DYNAMIC SPHERICAL MODEL FOR SOLVATION IN A DIPOLAR LATTICE

The spherical model for a dipolar lattice is extended to the dynamic r egime to provide a theory for nonequilibrium solvation. In this extens ion the dynamic susceptibility takes the same expression as the static one in the spherical model, but the dielectric constant is replaced b y the dielectric function. This leads to the same result as what is ob tained from the Smoluchowski-Vlasov equation if the dielectric functio n takes the Debye form. Otherwise it can be derived from a generalized Smoluchowski-Vlasov equation. The solvation dynamics of an ion is fou nd by summing the product of the dynamic polarization of the homogeneo us lattice and the electric field of the ion at each lattice site (exc ept the ionic site). This constitutes the dielectric approximation. By use of dielectric functions from previous simulations, the dynamic sp herical model produces results that agree very well with simulated ion ic solvation dynamics. However, the dynamic spherical model fails for dipolar solvation as a result of the inherent dielectric approximation . By using the spherical model expression for the static dipolar solva tion energy and ''tending it to the dynamic regime, an expression is o btained for dipolar solvation dynamics. Its results agree moderately w ell with simulations. Several implications for solvation dynamics in d ipolar liquids can be drawn from this study. It is suggested that the dielectric function plays an essential role in theories of solvation d ynamics. It is also shown that the memory function theory of Fried and Mukamel can be derived from a generalized Smoluchowski-Vlasov equatio n. Lastly it is concluded that the dielectric approximation has to be improved for dipolar solvation.