# Effect of size polydispersity on the pitch of nanorod cholesterics

## TL;DR

This study explores how size polydispersity in nanorod cholesterics influences their pitch, revealing that polydispersity increases the twist elastic modulus and can significantly reduce the pitch, with effects amplified in bimodal distributions.

## Contribution

It provides a theoretical analysis of the impact of length polydispersity on cholesteric pitch using Onsager-Straley theory, highlighting the enhancement of twist elastic modulus and pitch reduction.

## Key findings

- Polydispersity increases the twist elastic modulus by up to 50%.
- The cholesteric pitch is unaffected by polydispersity at high aspect ratios.
- Bimodal distributions further reduce the pitch, especially with very long rods.

## Abstract

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.