A SOLUTION OF THE MULTIPLE-BINDING MEAN SPHERICAL APPROXIMATION FOR IONIC MIXTURES

The mean spherical approximation (MSA) for an arbitrary mixture of cha rged hard spheres with saturating bonds is solved in the Wertheim form alism. Any number of bonds is allowed. It is shown that the general so lution is given in terms of a screening MSA-like parameter Gamma(T), a cross-interaction parameter eta(B) that will depend on the binding as sociation 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 o n the particular closure that is used to compute the contact pair corr elation Function. The full solution requires, as in the dimer case rec ently solved by Blum and Bernard, solving m + 2 equations and addition ally the inversion of a matrix of size [(v-l)rn] for a system with m c omponents and v bonds. We recall that when v = 1, only dimers are allo wed; 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.