Dipoles of Disclination Lines of Half-Integer Strength in Nematics

Abstract

The equilibrium equation for the director field in the presence of a pair of parallel disclination lines of strength ± 1/2 is considered. A perturbation procedure is employed, where the expansion parameter is the difference between the two elastic constants that play a role in this planar problem. It is demonstrated that the total energy, truncated to the first order, is minimized by one or the other of two special configurations, i.e., the problem generally admits only two possible orientations of the dipole axis with respect to the undistorted background. Between these two configurations, the “true” one is determined by the relative values of the elastic moduli.

Key Words:

• disclination lines
• nematic disclinations
• strength one half disclinations