Exact solution of the mean spherical model for simple polar mixtures

Abstract

Wertheim's solution of the mean spherical model (MSM) for pure fluids composed of hard spheres with embedded dipoles [J. Chem. Phys. 55, 4291 (1971)] is extended to multicomponent polar fluid mixtures. The components are restricted to have equal hard sphere radii but may have different dipole moments. The anisotropic part of the pair correlation functions for an m-component fluid characterized by hard sphere diameter d, temperature parameter β, dipole moments μ1, μ2, ···,μm, and densities ρ1, ρ2, ···,ρm are shown to be expressable in terms of the corresponding functions for an effective pure MSM polar fluid with the same hard sphere radius and the same temperature parameter but with an effective dipole moment μ̂ = [m−1 (μ12 + μ22 + ⋯ + μm2)]1/2 and an effective density ρ̂ = μ̂−2(μ12ρ1 + μ22ρ2 + ⋯ + μm2ρm). The excess thermodynamic properties of the mixture (relative to a pure hard sphere Percus-Yevick fluid) are shown to be those of the effective pure fluid. The dielectric constant of the mixture is also that of the effective pure fluid. The case of polar-nonpolar mixtures is considered by allowing one or more of the dipole moments to vanish. It is found that the potential of mean force and spatial distribution of the nonpolar molecules is independent of the magnitude of the dipoles while the anisotropic correlations between the polar molecules are independent of the presence of the nonpolar species.