Fluctuation Theory of Ionic Solvation Potentials

Abstract: This work presents a rigorous statistical mechanical theory of solvation free energies, specifically useful for describing the long-range nature of ions in an electrolyte solution. The theory avoids common issues with field theories by writing the excess chemical potential directly as a maximum-entropy variational problem in the space of solvent 1-particle density functions. The theory was developed to provide a simple physical picture of the relationship between the solution's spatial dielectric function, ion screening, and the chemical potential. The key idea is to view the direct correlation function of molecular Ornstein-Zernike theory as a Green's function for both longitudinal and transverse electrostatic dipole relaxation of the solvent. Molecular simulation data is used to calculate these direct correlation functions, and suggests that the most important solvation effects can be captured with only a screened random phase approximation. Using that approximation predicts both the Born solvation free energy and a Debye-Huckel law in close agreement with the mean spherical approximation result. These limiting cases establish the simplicity and generality of the theory, and serve as a guide to replacing local dielectric and Poisson-Boltzmann approximations.