Numerical Solution of a Liquid Crystal Problem by Optimization

Abstract

The deformation of a nematic liquid crystal layer sandwiched between parallel metallically coated glass plates and subjected to an external electric field perpendicular to the plate, is of interest in the design of optical devices. Schadt and Helfrich [5] showed how such layers can be switched from light to dark and dark to light. Leslie [3] obtained equations describing the deformation of a twisted orientation pattern in a magnetic field. Deuling [1] considered the deformation of a nematic layer contained between metallized glass plates in an electric field when one plate is twisted through an angle ωm around an axis perpendicular to the plates. The nematic layer exhibits a helical orientation pattern even for small electrical fields. In practical applications, it is important to describe these twisted orientation patterns in terms of twist and tilt angles of the liquid crystal molecules as a function of depth in the layer. We have developed an algorithm to solve Deuling’s equations by a nonlinear optimization technique applied to an integral formulation of the governing equations. The effective implementation of this technique is facilitated by the availability of high quality optimization software found in the IMSL and NAG Libraries.