Structures and Energies of Grandjean-Cano Liquid-Crystal Disclinations

Abstract

Closed analytical expressions for the orientation of the director and the total distortional elastic energy are given for de Gennes's model of a Grandjean-Cano disclination. The director expression is shown to be equivalent to de Gennes's infinite-sum solution. This model is generalized and similar expressions for single disclinations on one of the parallel surfaces and for double disclinations between the boundaries are derived. Approximate energies are computed for these singularities in the case of nonparallel surfaces, and comparisons are made to predict the conditions for their stability. A more realistic model where many equally spaced disclinations occur within wedge-shaped boundaries is proposed and elastic distortion energies are calculated for this case.