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Quasi-stable liquid crystal configurations in polyhedral geometries

Majumdar, Apala; Robbins, Jonathan; Zyskin, Maxim; Newton, Chris


Keyword(s): liquid crystals; bistability; topological classification

Abstract: Bistable director configurations are of great interest in liquid crystal display technologies, offering the possibility of higher resolution combined with reduced power consumption. One way to achieve such bistability is to use the cell geometry. As part of an ongoing programme to analyze quasi-stable configurations of liquid crystals in polyhedral geometries, we construct a topological classification scheme of unit-vector fields in convex polyhedra subject to tangential boundary conditions and obtain a general lower bound on the energy of these configurations. We also study the specific case of a unit cube, where we obtain lower and upper bounds for the energies of a family of topological types. This paper will be published in the Proceedings of the XV Conference on Liquid Crystals: Chemistry, Physics, and Applications, 2003, Zakopane, Poland and is made available as an electronic preprint with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. Notes: Apala Majumdar, Jonathan Robbins and Maxim Zyskin, Dept of Mathematics, University Walk, University of Bristol, Bristol, BS8 1TW UK

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