Simulations of solvation in a Brownian dipole lattice

Abstract

We have simulated the solvation of ions in a solvent consisting of point dipoles which undergo diffusive reorientation while translationally fixed to the sites of a cubic lattice. The simplicity of this model allows us to thoroughly explore how the energetics and dynamics of solvation depend on factors such as solute charge, solvent polarity, and number of solvent molecules. Some of the main features observed are as follows. The orientational response of first solvation shell dipoles saturates for moderate solute charges, resulting in a nonlinear dependence of the reaction potential on solute charge. This nonlinearity is to a good approximation independent of solvent polarity and can be rationalized on the basis of a simple phenomenological model. One effect of the nonlinear solvent response is to cause solvation free energy wells of the sort considered in electron transfer theories to be significantly anharmonic. Surprisingly, this deviation from harmonic behavior has little apparent impact on solvation barriers to charge transfer. The time dependence of the solvation response deviates substantially from exponential behavior in the more polar systems studied. Solvation times (1/e times of the solvation response) are directly related to the magnitudes of fluctuations in the solvation potential. The dynamics of solvation for times ≤t1/e can therefore be understood in terms of purely static correlations between solvent molecules. Dynamical interparticle correlations are only important in determining the longer time behavior of the solvation response. In contrast to the long-ranged character of the solvation energy, only 20–30 solvent molecules are required to produce solvation times characteristic of bulk solvent.