Exact banded patterns from a Doi-Marrucci-Greco model of nematic liquid crystal polymers

Elements of pattern formation in nematic liquid crystal polymers are presented using the Doi-Marrucci-Greco (DMG) moment-averaged theory. The theory yields a full tensor orientation equation, accounting for excluded-volume and distortional elasticity potentials, with rotational molecular diffusion. Spinodal decomposition associated with unstable homogeneous phases is described first by way of an exact solution of the linearized DMG model. A variety of uniaxial and biaxial banded spatial patterns are then explicitly constructed from the DMG model. Exact solutions are given that possess order parameter spatial variations as well as solutions whose banded intensity patterns arise from sinuous director heterogeneity. These constructions pose as analytical models for banded structures observed during and after cessation of simple shear or elongation.