Microscopic expression for dielectric friction on a moving ion

Abstract

A theoretical study of the dielectric friction on an ion moving through a dipolar liquid is presented. A microscopic expression for the dielectric friction is derived from linear response theory for a Brownian ion. This expression supports the picture of a ‘‘dynamic solventberg’’ model in the sense that much of the contribution to dielectric friction (ζDF) comes from the nearest-neighbor molecules. The translational modes of the solvent are found to have a very strong influence on the dielectric friction, in agreement with the observation of Colonomos and Wolynes [J. Chem. Phys. 71, 2644 (1979)]. In fact, except in the limit of small ion size, the microscopic ζDF is significantly larger than the continuum ζDF in the absence of the translational motion of the solvent molecules, but the reverse is obtained in the presence of a substantial translational contribution. It is found that the recovery of the continuum limit results from the molecular expression requires serious assumptions, some of which are hard to justify. It is also found that the point dipole approximation for the dipolar solvent molecule leads to improper results for ζDF because this approximation gives a wrong wave vector (k) dependence of the wave vector dependent dielectric function (ε(k)) of the liquid at large k (kσ≫2π, where σ is the solvent molecular diameter). We show that within a linear equilibrium theory for dipolar liquids, the cross correlations between the short ranged hard force and the long ranged dipolar force is zero so the calculations of Colonomos and Wolynes are internally consistent. However, this cross correlation can be quite important if the soft force also contains a spherically symmetric part. The similarity between the solvent role in ζDF and in the time-dependent fluorescence Stokes shift is discussed. The limitations of the present theory are also pointed out.