAGULATION AND STABILITY FACTOR. In most cases the rate of coagulation was determined from turbidity. In the case of coagulating hydrophobic systems, light scattering is not suited to determine absolute values for the number of particles because the scattered light is not in a simple way related to the size of the aggregates. It may be assumed, however, that the scattering is uniquely determined by the state of coagulation, irrespective of the rate at which it is reached.Therefore rates of coagulation can be compared with each other by measuring the times after which a certain amount of scattering is obtained. This comparison is simplified by the fact that extinction-time curves all start with a linear part in agreement with calculations and observations by Troelstra 21 and Oster.22 Fig. 5 gives a few of our observations on the flocculation of Sol A with Ba(N03)~.H. REERINK A N D J . TH. G. OVERBEEK 81 The slopes of the curves for zero time are proportional to the rate of coagulation or inversely proportional to the stability factor W, dE/df cc 1/W. (8.1) In order to cover a large range in W without getting involved in measurements at very short or inconveniently long times the sol concentration was varied.As coagulation is essentially a " bimolecular " process the rate of change of extinction is given by dE/dt cc C,2d/W, or 1/W cc (dE/dt)/(CS2d), (8.2) where C, is the sol concentration and d the length of the light-path in the sol. It was verified that the Lambert-Beer law holds up to extinctions of about 1.2. This method of determining W from eqn. (8.2) was very successful for flocculations with bi- and trivalent ions, With monovalent ions some complications arose. The ex- tinction was too high, probably due to a rearrangement of the primary particles in the aggregates. The stability curves ( W against ce) were therefore extrapolated to infinite sol concentration where the rate of this secondary rearrangement could be neglected compared to the rate of flocculation.E x 103 I I I 5 10 15 M inutcz s FIG. 5.-Extinction against time for different Ba(N03)~ concentrations indicated by the numbers (in mmole/l.). Sol A. Concentration 0.1 mmole/l . AgI. For the very coarse sol E the extinction changed only very little during flocculation. In this case the rates of flocculation were evaluated by counting the particles in the ultra- microscope. For a single example (sol C with Ba(NO&), table 3 shows all the values of the stability factor obtained at different sol concentrations and electrolyte concentrations. TABLE 3.-vALUES OF 103/C,2d X dE/dt = Const/ W FOR SOL C AS A FUNCTION OF Ba(N03)z CONCENTRATION. &L CONCENTRATIONS IN MMOLE/l. PI = 4 ce = 5.0 2.5 2.2 2.0 1.8 1.65 1.5 1.4 1.2 rapid flocculation C, =1.16 - - - - 28 14 6.2 2.8 0-52 0.58 - 285 137 74 25 12 5.9 0-145 2040 238 - 71 0.29 I - 143 - The proportionality constant is evaluated from rapid flocculations, where W = 1.82 RATE OF COAGULATION 9.DISCUSSION OF THE. STABILITY CURVES Stability curves for the AgI sols A-E are pictured in fig. 6. The linear relationship required by the theory is confirmed. In fig. 7 stability curves are given which are calculated from coagulation measure- ments by other authors. In addition it may be mentioned that already in 1912 Paine 23 gave an empirical relation : log W = k - p log ce, with p as a constant between 5 and 6. The slopes in fig. 7 range from - 2 to - 14. FIG. 110 63 C e 6-Stability curves for silver iodide sols.Electrolyte concentration in mrnole/ 1. 4BsolA; OsolB; CIsolC; x solD; AsolE. W " \ FIG. 7.-Stability curves for various sols. AgI sol, Lepin and Bromberg ; 24 V gold sol (steep curve), Tuorila ;I6 8 WO3 sol, Hermans ;25 0 AgI sol, Hermans;25 V gold sol (flat curve), Westgren ;26 x &2S3 sol, Hofmann, and Wannow ;27 + selenium sol, Van Arkel and Kruyt.*s Although the linear relationship is in accord with theory, eqn. (6.11) is not con- firmed as far as the proportionality between slope and partide radius is concerned. For Ba(NO3)2 there is no significant difference between the fine sol B on the one hand and sols A, C and D on the other. The coarse sol E shows qualitatively the predicted effect that its stability curve is steeper than and intersects the curveH .REERINK AND J . TH. G . OVERBEEK 83 of the finer sols but the slopes d log W/d log Ce are not proportional to a. For KNO3 the results are still worse, the fine sol B having the steepest slope. There are only very few older publications on the influence of particle size on slow coagulations. Westgren 26 measured rates of coagulation of three mono- disperse gold sols with particle radii of 490 A, 770 A and 1200 A at various electro- lyte concentrations, and could not find any difference between them. Tuorila 16 on the other hand showed that in a mixture of two gold sols (a = 20A and 250A) at a rather high electrolyte concentration the coarse particles coagulated at a much higher rate than the small ones. It may be assumed that had the same value for both kinds of particles in this mixture, while in Westgren's experiments may have had different values for the various sols.Holliday28 demonstrated a higher stability for larger particles. In a very fine gold sol the primary particles became unstable upon dialysis (low ce!) and coagulated, forming aggregates of two primary particles which did not flocculate any further. Application of the theory of Verwey and Overbeek leads to the plausible value of The results of van Arkel and Kruyt 15 on selenium sols show rather large differ- ences in coagulating rate at nearly the same particle size. Here, too, nothing was known about t,b&. It seems permissible to draw the conclusion that there is an influence of particle size, but this influence is over-estimated by eqn. (6.11).Possible reasons for this discrepancy may be deviations from spherical shape, or imperfections of the theory of interaction of spherical double layers. Yet we have used eqn. (6.11) to evaluate #d and A (see $ 5). The results are given in table 4 for our silver iodide sols and in table 5 for those sols of fig. 7 for which particle sizes are known. w 100 mV. TABLE 4.-vALUEs OF STERN-POTENTIAL AND VAN DER WAALS CONSTANT electrolyte sol a A A x 1012 erg $6 dlog W d Iog ce mV KNO3 A 520 - 5.9 - 24 0.05 B 250 - 10.6 - 48 0.2 E 2000 - 7.3 - 14 0.02 Ba(N03)2 A 520 - 8.0 - 30 0.4 B 250 - 8.0 - 53 0.9 C 520 - 8.0 - 30 0.4 D 650 - 8.0 - 26 0.3 E 2000 - 11-0 - 12 0.2 La(N03)3 A 520 - 5.8 - 28 1.0 TABLE 5.-vALUES OF STERN-POTENTIAL AND VAN DER WAALS CONSTANT sol electrolyte a A author8 dlog W $8 A X 1012 dlogc, mV erg gold LiCl 350 - 14 - 48 0.6 Tuorila 16 KCI 350 - 14 - 48 0.6 CSCl 3 50 - 14 - 48 0.6 gold LiCl 900 - 4.0 - 15 0.1 Westgren 26 NaCI 900 - 2.0 - 10 0.05 selenium KCl 500 - 13.0 - 37 0.2 Van Arkel 520 - 4.7 - 20 0.05 and Kruyt 15 620 - 5.8 - 20 0.1 560 - 6.2 - 24 0.2 and Kruyt 15 620 - 11.8 - 35 0.5 selenium BaC12 560 - 5.0 - 21 0.2 Van Arkel84 RATE OF COAGULATION The values of $d have the expected order of magnitude (10-100 mV) although as a rule they are rather on the low side.This is especially striking for the coarse sol E and Westgren’s gold sol. On the other hand the rule of Schulze and Hardy is obviously obeyed in all cases mentioned and this points to (see ref.