A solution of the multiple-binding mean spherical approximation for ionic mixtures

The mean spherical approximation (MSA) for an arbitrary mixture of charged hard spheres with saturating bonds is solved in the Wertheim formalism. Any number of bonds is allowed. It is shown that the general solution is given in terms of a screening MSA-like parameter Gamma(T), a cross-interaction parameter eta(B) that will depend on the binding association equations, the set of binding association fractions, and an additional algebraic equation. The equation for Gamma(T) is given for the general case. The equation for eta(B), however, depends strongly on the particular closure that is used to compute the contact pair correlation Function. The full solution requires, as in the dimer case recently solved by Blum and Bernard, solving m + 2 equations and additionally the inversion of a matrix of size [(v-l)rn] for a system with m components and v bonds. We recall that when v = 1, only dimers are allowed; for v = 2, only linear chains are formed, and when v greater than or equal to 3, branching of the polymers occurs. It can be shown that the excess entropy for the polymer case is as before, Delta S-MSA = (Gamma(T))(3)/3 pi + sticky terms, where the sticky terms depend on the model and will be given in Future work.