The conditions governing the specific adsorption of counter-ions in the interaction of two parallel plate-like colloidal particles

Abstract

Frens and Overbeek have proposed that during the Brownian collision of two colloidal particles in a hydrophobic sol, the surface charge density due to potential-determining (p.d.) ions remains virtually unchanged. It is argued here that the cause of this behaviour is the low concentration of p.d. ions in the diffuse layer. However, equilibrium can be maintained with respect to counter-ions adsorbed into the Stern region from the supporting electrolyte, because the concentration of such electrolyte in the dispersion medium is considerably greater than that of p.d. ions. A general expression is quoted from earlier work for the electric double layer interaction between two parallel plate-like particles in the case where surface charge due to p.d. ions is fixed, but where counter-ions adsorbed into the Stern region can equilibrate with ions of the same species in the diffuse layer. Incorporating discreteness-of-charge and ion-size effects into the adsorption isotherm of the counter-ions, the double layer interaction energy of the two plates is calculated at contact of the two outer Helmholtz planes (o.h.p.'s). It is shown that although this energy exceeds the classical expression obtained by assuming the potential at the o.h.p. to be independent of plate separation, it remains finite.