© 1974 by Oxford University Press
A CONTINUUM MODEL FOR DISCLINATION LINES IN NEMATIC LIQUID CRYSTALS
( Department of Mathematics, University of Strathclyde )
Employing continuum theory, this paper examines orientation patterns in a sample of nematic liquid orystal contained in an infinitely long circular tube, when a disclination line is coincident with the tube axis. Accepting Ericksen's hypothesis (1) that the disclination line consists of a cylindrical core of isotropic fluid, we associate an anisotropic surface energy with the nematic liquid crystal-isotropic core interface. A uniform circumferential orientation is assumed to obtain at the tube surface, and particular forms of solution of the field equations relevant to this arrangement are discussed. For each form considered, a variety of solutions satisfying the applied boundary conditions is possible, provided the tube radius exceeds certain critical values, and it is anticipated that the solution with the least energy is the one most likely to occur. A particularly interesting and surprising result is obtained when the surface energy prefers a parallel orientation at the interface. In this event our calculations suggest that the solution most likely to occur is a distortion in which the molecules lie in curved surfaces parallel to and concentric with the tube axis. It is interesting to observe the obvious similarity between this solution and the axi-symmetric solution in which the molecules lie in planes containing the tube axis, discussed by Barratt (2) for a similar arrangement, when a radial orientation obtains at the tube wall. In both cases the free energy may be reduced and kept finite for all sample volumes, provided one allows the molecules to relax out of planes perpendicular to the tube axis.