Frank-Read Mechanism in Nematic Liquid Crystals

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 generates 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 degrees 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. Lastly, we discuss potential use of Frank-Read sources to modify microstructural evolution in both passive and active nematics.

Kinematics and dynamics of disclination lines in three-dimensional nematics

“…We note that equation (4.6) is the analogue of the Peach–Koehler relation of dislocation mechanics [15,17]. The Peach–Koehler force applied to nematic liquid crystals was first introduced by Kléman [53] and has been recently used to study disclination line motion in various scenarios [26,54]. Our analysis here using equation (3.6) represents an alternative derivation of this result that does not directly compare disclinations to dislocations in solids.…”