Statistical Models for Liquid Crystals

Abstract

In this project, we pretend to study liquid crystals with modulated structures from discrete models defined on lattices, with emphasis on the structural understanding of thermotropic liquid crystals, in particular the cholesteric phase.Based on ferromagnetic models with interactions like ANNNI (Axial-Next-Nearst-Ising) and like Dzyaloshinsky-Moriya, responsible for the existence of modulated phases, we consider competing interactions in the discrete Maier-Saupe model, known in the literature as Maier-Saupe-Zwanzig. In this model, the orientations of the symmetry axis of the molecules on the lattice are restricted to the three cartesian axis perpendicular to each other. Essentially, the competition is introduced in the following ways: competition between two molecules located at nearest and next-nearest-neighbors lattice sites along a direction and competing interactions between different alignments of two molecules located at nearest-neighbors lattice sites.