Theory of nonprimitive electrolyte solutions: generalized electrostatic model for the equilibrium properties of ionic–polar mixtures

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Abstract
A new electrostatic method for the equilibrium properties of nonprimitive electrolyte solutions is proposed. The theory is developed in detail for a 1‐1 symmetric electrolyte composed of equal radius rigid spheres with embedded charges and dipoles. The theory is based on the following key ideas. The microscopic electrostatic equation for the ionic–polar mixture is reduced by averaging to a coupled hierarchy of effective electrostatic equations which depend, respectively, on the coordinates of 0, 1, 2, 3, etc., molecules. The first member of the hierarchy, which determines the macroscopic electrostatics in the solution, involves a salt concentration dependent dielectric constant ε and a generalized Debye inverse screening length κ. These constitutive parameters are determined self‐consistently from the solutions of the second set of hierarchy equations. These are rendered tractable by a mean field closure of the hierarchy which is tantamount to assuming the constitutive parameters of the solution when one molecule is fixed are identical to the macroscopic constitutive parameters. The resulting first hierarchy equations are of generalized Poisson–Boltzmann form and involve dielectric and Debye screening functions which mirror the reference fluid hard sphere distribution function gHS(r). The theory is solved analytically by assuming gHS(r) has its low‐density limit to yield a finite ionic strength generalization of the Onsager polar fluid theory. A more realistic approximation to gHS(r) yields a theory including local structure (i.e., Kirkwood) corrections to the Onsager model. The ion–ion potential of mean force predicted by this latter model is calculated at both zero and finite ionic strength. The significant differences between results of the nonprimitive electrolyte theory and an analogous primitive model theory also developed here are identified and discussed qualitatively for low, intermediate, and high dielectric constant solvents. Salt concentration and local structure effects on the dielectric behavior of the solution are also examined quantitatively.