Curvature-induced ordering in cylindrical nematic shells

Abstract

In this paper we study theoretically the equilibrium configurations of two-dimensional nematic liquid crystals on a cylindrical surface. Configurations are described through a tensor-order parameter that provides information about the tangential optical axis and the dispersion of the molecules around it. Equilibrium equations are obtained by the surface Landau–de Gennes energy recently proposed in Napoli and Vergori [Physical Review E 061701 (2012)]. We show that, whenever free boundary conditions are applied, the extrinsic curvature induces the alignment of the optical axis along the cylinder axis. On the contrary, when strong planar anchoring is imposed on the boundaries, the curvature triggers a sort of Freédricksz-like transition in the alignment. We provide the asymptotic solution of the non-linear problem with strong planar anchoring boundary conditions for elongated cylindrical shells.