Recently developed bistable nematic devices such as the ZBD and PABN displays
use complex surface morphologies, defect interactions and flexoelectricity in
order to achieve bistability, which reduces power consumption and thus benefits
hand-held devices. To understand and optimise such devices, the predictions of
flexoelectric and surface coefficients from Projects 1, 2 and 5 are to be used
in mesoscopic models which allow an accurate description of regions of low
order.

Two methods will be used and compared in this project, lattice-Boltzmann and finite difference/element techniques, both of which will model fluid flow and order variations.

A number of lattice Boltzmann (lB) approaches have been developed for solving the equations of nemato-dynamics with a variable order parameter [1-3]. The variable order schemes are more readily adapted to lB solvers, particularly in three dimensions, and have the additional merit that they allow a more correct description of both defects and surface interactions. There are a number of approaches to the introduction of a variable order parameter into nemato-dynamics (see eg [4]) and the lB schemes are, in principle, able to recover all of these schemes. It is likely that it will be necessary to use an adaptive mesh in order to more accurately describe the behaviour near walls and defects; similar approaches have been adopted by Svencek [5] to model defect motion. The lB methods have been shown to be successful in modelling device scale properties and, in particular, bistability and defects [6,7]. Also, flexo-electric and surface effects can be readily incorporated through appropriate modifications of the free energy functional and, hence, the molecular field tensor.

Finite difference and finite element numerical techniques will also be used to solve a recently developed mesoscopic dissipation theory by Sonnet (Strathclyde) and Virga which extends the classic Ericksen-Leslie theory and allows for changes in mesoscopic order. By using multigridding and adaptive grid refinement we will be
able to model lengthscales many orders of magnitude smaller than the typical device size which will be essential to describe the behaviour near walls and defects. Similar approaches have been used successfully by Svencek. The use of adaptive grid methods will also be explored within the lB solver.

The results of both models will be compared with each other (in terms of solution accuracy and efficiency) and compared with experimental results from Hewlett-Packard and Dr Elston. Having established, and validated, modelling routes from molecular to device length scales, the development of novel materials and device geometries will be explored through collaborative interactions with Projects 1, 2, 5 and 11.


[1] C M Care, I Halliday and K Good (2000) J Phys; Condensed Matter 12, L665-L671.

[2] Denniston C, Orlandini E and Yeomans J M (2001) Phys Rev E 63, 056702.

[3] Care C M, Halliday I, Good K and Lishchuk S V (2003) Phys Rev E 67, 061703.

[4] Sonnet A and Virga E, Dissipation theory for nematodynamics, (2003), to appear in Continuum Mechanics and Thermodynamics.

[5] Svencek D and Zumer S (2002) Phys Rev E 66, 021712.

[6] Toth G, Denniston C, Yeomans J M (2002) Comput Phys Commun 147, 7.

[7] Toth G, Denniston C, Yeomans J M (2002) Phys Rev Lett 88, 105504.