THEORY OF THE STABILITY OF LYOPHOBIC COLLOIDS E. J. W. VERWEY Natuurkundig Laboratorium der N . V . Philips’ Gloeilampenfabrieken, Eindhoven, Holland Received November 14, 1946
Hamaker (4)has given a general theory of the stability of lyophobic colloids in terms of potential curves, giving the potential energy of two particles with respect to each other as a function of their mutual distance. He considered different types of potential curves, all being a superposition of an attractive potential due to London-van der Waals forces between the particles and a repulsive potential due to the interaction of the double layers surrounding the particles. He gave expressions for the London-van der Waals potential for various cases (two spherical particles, two parallel plates, etc.). The theory of the interaction of the double layers, however, offered considerable difficulties. This is especially shown by the circumstance that later work by different authors led to completely divergent results. Hamaker gave only a rough estimate of the double-layer interaction potential but assumed it to be repulsive for all distances between the particles. Hamaker’s conclusions have been challenged by Langmuir, who argues that a system of charged colloidal particles and oppositely charged counter ions will show an attraction between the particles for certain distances. An entirely different point of view is presented in the work of Levine and Dube, and in that of Corkill and Rosenhead. They consider different cases, but in both instances the conclusion is reached that even for the case of two particles, attractive forces may result from the double-layer interaction. We have been reconsidering this problem (8, 9, 10, ll), and a brief outline of our results is given here. Full details are to be published in book form (12). I t occurred to us that the conclusions of those authors who find an attraction between the particles ought to be incorrect, as the net result of an interaction under reversible conditions will generally be a partial suppression of the doublelayer charge. This will especially be true for lyophobic colloidal particles, for which the double-layer potential is fixed by the concentration of the potentialdetermining ions in the sol medium, and therefore will be independent of the particle distance. The double layer is formed autogenously when the particles are brought into contact with the solution. This formation is accompanied by a decrease of the free energy of the system. The interaction of two double layers must therefore be associated with an increase of the free energy, leading to a repulsion between the particles. This could be confirmed quantitatively by a careful consideration of the free 1 Presented at the Symposium on the Stability of Colloidal Dispersions, which wa8 held under the auspices of the Division of Colloid Chemistry a t the 110th Meeting of the American Chemical Society, Chicago, Illinois, September, 1946. 631
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energy of a system of particles surrounded by an electrolytic double layer. The theory has been applied t o a number of special cases, e.g., two flat plates parallel to each other, two spherical particles, and a hexagonal pattern of parallel cylinders. In most cases we started from the complete differential equation determining the electrical potential in the electrolytic solution in the neighborhood of the particles. For a single flat double layer this equation leads t o the well known Gouy-Chapman theory of the diffuse double layer. In some cases we also tried a better approach to the electrical conditions in the double layer, similar to Stern’s theory. In colloidal systems containing a small amount of electrolyte, the thickness of the double layer will generally be smaller than the particle dimensions. The linear approximation used in the Debye-Hiickel
FIG.1. Potential energy us. distance for two parallel plates in a solution of monovalent ions, for different values of the double-layer potential, 2, measured in units k T / e (see text).
theory of electrolytes cannot be applied in such systems, as it would lead to completely unsatisfactory results. Calculating in this way the repulsive potential between the plates or particles, and adding the London-van der Waals attractive potentials as calculated by Hamaker, we found potential os. distance curyes of the type given in figure 1. The graph refers t o the case of two parallel plates in a solution of monovalent ions and shoivs a set of curves\\ ith increasing values of the double-layer potential, z , measured in units k T / e ( z = 1 means therefore 26.6 mv. at room temperature, z = 2 is 51.2 mv., etc.). The units of the coordinates depend on the electrolyte concentration, n, measured by Debye’s viell-knon-n quantity K = (8rme2/e k T ) * ; A is K = 10‘ holds approximately for a 0.1 n solution, K = 106 for 0.001 n,etc. a proportionality factor for the London-van der Waals potential; it will depend on the nature of the participating atoms, but for most colloidal systems it appears to be in the neighborhood of a few times lo-’’
