On the rotational diffusion of asymmetric molecules in liquid crystals

We present a nonperturbative solution of the rotational diffusion equation for an asymmetric rotor reorienting in a uniaxial liquid crystal, such as a nematic, smectic A or membrane bilayer covering the full range of order parameters from isotropic to complete order for rod-like and plate-like molecules. We obtain explicit expressions for the rotational diffusion matrix elements for a potential containing arbitrary rank interactions. For the actual numerical computations we consider the rotor with biaxial diffusion tensor to be subject to a second rank biaxial orienting potential. We study in detail the influence of changes in diffusion tensor and ordering matrix biaxiality on correlation functions and correlation times of first and second rank and we comment on experiments that can be sensitive to biaxiality effects in the diffusion tensor. We give a comparison with approximate results that have appeared in the literature.