Equilibrium Configuration in a Nematic Liquid Crystal Droplet with Homeotropic Anchoring of Finite Strength

Equilibrium configuration of order parameter in a nematic liquid crystal droplet with homeotropic anchoring of finite strength at the surface is studied numerically by using the Landau–de Gennes approach. It is found that a hedgehog-like configuration with a disclination loop of a small radius is stable for strong anchoring while an axial configuration without defect is stable for weak anchoring. A first-order phase transition from one configuration to the other occurs as the strength of the anchoring is varied. The critical anchoring strength turns out to increase almost linearly with the inverse of the droplet radius.