Numerical study of chiral structures from achiral liquid crystals using Ball-Majumdar singular potential model

Recent experiments have shown that certain species of lyotropic chromonic nematic liquid crystal (LCLC) systems have spontaneously exhibited chirality when confined to particular domains, despite the molecules themselves being achiral. For a cylindrical domain with homeotropic anchoring, so-called twisted escaped radial (TER) configurations in which a single +1 disclination escapes to the third dimension via twisting, and twisted polar planar (TPP) configurations in which two +1/2 disclinations form a double-helix structure are formed as systems relax. These configurations are made possible by the small twist elastic constants of LCLCs relative to their bend and splay elastic constants, though energetic arguments on this point are still under debate. We present a study of these systems using a Ball-Majumdar singular potential computational field theory. With this model we are able to sweep through parameters controlling the elastic twist constant and the domain dimensions in order to characterize stability and decay paths of twisted configurations. This analysis is supplemented by using the disclination kinematic law to understand defect motion in the case of the TPP configuration.