Fast Switching of Nematic Liquid Crystals by an Electric Field: Effects of Dielectric Relaxation on the Director and Thermal Dynamics

Abstract

Liquid crystals (LCs) represent a special state of soft matter in which the anisotropic molecules or their aggregates demonstrate a long-range orientational order but little or no positional long-range order [1]. In the simplest case of a uniaxial nematic LC (NLC), the long-range positional order is absent altogether; the molecules form a uniaxial centrosymmetric medium, as they are predominantly aligned along a single direction called a director and described by a unit vector n (such that n≡−n . The director can be realigned by electric and magnetic fields that thus change the optical properties of sample. The orientational dynamics of director in the applied electric field is a fundamental physical phenomenon that is at the heart of modern display technologies. Discovered in 1930s by Frederiks (initially for the magnetic case) [2], this phenomenon, rather surprisingly, still poses a fundamental unanswered question regarding the behavior of NLCs with the finite rate of dielectric relaxation. The problem can be understood as follows. The dielectric torque that reorients the director has the densityM t =D t ×E t , where E t is the electric field and D t is the electric displacement at the moment of time t. In the widely accepted standard approach [1, 3, 4], the director response is assumed to be instantaneous, i.e., the displacement D t is determined by the electric field at the very same moment D t = 0 E t , where 0 is the free space 277