(l), p. 119) a rather high value of the surface potential (> 25 mv). It may be that the particle radius a has been over-estimated in so far that it is rather the radius of curvature at protrusions on the particle than half its diameter that determines its interaction with other particles. Tables 4 and 5 also give the van der Waals constant A calculated in the way described in 6 5. The values are in agreement with other estimates derived from flocculation values and from London’s theory. The great scatter in A for one sol shows that there are still serious shortcomings in the theory, but the assumption of a lower value for the effective particle radius a as indicated above would bring the van der Waals constants more in line with the values found for the smallest sol particles.Our results might be summarized in the following way. Taking into account the comparative crudeness of the theoretical approach the agreement with experi- ments is satisfactory. The straight line relationship and the fact that we find the correct order of magnitude of surface potential and van der Waals constant confirm the present picture of the stability of hydrophobic colloids. It certainly is desirable to improve both theory and experiments. Good experiments with truly spherical particles (e.g. with emulsions) are especially desirable. 1 Verwey and Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier, 2 Harmsen, van Schooten and Overbeek, J. Colloid Sci., 1953, 8, 64. 3 Mackor, Rec. trm. chim., 1951, 70, 841. 4 Stern, 2. Elektrochem., 1924, 30, 568. 5 Gouy, J. Physique Rad. (4), 1910, 9, 457; Ann. Physique (9), 1917, 7, 161. 6 Chapman, Phil. Mag. (6), 1913, 25, 475. ’ref. (l), p. 140. 8 Debye and Huckel, Physik. Z., 1923,24, 185; 1924, 25,97. 9 Kallmann and Willstaetter, Naturwiss., 1932, 20, 952. 10 de Boer, Trans. Faraday SOC., 1936, 32,21. 11 Hamaker, Physica, 1937, 4, 1058. 12 Overbeek and Spamaay, Proc. K. Akad. Wetensch. B, 1951, 54, 387. 13 von Smoluchowski, Physik. Z., 1916, 17, 557, 585; 2. physik. Chem., 1918,92, 129. 14 Mueller, Kolloidchem. Beih., 1928, 26, 257 ; 1928, 27, 44. 15 van Arkel and Kruyt, Rec. trav. chim., 1920, 39, 656 ; 1921,40, 169 16 Tuorila, Kolloidchem. Beih., 1926, 22, 191 ; 1928, 27,44. 17 Fuchs, 2. Physik., 1934, 89, 736. 18 Reerink, Thesis (Utrecht, 1952). 19 de Bruyn and Troelstra, Kolloid Z., 1938, 84, 192. 20 Troelstra, Thesis (Utrecht, 1941). 21 Troelstra, Kolloidchem. Beih., 1943, 54, 225. 22 Oster, J. Colloid Sci., 1947, 2, 290. 23 Paine, Kolloidchem. Beih., 1912, 4, 24. 24 Lepin and Bromberg, Acta physicochim., 1939, 10, 83. 25 Hermans, Rec. trm. chim., 1939, 58, 139, 725. 26 Westgren, Arkiv. Kemi, Mia Geol., 1918, 7, no. 6. 27 Hofmann and Wannow, Kolloid Z., 1938,83,258. 28 Holliday, Trans. Faraduy Soc., 1950, 46,440, 447. Amsterdam, 1948).

ISSN:0366-9033    

DOI:10.1039/DF9541800074

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

A THEORY OF THE HETEROCOAGULATION, INTER- ACTION AND ADHESION OF DISSIMILAR PARTICLES IN SOLUTIONS OF ELECTROLYTES BY B. V. DERJAGUIN* Academy of Science of U.S.S.R., Institute of Physical Chemistry, Laboratory of Surface Phenomena Received 3rd August, 1954 The theory of interaction of charged surfaces in electrolyte solutions based on com- puting the energy of overlapping of ionic atmospheres has up till now been applied only to the symmetrical case of two equally charged surfaces, or to wetting films with zero charge at their outer boundary when it is easy to reduce this system to the symmetric one. But there exist many phenomena, for instance coagulation of mixtures of sols, coacerva- tion, dyeing, flotation? etc., which require consideration of the asymmetric case of unequally charged surfaces.Using the method of “ isodynamic curves ” it is possible to obtain the solution of the problem for any electrolyte and any constant value of the surface potentials. The most important property of electric repulsion of surfaces having charges of like signs is the existence of a maximum value of the repulsion at a definite gap-width between both surfaces which is independent of the maximum potentials of both surfaces. This rule holds strictly being independent of the form of either surface. Diverse criteria of stability are found theoretically. Two fundamentally distinct cases should be distinguished according to whether the net result of van der Waals’ inter- actions leads to mutual attraction or mutual repulsion of both bodies-the latter case being impossible when both bodies are similar in material.In the former case a modifica- tion of Eilers and Korff’s rule is given, which is adapted to the case when one surface remains always strongly charged and the charge of the other one may acquire any value near to zero. In the other case the adhesion of surfaces or coagulation is only possible when the charges of both surfaces have unlike signs and the electrolyte concentration is not very high. When in addition both surfaces are strongly charged, an equation is obtained giving the critical concentration beIow which coagulation begins. This equation is very similar in form to that deduced by Landau and myself and includes the modified Hardy- Schulze’s and Wolfe-Ostwald’s rules, but in contrast to it contains the valencies of anions and cations symmetrically.Such a reversed Hardy-Schulze’s rule is in accordance with the experiments of Frumkin, Gorodetskaja and Titijevskaja on adhesion of mercury drops to glass in electrolyte solutions on dilution. Both these experiments and the theory developed can explain the mechanism of the bipolar coacervation. The present theory of interaction of unlike surfaces is in accordance with many facts in the fields of heterocoagulation and mutual coagulation of sol mixtvres. For instance, this theory explains the existence of group coagulation in some cases and disorder coagulation-in other ones, the fixation of dye particles prior to the onset of homogeneous coagulation, and many other phenomena. 1. In the preceding papers of the present author published in 1937-41 a theory of interaction of particles 1 and coagulation of hydrophobic colloids was developed.It led to the establishment of criteria for the adhesion of particles and coagulation of hydrophobic sols and suspensions, both weakly 2 and strongly 3 charged. These criteria theoretically substantiate the revised rules of Hardy and * The content of 6 1 is based on the work performed in collaboration with Prof. V. G. Levich. 8586 THEORY OF HETEROCOAGULATION Schultze,*3 Ostwald,3 and Eilers and Korff.” 