Multiple discrete energy levels and the bistable state of weak anchoring NLC cells

Abstract

The weak anchoring nematic liquid crystal (NLC) cell is investigated with regard to energy. Because the Gibbs free energy of liquid crystal system used in theory does not include temperature and entropy, and because the equations and boundary conditions for δG=0 are also the mechanical equilibrium conditions of the continuum, the Gibbs free energy G is equivalent to the energy E of the liquid crystal continuum. There are multiple solutions which satisfy these equations and boundary conditions, each solution corresponding to a certain energy value. We call these discrete energy values and energy levels. Adopting a simple liquid crystal cell model, the energy levels are calculated in detail by means of analytical and numerical methods. The results show that there are three energy levels (or more in certain cases). The values and sequence of the energy levels are related to the external field and anchoring parameters. The relationships between the energy level structure and the bistable. Fréedericksz transition are disussed, together with their influence on the response time. The physical condition for the existence of more than three energy levels is also given.