Orientational defects near colloidal particles in a nematic liquid crystal

We study the interaction between a surface-anchoring colloidal particle and a liquid-crystalline host, and in particular the formation of orientational defects near the particle. A mean-field theory based on the nonlocal Marrucci-Greco nematic potential is used to represent molecular interactions in an inhomogeneous orientational field. An evolution equation for the molecular configuration tensor is solved numerically whose steady state minimizes the total free energy of the system. With strong homeotropic anchoring on the particle surface, three types of solutions may appear depending on initial conditions and particle size: Saturn rings, satellite point defects, and polar rings. The Saturn ring remains stable on micrometer-sized particles, contrary to previous calculations but consistent with experiments. A phase diagram is constructed for the three regimes. Based on the free energy, the most stable state is the Saturn ring for smaller particles and the satellite defect for larger ones.