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.
Acknowledgements
We acknowledge financial support from Ministerio de Educación y Ciencia (Spain) under Grant numbers FIS2008-05865-C02-02, FIS2007-65869-C03-C01, FIS2008-05865-C02-01, and Comunidad Autónoma de Madrid (Spain) under Grant No. S-0505/ESP-0299.