Formação de listras na transição de fase isotrópica-colestérica pelo método de Monte Carlo

Abstract

This dissertation is focused in the pattern formation during the isotropic-nematic phase transition in a cholesteric from the simulation viewpoint. Experimentally, this formation occurs immediately after the wetting transition and has been reproduced by simulations using the Monte Carlo method attached with Metropolis algorithm. The liquid crystal is considered as a mesophase between the solid crystalline state and isotropic liquid. Among these states interval there are mesophases. The nematic is one of them. In a nematic medium, the director vector (the representative of alignment average direction of molecules in a little domain) is obtained by analysing the torsions found in the bulk. These torsions were fundamental tools, when studied in short scales, to find the free energy density in the bulk of a liquid crystal sample. Topic of great interest, the interaction between pairwise domains well ordered is found by using some molecular models, like the proposed by Lebwohl-Lasher (the interaction depends just on the angle between the directors of each domain in nematic), the Gruhn-Hess-Romano-Luckhurst (the GHRL interaction depends on the three elastic constants stemming from the torsions studied, in addition to angle between the directors of nematic) and the Luckhurst one (the GHRL interaction is proposed for cholesterics). Experimental samples of cholesterics have been studied in the isotropic-nematic phase transition. Some of them present, after the wetting, the stripe/fringe formation according to the pitch variation. Besides, there are defects that arise in the stripes, which are treated briefly too. The Monte Carlo method takes action in simulation together with the interaction potential model obtained for the cholesterics generating simulated textures. Stripes and defects have been arisen, enabling a comparison with the experimental phenomena, what heretofore has never been done by this method. Either the stripes formation (first or second order) or its behaviour (topological defects formation, rotation, etc.) has been reproduced faithfully to experiment. The simulations can also predict the elastic constants range for which stripes arise and the results can be interpreted in terms of phenomenological parameters present in the simulation with the Luckhurst pairwise potential.