SURFACE FORCES IN THE DEPOSITION OF SMALL PARTICLES 721 The effect on the zeta-potential, in the case of ionic adsorbed compounds, must obviously be taken into account in calculating VR. The presence of an adsorbed layer also influences VA. On classical lines, Vold (11) developed the theory for calculating the interaction of layered particles, and the same problem can now be tackled by Lifshitz theory (13, 18), probably with rather different results in particular cases. Naturally, if the adsorbed layer is a highly solvated macromolecular substance, its effective London-Hamaker (or Lifshitz) constant is rather close to that of water, and then the layer itself may contribute only a weak inter-particle attractive force. Under these circumstances, and quite apart from any double-layer forces, the absorbed layers will have a predominantly 'protective colloid' action--the van der Waals attraction being too weak at the point when the layers 'touch' to overcome the compressive resistance of these layers. (A solvated adsorbed layer naturally resists compression with a force analogous to osmotic pressure.) Even if the zeta-potential is reduced towards zero by alteration of the concentration of potential- determining ions or by large additions of indifferent salts, colloidal particles protected by a thick lyophilic colloid layer will neither coagulate nor deposit. The stabilizing effect of adsorbed layers is obviously of first rank im- portance but unfortunately the magnitude of the protection is difficult to calculate theoretically. With relatively small adsorbed molecules, the problem amounts to calculating the force (per unit area) required to 'crush' these molecules. This force mechanism is sometimes called 'steric stabilization'. With extended (i.e. solvated) polymer chains, it is possible to try the theory of configuration of polymers to calculate the elastic force required to compress the layer alternatively, it can be regarded as an osmotic pressure required to remove solvent from this coating of polymer solution. Such theoretical treatments can only be regarded as 'schematic', and as far as the writer is aware, it has not been possible to check theory against experiment in any test system. Work on this problem has been well reviewed by Lyklema (39) and more recently by Napper and Hunter (40). Flocculation by polymer bridging An exception to the statements made in the previous paragraph is sometimes encountered when very small quantities of a lyophilic colloid (insufficient to surround the particles) are present. The phenomenon of 'sensitization' of flocculation by proteins was recognized early in the

722 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS century, and is now widely exploited as a means of removing suspended particles. The modern linear synthetic polymers, such as polyacrylamide with molecular weights above 106, are particularly effective flocculants. Their mode of action has been reviewed recently (41) and undoubtedly depends on bridging adsorption in which these very long molecules are partly adsorbed on one particle and partly on the next. The result is literally an elastic linkage, which permits large flocs to be built up. The same principle can be expected to operate in non-aqueous media (43). Polymeric flocculants can certainly also cause attachment of single particles to smooth surfaces. The effect has been confirmed with quartz particles and silica plates in the writer's laboratory. The better the floccu- lant, the more strongly do the particles adhere. Another variation is the pre-adsorption of oeolyelectrolytes of high molecular weight to the substrate, followed by electrostatic deposition of particles of opposite electric charge. And a not-dissimilar phenomenon is the successive deposition of alternate mono-layers of a negative colloid (e.g. silica sol) and a positive colloid (e.g. alumina sol), as beautifully demonstrated by Iler (37, 42). (Received: 23rd February 1973) SELECTED LITERATURE Extension of DL VO theory: heterocoagulation (1) Derjaguin, B. V. A theory of the heterocoagulation, interaction and adhesion of dissimilar particles in solutions of electrolytes. Discuss. Faraday $oc. 18 85 (1955). (2) Bierman, A. Electrostatic forces between non-identical colloidal particles. J. Colloid $ci. 10 231 (1955). (3) Hogg, R., Healy, T. W. and Fuerstenau, D. W. Mutual coagulation of colloidal dispersions. Trans. Faraday $oc. 62 1638 (1966). (4) Wiese, G. R. and Healy, T. W. Effect of particle size on colloid stability. Trans. Faraday $oc. 66 490 (1970). (5) Usui, S. Heterocoagulation. Progr. Surf. Membrane $ci. 5 223 (1972). (6) Muller, V. M. Theory of the stability of a hydrophobic colloid. Res. Surface Forces (Trans. Consultants Bureau, New York) 3 236 (1971). (7) Pugh, R. J. and Kitchener, J. A. Theory of selective coagulation in mixed colloidal suspensions. J. Colloid Interface $ci. 35 656 (1971). (8) Honig, E. P., Roebersen, G. J. and Wiersema, P. H. Viscous correction. Effect of hydro- dynamic interaction on the coagulation rate of hydrophobic colloids. J. Colloid Interface $cL 36 97 (1971). Theory of van der Waals forces between particles: Hamaker method (9) Gregory, J. The calculation of Hamaker constants. Advan. Colloid Interface $ci. 2 396 (1969).