Interactions between charged plates. Proof and applications of a useful theorem

Abstract

Two dissimilar semi-infinite charged plates separated by an electrolyte solution are considered. When the ion distribution in the solutions between surfaces s and s′ placed close to the plate surfaces is described by the Poisson–Boltzmann equation, and transfer of material across s and s′ is forbidden, it is shown that the state of material on the solid side of s or s′ is independent of plate separation and solution composition. This result justifies procedures used in previous work concerning the interaction between charged plates. It also leads to a method for the estimation of specific adsorptions of both potential determining ions and counterions from electrokinetic data alone, without recourse to a detailed model of the inner regions of the double layer.