Spherical particle immersed in a nematic liquid crystal: effects of confinement on the director field configurations

The effects of confinement on the director field configurations are studied for a spherical particle immersed in a nematic liquid crystal. The liquid crystal is confined in a cylindrical geometry and the particle is located on the axis of symmetry. A finite element method is used to minimize the Frank free energy for various sizes of the system. The liquid crystal is assumed to possess strong anchoring at all the surfaces in the system. Two structures are examined for strong homeotropic anchoring at the surface of the particle: configuration with a Saturn ring disclination line and configuration with a satellite point defect (hedgehog defect). It is shown that the equilibrium locations of the Saturn ring and of the hedgehog point defect change with confinement. It is also found that confinement induces an increase in the elastic free energy that differs substantially with the type of topological defect under consideration. In particular, the evaluation of the total free energy that includes an approximate contribution for the core defect shows that, for micrometer-sized particles in confined systems, the Saturn ring configuration appears to be more stable than the hedgehog defect. This result is in contrast to the bulk situation, where the hedgehog is more stable than the Saturn ring, and it helps explain recent experimental observations of Saturn ring defects around confined micrometer-sized solid particles.