On the Mathematical Modeling of Textures in Polymeric Liquid Crystals

Abstract

I consider the problem of development of domain structures in polymeric liquid crystal materials, in the absence of flow. The model emploid is that due to Ericksen. In one-space dimension, the optic variables of the problem satisfy a system of nonlinear parabolic partial differential equations. An analysis of traveling wave solutions and energy minimizers is carried out, using phase plane arguments. In particular, the presence of isotropic fronts in the material is discussed. Solutions to the governing equations that exhibit banding structures are also analyzed, in the framework of singular perturbations. The motivation of the present analyses is the modeling of banding textures that result from shear relaxation processes.