A Mean-Field Study of Defects near Colloidal Particles in a Nematic Liquid Crystal

J. J. Feng & C. Zhou
J. Colloid Interface Sci. 269, 72-78 (2004).
Abstract - We study the defects near a sphere with strong homeotropic anchoring in a nematic liquid crystal. The mean-field theory is based on a nonlocal nematic potential representing molecular interactions in an inhomogeneous orientational field. An evolution equation for the configuration tensor is solved numerically whose steady state minimizes the total free energy of the system. 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 micron-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.