A hydrodynamic theory for solutions of nonhomogeneous nematic liquid crystalline polymers of different configurations

Abstract

A hydrodynamic theory is developed for solutions of nonhomogeneous nematic liquid crystalline polymers (LCPs) of a variety of molecular configurations in proximity of spheroids, extending the Doi kinetic theory for rodlike molecules. The new theory accounts for the molecular aspect ratio as well as the finite range molecular interaction so that it is applicable to liquid crystals ranging from the rodlike liquid crystal at large aspect ratios to the discotic one 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. When restricted to uniaxial symmetry in the weak flow limit, the theory recovers the director equation of the Leslie–Eriksen (LE) theory, but the stress tensor contains excessive gradient terms in addition to the LE stress tensor. The theory predicts that the elastic moduli K1, K2, and K3 obey the ordering K3<K1<K2 for stable, discotic (oblate spheroidal) LCPs in the weak flow limit. The ordering is reversed for rodlike (prolate spheroidal) LCPs. It yields a positive Leslie viscosity α2 (α3) in the flow-aligning (tumbling) regime for oblate (prolate) spheroidal LCPs. Moment averaged, approximate, mesoscopic theories for complex flow simulations are obtained via closure approximations.