Mixtures of hard ions and dipoles against a charged wall: The Ornstein–Zernike equation, some exact results, and the mean spherical approximation

Abstract

The Ornstein–Zernike equation for a mixture of ions and dipoles near a hard charged wall is obtained. It is shown that the same exact contact and monotonicity theorems, previously derived for the primitive (continuum dielectric) case, also are valid for this model. Rather simple expressions for the contact density, potential difference, capacitance, and distribution functions are obtained in the mean spherical approximation (MSA). These expressions reduce to previously known results in the limits of low and high concentrations of ions. It is found that cooperative alignment of the dipoles near the wall results in an increased potential difference and reduced capacitance of the double layer compared to that calculated when the solvent is represented by a continuum dielectric.