Shape enantiomerism in semi-rigid polymer liquid crystals

Abstract

Weakly flexible, directed polymers can adopt a potentially infinite variety of conformations, some of them chiral. We develop a second-virial theory for semi-rigid polymers embedded in a nematic environment based on the assumption that the chains possess no intrinsic molecular chirality but can take on weakly helical conformations of either handedness. We demonstrate how these transient helical fluctuations can be exploited to predict the degree of chain stiffening induced by molecular crowding. The theoretical predictions are in good agreement with large-scale molecular dynamics simulations of bead-spring polymers with tunable backbone flexibility. Although both theory and simulations rule out spontaneous global chiral symmetry breaking imparted by chain conformations alone, they do reveal that polymers can develop pronounced enantiomeric shapes. Nematic fluids of semi-rigid polymers can be viewed as compensated cholesterics composed of transiently helical polymers with zero enantiomeric excess. By quantifying the degree of compensated chiral order developed over a broad range of concentrations and persistence lengths, two distinct regimes of weak and strong enantiomerism can be identified. A crossover between the two occurs when the chain persistence length drops below roughly three times the contour length.