One order parametertensor mean field theory for biaxial liquid crystals

Xiaoyu Zheng; Peter Palffy-Muhoray

doi:10.3934/dcdsb.2011.15.475

Article Contents

2011, Volume 15, Issue 2: 475-490. Doi: 10.3934/dcdsb.2011.15.475

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One order parameter tensor mean field theory for biaxial liquid crystals

Xiaoyu Zheng^1, and
Peter Palffy-Muhoray^2,

1.
Department of Mathematical Sciences, Kent State University, Kent, OH 44242
2.
Liquid Crystal Institute, Kent State University, Kent, Oh 44242

Received: October 31, 2009

Revised: January 31, 2010

Published: August 2011

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Abstract

In this paper, we present a simple one tensor mean field model of biaxial nematic liquid crystals. The salient feature of our approach is that material parameters appear explicitly in the order parameter tensor. We construct the free energy from a mean field potential based on anisotropic dispersion interactions, identify the order parameter tensor and its elements, and obtain self-consistent equations, which are then solved numerically. The results are illustrated in a 3D ternary phase diagram. The phase behavior can be simply related to molecular parameters. The results may be useful for designing molecules that show a thermotropic biaxial phase.

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Mathematics Subject Classification: Primary: 82B26.

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