Prolate and oblate nematic shells under equal and hybrid alignments

Using the Landau-de Gennes free-energy formalism with the fast inertial relaxation engine relaxation method, we investigate the role of geometry and anchoring conditions in nematic liquid crystal shells. Both prolate and oblate geometries are explored for four distinct anchoring configurations: degenerate planar on both surfaces, homeotropic on both surfaces, and hybrid cases with planar-homeotropic and homeotropic-planar alignments. Our simulations reveal a rich variety of topological defect arrangements, including bipolar configurations with boojums; tetrahedral patterns featuring disclination lines, boojums, and hedgehogs; Saturn-ring structures; and twisted director fields in the equatorial plane. Detailed energy analyses demonstrate that elastic distortions-splay, bend, and twist-are strongly influenced by parameters such as inner and outer radii, shell thickness, and aspect ratio, which in turn dictate the stabilization of specific defect structures. These findings provide insights into the curvature-driven mechanisms that control the formation of defects in nematic shells, with potential applications for the design of advanced photonic and sensing devices.