5#7 This theory is based on calcula- tions for the symmetrical case of interaction in an electrolyte solution (taking account of the van der Wads forces) for similar particles charged to the same potential. However, the development of the theory of heterocoagulation, i.e.coagulation of mixtures of dissimilar particles, as well as the theory of adhesion of particles to surfaces of a different nature-adagulation t according to Smoluchowski 8 -requires a consideration of the general “asymmetrical” case. In that case the sign (direction) can be reversed not only for the electrostatic force but also for the resultant van der Waals interaction. Let us first consider a plane-parallel layer $ of thickness h formed by a solution of a binary electrolyte between the surfaces of plates 1 and 2 charged to potentials $1 and $2 > $1, respectively. We shall assume that the potential in the electro- lyte solution obeys the equation : where b = elkT = F/RT, e is the electron charge, F the faraday,l k is the Boltz- mann constant, Tis the absolute temperature, z1 and 22 are the valencies of the anion and cation, respectively ; a = (8rr/D) eNC = (871.10) ez1nlNy = (8n-/D)ez2n2Ny ; D is the dielectric constant, N is the Avogadro number, C is the concentration in g equiv.lcm3, y is the concentration in moles cm-3, rtl and n2 are the number of anions and that of cations, respectively, in a molecule of the electrolyte. On introducing the parameter #I = 22/21 and the dimensionless variables, 4 = qb$, x = xld = KX, where K = lfd = d a z , (2‘) eqn.(1) reduces to d2+/dx2 = 4 {exa (+I - exp (-- P+).) On integrating eqn. (2) we obtain : (d+/dX)2 = exP + - U / P ) exp (- P4) - c, (3) where the value of C must be so chosen as to make the difference x1 - x2 between the values x = x1 and x = ~2 for which 4 = $1 = zlb$l and 4 = 42 = zlb$2 respectively, be equal to H = hJd.* The derivation of the same rules by Venvey and Overbeek (the one of them is not entitled as that of Eilers and Korff) was published considerably later.4 In this publication the authors failed to quote our papers containing the derivation of these ruIes and wrongly assumed their priority for the explanation of the stability of strongly charged sols (cf. pp. vi and 188). By heterocoagulation we mean the mutuaI adhesion of particles of a dissimilar nature as a result of their Brownian motion. Adagulation is an expedient term to be used to distinguish the adhesion of Brownian particles to macrosurfaces or fibres and other macroscopic particles whose Brownian motion may be neglected owing to their large mass. In cases in which it is essential also to emphasize the difference in the nature of the Brownian and macroscopic particles (their nature being in some cases the same) the term ‘‘ heteroadagulation ” should be logically used.It should be noted in this connection that the terms heterocoagulation and adagulation are in no wise equivalent : the former implies a difference in the nature of the particle surfaces, whilst the latter emphasizes a difference in their sizes and masses and eventually in their Brownian mobility. $ This case has been considered by the author and V. G. Levich.3. V. DERJAGUIN 87 The repulsion P between the plates per unit area, has been shown 1 to be equal to P = ~ T N W C / Z ~ , (4) (5) where w = c - 1 - (l/P>.Instead of establishing the relation between N and w by determining the values of w corresponding to various values of H, it is much simpler to adopt the opposite sequence, viz. determining H as a function of w (for various values of $1, $2 and parameter /3), For this purpose, let us consider in fig. 1 a set of integral curves $ = +(x, C) plotted according to eqn. (3) for various values of C and, consequently, of w and passing through the point x = 0, + = co, i.e. having the x axis as an asymptote. I FIG. 1.-The schematical drawing of the set of isodynamic curves for the interaction of two unequally charged.surfaces in electrolyte solution. For w < 0, d+/dX differs from zero for any values of $, and the integral of eqn. (3) may be expressed in the form : Pco dd When w = 0, the integral curve (shown in fig.1 by a dotted line) has the axis of abscissae as an asymptote. When w > 0, each integral curve has a minimum with an ordinate $ = 40 defined by the equation which has one positive root. The abscissa of the minimum is given by88 THEORY OF HETEROCOAGULATION For x < xm, the integral of eqn. (3) is also expressed by eqn. (6). For x > xm we have : ___ I_ (9) dS1 The intersections of one of these “isodynamic” curves, which corresponds to a definite value w = const., with two straight lines parallel to the axis of abscissae drawn at the heights of + = $1, and # = $2 give the possible abscissae of the re- spective surfaces, x1 and x2 whose difference equals H. For w < 0, each of these straight lines intersects the isodynamic curve in one point and from eqn.(6) we obtain For w -+ 00, H evidently tends to zero according to the asymptotic law: When w = 0 (absence of interaction) we have w - ($2 - +1)~1H2. (1 1) w > 0 results in repulsion instead of attraction. In this case each straight line + = const. > $0 crosses the isodynamic curve twice. The intersection points situated on one side(e.g., on the left) of the minimum of the isodynamic curve give the values of H which are also given by eqn. (10). The intersection points situated on different sides of the minimum will give larger values, H = H’, which, according to eqn. (6) and (9) are equal to It will be readily seen that when $0 = $1, and hence when (14) 1 1 w = w*=exp(41)+pexP(--#l)- 1 - p , the straight line 4 - $1, will be tangent to the isodynamic curve and H‘ will equal H.When w > w, the straight line 4 = $1 will fail to intersect the isodynamic curve, so that such values of w can OCCLE at no value of H. It follows that for any values of$1 and 4 2 of like signs the repulsive force reaches a maximum at aB . V. DERJAGUTN 89 certain value of H which is given by It is remarkable that w is independent of $2, Le. of the potential of the more strongly charged surface. w c FIG. 2.-The repulsion between two unequally charged surfaces in electrolyte solution as a function of their distance (schematic drawing). FIG. 3.-The repulsion against distance for a strongly charged surface and for different potentials of another surface in a solution of a symmetrical electrolyte (exact drawing).The form of the w(W> graph resulting from the above analysis is shown in fig. 2. The more trivial case is that of $2 > 0 > in which w is negative for all values of H and steadily increases in absolute magnitude as H decreases. For ,6 = 1 the relation between H and w is expressed by elliptic integrals, viz., when w < 0, eqn. (10) gives for H, where 1 du d ( 1 - G)(1 - klU2)’ H = kl whilst for H’ we obtain from eqn. (13) : where M = l/cosh ($012) ; ~ 2 . = cash ($0/2)lcosh (#2/2). Fig. 3 and 3a reproduce the exact form of the set of curves w = w(H, $1) for 18 L= 1 for the particular values +2 = 10 (which is close to co) and $2 = 1 (fig. 3 4 , ” respectively. * In fig. 3a curves are also drawn for which 41 > 4 2 .~1 = cash (+o/2)/~0sh (461/2) :90 THEORY OF HETEROCOAGULATION The thickness HO at which the sign of w is reversed is given by For w, we obtain whilst for H, we have w, = exp ($1) + exp (- $1) - 2 = 4 sinha (#q/2), 1 dU H , = k f, d ( l - u2)(1 - k2u2) ' where k = llcosh (41/2), uo = cash ($l/2)/~0sh ($212). FIG. 3a.