Solution of the generalized mean spherical approximation for charged hard-sphere mixtures

Abstract

We discuss in detail the method of solution of the GMSA for charged hard spheres of unequal sizes, briefly reported in a preceding paper. The theoretical approach is based on the use of the Wiener-Hopf factorization technique. It is shown that the solution of the Ornstein-Zernike equation with Yukawa closure can be obtained in terms of a system of coupled nonlinear equations, which can be solved numerically. Since the solution is manifold, we face the problem of how to choose the physically meaningful branch. To this aim we devise a procedure, which, starting from the well-known GMSA for equally sized charged hard spheres, builds up the solution for the present case by «perturbative» steps. The equal-size limit is then investigated in detail and close contact of our results with those obtained by other authors is established. The problem of the thermodynamic consistency of the GMSA and the usefulness of a comparison of the different ways one can impose it are also discussed.