Equilibrium locations of defects in two-dimensional configurations of the NLC director field

Abstract

ABSTRACT We revisit the problem of finding the equilibrium location of the defect in two-dimensional configurations of the nematic liquid crystal (NLC) director field within the framework of the Frank-Ozeen formalism. Our analytical approach can be used for a wide class of nematic-filled regions, on the boundary surfaces of which there is a strong anchoring for the director with a piecewise constant pretilt. First, we use complex analysis to find a nematic director profile as a superposition of contributions from a set of virtual defects with appropriate topological charges acting on the defect in question. Then, we use the net zero force principle to find the equilibrium location of the defect. Our method generates the set of virtual defects automatically without using ad hoc symmetry considerations as it is in the standard method of images. We reproduce some known results using very simple calculations. We also consider several simple yet original problems. Namely, we find the equilibrium location of a disclination line near a long cylindrical particle with strong combined homeotropic-circular anchoring on its lateral surface and the equilibrium location of the disclination line in the NLC bounded by a parabolic cylinder with strong circular anchoring.