Analog of the Frank-Read Source in Nematic Liquid Crystals

Under external stress, a pinned dislocation segment in a crystalline solid can deform and continuously generate dislocation loops, known as a Frank-Read source. We investigate an analogous mechanism of defect multiplication for disclination lines in nematic liquid crystals. We model a liquid crystal cell containing a disclination half loop pinned to one substrate via patterned surface anchoring. External stress is imposed by gradually rotating the uniform planar anchoring orientation on the opposite substrate. As stress increases, the half loop stretches until a threshold stress is reached and a disclination loop is emitted, leaving the original pinned half loop intact such that the process can repeat. To understand this finding, we develop a simple theory based on the free energy of the system, and explain the behavior of this nematic Frank-Read source by the balance of the Peach-Koehler force and the tension of the disclination line. We compare our findings to related experiments [1] and discuss implications for disclination nucleation mechanisms in both passive and active nematic liquid crystals. [1] J. Angelo et al, DOI: 10.1080/15421406.2017.1287486.