A Simple Model for the Diffuse Double Layer Based on a Generalized Mean Spherical Approximation

Abstract

A semiempirical method of including the effects of ionic size in a simple analytical model of the diffuse double layer is described. Guided by earlier work in the hypernetted-chain approximation, the ion−wall correlation functions are modified from their Gouy−Chapman approximations by addition of two new parameters. The first is a constant related to the osmotic pressure and thus to the volume of the ions. The second is related to the effect that ion size has on the thickness of the ionic atmosphere in the electrolyte system, and depends on the electrical field at the wall. The exact form of the potential-dependent correction is found using Monte Carlo estimates of the potential drop across the diffuse layer φd. In this way, an analytical expression for the potential drop is derived and used to estimate φd as a function of electrolyte concentration and charge density on the wall for 1−1 electrolytes assuming that the component ions have a diameter of 425 pm.