Equilibrium configuration of a nematic liquid crystal confined to a cylindrical cavity

A nematic liquid crystal confined to a cylindrical capillary with homeotropic anchoring to the sidewalls is considered. An analytic description of the planar polar director field configuration is proposed for arbitrary values of the system material parameters. Conditions for orientational transitions between planar radial, planar polar, and escaped radial structures are determined, with a discussion of similar considerations for planar-circular anchoring.