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Modelling post-aligned bi-stable nematic liquid crystal display

M. Zyskin
University of Bristol, UK

Keywords:
liquid crystal, PABN, numerical simulations, initial configuration, topological classification, energy bounds, harmonic maps

Abstract:
In existing liquid-crystal display technologies, each display cell supports just a single stable configuration. To produce optical contrast, a voltage must be applied to re-orient the molecules. Refreshing the pixels in this way consumes substantial power and limits the resolution of the display. A number of research groups world-wide are seeking to develop alternative technologies based on bi-stable liquid crystal cells. Bi-stable cells support two (or more) stable configurations with contrasting optical properties. Power is needed only to switch from one stable configuration to another. Successful implementation would lead to displays with higher resolution and requiring significantly less power than is currently possible, and would constitute a breakthrough in display technology.
One of mechanisms where bi-stability was shown to exist is post-aligned bi-stable nematic device (PABN): in a geometry of periodic arrays of rectangular posts, there are two stable configurations of nematic, tilted and planar, with optically distinct properties.
 
We propose a new approach towards modelling stable configurations of nematic in geometry of polyhedral posts (periodic or otherwise), which require less computational resources then existing methods. Using director field model, we establish topological classification of nematic configurations in polyhedral geometry with appropriate boundary conditions (often a mixture of tangent, normal and periodic), and allowing for defects. We give minimal energy bounds for configurations of various topologies, and identify topological types with low energies. We produce test configurations of a given topology, with a small number of free parameters (in one-constant energy approximation, those test configurations can be constructed in such a way that they are close to actual energy minimizers). Numerically minimizing energy with respect to free parameters gives a good insight on stable configurations of nematic, in particular on singularities which it may develop, and provide very good trial configurations for a more realistic, but requiring substantially more computational resources numerical modelling (such as Q tensor and molecular simulations).
 
For periodic arrays of rectangular posts, with tangent boundary conditions on faces, our results include topological classification of director fields, energy bounds, and simple test configurations close to energy minimizers. We use those test configurations to find numerically two topologically distinct energy-minimizing configurations.

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