Tunable Architecture of Topological Defect Lines in a Nematic Liquid Crystal

In this talk, I will introduce a theoretical framework to tailor three-dimensional defect line architecture in nematic liquid crystals. By drawing an analogy between nematic liquid crystals and magnetostatics, I will show that: i) disclination lines connect defects with the same topological charge on opposite surfaces and ii) disclination lines are attracted to regions of maximal twist. Using these principles, I will show quantitative predictions for the connectivity and shape of defect lines in a nematic confined between two thinly spaced glass substrates. I will demonstrate experimental and numerical verification of these predictions, and identify critical parameters that tune the disclination lines' curvature within an experimental setup, as well as non-dimensional parameters that allow matching experiments and simulations at different length scales. Our framework provides both physical insight and powerful tools to induce desired shape changes of defect lines, opening opportunities to design new types of smart materials and devices.