Domain growth dynamics and Freedericksz transitions of liquid crystals: Brownian dynamics simulations on lattices

Abstract

A Brownian dynamics simulation using the Lebwohl-Lasher (LL) nematogen model is developed to investigate liquid crystals (LCs) on two-dimensional lattices. According to the examination of defect annihilation and domain growth, this methodology appears to be a successful approach in studying the LC dynamics, its main advantage being that the time evolution in the simulation mimics the physical time, in contrast to related modellings published recently. In addition, the Freedericksz transition of an LC under static magnetic fields is reproduced. Further analysis of the simulation outputs and the associated continuum theory of LC elasticity reveals that the LL potential can, by analogy, be obtained from the Frank energy. As a result, the methodology of the combination of Brownian dynamics simulation with the LL model is proven valid and can be extended to study the director dynamics of LCs subjected to external fields.