Estudos numéricos da formação e dinâmica de defeitos topológicos em cristais líquidos nemáticos - Oliveira, Breno Ferraz de (2012)
In this work we study numerically the generation and dynamics of topological defects in nematic liquid crystals. Our study is based on a Ginzburg-Landau model describing the evolution of the orientational order of a liquid crystal in terms of a symmetric, traceless, second-rank tensor. This phenomenological model allows studies of nematic phases at scales ranging from few nanometers to few micrometers (mesoscopic scale). Within this framework we developed a software named LICRA (Liquid CRystal Algorithm) that combines standard finite difference algorithm for the spatial derivatives with a Runge-Kutta temporal integration to solve the relaxational equations of nematodynamics without thermal fluctuations and hydrodynamic flow. Using this software we investigate the coarsening dynamics of defects of two- and three-dimensional uniaxial nematic liquid crystals. The time dependences of the structure factor and characteristic length scale were computed. The characteristic length scale is expected to grow as a power law in time, L ∝ tα. From dimensional analysis α = 1/2 and we found α = 0, 45±0, 01 in two-dimensions and α = 0, 350±0, 003 in three-dimensions. Furthermore, in all cases Porod s law is satisfied for large values of wave number k. We also investigate, using LICRA, the coarsening dynamics of liquid crystal textures in a two-dimensional nematic under applied electric fields. We consider both positive and negative dielectric anisotropies and two different possibilities for the orientation of the electric field parallel and perpendicular to the two-dimensional lattice. We determine the effect of an applied electric field pulse on the evolution of the characteristic length scale and other properties of the liquid crystal texture network. In particular, we show that different types of defects are produced after the electric field is switched on, depending on the orientation of the electric field and the sign of the dielectric anisotropy. Finally, we present the effect of the rotation of an external electric field on the dynamics of half-integer disclination networks in two and three dimensional nematic liquid crystals with a negative dielectric anisotropy. We show that a rotation of π of the electric field around an axis of the liquid crystal plane continuously transforms all half-integer disclinations of the network into disclinations of opposite sign via twist disclinations. We also determine the evolution of the characteristic length scale, thus quantifying the impact of the external electric field on the coarsening of the defect network.