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We note the following features: 1. For small values of the double-layer potential the London-van der Waals potential appears t o prevail for all plate distances. The plates (or particles) will be attracted when they approach each other and the corresponding colloidal systems mill flocculate. 2. For sufficiently large values of the double-layer potential the repulsion due t o the interaction of the double layers appears t o dominate for intermediate distances (in the neighborhood of Kd = 1) and the curves show a more or less pronounced maximum. The resulting potential barrier, if sufficiently high with respect to k T , will prevent agglomeration of the particles and the colloidal system will behave as a stable sol. 3. The curves showing a maximum have two regions for which the Londonvan der Waals potential again prevails: uiz., for very small distances, and for comparatively large distances. The weak minimum at large distances will be of importance if its depth is larger than kT. The curves of figure 1 have been calculated under the assumption that the London-van der Waals potential betmen two atoms is proportional to r-'. Later on, doubt arose as to whether this law would still be correct for large distances between the atoms, of the order of magnitude of the wave lengths corresponding t o the fundamental frequencies of the atoms (say cm.). Casimir has therefore reconsidered the theory of r a n der Waals forces, including retardation, and found that for large distances the potential decays much more rapidly (approaching an F7law). The actual minima are therefore still weaker than those in figure 1. Provisional calculations suggest that minima larger than k T can only be experted in certain favorable cases; for instance, in the case of blade-shaped particles (approximated by the case of two flat plates) or cylindrical particles of sufficient size n hen oriented parallel to each other. The phenomena observed in aged ferric oxide sols by Heller ( 5 ) and Zocher and in tobacco mosaic virus sols by Bernal and Fankuchen (1) must probably be explained in this way (formation of tactoids). The theory shows that in systems containing sufficiently small amounts of electrolytes the height of the potential maximum may very easily reach a value of several times k T . The influence of the electrolyte concentration is shonn by figure 2 , for a rather low value of the double-layer potential ( z = 1, i.e., the surface potential is 25 G mv.). The graph refers to the case of two spherical particles with radius a = cm., using the London-van der Waals constant A = lo-''; s = R ' a is the distance betneen the particle centers measured in units a. It is seen that 11-ith increasing values of K , L e , with increasing electrolyte concentration, the potential barrier shifts gradually to smaller particle distances and is finally entirely suppressed. This behavior is obviously associated with the circumstance that for larger electrolyte concentrations the charge in the liquid is so strongly concentrated in the neighborhood of the surface of the particles that the repulsive field of the double layers falls entirely within the attractive sphere of the van der Waals forces and can no longer be active. The curves obtained for two spherical particles are not much different from
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those for two flat plates, so that, especially if the particles are not extremely small, the case of two plates can often be used as a first approximation. For large values of the double-layer potential we may then derive a very simple expression for the eiectrolyte concentration for which the maximum in the potential curve touches the axis of abscissas, Le., an approximate value of the electrolyte concentration for which the maximum will be insufficient to prevent agglomeration. This concentration is known as the flocculation value, and it is a well-known fact that it depends strongly on the valency of the ions with a
r
-,?OH I
FIG.2 . Potential energy of interaction us. distance between centers
of two spherical particles (in units of particle radius a = 10-6 cm., for z = l ) ,showing the influence of electrolyte concentration.
charge opposite to that of the particles (Schultze-Hardy rule). The simplified theory leads to the result that for monovalent, divalent, and trivalent ions the flocculation concentrations should be in a ratio
1:(1/2)8:(1/3)6 = 100:1.6:0.13 which is very close to the actual ratio found for all sorts of colloidal systems. Although the theory appears to be in agreement with various colloid-chemical data, a large amount of work remains to be done t o fit the complicated facts into the theory. One handicap in making comparisons with experimental data is that the potential drop in the diffuse layer has usually been calculated from elec-
