LMP Seminar: Investigating Order and Defects in Models of Nematic Liquid Crystals

The Lebwohl-Lasher model is a simple potential that can model the behavior of nematic liquid crystals. We modify the Lebwohl-Lasher potential to investigate two cases of nematic behavior. The first case investigates the Frank-Read source of topological defects in nematic liquid crystals by drawing analogies to dislocation multiplication in crystalline solids. We consider a disclination half-loop pinned to an anchoring layer. This half-loop will expand and snap off a new disclination loop under applied twist. We model this mechanism in a uniaxial nematic via a Lebwohl-Lasher rotor model and study this analogous Frank-Read mechanism to explore the effects of temperature and twist rate. We propose that a liquid crystal cell with a patterned array of Frank-Read sources will demonstrate a rheological response that depends on disclination half-loop sizes, density, orientation, and pattern. The second case investigates the effect of cooperative ordering in achiral nematic liquid crystals resulting in chiral amplification of helical twist from a small amount of chiral dopant. To explore this concept, we present a modified Lebwohl-Lasher model where each spin has an additional chiral degree of freedom, representing degenerate left- and right-handed isomers of n-CB liquid crystal molecules. Monte Carlo simulations show racemic isotropic and nematic phases, plus a deracemized nematic phase composed of layered chiral domains with alternating cholesteric pitch. We compare with Maier-Saupe theory which predicts a similar phase diagram and shows that chiral amplification is enhanced near a phase transition to the deracemized nematic phase.