Ionic solution theory for nonideal solvents

A statistical‐mechanical study is made of the deviations from the primitive model (PM) of an ionic solution. In the PM, the solvent is treated as an ideal continuum that manifests itself only through the appearance of a dielectric constant ε ≠ 1. This paper begins with the introduction of a simple model that complements the PM, the NCDM (no charge‐dipole model) in which the granularity of the solvent is treated exactly. A second more realistic model, the EISIM (exact ion‐solvent interaction model), is then defined and discussed, as is the limit in which the PM approximation becomes an exact result. Like the PM the EISIM can be used as an ``ideal‐solvent'' approximation in which the solvent‐solvent interaction is idealized so that it manifests itself only through the appearance of ε. However, in the EISIM the solute‐solvent interaction is treated exactly. A cluster expansion for $W_n^{\text{(0)}}$ , the n ‐point potential of mean force, is derived and a thermodynamic perturbation theory for the problem is developed; an alternative treatment is also noted in which the mean‐spherical approximation can be used to bypass the McMillan‐Mayer theory and the attendant necessity for knowing $W_n^{\text{(0)}}$ , n > 2. The connection between the expressions herein derived and the phenomenologically developed Gurney‐Frank picture is pointed out; one term in the EISIM is shown to be identifiable with the solute‐solvent contribution to the Gurney cosphere‐intersection potential. Part of that term can be further isolated and identified as the exclusion‐volume contribution to the cosphere‐intersection potential.