Chirality amplification and deracemization in achiral nematic liquid crystals

Small amounts of chiral dopant induce helical twist in achiral nematic liquid crystals, resulting in a cholesteric phase with uniform pitch. We hypothesize that this high chiral amplification is the result of cooperative chiral ordering which enables a dopant molecule's influence to extend well beyond its immediate neighbors. To explore this concept, we present a modified 3D Lebwohl-Lasher model where each spin has an additional chiral degree of freedom, representing degenerate left- and right-handed isomers of the 5CB liquid Crystal molecule, separated by a low energy barrier. Monte Carlo simulations show racemic isotropic and nematic phases, plus a deracemized nematic phase composed of layered chiral domains with alternating cholesteric pitch. Maier-Saupe theory predicts a phase diagram containing a tricritical point, and shows that chiral amplification, e.g. by a chiral dopant, is enhanced near a phase transition to the deracemized nematic phase. Though the deracemized phase may be obscured by a transition to other liquid-crystalline or crystalline states, we argue that chirality amplification (helical twisting power) is a tell-tale sign of its existence.