The dynamics of polar solvation: Inhomogeneous dielectric continuum models

The influence of an inhomogeneous dielectric response on the dynamics of solvation of ions and dipoles is investigated. Solvent models considered include discrete shell models as well as models in which the solvent dielectric constant varies continuously as a function of distance from a spherical solute. The effect of such dielectric inhomogeneity is to introduce additional, slower relaxation times into the solvation response when compared to the homogeneous case. For all models studied, the deviation of the average relaxation time from that predicted for a homogeneous continuum solvent increases as the dielectric constant and the length parameter, which specifies the rapidity of approach to bulk behavior, increase. For a given solvent model the solvation response to a change in a point dipole moment is slower than the response to a charge jump. The continuum results are compared to a recent molecular model based on the mean spherical approximation. The comparison suggests that deviations from homogeneous continuum behavior in the molecular model can be accounted for by inhomogeneity of the solvent dielectric constant extending only over the first solvation shell. Predictions of inhomogeneous continuum models are also compared to experimental data. Both the observed dependence of average relaxation time on dielectric constant, and the detailed time dependence of the relaxation in high dielectric constant solvents can be rationalized on the basis of such models.