- Email: [email protected]
Investigations of the forces of interaction of surfaces in different media and their application to the problem of colloid stability
INVESTIGATIONS OF THE FORCES OF INTERACTION OF SURFACES IN DIFFERENT MEDIA AND THEIR APPLICATION TO THE PROBLEM OF COLLOID STABILlTY BY B. V. DERJAOTJIN, A. S. T~T~JWSKA~A (5 2), I. I. ABRICW~~VA(5 3) AND A. D. MALKINA($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 arb in quantitative accordance with the corresponding theory, under the condition of introducing the important correction for the thickness (about 40A) 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 highsensitivity 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 uucuo. After extreme care had been taken to remove all traces of surface electric charges and organic impurities, we succeeded to obtain quite reproducible results. Tbe force values are the same when measured in air and in uucuo and are proportional to the radius of curvature of the spherical surface in accordance with the formula for molecular interaction of macrobodies deduced by me 20 years ago. The measured force values are about l-2 orders smiler than the values that result from the London-Hamaker formula. Some years ago we obtained as Prof. Overbeek and Dr. Spamaay still do, results about one order of magnitude higher than those calculated by the London-Hamaker formula and of very bad reproducibility. This unexpectedly large discrepancy seems to be caused by surface charges and points to the exceptional diiculty in removing them. The last part of thii 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 Buxag’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 Buxag’s
experiments and the much smaller one is ours. $ 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. 74
Selected Works - 1 Costichev 1 was the tirst to assume the existence of such repulsion forces in thin liquid films. Hardy 2 developed the same idea and attempted to subsmtiate 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.46 Elton made an attempt to attribute the results of these experiments to the effect of “ elfxtroviscosity “.7 The groundl~ness of Elton’s argument and the errors involved in his reasoning were, however, elucidated in detail by Kussakow and the present author.8 The experimental relation 4 of the disjoiig pressure isotherms to the electrolyte concentration supplied a basis for calculating the repulsion forces in thin fihns due to the interaction of the electric double layers 9 situated at the interfaces between the film and the adjacent phases. The latter paper was the first to develop a method for calculating both the efiergy and the forces of this interaction. This method was subsequently also applied to strongly charged surfacesJO-13’ An attempt to calculate the interaction of similarly charged surfaces in electrolyte solutions was also made by Levine.14 and Corkhill and Rosenheed. Levine’s statistical derivation of the expression for the energy of interaction of particles, using Debye and Hiickel’s method of charging ions, involves an error which, in particular, leads at long distances to attraction instead of repulsion 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 Rosenheed. 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 properties of colloids, in the first place their stability. The author at first 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 Kofls rule9 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 HardySchultze and Ostwald’s rules to be substantiated and quantitatively revised.t 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 fomm1a.a An exact method of allowing for the effect of polymolecular adsorption layers on capillary condensation was simultaneously deve1oped.m 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 *see, e.g. Derjaguin, Trans. Faraday Sot.. 1940, 36, 209, the second psssage. An analogous reasoning was subsequently developed in extended and mbrc elaborated form by Venvey and Overbeek 17 (1948). t This shows the fallacy of the critical remark made by Verwey and Ovcrbex?kin their paper 17 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 dcr Waals forces. The latter remark is also wholly in&rrect inasmuch as the van der Waals forces have been taken into account by the present author in the theory of the stability of strong& charged sols in the same paper quote-d above. 13 For weakly charged sols these forces have already been taken into account in the derivation of the Eilers-KortT rule in the addendum to the paper presented to the discussion on the double layer (TMs. Furuday sac, 1940,36,730). All these incorrect statements in the historical review of the.quesGon have unfortunately remained uncorrected in the subsequent publications by Venvey and Over&k.
75
B. V. Derjaguin
76
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 5.21 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 tilms 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. ‘Ihe possibility of a rigorous, general and simple method $ of such recalculation or transition is presented by the following previously derived ~2 formula : N=G
co R(h)dh, (1) sh 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 f 4). For a sphere and a plane we have G = 2mr;
(2)
G=nr;
(2’)
for two spheres of radius r, and for two filaments
22 of radii rl and r2 meeting at an angle w,
G=2.nz/;;;; -. sin w
(3)
$ The method of direct calculation of theelectrostatic interaction developed by Levine *? 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.
experiments and the much smaller one is ours. $ 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. 74
Selected Works - 1 Costichev 1 was the tirst to assume the existence of such repulsion forces in thin liquid films. Hardy 2 developed the same idea and attempted to subsmtiate 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.46 Elton made an attempt to attribute the results of these experiments to the effect of “ elfxtroviscosity “.7 The groundl~ness of Elton’s argument and the errors involved in his reasoning were, however, elucidated in detail by Kussakow and the present author.8 The experimental relation 4 of the disjoiig pressure isotherms to the electrolyte concentration supplied a basis for calculating the repulsion forces in thin fihns due to the interaction of the electric double layers 9 situated at the interfaces between the film and the adjacent phases. The latter paper was the first to develop a method for calculating both the efiergy and the forces of this interaction. This method was subsequently also applied to strongly charged surfacesJO-13’ An attempt to calculate the interaction of similarly charged surfaces in electrolyte solutions was also made by Levine.14 and Corkhill and Rosenheed. Levine’s statistical derivation of the expression for the energy of interaction of particles, using Debye and Hiickel’s method of charging ions, involves an error which, in particular, leads at long distances to attraction instead of repulsion 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 Rosenheed. 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 properties of colloids, in the first place their stability. The author at first 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 Kofls rule9 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 HardySchultze and Ostwald’s rules to be substantiated and quantitatively revised.t 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 fomm1a.a An exact method of allowing for the effect of polymolecular adsorption layers on capillary condensation was simultaneously deve1oped.m 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 *see, e.g. Derjaguin, Trans. Faraday Sot.. 1940, 36, 209, the second psssage. An analogous reasoning was subsequently developed in extended and mbrc elaborated form by Venvey and Overbeek 17 (1948). t This shows the fallacy of the critical remark made by Verwey and Ovcrbex?kin their paper 17 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 dcr Waals forces. The latter remark is also wholly in&rrect inasmuch as the van der Waals forces have been taken into account by the present author in the theory of the stability of strong& charged sols in the same paper quote-d above. 13 For weakly charged sols these forces have already been taken into account in the derivation of the Eilers-KortT rule in the addendum to the paper presented to the discussion on the double layer (TMs. Furuday sac, 1940,36,730). All these incorrect statements in the historical review of the.quesGon have unfortunately remained uncorrected in the subsequent publications by Venvey and Over&k.
75
B. V. Derjaguin
76
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 5.21 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 tilms 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. ‘Ihe possibility of a rigorous, general and simple method $ of such recalculation or transition is presented by the following previously derived ~2 formula : N=G
co R(h)dh, (1) sh 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 f 4). For a sphere and a plane we have G = 2mr;
(2)
G=nr;
(2’)
for two spheres of radius r, and for two filaments
22 of radii rl and r2 meeting at an angle w,
G=2.nz/;;;; -. sin w
(3)
$ The method of direct calculation of theelectrostatic interaction developed by Levine *? 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.