The physics of liquid crystals is an exciting field of research with important practical applications. In this dissertation we present the results of simulation studies of nematic liquid crystals using Monte Carlo and molecular dynamic techniques. In our first project we performed Monte Carlo Simulations of the Lebwohl-Lasher (LL) model of nematic liquid crystals confined to cylindrical cavities with perpendicular anchoring. In this particular geometry one has an interesting interplay between bulk and surface energies, which results in different director configurations inside the cylinder. Our work reconciled the apparent contradictions between the results of earlier simulations and approximate analytics theories. In another project we simulated the nematic-isotropic transitions in the LL model using a single cluster Monte Carlo algorithm. We calculated the finite size scaling of the free energy barrier at the transition and obtained a reliable estimate of the value of the transition temperature in the thermodynamic limit for the first time. We also used the cluster algorithm to the study the behavior of disclination loop defects in the vicinity of the of the nematic-isotropic transition in the LL and related models. We calculated the distribution of these defects and were able to draw interesting conclusions about their behavior at the transition, and contrast the behavior with analogous magnetic systems. In our last project we studied the coarsening dynamics of biaxial nematics using Langevin molecular dynamics. We used a model with no a priori relationship among the three elastic constants associated with director deformations. We found a rich variety of coarsening behavior, including the simulataneous decay of nearly equal populations of the three classes of half-integer disclination lines. The behavior we observed can be understood on the basis of the relative values of the elastic constants and the resulting decay channels of the defects.
Priezjev, N. V.
(2002). Simulations of Nematic Liquid Crystals: Confined Geometries, Phase Transitions and Topological Defects. .