Topological defects in a two-dimensional liquid crystal confined in a circular nanocavity.

Using a microscopic theory based on excluded-volume interactions, we analyze the structure and thermodynamic stability of configurations in a two-dimensional liquid crystal confined into a (small) circular nanocavity. Weak homeotropic anchoring conditions are considered, and topological defects of total charge k=+1 are discussed. It is found that, for small cavity radii, the cavity is free of defects at the expense of surface free energy not being optimized. For larger cavities, a configuration with two repulsive k=+1/2-charge point defects is always stable. The two configurations are equally stable thermodynamically (structural or Frederiks transition) on a curve in the chemical potential-cavity radius plane. This curve ends for chemical potential and cavity radius below some critical values. Elastic-theory arguments are used to explain the stability of the defected structure compared with the one free of defects. Our results indicate that the two-defect structure is always more stable than the one with a single point defect of charge k=+1 at the cavity center, which, in agreement with computer simulation, is never found to be stable. Finally, the relation with the bulk behavior of the fluid is discussed.