Hedgehog defects in mixtures of a nematic liquid crystal and a non-nematogenic component

Abstract

A theoretical study of the core structure and composition of a hedgehog defect in a mixture of a nematic liquid crystal and a second non-nematogenic component is presented. Fractionation of the components between the bulk and the defect core is rigorously considered by using solution thermodynamics. Two complementary approaches are used to analyze this problem: a multiscale model based on a Landau–de Gennes free energy functional that is solved numerically, and a macroscopic sharp interface phase-equilibrium model, which considers the defect core as an isotropic phase in equilibrium with a distorted nematic phase and that under certain limiting conditions yields equations that reveal the mechanisms that select defect core structure, geometry, and composition. It is found that the non-nematogenic component segregates preferentially to the defect core, and the defect radius increases as the concentration of the second component and the temperature are increased. As previously predicted for pure liquid crystals, close to saturation conditions the radius increases significantly, and a small range of supersaturation or superheating is observed.