MSE8: Defects in liquid crystals - mathematical and experimental studies

Background

Liquid crystals are an intermediate phase of matter between the solid and liquid states. They are widely used in electronic device displays due to their anisotropic optical properties. Most current liquid crystal displays are monostable and require a constant source of power to maintain optical contrast.  Bistable liquid crystals displays are a new generation of high-performance and high-resolution displays that can support multiple optically-contrasting states. These have reduced power consumption compared to monostable devices since power is only require to switch between states but not to maintain a static image [1].

Techniques and Challenges

We model a planar two-dimensional bistable device [2] within the continuum Oseen-Frank model on square and rectangular domains with tangent/planar boundary conditions. In the isotropic one-constant approximation, the governing equation for the director field can be solved analytically. In the general anisotropic case, the governing equation is highly nonlinear and can be explored using a combination of asymptotic techniques and numerical finite element methods to resolve the boundary layers near the domain edges.

Results

In the one-constant case, we have obtained explicit analytic solutions for the stable equilibria along with analytic estimates for the energy in terms of the geometrical aspect ratio. For a square domain, two distinct states are identified, whereas for a rectangular domain, there are three distinct stable states. The global energy-minimiser is identified in both cases. Numerical simulations of the anisotropic case show qualitatively similar behaviour.

The Future

To make the model more physically realistic, we will model the planar boundary conditions with realistic surface anchoring energies. In the long term, we will study the nonequilibrium properties and the switching mechanisms in this device. We hope to fabricate these devices in collaboration with researchers in the Department of Physical and Theoretical Chemistry.

References

[1] Majumdar A., Newton C.J.P., Robbins J.M., Zyskin M.: Topology and Bistability in Liquid Crystal Devices, Physical Review E, 2007

[2] Tsakonas C., Davidson A.J., Brown C.V., Mottram N. J.: Multistable alignment states in nematic liquid crystal filled wells, Applied Physics Letters, 2007