A theory of dielectric relaxation in anisotropic systems

Abstract

There is no complete theory of dielectric relaxation for liquid crystals, in particular, or for anisotropic polar dielectrics, in general. Here we develop a relation between the complex frequency-dependent permittivity tensor and the autocorrelation matrix for the net permanent dipole moment of an ellipsoidal cavity within the dielectric. The relevant equations are derived for both non-polarizable and polarizable molecules. The choice of the cavity geometry and simple reductions of the macroscopic autocorrelation matrix to that for a single particle are discussed.