Discotic liquid crystal shells under mixed anchoring: Monte Carlo simulation study

The formation of topological defects (TDs) in ordered phases under spherical confinement is inevitable, as exemplified by liquid crystal (LCs) shells and droplets. In this work, we present Monte Carlo simulations of discotic LCs confined between two concentric spherical surfaces with mixed anchoring conditions, considering two scenarios: (1) an inner surface with face-on (homeotropic) anchoring and an outer surface with edge-on (planar) anchoring, and (2) the reverse configuration, across three different shell thicknesses. We report the emergence of multiple disclination lines that satisfy the Poincaré-Hopf theorem. In thicker shells, two+1/2disclination arches appear in the nematic phase with their ends anchored at the edge-on surfaces, while the face-on anchoring promotes the formation of a disclination ring. In contrast, in thinner shells, only two disclination lines are observed in the nematic phase: a wedge disclination and a twist disclination, both terminating at the edge-on surface. Although the twist disclinations change sign along their length (from+1/2to-1/2and back), they contribute+1/2charges at the edge-on boundary, thereby yielding the required total topological charge of +2 at the surface. Additionally, confinement induces a continuous isotropic-nematic transition, consistent with previous studies. These findings provide new insights into the interplay between anchoring conditions, confinement geometry, and TD formation in discotic LCs.