Exact solution of the mean spherical model for strong electrolytes in polar solvents

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Abstract
The mean spherical model (MSM) for dense fluids is solved for an arbitrary mixture of equal radii charged hard spheres with permanent embedded dipole moments. The model provides a treatment of ionic solutions that includes the feature of a molecular solvent. Thus, it gives a basis for investigating deviations from the familiar continuum dielectric model in ionic solution theory. The arbitrary polar‐ionic mixture is first reduced to an effective two component problem. One component is an effective charged species while the other is an effective polar species. This two component problem is solved in terms of three parameters closely related to the thermodynamic functions of the fluid. Nonlinear algebraic equations for these parameters are obtained. Although these equations appear to be analytically intractable for arbitrary ionic and dipolar strengths, explicit results are obtained for low ionic strength. In this limit, the ion‐ion contribution to the Helmholtz free energy is given by the classical Debye‐Hückel result. The dielectric constant in the Debye‐Hückel formula is that of the MSM polar fluid mixture that results if the ionic components of the polar‐ion solution are discharged. The self‐energy of charging, however, differs from the classical result. The model also exhibits Debye shielding of the solven‐solvent and solvent‐solute interactions as well as the more familiar solute‐solute shielding.