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

We examine orientational patterns of liquid crystalline polymers (LCPs) using a mesoscale Doi theory that couples short-range, excluded-volume molecular interactions, rotary molecular diffusion, and the Marrucci–Greco potential for finite-range distortional elasticity. The model is a full tensor, polymeric generalization of small-molecule liquid crystal (Ericksen–Leslie) theory. The symmetric, traceless, rank 2 orientation tensor corresponds to micron-scale, averaged 3D microstructure through an orthogonal frame of eigenvectors (the directors, or principal optical axes) and corresponding eigenvalues (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 spatial patterns, both steady and time-dependent. Our constructions arise from posited tensor representations in spectral variables, separating spatial structure arising from optical axes variations versus order parameter variations. The reduced equations are solved to generate a variety of mesoscale structures, presented both in terms of the geometric content of the orientation tensor and in terms of the light scattering intensity patterns which would result from these exact macromolecular structures.