In this work the dynamics of liquid crystal ordering in a cylindrical geometry are considered. We study a system with liquid crystalline properties that exhibits translational symmetry along the cylinder axis and, therefore, the problem is effectively two-dimensional. The orientation of liquid crystals is described by a tensorial order parameter and the dynamics are governed by a balance between the dissipation and the rate of change of free energy, which includes the elastic, thermotropic and surface energy terms. The evolution of the + 2 defect differentiating first into two + 1 disclinations and subsequently into four + 1/2 defects is analysed. Different boundary conditions, namely strong and weak or no anchoring, have been considered and the critical value for the anchoring strength, at which + 1/2 defects are very close to escaping through the boundary but still remain there at equilibrium, has been identified.
- dislocation dynamics
- free energy
Miroshnychenko, D., Hill, N. A., Mottram, N. J., & Lydon, J. E. (2005). Evolution from A +2 Defect to +1/2 Defects in a Cylindrical Geometry. Molecular Crystals and Liquid Crystals, 437, 1495-1512. https://doi.org/10.1080/15421400590955334