Anomalous Elasticity of Polymer Cholesterics

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 (nonchiral) concentration $c^{*}$ diverges similar to $|{c-c}^{*}{|}^{-\nu }$, with $\nu =1.43\mathrm{}\pm 0.04$ (for short molecule cholesterics, $\nu =1\mathrm{}$). The short molecule law is recovered for polymers of finite molecular length $\ell$ once the pitch is longer than a length that diverges similar to ${\ell }^{\gamma }$ with $\gamma =0.67\mathrm{}\pm 0.01$. Our predictions could be tested by measurements of the pitch in DNA.