Methods for the exact construction of mesoscale spatial structures in liquid crystal polymers

We examine orientational patterns of liquid crystalline polymers (LCPs) usi ng a mesoscale Doi theory that couples short-range, excluded-volume molecul ar interactions, rotary molecular diffusion, and the Marrucci-Greco potenti al for finite-range distortional elasticity. The model is a full tenser, po lymeric generalization of small-molecule liquid crystal (Ericksen-Leslie) t heory. The symmetric, traceless, rank 2 orientation tenser corresponds to m icron-scale, averaged 3D microstructure through an orthogonal frame of eige nvectors (the directors, or principal optical axes) and corresponding eigen values (the order parameters) which convey the degrees of orientation with respect to the optical axes. These model quantities are directly related to intensity data from light scattering experiments. We focus on a classical method, separation of variables, to provide an exact construction of spatia l patterns, both steady and time-dependent. Our constructions arise from po sited tenser representations in spectral variables, separating spatial stru cture arising from optical axes variations versus order parameter variation s. The reduced equations are solved to generate a variety of mesoscale stru ctures, presented both in terms of the geometric content of the orientation tenser and in terms of the light scattering intensity patterns which would result from these exact macromolecular structures. (C) 2001 Elsevier Scien ce B.V. All rights reserved.