On the effects of association in the statistical theory of ionic systems. Analytic solution of the PY-MSA version of the Wertheim theory

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Abstract
The statistical mechanical approach to a fluid of dimerizing hard spheres proposed recently by Wertheim is extended to a two-component mixture of oppositely charged hard spheres. The pair potential is represented as a sum of the short-range hard-sphere potential, an intermediate-range square-well potential between the oppositely charged spheres, and a long-range Coulomb potential. The square-well potential, which is responsible for association, results from a single auxiliary site. If the site is located in such a way that only dimers are formed, the model presented here can be viewed as a model of chemical association in a fluid consisting of molecular ions. The model with the site located in the centre of hard sphere can be used to describe the formation of contact ion pairs in ionic systems. An analytical solution of the Ornstein-Zernike-like integral equation is obtained within a mixed Percus-Yevick and mean spherical approximation closure. The fraction of unbonded ions and the radial distribution functions are presented, and are studied as a function of the system density, the inverse reduced temperature, and the depth of the square well.