Generalized mean spherical approximation for charged hard spheres: The electrolyte regime

Abstract

A study of a generalized mean spherical approximation (GMSA) proposed by Ho/ye, Lebowitz, and Stell in J. Chem. Phys. 61, 3253 (1974) is made for a system of charged hard spheres. The complete solution of the GMSA is given explicitly. It yields a fully analytic theory—that is, both the thermodynamic properties of the GMSA and the structure factors associated with its distribution functions can be found in simple closed form. Moreover, the GMSA is constructed in such a way to insure that use of the virial theorem, fluctuation theory, and the expression for its internal energy all lead to identical thermodynamics, characterized by the same simple algebraic equations that appear in the mean spherical approximation (MSA). Quantitative results are given for the restricted primitive model electrolyte under conditions typical of 1–1 electrolytes. They demonstrate that the GMSA represents a significant improvement over the MSA, which is seriously lacking in thermodynamic self–consistency for charged spheres and is associated with negative pair distribution functions at low densities for spheres of like charge.