Spatial structure of topological defect lines in three-dimensional nematic liquid crystals

Topological defects in nematic liquid crystal systems often exhibit intricate spatial structures with nontrivial morphology. Using the the Landau-de Gennes framework, we theoretically and numerically study the structure and energetics of topological defect configurations that arise in various nematic liquid crystal systems. We investigate the role of different experimentally tunable parameters such as system size and boundary condition in dictating the minimum-energy form of the topological defects. In particular, motivated by experiment, we study the equilibrium structure of the defect patterns in the presence of non-matching surface disclinations at the two opposite boundaries of the system. Interestingly, we find that the morphology of the three-dimensional disclination lines that connect different surface defects crucially depends on the thickness of the system and other system parameters. These structures and transitions arise from the geometric conflict, inflicted by boundary conditions, between having short defect paths and having small elastic distortion around them. Some of our theoretical findings corroborate experimental observations. We point to the crucial effect that these nematic structures may have on the topology of defects that will emerge in such a system once cooled into a smectic phase.