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Monte Carlo Simulation of the Director Field of a Nematic Liquid Crystal with Three Elastic Coefficients

Gruhn, Thomas; Hess, Siegfried

In this article, a Monte Carlo simulation is presented, which generates the equilibrium director field of a nematic liquid crystal under the influence of an external field and fixed boundary conditions. The liquid crystal is characterized by a set of directors on a spatially fixed lattice. The simulation is based on an expression for the Frank free energy with three elastic coefficients. The chosen discretisation conserves the nematic symmetry, which means n and - n are equivalent. The results for several Frederiks geometries with homogeneous and spatially modulated external fields are shown, as well as an investigation of a capillary with homeotropic boundary conditions. Further we compare our method with the Lebwohl-Lasher model and introduce an extension of the latter which distinguishes between splay-, twist-and bend-configurations.
Published in: Zeitschrift fĂĽr Naturforschung A, 10.1515/zna-1996-1-201, De Gruyter