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

Qi Wang

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-Ericksen (LE) theory, but the stress
tensor contains excessive gradient terms in addition to the LE stress
tensor. The theory predicts that the elastic moduli $K_1, K_2$ and
$K_3$ obey the ordering $K_3