A Kinetic Theory for Solutions of Nonhomogeneous Nematic Liquid Crystalline Polymers With Density Variations

Abstract

The kinetic theory developed in [1] for solutions of nonhomogeneous nematic liquid crystalline polymers (LCPs) of spheroidal molecular configurations is extended to account for the translational diffusion and the related spatial density variation. The new theory augments the effect of the density variation to the intermolecular potential, Smoluchowski equation and the elastic stress. It accounts for the molecular aspect ratio as well as the finite range molecular interaction so that it is applicable to liquid crystals ranging from rodlike liquid crystals at large aspect ratios to discotic ones at small aspect ratios. It also exhibits enhanced shape effects in the viscous stress and warrants a positive entropy production, thereby, the second law of thermodynamics. Moment averaged, approximate, mesoscopic theories for complex flow simulations are obtained via closure approximations. In the limit of weak distortional elasticity, weak translational diffusion, and weak flows, the theory yields the torque balance equation of the well-known Ericksen-Leslie theory.