Dielectric theory for polar molecules with fluctuating polarizability

Abstract

The dielectric properties of a classical system of interacting particles, each bearing a permanent dipole moment and thermally fluctuating polarizability, is considered. It is shown how a useful class of approximations initially defined for a system of nonpolarizable particles can be generalized to include fluctuating polarizability. For the case in which the mean polarization of an isolated particle is linear in applied field (i.e., harmonic fluctuations) it is further shown that the dielectric constant can be explicitly computed in these approximations, which include the mean spherical approximation and the single super-chain approximation (equivalent to the ’’reference’’ version of the linearized hypernetted chain approximation). The resulting ε is identical to that in a corresponding approximation defined for dipolar particles with nonfluctuating polarizability. In the limit of a closed-packed system of nonpolar particles with cubic symmetry, it is found that the resulting approximations for ε all reduce to the Claussius–Mossotti result, which is known to be exact for systems of such symmetry in the case of either fluctuating or constant polarizability. The inclusion of nonlinear effects is discussed briefly; in particular it is noted that a permanent dipole moment is equivalent to a certain limiting case of anharmonic fluctuations.