Anomalous Elasticity of Polymer Cholesterics

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 $\vert c-c^*\vert^{-ν}$ with $ν=1.43 \pm 0.04$ (for short molecule cholesterics $ν=1$). The short molecule law is recovered for polymers of finite molecular length $\ell$ once the pitch is longer than a length that diverges like $\ell^γ$ with $γ=0.67 \pm 0.01$. Our predictions could be tested by measurements of the pitch in DNA.