Stability of Disclinations in Nematic LiquidCrystals

Abstract

In the light of ϕ-mapping method and topologicalcurrent theory, the stability of disclinationsaround a spherical particle in nematic liquid crystals is studied.We consider two different defect structures around a sphericalparticle: disclination ring and point defect at the north or southpole of the particle. We calculate the free energy of thesedifferent defects in the elastic theory. It is pointed out thatthe total Frank free energy density can be divided into two parts.One is the distorted energy density of director field around thedisclinations. The other is the free energy density ofdisclinations themselves, which is shown to be concentrated at thedefect and to be topologically quantized in the unit of(k−k24)π/2. It is shown that in the presence ofsaddle-splay elasticity a dipole (radial and hyperbolic hedgehog)configuration that accompanies a particle with strong homeotropicanchoring takes the structure of a small disclination ring, not a point defect.