Line defects in nematic liquid crystals as charged superelastic rods with negative twist--stretch coupling

Topological defects are a ubiquitous phenomenon in diverse physical systems. In nematic liquid crystals (LCs), they are dynamic, physicochemically distinct, sensitive to stimuli, and are thereby promising for a range of applications. However, our current understanding of the mechanics and dynamics of defects in nematic LCs remain limited and are often overwhelmed by the intricate details of the specific systems. Here, we unify singular and nonsingular line defects as superelastic rods and combine theory, simulation, and experiment to quantitatively measure their effective elastic moduli, including line tension, torsional rigidity, and twist--stretch coefficient. Interestingly, we found that line defects exhibit a negative twist--stretch coupling, meaning that twisted line defects tend to unwind under stretching, which is reminiscent of DNA molecules. A patterned nematic cell experiment further confirmed the above findings. Taken together, we have established an effective elasticity theory for nematic defects, paving the way towards understanding and engineering their deformation and transformation in driven and active nematic materials.