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Modelling postaligned bistable 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 liquidcrystal display technologies, each display cell supports just a single stable configuration. To produce optical contrast, a voltage must be applied to reorient the molecules. Refreshing the pixels in this way consumes substantial power and limits the resolution of the display. A number of research groups worldwide are seeking to develop alternative technologies based on bistable liquid crystal cells. Bistable 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 bistability was shown to exist is postaligned bistable 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 oneconstant 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 energyminimizing configurations.
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