Characterising texture formation in fibre lattices embedded in a nematic liquid crystal matrix

Abstract

A two-dimensional computational study is performed on the texturing of fibre-filled nematic liquid crystals using the Landau-de Gennes model describing the spatio-temporal evolution of the second moment of the orientation distribution function or quadrupolar tensor order parameter. The investigation is performed on a consistent computational domain comprising a square array of four circular fibres embedded within a unit square containing a uniaxial low molar mass calamitic liquid crystal. Interest is focused on the role of temperature, boundary conditions and their effect on the nucleation and evolution of defect structures. Thermal effects are characterised below and above the temperature at which the nematic state is stable. Simulations in the stable nematic state serves as a scenario for investigating the effect of imposing different external boundary conditions, namely periodic and Dirichlet; the former describes a square lattice array of fibres embedded in a nematic liquid crystal, and the latterdescribes a four-fibre arrangement in an aligned nematic material. In each case, the influence of temperature is characterised, with defect structures forming and either remaining or splitting into lower strength defects. For fibre lattices, splitting transitions of defects at the centre of the domain occur at a critical temperature, but for the four-fibre arrangement, defect transitions occur continuously over a temperature range. The discontinuous defect splitting transition in fibre arrays occurs at lower temperatures than the continuous defect transformation in the four-fibre arrangement. At sufficiently low temperatures, the four-fibre arrangement and the fibre lattice give the same texture consisting of two disclination lines close to each fibre. The evolution of the texture with respect to temperature can be characterised as a change from single-fibre mode at low temperature to a collective mode with a centre-located heterogeneity at higher temperature. At higher temperatures, in the stable isotropic state, it is shown that surface-induced ordering arising from the fibre/liquid crystal interaction propagates into the bulk forming thin disclination lattices around the four-fibre configuration.