Chiral assembly of weakly curled hard rods: Effect of steric chirality and polarity

We theoretically investigate the pitch of lyotropic cholesteric phases composed of slender rods with steric chirality transmitted via a weak helical deformation of the backbone. In this limit, the model is amenable to analytical treatment within Onsager theory and a closed expression for the pitch versus concentration and helical shape can be derived. Within the same framework, we also briefly review the possibility of alternative types of chiral order, such as twist-bend or screw-like nematic phases, finding that cholesteric order dominates for weakly helical distortions. While long-ranged or "soft" chiral forces usually lead to a pitch decreasing linearly with concentration, steric chirality leads to a much steeper decrease of quadratic nature. This reveals a subtle link between the range of chiral intermolecular interaction and the pitch sensitivity with concentration. A much richer dependence on the thermodynamic state is revealed for polar helices where parallel and anti-parallel pair alignments along the local director are no longer equivalent. It is found that weak temperature variations may lead to dramatic changes in the pitch, despite the lyotropic nature of the assembly.