-The repulsion against distance for a weakly charged surface and for different potentials of another surface in a solution of a symmetrical electrolyte (exact drawing). For < $2 < 1, for any values of /3, we obtain instead of eqn. (7), (16), (17), (22 1 (18), (19) and (20) : w = ((1 + P)/2)+02?B . V . DERJAGUIN 91 2. The force iV of interaction for any charged convex surfaces may be obtained by the general formula (5) derived before : 5 N = GJ)yh)dh = Gd- kTNC fl" w(H)dH, where y is the gap width at the narrowest region, Y = y/d; G is a form facto which depends on the radii of curvature of both surfaces at the zone of approach and on the mutual orientation of the principal normal sections; for two spheres of radius CG = ~ 5 .Formula (27) is valid as long as the radii of curvature are much larger than the range of the interaction forces between the surfaces : z > d. (28) Without reproducing the respective computations, we shall confine ourselves to stating the following results. When 41 and $2 are of like signs, according as y and Y decrease N increases, reaches a maximum N = N, whose asscissa Y, evidently equals HO in formulae (12), (18) and (24) and then decreases again changing the sign and tending to - c;o as h tends to zero according to the formula : The height of the maximum is Now, according to (lo), (13) and (S"), we have Hence where #O is defined as a function of w from eqn.(7) whilst w, is determined as a function of 41 from eqn. (14) which is identical in form with eqn. (7). Eqn. (32) thus leads to a remarkable result: the force barrier Nm depends like w, exclusively on the potential of the weaker charged surface. Reversing the order of integration in eqn. (32) it may be reduced to the form : (33) 1 1 k:Nc 1%' J exp ($1 + p exp (- ,&) -- 1 - - d+. B N,= 4Gd- In particular, for 461 > 1, we have kTNc Nm w 8Gd - exp (+1/2), whilst for $1 < 1 we obtain kTNc r p N, 2Gd- -2- $12. Z J (34) (35) When p = 1, eqn. (33) gives on integration : kTNc N . = 8Gd- (exp ($112) + exp (- 4112) - 2) = 32CdkT* sinh2 9:.(36) 292 THEORY OF HETEROCOAGULATION It will be noted that is the height of the energy barrier for the thinning of a plane layer. 3. Let us now consider the resultant energy of the dispersion interaction of two dissimilar particles in a liquid medium. If we assume that the interactions of the individual elements of volume are additive * and that they obey the London formula, then in the case of two plates separated by a plane-parallel gap of width h the attractive force per unit area in vacuo will be given by NJG = 32dkTNclz where A12 is the constant of the dispersion interaction of the volume elements of the first and second particles. If the particles are immersed in a liquid medium,ls then we obtain instead of (37) : If the particles 1 and 2 are of the same nature, there are reasons 9 to believe that Q is always positive.For dissimilar particles under consideration there are no such reasons and the cases are undoubtedly possible in which (39) A = A12 4 A33 - A13 - A23 < 0. For the resultant of dispersion forces S of convex particles we shall have GA S = G 1; Q(h)dh = GU(y) = - 12 ny2 It should be mentioned that for distances exceeding the dispersion wavelengths the electromagnetic retardation must be allowed for according to Casimir and Polder 10 and Abrikossowa and present author.11 This results in the replacement of eqn. (38) and (40) by the following equations : Q = ~ 1 ~ 4 , (41) and S = GBj3y3. (42) Let us now separately consider the application of the theory developed to the cases of A > Oand A < 0.CASE OF A > 0 In this case the existence of a force (or energy) barrier is only possible when the particles are similarly charged. In the theory of coagulation of hydrophobic sols and suspensions 3 it has been shown that there exist two characteristic types of coagulation : (i) Coagulation due to a fall of the potential of the surface below some critical value &, which satisfies the relation : 2 Dd$c2/A = const. (43) (ii) Coagulation due to a contraction of the ionic double layer on increasing the electrolyte concentration above a critical value which satisfies the relation : 3 * This assumption is obviously incorrect for condensed systems. Yet the relation between the interaction of particles and their distance apart (eqn.(37)) which results from this assumption is apparently valid for small distances.B. V. DERJAGUIN 93 Accordingly, in the instance of 4 2 + 41 under consideration the cases of funda- mental interest are those of adhesion due either to contraction of the double layer when 4 2 > $1 > 3, or to a decrease in potential +I.* For $2 > 41 >> 1, according to eqn. (12) and (15), the interaction of particles will appreciably depart from the symmetrical case for very small values of H only. This will affect the strength of adhesion and the conditions of repeptization but not the condition of its onset. We therefore shall confine our- selves to adhesion due to a drop in $1, assuming for simplicity and definiteness in what follows that (45) As a condition for the ad- hesion of plane surfaces we shall3 set the requirement of the disappearance of the force barrier (resulting from both electrostatic and molecular interaction) in which case the force diagram P - Q against 4 2 9 1 5 +l.FIG. 4.-The interaction of two plates in a solution of electrolyte for different potentials of one of them near the disappearance of the force barrier (schematic drawing). h has the form shown in fig. 4 by the dotted line. In this case we must evidently consider the values of w and P whose abscissae lie on the right of the maxima (i.e. H > Hm). Hence the values of 40 will be real and will satisfy the inequality (46) Then we have to use eqn. (13) from which, taking into account eqn.(8) and (45), we obtain 4 0 < 41 < 1- An approximate value of .loo for small values of $0 may be obtained by making use of the fact that the relation between Jo0 and $0 is identical with that between (~'h/2) and rjq in eqn. (14) of the paper quoted above 3 for z1 = 1. As follows from eqn. (21) of the same paper,3 for small values of $0, .Ico is large and is asymptotically expressed as where K is a function of only ; for p = 1, K = 8. On simplifying the expression for J1 taking account of (22) and (46) we obtain * The cases of a simultaneous decrease in 41 and $2 are less frequent and characteristic. We therefore shall not consider them, especially as they may be readily analyzed using approximation formulae (22-26).94 THEORY OF HETEROCOAGULATION The conditions for the disappearance of the force barrier are given by the equations : dP - d Q dh--dh' P = Q = AIGrrh3, (51) whence d In P/d In h = - 3 .(52) Hence the abscissa ho of the force barrier (see fig. 4) may be determined. Sub- On passing to the dimensionless quantities w and H' taking account of eqn. (4), stituting it in eqn. (51) we obtain the criterion of adhesion. we shall have instead of eqn. (52) and (51) : dH'/d In $0 = - 3 H', (53) Az1/(6nd3kTNc) = wH'3. (54) From eqn. (49) and (53) we obtain The equations obtained enable one to find t - ~ = $1/#0 when $1 is known, and vice versa. FIG. 5. In fig. 5 the graph is given for u = $1140 as a function of $1, which shows that u is close to unity when 41 < 0.3. After determining u as a function of 41, we may find $1 = +l/u and inserting in (54) obtain the criterion sought for. Assuming for simplicity u M 1 and $0 M $1 we have the criterion of adhesion in the form : or replacing $1 and dz according to eqn.