Mean Spherical Model Integral Equation for Charged Hard Spheres I. Method of Solution

The thermodynamic properties and radial distribution function of a ``primitive model electrolyte'' are calculated in the Mean Spherical Model (MSM) approximation. The system considered is formally described as a classical fluid of charged hard spheres (hard sheets in one dimension). The interaction potential between an ion of species i and an ion of species j, vij(r) is the sum of a Coulomb part and a hard core part qij(r)=∞ for r Rij or 0 otherwise. The MSM approximation consists of supplementing the fact that the radial distribution function gij(r) is zero for r Rij by equating the Ornstein—Zernike direct correlation function Cij(r) to -βvij(r) for r Rij, β being the inverse temperature. In this paper, which is the first of two in this topic, we give the method of solution for this approximation and obtain Cij(r) for r Rij as polynomials in r, which have a structure similar to that found in the PY approximation for a mixture of uncharged hard spheres. We give the solution up to a set of algebraic equations in the polynomial coefficients. In the second paper we discuss the explicit solution and derived thermodynamic quantities.