Geometry and mechanics of disclination lines in 3D nematic liquid crystals

Abstract

In 3D nematic liquid crystals, disclination lines have a range of geometric structures. Locally, they may resemble $+1/2$ or $-1/2$ defects in 2D nematic phases, or they may have 3D twist. Here, we analyze the structure in terms of the director deformation modes around the disclination, as well as the nematic order tensor inside the disclination core. Based on this analysis, we construct a vector to represent the orientation of the disclination, as well as tensors to represent higher-order structure. We apply this method to simulations of a 3D disclination arch, and determine how the structure changes along the contour length. We then use this geometric analysis to investigate three types of forces acting on a disclination: Peach-Koehler forces due to external stress, interaction forces between disclination lines, and active forces. These results apply to the motion of disclination lines in both conventional and active liquid crystals.

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• Kinematics and dynamics of disclination lines in three-dimensional nematics
• Scaling and spontaneous symmetry restoring of topological defect dynamics in liquid crystal
• Chirality, anisotropic viscosity and elastic anisotropy in three-dimensional active nematic turbulence
• Coexistence of defect morphologies in three dimensional active nematics
• Frank-Read Mechanism in Nematic Liquid Crystals
• Hierarchies of Critical Points of a Landau-de Gennes Free Energy on Three-Dimensional Cuboids
• Analytical model for the motion and interaction of two-dimensional active nematic defects
• Approach and rotation of reconnecting topological defect lines in liquid crystal
• Applications of the Peach-Koehler Force in Liquid Crystals
• Simulations of Three-dimensional Nematic Guidance of Microswimmers
• Coarse-grained theory for motion of solitons and skyrmions in liquid crystals