The stability diagram of a nematic liquid crystal confined to a cylindrical cavity

Abstract

Different nematic structures confined to a long cylindrical cavity with homeotropic surface anchoring are studied using a numerical minimization of the free energy of the uniaxial nematic liquid crystal. The stability of escaped radial structures and planar polar structures (with and without line defects) is analysed in terms of the ratio of elastic constants K ₂₄/K ₁₁, K ₃₃/K ₁₁, anchoring strength and external magnetic field applied perpendicular to the symmetry axis of the cylinder. We draw the analogy between the stability diagram of the cylindrical structures and structures in a spherical droplet. In particular, a simple way extracting the value of the saddle-splay elastic constant K ₂₄ from the stability studies is discussed.