Fluctuations at the domain edges of nematic liquid crystals in two dimensions

Abstract:

Capillary waves and director fluctuations reduce the surface tension of a non-anchoring unbound nematic surface by comparable amounts. These are relatively small effects in three dimensions, but in two dimensions they become more significant. We examine the conditions in two dimensions under which they dominate explicitly within the framework of a model of the Maier-Saupe type. We find that for reasonable physical parameters of the model the onset of the fluctuation dominated regime generally preempts the nematic-isotropic transition. We conclude that processes which are sensitive to line tension, such as Ostwald ripening during two-dimensional liquid-gas phase separation, are much more strongly coupled to anisotropic molecular interactions and associated nematic ordering than in three dimensions.