Effect of size polydispersity on the pitch of nanorod cholesterics

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, $K_{2}$, of the cholesteric material without affecting the effective helical amplitude, $K_{t}$. 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

Generalized van der Waals theory for the twist elastic modulus and helical pitch of cholesterics

We present a generalized van der Waals theory for a lyotropic cholesteric system of chiral spherocylinders based on the classical Onsager theory for hard anisometric bodies. The rods consist of a hard spherocylindrical backbone surrounded with a square-well potential to account for attractive (or soft repulsive) interactions. Long-ranged chiral interactions are described by means of a simple pseudo-scalar potential which is appropriate for weak chiral forces of a predominant electrostatic origin. Based on the formalism proposed by Straley [Phys. Rev. A {\bf 14}, 1835 (1976)] we derive explicit algebraic expressions for the twist elastic modulus and the cholesteric pitch for rods as a function of density and temperature. The pitch varies non-monotonically with density, with a sharp decrease at low packing fractions and a marked increase at higher packing fractions. A similar trend is found for the temperature dependence. The unwinding of the helical pitch at high densities (or low temperatures) originates from a marked increase in the local nematic order and a steep increase of the twist elastic resistance associated with near-parallel local rod configurations. This contrasts with the commonly held view that the increase in pitch with decreasing temperature as often observed in cholesterics is due to layer formation resulting from pre-smectic fluctuations. The increase in pitch with increasing temperature is consistent with an entropic unwinding as the chiral interaction becomes less and less significant than the thermal energy. The variation of the pitch with density, temperature and contour length is in qualitative agreement with recent experimental results on colloidal {\em fd} rods.Comment: 17 pages, 6 figures, to appear in J. Chem. Phy