Energetics of disclinations in liquid crystals

Abstract

Continuum mechanics has been used to work out the structure and properties of disclinations in nematic and cholesteric liquid crystals. After a brief review of the earlier works on the energetics of disclinations in the one constant approximation, we consider the effect of elastic anisotropy. Elastic anisotropy not only alters the energies and director patterns of individual defects, but appears to favor the presence of wedge disclination in nematics in preference to twist disclinations. Disclination interactions are also considerably affected. The radial force of interaction can be worked out in terms of single defect solutions. In addition, there arise angular forces of interaction between defects in the presence of anisotropy. We next consider cholesteric liquid crystals. Elastic anisotropy appears to favor helicoidal pairings between disclinations of the χ-screw type. We reanalyze the defect solutions in the coarse-grained approximation. It emerges that the χ-edge disclination should be like the smectic A edge disclination from the point of view of energetics. The problem of slow motion of disclinations and disclination pairs has also been considered. Elastic anisotropy is found to increase the frictional coefficient. Like and unlike pairs behave differently in motion.