Rotational diffusion and orientation relaxation of rodlike molecules in a biaxial liquid crystal phase

The longitudinal relaxation time and the complex dielectric polarizability of rod-like molecules with dipole moment parallel to the long axis in a biaxial nematic liquid crystal are calculated using as model the rotational Brownian motion in a mean field potential so reducing the problem to a solution of a set of linear differential-recurrence relations for statistical moments (the appropriate equilibrium orientational correlation functions). The solution of this set is obtained by matrix continued fractions. Moreover, simple analytic equations (based on the exponential separation of the time scales of the intrawell and overbarrier (interwell) relaxation processes), allowing one to understand the qualitative behavior of the system and accurately predicting the longitudinal complex polarizability for wide range of the barrier height and anisotropy parameters, are proposed.