THE GENERAL-SOLUTION OF THE BINDING MEAN SPHERICAL APPROXIMATION FOR PAIRING IONS

The mean spherical approximation (MSA) for an arbitrary mixture of charged hard spheres with saturating bonds is solved in the Wertheim formalism. Only pairs are allowed. It is shown that the general solution is given in terms of two scaling parameters and the set of binding fractions. One of the scales is the screening parameter, and the other is a coupling parameter analogous to that of the simple MSA, but that now is found solving a cubic equation. Therefore the full solution requires solving m+2 nonlinear algebraic equations for a system with m components. A brief discussion of the thermodynamics is given.