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.
Discrete and Continuous Dynamical Systems, Series B
Copyright 2011 American Institute of Mathematical Sciences. Available on publisher's site at http://dx.doi.org/10.3934/dcdsb.2011.15.475
Zheng, Xiaoyu; Palffy-Muhoray, Peter (2011). One Order Parameter Tensor Mean Field Theory for Biaxial Liquid Crystals. Discrete and Continuous Dynamical Systems, Series B 15(2) 475-490. doi: 10.3934/dcdsb.2011.15.475. Retrieved from https://oaks.kent.edu/cpippubs/231