Frank-Read Sources in Nematic Liquid Crystals: Temperature and Strain-Rate Effects

In a crystalline solid under stress, a Frank-Read (F-R) source is a pinned dislocation segment that repeatedly bows out and detaches, generating concentric dislocation loops. We study an analogous F-R mechanism in nematic liquid crystals, where a pinned disclination segment bows out and generates concentric disclination loops. We model this mechanism via a 3D Lebwohl-Lasher rotor model with a Langevin thermostat, representing a uniaxial nematic with equal Frank constants. We model a disclination half-loop pinned to a planar anchoring surface containing two point defects; loop emission is driven by applied director twist. We find that the critical elastic stress to produce loop emission drops with increasing temperature; and that the critical strain for loop emission rises as a function of increasing twist-rate. We also demonstrate that a tethered loop below the critical strain is stable at low temperature, but expands and can become unstable when heated. We compare our results with an analytical model; speculate on how engineered F-R sources can be used to modify rheology and microstructural evolution; and compare with behavior of F-R sources in crystals; and discuss other stimuli that could drive loop emission in passive and active nematics.