Stability of equilibria of nematic liquid crystalline polymers
Abstract
We provide an analytical study on the stability of equilibria of rigid rodlike
nematic liquid crystalline polymers (LCPs) governed by the Smoluchowski equation with
the Maier-Saupe intermolecular potential. We simplify the expression of the free energy
of an orientational distribution function of rodlike LCP molecules by properly selecting
a coordinate system and then investigate its stability with respect to perturbations of
orientational probability density. By computing the Hessian matrix explicitly, we are
able to prove the hysteresis phenomenon of nematic LCPs: when the normalized polymer
concentration b is below a critical value b∗ (6.7314863965), the only equilibrium state is
isotropic and it is stable; when b∗ <b< 15/2, two anisotropic (prolate) equilibrium states
occur together with a stable isotropic equilibrium state. Here the more aligned prolate
state is stable whereas the less aligned prolate state is unstable. When b > 15/2, there are
three equilibrium states: a stable prolate state, an unstable isotropic state and an unstable
oblate state.
Description
Acta Mathematica Scientia, 31B(6), 2289-2304, 2011
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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