Regulation of surface potential at amphoteric surfaces during particle–particle interaction

A model is presented whereby a system of two interacting electrical double layers can minimise its electrical free energy at all distances of separation. The surface charge on each particle is described in terms of surface site equilibria which maintain constant chemical potential of potential determining ions. The ability of the system to react (i.e. buffer) to changes in the interparticle medium during approach, depends on the surface site dissociation constants, the point of zero charge of the surface and the ionic strength. It is shown that essentially perfect regulation, i.e. essentially infinite buffer capacity, is observed with systems such as AgI for which the potential of the single double layer is given by the Nernst equation; for such a system the usual assumption of interaction at constant potential is sensibly correct. For systems where the activity of potential determining ions is set at a value far removed from a surface dissociation constant the interaction is well approximated by constant charge interaction. The interaction with regulation involves solving a set of transcendental equations for self consistent values of surface charge and potential at all separations for any given set of bulk parameters. It is a general treatment that replaces constant charge and constant potential assumptions and is applicable to oxide colloids and amphoteric biosurfaces in particular.