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

Abstract

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 parameterΓ ^T, a cross-interaction parameterη ^β that will depend on the binding association equations, the set of binding association fractions, and an additional algebraic equation. The equation forΓ ^T is given for the general case. The equation forη ^β, 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, solvingm+2 equations and additionally the inversion of a matrix of size [(ν−1)m] for a system withm components and ν bonds. We recall that when ν=1, only dimers are allowed; for ν=2, only linear chains are formed: and when ν≥3, branching of the polymers occurs. It can be shown that the excess entropy for the polymer case is as before,ΔS ^MSA=(Γ ^T)³/3π + sticky terms, where the sticky terms depend on the model and will be given in future work.