Defect structures of nematic liquid crystals in cylindrical cavities

Abstract

Equilibrium axial-radial director fields of a nematic liquid crystal confined to micrometer cylindrical cavities are examined in the approximation of one elastic constant K and spatially homogeneous nematic order parameter. It is shown that, in the strong-anchoring regime with homeotropic boundary conditions, a metastable partially escaped domain structure with an array of alternating radial and hyperbolic point defects is locked in. It can be unstable for very small domain sizes (length less than or approximately equal to 0.25 times the radius), where the two adjacent defects annihilate and thus increase the domain size. Furthermore, it is unstable for larger domain sizes (length greater than or approximately equal to R) if the surface anchoring strength is weaker (${\mathit{w}}_{0}$\ensuremath{\lesssim}5K/R). Here, the radial defects disappear and transform into axial domain walls while the hyperbolic defects remain unchanged. The corresponding phase diagram is presented.