(2') we get instead of (56) :B. V. DERJAGUIN 95 The condition obtained is rather similar to that of adhesion of two plates charged to equal small potentials (corrected Eilers and Korff’s rule) : A/Dd#l2 = const. (58) However, in the case under consideration, viz., that of small values of $1, the right-hand side of eqn. (57) is larger than that of eqn. (58) (the latter being of the order of unity).2 It follows that the critical potential initiating adhesion is lower than that of the symmetrical case. CASE OF A < 0 In this case repulsion always predominates both at short and long distances; it follows that there exist two force barriers, either distinct or fused together: yet when $2 $= $1 * the graph of the force plotted against the distance may have a well of depth Rdn as shown in fig.6. If the right-hand barrier of height Rma, is overcome under the action of an external force and the system gets into the well, then R d n will evidently express the adhesion force. R 8 h i FIG. &-The force diagram for two plates in a solution of an electrolyte, for A < 0 (repulsion resulting from van der Waals interaction energy). A change in the electrolyte compositioh and in potentials $1 and $2 will affect Rmin and R,, simultaneously. When the concentrations are low and the values of $1 and t,b2 are of the same sign though not too close in magnitude, then R,, may be calculated neglecting the van der Waals forces, by formulae (21, (4) and (14) from which we obtain When c and $1 are small, this “ activation ” force barrier is not high and adhesion occurs readily.According as c and are raised Pmax increases, whilst Pmin decreases and reaches zero when c assumes some value cc. The condition for the complete disappearance of adhesion for #2 > 1 may be obtained from the same eqn. (501, (51), (52) and (54) as before. Instead of H‘, however, it is now necessary to substitute H from eqn. (10) whereupon instead of eqn. (53) we obtain where, assuming 41 < 1 and w < 0, d H / d h w = - $ H , (60) * $2 will be considered positive in all cases, whilst $1 may be of either sign.96 THEORY OF HETEROCOAGULATION From eqn.(60) we obtain instead of eqn. (55) Assuming K > 1 and taking into account eqn. (60) we hence obtain approximately (For /I = 1 this gives wo' w 3 since X = 8.) Hence we have He 312. (64) Substituting H and wo in eqn. (54) we obtain the condition for the disappear- ance of adhesion : A'z 6rrkTNcd3 where A' and w' denote (- A) and (- w), respectively ; hence the condition for the complete impossibility of adhesion and, simultaneously, for " peptization " in the case of 1 > $1 > 0 is given by If +2 > 0 > # I , w is always negative and there is likewise a " force well " (67) (68) A'~ij(6rd3kTN~) = w'H3, (69) when c is small. Let us consider the simplest limiting case in which #2 > 1 < - $1. dH/d In w' = - *H7 By analogy with the foregoing treatment we may write the conditions : Substituting this expression for H in eqn.(68) we obtain the values of Hc and wc' which evidently depend on /3 alone. Then using eqn. (69) we find the stability criterion in the form : C' D3(kT)5 f '(p) e6zl6nlNA2 Y=- Adhesion will occur when the following condition is fulfilled : (71) For identical, strongly charged surfaces the stability criterion has 3 the same form as in eqn. (71), though with a different numerical coefficient c/f(p). How- ever, the condition of adhesion in that case is expressed by an inequality the reverse to that of (72). In other words, for dissimilar particles adhesion or coagulation can be produced not by addition but by dihtiun of the electrolyte, owing to an increase in the double layer thickness." An example of this kind of coagulation * Another distinction lies in the fact that for obvious reasons the stability criterion must be expressed in terms of the charges of both kinds of ions, zl and 22 symmetrically ; the function f'(P) in eqn.(71) must therefore satisfy the condition z16f'c[j) = z@f'(l/p), or the condition f'(P)P-3 = f ' ( l l P ) (1/P)3.B . V. DERJAGUIN 97 is supplied by the observation of Frumkin12 and co-workers on adhesion of mercury and glass in dilute solutions of electrolytes. To determine the adhesion force for a given concentration it is necessary first to find the abscissa of the force well, h ~ n from eqn. (50) which may be written in the form : 1 dH' - 2mkTNd3 (H'>4 dw' ZlA' - After finding w' and H e from this equation and then hhn we obtain (73) For small values of c the right-hand part of eqn. (73) is large (- c-4) whence it follows that H' < 1, whilst w' > 1. In this case the following formula which is equivalent to eqn.(1 1) is applicable : (75) After simple transformations we obtain from eqn. (73), (74) and (75) H' = (42 - + l ) / V T This simple result may also be obtained by less lengthy reasoning. 5. The results obtained may be readily generalized to cover adhesion between convex surfaces, In view of the laboriousness of the computations, however, we shall confine ourselves to stating some principal conclusions. CASE OF A > 0 ; $2 > 1 > 41 complex in the right-hand side. Similarity to eqn. (58) is retained. Instead of criterion (56) we obtain a criterion of a similar kind though more CASE OF A < 0; 4 2 1 ; (- 41) > 1 The stability criterion differs from eqn.(71) and (72) in the value of the co- efficient clfcp) alone. As for plane surfaces, adhesion and coagulation must occur on dilution of the electrolyte. 6. The theory developed may primarily be applied to interpreting the phenomena of coagulation in a mixture of two sols. As is clear from the whole foregoing treatment, especially from the possibility that the quantity A for dis- similar particles can not only possess abnormally low values but even become negative, the theory accounts for the phenomenon of " group coagulation " 13 in which the aggregates formed only contain particles of the same kind but not the mixtures of both kinds.In this case three thresholds of concentration coagulation are possible of which the third, i.e. the one that signifies the beginning of formation of aggregates of dissimilar particles for A < 0, may not only be lower in concentration but even correspond to inversion of the Hardy-Schultze rule, i.e. signify the lower limit of concentrations imparting stability (with respect to aggregation of dissimilar particles). Similar considerations may also be applied to the coagulation of a sol in which the surface of the particles is non-uniform with respect to potential. In particular, these considerations may account for the interesting experimental results due to Bromberg, Chmutov, Lookyanovich, Radushkevich and Nemtzova.14 The theory may also be successfully applied to the phenomena of adhesion of particles, e.g. of dyes to fibres and to other surfaces, enabling one to account for the fact that on addition of electrolyte " adagulation " occurs before coagulation and exhibits a stronger linkage than for homogeneous adhesion. In the less frequent cases of A < 0, phenomena of an opposite nature may of course be observed. D98 COAGULATION OF EMULSIONS 1 Derjaguin, Bull. Acad. Sci. U.R.S.S., Classe Mathem. Natur. Skr. Chim. (Russ.), 1937, 5, 1153 ; Acta Physicochim., 1939, 10, 333 ; Trans, Favaday SOC., 1940, 36, 203 ; 1940, 36, 730. 