The discreteness-of-charge effect at charged aqueous interfaces: III. Smoothly varying dielectric constant in inner region at mercury interface

Abstract

The discreteness-of-charge potential for an adsorbed ion at the mercury/aqueous electrolyte interface is derived for a model of the inner region with a smoothly varying isotropic dielectric constant. Use is made of the work by Buff and co-workers, who solved the modified form of Poisson's equation for the potential due to a unit point charge situated in a region of smoothly varying dielectric constant. Similar equations are solved in this paper in a more direct manner and the exclusion-disc potential, the major contribution to the discreteness-of-charge potential, is then determined. The specific dielectric constant profile for the inner region, which can be changed by choosing different values for a variable parameter, is expressed in terms of circular and hyperbolic cosines. This particular form, which was used by Buff and co-workers, yields a relatively simple expression for the potential due to a unit point charge. The effect of the diffuse layer in the aqueous phase is included and is shown to be substantial. A comparison is made with the earlier model (papers I and II) where the Stern inner region was divided by the inner Helmholtz plane into two zones of different but uniform dielectric constants ε 1 and ε 2 ( ε 1 < ε 2 ) so that discontinuities were present at both the inner and outer Helmholtz planes, as well as at the mercury surface. It is found that for the same thickness of the inner and outer zones and equivalent mean dielectric constants for the continuous model equal to ε 1 and ε 2 , the discontinuous and continuous models of the dielectric constant profile give similar values for the discreteness-of-charge potential. A list of misprints in papers I and II is given at the end of this paper.