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trophoretic data. We know now that the {-potentials calculated in this way are more or less incorrect, because we cannot neglect the relaxation effect in electrophoresis. The interesting phenomena discussed by Stamberger (coagulation by stirring (7)) must be directly associated with this effect, as it seems rather certain that they must be explained by a local decrease of the potential barrier betxeen the particles caused by a lagging behind of the charge in the liquid phase when a particle is in motion with respect to the surrounding liquid. The theory may be especially useful in considering in more detail the phenomena of thixotropy and tactoid formation as discussed by Heller (5). It seems worthwhile to study more closely the significance of the quantity {"/Kput forward by Eilers and Korff, and discussed in the present symposium in the paper by Graham (3). For further details ive refer to the papers previously cited (8-12). There we have also considered extensively the work of previous authors, including some who have been mentioned above. We wish to add that an essentially correct theory for the interaction of tvio double layers can be found in earlier papers (2) by the Russian author Deryagin, though worked out in an unsatisfactory manner. It should also be mentioned that Langmuir, in the last part of his well-known paper (6) on tactoids and coacervation, gives a correct expression for the repulsive force between tvio plates, which can be directly derived from our more general theory. SUMMARY
The theory of the interaction of the double layers has been reviewed in relation to the stability of lyophobic colloids. It is concluded that the interaction must be associated with an increase of the free energy, leading to a repulsion between the particles. The repulsive potential calculated from a consideration of the free energy for certain special cases has been combined with the London-van der Waals attractive potential calculated by Hamaker to obtain curves of potential us. distance. Predictions based on these curves appear to agree well withvarious experimental data. For example, the influence of electrolyte concentration and of the valencies of the ions on flocculation is satisfactorily explained in terms of the theory, although many complicated phenomena remain to be correlated with it. REFERESCES (1) BERSAL,J. D . , A S D F a X K V C H E s , I.: J. Gen. Physiol. 26, 111-20, 147 (1941). (2) DERYAGIN, B.: Acta Physicochim. U.R.S.S. 10, 333 (1939); Trans. Faraday SOC.36, 203 (1940). (3) GRAHAM, D . P . : The Contribution of Solvation to the Stability of Anthraquinone Vat Dye Suspensions; Paper S o . 32 of the Symposium on the Stability of Colloidal Dispersions, !vh&cb was held under the auspices of the Division of Colloid Chemistry at the 110th Meeting of the American Chemical Society, Chicago, Illinois, September 19-16. (4) H.~MAKER, H . C.: Chem. Weeliblad 36, 47 (1938); (English language) Symposium on Lyophobic Colloids. ( 5 ) HELLER,W.:Thixotropy, Tactoid Formation, Syneresis, and Other Colloid Phe-
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(8) (9) (10) (11) (12)
C. W. CARR, W. F. JOHKSOK .4KD I. M. KOLTHOFF nomena, and their Dependence on Colloid Stability; Paper So. 27 of the Symposium on the Stability of Colloidal Dispersions, which was held under the auspices of the Division of Colloid Chemistry a t the 110th RIeeting of the American Chemical Society, Chicago, Illinois, September, 1916. LANGMUIR, I.: J. Chem. Phys. 6,873 (1938). STAMBERGER, P. : Flocculation of Lyophobic Dispersions by Slow Mechanical Stirring; Paper S o . 33 of the Symposium on the Stability of Colloidal Dispersions, which was held under the auspices of the Division of Colloid Chemistry a t the 110th 3Ieeting of the American Chemical Society, Chicago, Illinois, September, 1946. VERWEY, E. J. W . : Chem. Xeekblad 39, 563 (1912). VERWEY, E . J. W.: Contribution to a symposium held by the Xederlandsche Chemische Vereniging on July 3-4, 1944. VERWEY, E. J. W . : Philips Research Reports 1.33 (1945). VERWEY, E. J. W., A K D OVERBEEK, J. TH.G . : Trans. Faraday Soc., in press. VERWEY,E. J. W., ABD OVERBEEK, J. TH. G., with the collaboration of K . van Xes: Theory of the Stability of Lj/ophobic Colloids, in press. Elsevier Publishing Company, Amsterdam, Holland.
T H E USE OF MEMBRASE ELECTRODES I S THE STUDY OF SOAP SOLUTIONS' C. W. CARR,
W.F. JOHSSOS, . ~ N DI. 11,KOLTHOFF
School of Chemistry, Institute of Technology, C-niversity of Minnesota, IMinneapolis, Minnesota Received November 14, 1946 I. INTRODUCTION
In studies of the properties of soap solutions several different physicochemical methods have been applied. These methods include such diverse measurements as that of the electrical conductance, the degree of solubilization of an oil or dye, the freezing-point loivering,the viscosity, and the surface tension of the solutions. The present paper is concerned with the use of recently developed membrane electrodes (1, 2, 4, 8) for the determination of the cation and anion activity in soap solutions. The collodion membranes are negatively charged in electrolyte solutions and behave as electrodes for cations in much the same may as the glass electrode behaves toward hydrogen ions. Similarly, the protamine-collodion membranes, being positively charged, behave as anion electrodes. These membranes differ from the glass electrode in that they are not specific for any one ion. For that reason they cannot be used for determining directly the activity of one ion in the presence of another of the same sign. However, they have been applied with success to a number of solutions containing a single electrolyte (3). Since the membranes are not always perfectly selective, especially a t concen]This investigation was carried out under the sponsorship of the Office of Rubber Reserve, Reconstruction Finance Corporation, in connection with the synthetic rubber program of the United States Government.
