Non-equilibrium orientational dynamics of pinned topological defects in two-dimensional nematic liquid crystals

Abstract

The long-wavelength dynamics of two-dimensional (2D) nematic liquid crystals (LCs) is dominated by the motion of topological defects, which behave like interacting particles endowed with both topological charge and orientation. In experimentally relevant regimes, the translational dynamics of the defect positions can be accurately described by effective nematoelastic particle-particle interaction forces. By contrast, analogous quasistatic torque descriptions for the orientational dynamics typically fail due to a breakdown of time-scale separation, severely hindering the inverse design of texture response dynamics in nematic LCs. To overcome this obstruction, we introduce a linear phase-diffusion formulation that accurately predicts the orientational relaxation dynamics of pinned topological defects in the nonlinear 2D Landau-de Gennes theory. The broad practical potential of this approach is demonstrated by showing how it enables the inverse design of transient nematic patterns as well as the inference of hidden defect configurations from sparse measurements.