The discreteness-of-charge effect at charged aqueous interfaces: I. General theory for single adsorbed ion species

Abstract

A general method is developed for determining the discreteness-of-charge potential of an adsorbed ion located on the inner Helmholtz plate (i.h.p.) within the Stern region at a charged non-aqueous medium/aqueous electrolyte interface. The Stern region is divided by the i.h.p. into two zones of different dielectric constants both lower than that of the aqueous medium. The potential distribution characterizing the ionic self-atmosphere which surrounds the ion in its inhomogeneous environment is treated as a perturbation on the mean potential distribution at the interface and the equations for this potential perturbation are linearised. The theory accounts for the screening effect on the self-atmosphere of the adsorbed ion of both the diffuse layer and the “primary” charge (due to electrons or potential-determining ions) situated on the boundary of the non-aqueous phase. The thermal motion of other adsorbed ions is also taken into account by introducing a two-dimensional Boltzmann distribution law in the neighbourhood of the specified adsorbed ions on the i.h.p. It is shown that, by the appropriate use of Fourier-Bessel integrals, an integral equation can be obtained for the potential distribution describing the two-dimensional ionic cloud on the i.h.p. surrounding the given ion.