Ionic solution in a molecular polar solvent

Abstract

We treat here the statistical mechanics of a solution of ions in a polar nonpolarizable solvent. In our model the ions are taken to be charged spheres of equal diameter σ, half of them bearing charge e and the remaining half bearing charge −e. The solvent consists of dipolar spheres of the same diameter σ and the solvent–ion interaction is taken to be a charge–dipole interaction with a hard core, also of diameter σ. Our major interest in the model is its treatment of the molecular solvent on an equal statistical mechanical footing with the ions, rather than as a structureless continuum as in the primitive model. We consider a lowest-order γ-ordered approximation that is exact in the limit of infinite Debye length. Our results yield for the first time the explicit large-r form for the ion–ion, ion–solvent, and solvent–solvent pair distribution functions at arbitrary solvent densities in the limit of vanishing ion charge or ion concentration. A number of new thermodynamic expressions valid in these and related limits are also obtained.