Rigid linear particles confined on a spherical surface: phase diagram of nematic defect states

A thin film of liquid crystal confined on a spherical surface displays topological defects, as demonstrated by experimental observation of micron-sized double-emulsion droplets. Proposals have been made in practical applications to design novel materials by using these patterned textures. Recent phenomenological models and Monte Carlo computer simulations revealed organized defect structures with different characteristics. Here, we theoretically investigate the structure of the nematic ordering resulted from the excluded-volume interaction between rigid molecules confined on a spherical surface. The free-energy model follows a basic idea originally proposed by Onsager for studying a nematic fluid made of rigid particles. We tackle this fundamental model numerically to produce high-precision free-energy branches that enable structural determination.