Controlling topological defects within achiral and chiral nematics using surface geometry and anchoring

System boundary conditions are significant in determining the arrangement and dynamics of topological defects in passive nematics. In this talk, I will present two systems that demonstrate the use of boundary geometry to control defects. The first system comprises of an array of holes suspended within a planar nematic cell [1]. Each hole necessitates, topologically, the presence of an accompanying defect. Within an array, the defects within each hole can interact to create intricate defect structures, such as a network of disclination lines that span the system. These structures are determined by the saddle deformations of each hole, the elastic constants of the liquid crystal, and the anchoring of the cell. The second system confines chiral nematics into spherical shells. Adjusting the shell geometry as well as the type and strength of anchoring at the shell surfaces determines the kind and assembly of chiral nematic defects [2]. Outside of equilibrium configurations, I will present recent results where dynamically changing the surface anchoring can undulate the chiral nematic to produce defects, in a manner reminiscent of the classic Helfrich-Hurault instability [3]. Topological defects in passive nematics can be finely tuned through the command of surface boundary conditions using techniques and principles that could also translate for active nematic systems.

[1] L. Tran, et. al., Proc. Natl. Acad. Sci. U.S.A. (2016) 113:7106.
[2] L. Tran, et. al., Phys. Rev. X (2017) 7:041029.
[3] M.O. Lavrentovich and L. Tran, Phys. Rev. Research (2020) 2:023128.