2 Derjaguin, Trans. Faraday SOC., 1940, 36, 730. 3 Derjaguin and Landau, Acta physicochim., 1941, 14, 633 ; J. Expt. Theor. Physics (Russ.), 1941,11,802 ; reprint in J. Expt. Theor. Physics (Russ.), 1945,15,662. 4Verwey and Overbeek, see e.g. Theory of the Stability of Eyophobic Colloids, New York, Amsterdam, 1948). 5 Derjaguin, Trans. Faraday Soc., 1940, 36, 730 ; Kolloid-Z., 1934, 69, 155. 6 Verwey, Trans. Faraday Soc., 1940, 36, 723. 7 Eilers and Korff, Trans. Faraday SOC., 1940,36,229. 8 Smoluchovski, Z. physik. Chem., 1918, 92, 129. 9 Hamaker, Physica, 193’7, 4, 1058. 10 Casimir and Polder, Physic. Rev., 1948,73,360. 11 Aurikossova and Derjaguin, C.R. Acad. Sci. U.R.S.S., 1953, 90, 1055. 12 Frbmkin, Gorodetzkaya and Titijevskaja, J. Physic. Chem. (Russ.), 1947, 21, 675. 13 Tyoku Matuhasi and Kunio Aoto, J. Colloid Sci., 1948, 3, 63. 14 Bromberg, Chmutov, Lookyanovich, Radushkevich and Nemtzova, J. Physic. Chem. 15 Derjaguin and Kussakov, Acta physicochim., 1939, 10, 25, 153. (Russ.), 1953, 27, 379.

ISSN:0366-9033    

DOI:10.1039/DF9541800085

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

98 COAGULATION OF EMULSIONS KINETICS OF THE COAGULATION OF EMULSIONS BY A. s. c. LAWRENCE AND 0. s. MILLS Dept. of Chemistry, The University, Sheffield 10 Received 6th August, 1954 The rate of coalescence of oil droplets in water and in soap solution has been in- vestigated by size frequency distribution measurements using an improved photomicro- graphic method. The results are analyzed in terms of the von Smoluchowski theory of coagulation kinetics and the presence of an energy barrier to coalescence demonstrated. One of us 1 has pointed out that the first step in the coagulation of any dis- persed system must be a collision process irrespective of considerations of free surface energy. Stabilization of a dispersion to a colloidal system involves provision, at the interface, of an energy barrier to coagulation subsequent upon collision.A perfectly stable colloidal system is one in which there is no decrease of the total number of particles with time : coagulation is a second-order collision reaction of a special kind whose kinetics have been derived first by Smoluchowski.2 Suggestions that no emulsion can be perfectly stable on account of the residual free surface energy are regarded as irrelevant, any limitation being kinetic, that is, due to the fraction of particles colliding with an energy greater than the energy barrier provided by the stabilizing agent. There has been a general refusal by workers on emulsions to make the necessary but very tedious particle size counts for this basic assessment of stability, i.e. the measurement of the change of the total number of particles with time.It is also curious, at first sight, that liquid-in-liquid systems have not been used to test the Smoluchowski equations on the grounds that the " coagulum " is spherical and its exact size measurable. There are, however, two serious limitations: (i) the original particles must be large enough for accurate measurement of drop diameter to be made : the magnification used in the counts cannot be increased more than about 500 times as the depth of field becomes so small that it is impossible to focus sufficient droplets; (ii) by the nature of the systems they are not mono- disperse and the effect of coalescence of a small drop into a large one is a veryA . S . C. LAWRENCE AND 0. S . MILLS 98 small increase of the diameter of the latter.Harkins and his collaborators 3 carried out large numbers of particle size counts and observed ageing effects. They were, however, only concerned with the amount of soap adsorbed per unit area of interface and the nature of the adsorbed film and not with the kinetics of the coagulation of the unstable systems. DISTRIBUTION PARAMETERS AS MEASURES OF EMULSION STABILITY Size -frequency distributions are unimodal and leptokurtic, the kurtosis be- Typical changes are shown in fig. 1. coming more pronounced with ageing. I 2 3 4 5 D i a m e t e r ,p FIG. 1 .-Variation of size frequency distribution with time ; unstabilized emulsion. From the sample size frequency distribution, various statistics may be derived, e.g. the arithmetic mean diameter, median diameter, modal diameter, etc.A tabulation of a number of these quantities and their inter-relations has been given by Jellinek.4 Each of these statistics varies with time in some related manner which is in general complicated. In particular it is possible to define three average diameters, namely, (i) the number average diameter defined as the average diameter over all particles, i.e. r = l I r = l where fr is the number of drops of diameter d r ; (ii) the average area diameter, i.e. the diameter of the drop with average surface area r = 00 r = m r = 1 r = 1 and (iii) the average volume diameter (ii) and (iii) are in addition to those given above. These three diameters in general differ due to the skewness of the distribution.loo COAGULATION OF EMULSIONS If coalescence of an emulsion follows the rate equations put forward by Smoluchowski for the region of rapid coagulation, in which every collision is effective, then supposing that there is initially a collection of unit sized particles (primary particles) of number No which coalesce so that 1-mer + 1-mer = 2-mer, and in general rn-mer + n-mer = (m + n)-mer, then the number of r-mer particles Nr at time t sec is given by No(PNot>r- 1 (1 + p l v o t w Nr = in which B = 4rrzD, where ?? is the effective radius of the emulsion droplet (here identified with the actual radius) and D is the diffusion coefficient.Putting 2 2- w i i 3 . i s ti $ 8 i? io;i 1'21'3 Time (hundreds of minutes) FIG. 2.-Variation of mean volume with time; unstabilized emulsion, 1 % phase volume at 25" C.Time (days) FIG. 3.-variation of mean volume with time ; emulsion stabilized with 1 % sodium oleate, 1 % phase volume at 25" C. D = kT/6~Xq, then p = 2kTI3~ and is hence a constant defined by the gas con- stant per molecule k, the absolute temperature Tand viscosity of the continuous phase 7. Then it follows that the mean drop volume at time t,Vt = ~ 4 3 1 6 , is given by r = o O r = c o Gt = NrVr Ni-7 r = l where v r = rvg is the volume of the rth-sized particle composed of r primary particles each of volume VO.A . S . C . LAWRENCE AND 0. S . MILLS 101 After substitution and summation we derive Ui 2 vo + PNovot. Now NOVO is the total oil emulsified in the unit concentration of emulsion, i.e. the phase volume fraction #, and hence Thus a plot of mean droplet size, or d y 3 , against time should be linear.If, on the other hand, every collision is not effective but only a fraction p , such that p = A exp (- E/RT), this fraction being a constant for any one system irrespective of the r values of the particles concerned, then vt = vo + &5t. from which we obtain by similar treatment, and so the ratio of slope observed to P# = p = A