Anomalous Elasticity of Polymer Cholesterics

TL;DR

This paper reveals that polymer cholesterics exhibit anomalously long pitches due to their unique elasticity, with a divergence near racemic concentration that differs from short molecule cholesterics, and provides testable predictions for DNA.

Contribution

It introduces the concept of anomalous elasticity in polymer cholesterics and quantifies how their pitch diverges near racemic concentration, differing from short molecule cholesterics.

Findings

Polymer cholesterics have longer pitches than short molecule cholesterics.

The pitch diverges as a7c - c^*a7^{- u} with u=1.43 b1 0.04.

Predictions can be tested through DNA measurements.

Abstract

We show that polymer cholesterics have much longer pitches than comparable short molecule cholesterics, due to their anomalous elasticity. The pitch $P$ of a chiral mixture with concentration $c$ near the racemic (non-chiral) concentration $c^*$ diverges like $\vert c-c^*\vert^{-\nu}$ with $\nu=1.43 \pm 0.04$ (for short molecule cholesterics $\nu=1$). The short molecule law is recovered for polymers of finite molecular length $\ell$ once the pitch is longer than a length that diverges like $\ell^\gamma$ with $\gamma=0.67 \pm 0.01$. Our predictions could be tested by measurements of the pitch in DNA.