Density-functional study of defects in two-dimensional circular nematic nanocavities

Abstract

We use density-functional theory to study the structure of two-dimensional defects inside a circular nematic nanocavity. The density, nematic order parameter and director fields, as well as the defect core energy and core radius, are obtained in a thermodynamically consistent way for defects with topological charge k = + 1 (with radial and tangential symmetries) and k = + 1/2. An independent calculation of the fluid elastic constants, within the same theory, allows us to connect with the local free-energy density predicted by elastic theory, which in turn provides a criterion to define a defect core boundary and a defect core free energy for the two types of defects. The radial and tangential defects turn out to have very different properties, a feature that a previous Maier–Saupe theory could not account for due to the simplified nature of the interactions, which caused all elastic constants to be equal. In the case with two k = + 1/2 defects in the cavity, the elastic regime cannot be reached due to the small radii of the cavities considered, but some trends can already be obtained.