exp ( - E/RT). The results given in fig. 2 and 3 show that for emulsions, both those stabilized by added stabilizing agent and those by electrical charge only, linear variations of 5t with time occur. EXPERIMENTAL APPARATUS AND MATERIALS. A photomicrographic method is required to analyze the size distribution so that sampling and recording can be rapidly performed and the measure- ments made subsequently. In order to reduce blurring due to Brownian motion it is necessary to have as short an exposure as possible.The source must be intense and at the same time the heating of the sample must be avoided whilst for sharpest focusing monochromatic light is desirable. All these points were achieved by using a 250-W compact source high-pressure mercury-vapour lamp with a Kodak no. 77 filter. The filter, whilst not being completely monochromatic, is very satisfactory because of its high transmission of the 546 mp line. The microscope was mounted on a horizontal optical bed and an enlarged image of the arc focused on to the aplanatic substage condenser by means of a Watson Conrady light-collecting lens. The various objectives used were (i) a 4 mm dry apochromatic, N.A. 0.95 with cover slip compensating device by Cooke, Troughton and Simms, (ii) phase contrast objectives by Cooke, Troughton and Simms, and (iii) an 8 mm apochromatic, N.A.0.65 by Watsons. The enlarged image was focused on to the screen of a &pl. reflex camera with the lens removed and coupled to the micro- scope tube by bellows. A roll film adapter allowed the use of standard 3& in. x 2) in. negatives. After fine grain development, enlargements were made on to Kodak foil card to prevent distortion during processing. With each series of film a photograph of a stage micrometer was included as a standard. The overall magnification was of the order of 1000 x , about 300-400 x being with the microscope. Under these conditions an exposure of 11200th sec was found to be convenient.The diameters of the drops were measured by a micrometer device used by Fresnel, and Joly, and Beckett.5 The scale was graduated so that each full division corresponded to approximately lp, and was subdivided into tenths. The scale was printed on to a positive transparency so that its emulsion side was in contact with the magnified print when in use. Two different oils were used during determinations. Initially Nujol weighted with carbon tetrabromide was used. This practice of weighting the oil with chloroform, carbon tetrachloride or carbon tetrabromide is, however, not to be recommended since (i) chloro- form is polar, (ii) carbon tetrachloride is volatile and carbon tetrabromide decomposes and bromide ions can be detected in the aqueous phase.A much more suitable oil is the pure hydrocarbon 3 : 3'-ditolyl, which has none of these disadvantages, and this was used in all subsequent experiments.6 Its high refractive index is particularly convenient for high contrast during microscopy. The oleic acid used in the preparation of sodium oleate solution was purified first by fractional crystallization from acetone solution at about - 20" C followed by fractionation from an alumina column. The acid, eluted from the column, when freed from solvent was quite colourless, almost odourless and remained so on standing. Conductivity water from a mixed resin column was used for the aqueous phase. vt = Do + PPq%102 COAGULATION OF EMULSIONS PREPARATION AND SAMPLING OF THE EMULSIONS.The emulsions were prepared by initially stirring the mixture of oil and aqueous phase in the annular space betweena stainless steel rotor and glass tube fitted with an inlet funnel and outlet lip. The emulsion could thus be circulated through the apparatus a number of times, usually six. The emulsion so produced was then homogenized with a cream mixer again passing the emulsion through some five or six times. All the apparatus was washed out first with warm soapy water, then repeatedly with boiling distilled water and finally steamed for a number of hours. The emulsion was sampled by withdrawing portions by means of a glass tube under suction. The slides consisted of a piece of gold foil cemented on to optically flat micro- scope slides by Canada Balsam so that the effective thickness was about 2-3 x 10-3 in.A suitable shape was then cut away and channels cut through the foil so that excess emulsion could drain away as the cover slip was applied. The cover slip was cemented into position by " just-molten " paraffin wax after the emulsion had been introduced. This procedure allowed the slides to be held vertically during photographing without the emulsion draining away. During ageing the emulsion was contained in a tube rotating vertically about its short axis and completely submerged in a thermostat at 25" C. This tube, which was completely filled with emulsion, was designed to overcome differing rates of coagulation due to sedi- mentation effects. The application of a slow rotary movement to the emulsion replaces the vertical sedimentation due to gravity by a much smaller displacement caused by weak centrifugal action.In practice the tube revolved some thirty times per minute. Emulsions with quite large density differences (0.1 g ml-1) have been suspended for long periods without creaming. This device coupled with the use of the pure hydrocarbon above makes sedimentation effects negligible. It was, however, found that after some considerable time had elapsed with unstabilized emulsions the oil particles which had diffused to the walls of the glass tube tended to stick there, thus reducing the concentration in the bulk. With soap- stabilized emulsions this effect was much less noticeable. When samples were withdrawn from the tube, soap solution of the same concentration was admitted so that no air remained in the tube after sampling.Approximately 100 ml emulsion was prepared each time. RESULTS AND DISCUSSION TEST OF THE SMOLUCHOWSKI EQUATION For a precise test of the Smoluchowski equation it would be necessary to follow the changes with time of the numbers of particles within each particular size range. Equal ranges will, however, contain different numbers of r-mers, those of larger diameter containing the greater number. This is because ar, pt-mer particle with volume proportional to n and to dn3 coalescing with an rn-mer to yield an (pt + m)-mer forms a drop whose diameter is not a linear combina- tion of dn and d, but is proportional to (dn3 + d,3)+. Although the frequency of the high r-mers will be small during relatively early stages of coagulation the larger numbers of successive r-mers within the common range gives a relatively larger frequency and thus contributes to the leptokurtic character of observed size frequency distributions.As a consequence of measuring distributions by their diameters it is impossible to identify the individual frequencies of the con- stituent r-mers and hence this rigorous testing of the Smoluchowski equation is impossible. The absolute measurements would also be more difficult as the standard deviation of the individual diameters would cause some overlapping between the ranges and the extent of this