MONTE-CARLO SIMULATION OF THE DIRECTOR FIELD OF A NEMATIC LIQUID-CRYSTAL WITH 3 ELASTIC COEFFICIENTS

In this article, a Monte Carlo simulation is presented, which generate s the equilibrium director field of a nematic liquid crystal under the influence of an external field and fixed boundary conditions. The liq uid crystal is characterized by a set of directors on a spatially fixe d lattice. The simulation is based on an expression for the Frank free energy with three elastic coefficients. The chosen discretisation con serves the nematic symmetry, which means n and - n are equivalent. The results for several Frederiks geometries with homogeneous and spatial ly 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-config urations.