# Twisting with a twist: supramolecular helix fluctuations in chiral nematics

## TL;DR

This paper extends the Onsager-Straley theory to analyze how weak concentration gradients influence the twist and fluctuations in chiral nematic liquid crystals, revealing control over helicity and divergence of correlation length at the compensation point.

## Contribution

It introduces a theoretical framework for understanding the effects of concentration gradients on chiral nematics, including control of handedness and fluctuation behavior near the compensation point.

## Key findings

- External fields can control helicity and twist magnitude.
- Director fluctuation correlation length diverges at the compensation point.
- Weak concentration gradients significantly influence cholesteric properties.

## Abstract

Most theoretical descriptions of lyotropic cholesteric liquid crystals to date focus on homogeneous systems in which the rod concentration, as opposed to the rod orientation, is uniform. In this work, we build upon the Onsager-Straley theory for twisted nematics and study the effect of weak concentration gradients, generated by some external potential, on the cholesteric twist. We apply our theory to chiral nematics of nanohelices in which the supramolecular helix sense is known to spontaneously change sign upon variation of particle concentration, passing through a so-called compensation point at which the mesoscopic twist vanishes. We show that the imposed field offers exquisite control of the handedness and magnitude of the helicoidal director field, even at weak field strengths. Within the same framework we also quantify the director fluctuation spectrum and find evidence for a correlation length diverging at the compensation point.