STABILITY OF EQUILIBRIA OF NEMATIC LIQUID CRYSTALLINE POLYMERS

doi:10.1016/S0252-9602(11)60401-3

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (6): 2289-2304.doi: 10.1016/S0252-9602(11)60401-3

STABILITY OF EQUILIBRIA OF NEMATIC LIQUID CRYSTALLINE POLYMERS

Hong Zhou¹, Hongyun Wang²

1.Department of Applied Mathematics Naval Postgraduate School, Monterey, CA 93943, USA|2.Department of Applied Mathematics and Statistics University of California, Santa Cruz, CA 95064, USA

收稿日期:2011-09-30 出版日期:2011-11-20 发布日期:2011-11-20
基金资助:
This work is partially supported by the National Science Foundation and by the Office of Naval Research.

STABILITY OF EQUILIBRIA OF NEMATIC LIQUID CRYSTALLINE POLYMERS

Hong Zhou¹, Hongyun Wang²

1.Department of Applied Mathematics Naval Postgraduate School, Monterey, CA 93943, USA|2.Department of Applied Mathematics and Statistics University of California, Santa Cruz, CA 95064, USA

Received:2011-09-30 Online:2011-11-20 Published:2011-11-20
Supported by:
This work is partially supported by the National Science Foundation and by the Office of Naval Research.

摘要/Abstract

摘要：

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.

关键词: equilibria, stability, nematic liquid crystalline polymers, hysteresis phe-nomenon

Abstract:

Key words: equilibria, stability, nematic liquid crystalline polymers, hysteresis phe-nomenon

中图分类号:

35Kxx

Hong Zhou, Hongyun Wang. STABILITY OF EQUILIBRIA OF NEMATIC LIQUID CRYSTALLINE POLYMERS[J]. 数学物理学报(英文版), 2011, 31(6): 2289-2304.

Hong Zhou, Hongyun Wang. STABILITY OF EQUILIBRIA OF NEMATIC LIQUID CRYSTALLINE POLYMERS[J]. Acta mathematica scientia,Series B, 2011, 31(6): 2289-2304.

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STABILITY OF EQUILIBRIA OF NEMATIC LIQUID CRYSTALLINE POLYMERS

STABILITY OF EQUILIBRIA OF NEMATIC LIQUID CRYSTALLINE POLYMERS

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