Chirality amplification and chiral segregation in liquid crystals

Liquid crystal mesophases of achiral molecules are normally achiral, yet in a few materials they spontaneously segregate and form right- and left-handed chiral domains. One mechanism that drives chiral segregation is molecular shape fluctuations between axial chiral conformations, where molecular interactions favor matching chirality and promote helical twist. Cooperative chiral ordering may also play a role in chirality amplification, as when a tiny fraction of chiral dopant drives a nematic phase to become cholesteric. We present a model of cooperative chiral ordering in liquid crystals using Maier-Saupe theory, and predict a phase diagram with a segregated cholesteric phase with alternating domains of left- and right-handed chiral twist, with opposite enantiomeric excess, in addition to racemic nematic and isotropic phases. Our model also demonstrates how chiral molecular fluctuations influence the helical twisting power of dopants in the nematic phase, which may be observed even in materials where the segregated cholesteric phase is preempted by a transition to another phase. We compare these results with Monte Carlo simulation studies of the switchable chiral Lebwohl-Lasher model, where each spin switches between right- and left-handed chiral states. Simulation results validate the predicted phase diagram, demonstrate chiral amplification in the racemic nematic phase, and reveal complex coarsening dynamics in the segregated cholesteric phase. These results suggest that molecular fluctuations between degenerate chiral configurations may be a common mechanism to produce cooperative chiral order in achiral liquid crystals.