  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.
