Many nanoparticle-based chiral liquid crystals are composed of polydisperse
rod-shaped particles with considerable spread in size or shape, affecting the
mesoscale chiral properties in, as yet, unknown ways. Using an algebraic
interpretation of Onsager-Straley theory for twisted nematics, we investigate
the role of length polydispersity on the pitch of nanorod-based cholesterics
with a continuous length polydispersity, and find that polydispersity enhances
the twist elastic modulus, K2, of the cholesteric material without
affecting the effective helical amplitude, Kt. In addition, for the
infinitely large average aspect ratios considered here, the dependence of the
pitch on the overall rod concentration is completely unaffected by
polydispersity. For a given concentration, the increase in twist elastic
modulus (and reduction of the helical twist) may be up to 50% for strong size
polydispersity, irrespective of the shape of the unimodal length distribution.
We also demonstrate that the twist reduction is reinforced in bimodal
distributions, by doping a polydisperse cholesteric with very long rods.
Finally, we identify a subtle, non-monotonic change of the pitch across the
isotropic-cholesteric biphasic region.Comment: 8 pages, 4 figure