ANALYTICAL SOLUTIONS FOR ROTATIONAL DIFFUSION IN THE MEAN-FIELD POTENTIAL - APPLICATION TO THE THEORY OF DIELECTRIC-RELAXATION IN NEMATIC LIQUID-CRYSTALS

A theory of dielectric relaxation in nematics is developed for a molec ular dipole moment directed at an arbitrary angle to the molecular lon g axis. Both exact and simple approximate analytical formulae for the longitudinal and transverse components of the complex dielectric permi ttivity tensor are obtained for the non-inertial rotational Brownian m otion of a molecule in the mean field potential of Maier and Saupe. It appears that both longitudinal and transverse relaxation processes ar e effectively described by two Debye type mechanisms with correspondin g relaxation times and dielectric strengths expressed in terms of the order parameter. The generalization of the theory for an arbitrary axi ally symmetric mean field potential is given.