would be unequal. It is therefore necessary to utilize only those equations which involve the total number of particles contained within the emulsion.This total, or the total per ml emulsion, decreases with time corresponding to an increase of the average volume. As shown this latter parameter is linear with time and hence the reciprocal of the total number should vary similarly. These two functions can be shown to be the only average properties which should possess linear variation should the above equations apply. Other statistics, e.g. number average diameter, area average diameter, mean specificA . S . C . LAWRENCE AND 0. S. MILLS 103 area all are non-linear. The latter statistic has been suggested by King and Mukherjee 7 as a measure of emulsion stability, who define this as the reciprocal of the rate of decrease of interfacial area of 1 g of emulsified material. They claim that their curves of specific interfacial area with time are approximately linear and that such non-linearity which does occur is due to inaccuracy during measurement.Where the plots are obviously curved the slope at a central portion was taken. The Smoluchowski theory predicts that this graph should not be linear but during the early stages of coagulation the specific interfacial area should diminish being proportional to 1 - klt + k2t2 - . . ., etc. With stabil- ized emulsions the proportionality should be 1 - pklt + p2k2t2 . . ., etc. These expressions are derived by setting up series similarly to those given earlier for the mean volume. Such series containing terms of the form PI3 x r - 1 where a has the value 3 for average volume function, 2 for the average area function and 1 for the average size function, cannot be summed explicitly, except when a = 3.When, however, (pt)2 is negligible compared to p t then the curve over such a range will be linear. This will be the case whenp is very small, i.e. for the most stable emulsions. With their most stable emulsions, in fact, this portion only is shown, whilst with those to which calcium chloride had been added so that breaking is fairly rapid the. fuller equation holds better. Further, King and Mukherjee's definition infers that - dsldt = so/k, where s and SO are values of the specific interfacial area at times t and 0 respectively and k is the stability factor as has been pointed out by Aherne and Reilly.8 Other workers 9 find a better approxim- ation to be - dsldt = s/k.The latter form would be closer to the Smoluchowski equation than the former. As it is impossible to calculate the mean volume size from the mean specific area unless the form of the distribution is known, it has been impossible to fit curves quantitatively to their figures. Further, their definition depends upon the unit of weight as a basis which makes it difficult to compare different oils. As they point out, however, emulsion stability is fre- quently independent of the nature of the oil, especially if non-polar and chemically inert. Thus they found similar results for kerosene and olive oil whilst we find somewhat similar results for ditolyl and Nujol. Experiments by the authors sought to test the agreement between the size variations and those predicted by the Smoluckowski equation, and to estimate values of p therefrom.For this purpose, initially an unstable system of hydro- carbon oil and water was used. Such systems rapidly separate should density differences be present. Nevertheless electrical stabilization must be present as is indicated by the stability of oil hydrosols. The cwves show, in fact, that only one collision in 10-3 leads to coagulation which corresponds to an energy of activation of E = 3.9 kcal mole-1, where p = A exp (- E/RT) and A is put equal to unity. For soap-stabilized emulsions we can compare our own results with 1 % phase volume and aqueous sodium oleate (1 % wlv) at 25" C with those of Jellinek and Anson 10 at 50 % phase volume at 70" C. The latter studied the relative stabilizing power of mixtures of a-monostearin and sodium stearate.'They found approximately linear variation of specific interfacial area with time for their most stable emulsions and consequently agreed with King and Mukherjee's definition of stability factor. At the same time they also plotted the time variation of the reciprocal of the total number of drops per g dispersed phase and showed this to be linear. These authors noted the formal agreement with Smoluchowski's equation but proceeded no further. Their most stable emulsion gives, as would be expected, fairly good straight lines on each plot. From the data for our sodium oleate graph whose slope is 3.2 x 10-18 ml sec-1 the value of p = 1.8 X 10-5 and E = 6.5 kcal mole-1. For Jellinek and Anson's emulsions their least stable one, B, gives a slope, when units are changed, of t = c O r = l104 COAGULATION OF NON-SPHERICAL PARTICLES 6.8 x 10-17 from which p = 8.8 x 10-6 and E = 7.9 kcal mole-1, whilst emulsion A gives p = 1-5 x 10-6 and E = 9.1 kcal mole-1.Due to the scatter on the points for their emulsion D it was not possible to estimate a value. In support of the view of an energy barrier stabilizing emulsions it will be noted that emulsions are temperature dependent, breaking more rapidly at elevated temperatures by factors greater than would be expected from collision frequencies variations. Further, the barrier would appear to be, at a first approximation at any rate, independent of the actual size of the drops coalescing. Before coalescence can take place the film of continuous phase between the two drops must drain away and finally puncture, whence the system becomes unstable and a single drop results.This initial puncture needs only be of molecular dimensions and hence is virtually independent of the size of drop. The origin of E must lie in a number of factors such as charge density on the droplets, surface viscosity of the interfacial layer and viscosity of the continuous phase. As has been indicated by Robinson 11 a high zeta-potential of itself need not necessarily lead to a low probability of coalescence, but if accompanied by a high surface viscosity would do so. The authors wish to thank the University of Sheffield for the award of an Ellison Research Fellowship to one of us (0. S . M.) and to the University Research Fund for a grant towards purchase of microscope objectives. . 1 Lawrence, Chem. and Ind., 1948, 615. 2 Smoluchowski, Z. physik. Chem., 1916,92, 129. 3 Harkins and Beeman, J. Amer. Chem. Soc., 1929, 51, 1674. 4 Jellinek, J. Sor. Chem. Ind., 1950, 69, 225. 5 see Beckett, Econ. Proc. Roy. Dublin Soc., 1927, 2, 303. 6 Mills, Nature, 1951, 167, 726. 7 King and Mukherjee, J. Soc. Chem. Ind., 1939, 58, 243. 8 Aherne and Reilly, Nature, 1944, 154, 86. 9 Lotzkar and Maclay, Ind. Eng. Chem., 1943, 35, 1294. Harper, Trans. Faraday Soc., 1934, Harkins and Fischer, 30, 636 ; 1935,31,774 ; and 1936,32, 1139. J. Physic. Chem., 1932, 36, 98. Berkman, J. Physic. Chem., 1935, 39, 527. 10 Jellinek and Anson, J. Soc. Chem. Ind., 1950, 69,229. *I Robinson, Trans. Faraday SOC., 1936, 32, 1424.

ISSN:0366-9033    

DOI:10.1039/DF9541800098

出版商:RSC    

年代:1954

数据来源: RSC