Frank-Read Mechanism in Nematic Liquid Crystals

TL;DR

This paper demonstrates an analogy of the Frank-Read dislocation source mechanism in nematic liquid crystals, showing how it can generate disclination loops under applied twist through combined experimental, simulation, and theoretical approaches.

Contribution

It introduces a novel Frank-Read mechanism in nematic liquid crystals, expanding understanding of defect dynamics and microstructural control in these materials.

Findings

Disclination loops are emitted repeatedly under applied twist.

Critical stress for loop emission scales inversely with segment length.

Loop emission depends on strain rate and temperature.

Abstract

In a crystalline solid under mechanical stress, a Frank-Read source is a pinned dislocation segment that repeatedly bows and detaches, generating concentric dislocation loops. We demonstrate that in nematic liquid crystals, an analogous Frank-Read mechanism can generate concentric disclination loops. Using experiment, simulation, and theory, we study a disclination segment pinned between surface defects on one substrate in a nematic cell. Under applied twist of the nematic director, the pinned segment bows and emits a new disclination loop which expands, leaving the original segment intact; loop emission repeats for each additional 180$^\circ$ of applied twist. We present experimental micrographs showing loop expansion and snap-off, numerical simulations of loop emission under both quasistatic and dynamic loading, and theoretical analysis considering both free energy minimization and the balance of competing forces. We find that the critical stress for disclination loop emission scales as the inverse of segment length, and changes as a function of strain rate and temperature, in close analogy to the Frank-Read source mechanism in crystals. Lastly, we discuss how Frank-Read sources could be used to modify microstructural evolution in both passive and active nematics.