# A simple theory of the electric double layer including solvent effects

## Abstract

The integral equations for the ionic and solvent profiles of a model electrolyte consisting of charged hard spheres (the ions) and dipolar hard spheres (the solvent) near a charged hard wall are examined. The mean spherical approximation (MSA), which is based upon a linearization in the strength of the charge density on the wall, leads to a set of coupled integral equations. In the limit of low concentrations, the ionic terms decouple from the solvent terms so that to obtain the ionic profiles it is only necessary to solve the MSA integral equation for a fluid of pure (i.e. without a solvent) charged hard spheres near a charged hard wall. The coupling of the ionic and solvent terms occurs in the integral equation for the solvent profile. In this paper it is assumed that the MSA integral equation for the solvent profile can be used with some more general and non-linear integral equation for the decoupled ionic contribution. This leads to a theory which is linear only in the response of the solvent to the charge on the wall. Some specific results are given for the case where the ionic terms are treated in the Gouy-Chapman theory. Generally good agreement with experiment is obtained without the use of semiempirical parameters. The discrepancies between the theory and experiment are most likely due to the completely symmetric model of the solvent molecule which has been used rather to the approximations used to obtain the integral equation. © 1982.