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 (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.Comment: 12 pages, Plain TeX, (1 postscript figure, compressed, uuencoded and appended to paper), minor corrections, IASSNS-HEP-94/4

Structure Function of Polymer Nematic Liquid Crystals: A Monte Carlo Simulation

We present a Monte Carlo simulation of a polymer nematic for varying volume fractions, concentrating on the structure function of the sample. We achieve nematic ordering with stiff polymers made of spherical monomers that would otherwise not form a nematic state. Our results are in good qualitative agreement with theoretical and experimental predictions, most notably the bowtie pattern in the static structure function.Comment: 10 pages, plain TeX, macros included, 3 figures available from archive. Published versio

Statistical Mechanics of Vacancy and Interstitial Strings in Hexagonal Columnar Crystals

Columnar crystals contain defects in the form of vacancy/interstitial loops or strings of vacancies and interstitials bounded by column ``heads'' and ``tails''. These defect strings are oriented by the columnar lattice and can change size and shape by movement of the ends and forming kinks along the length. Hence an analysis in terms of directed living polymers is appropriate to study their size and shape distribution, volume fraction, etc. If the entropy of transverse fluctuations overcomes the string line tension in the crystalline phase, a string proliferation transition occurs, leading to a supersolid phase. We estimate the wandering entropy and examine the behaviour in the transition regime. We also calculate numerically the line tension of various species of vacancies and interstitials in a triangular lattice for power-law potentials as well as for a modified Bessel function interaction between columns as occurs in the case of flux lines in type-II superconductors or long polyelectrolytes in an ionic solution. We find that the centered interstitial is the lowest energy defect for a very wide range of interactions; the symmetric vacancy is preferred only for extremely short interaction ranges.Comment: 22 pages (revtex), 15 figures (encapsulated postscript

Defects in Chiral Columnar Phases: Tilt Grain Boundaries and Iterated Moire Maps

Biomolecules are often very long with a definite chirality. DNA, xanthan and poly-gamma-benzyl-glutamate (PBLG) can all form columnar crystalline phases. The chirality, however, competes with the tendency for crystalline order. For chiral polymers, there are two sorts of chirality: the first describes the usual cholesteric-like twist of the local director around a pitch axis, while the second favors the rotation of the local bond-orientational order and leads to a braiding of the polymers along an average direction. In the former case chirality can be manifested in a tilt grain boundary phase (TGB) analogous to the Renn-Lubensky phase of smectic-A liquid crystals. In the latter case we are led to a new "moire" state with twisted bond order. In the moire state polymers are simultaneously entangled, crystalline, and aligned, on average, in a common direction. In the moire state polymers are simultaneously entangled, crystalline, and aligned, on average, in a common direction. In this case the polymer trajectories in the plane perpendicular to their average direction are described by iterated moire maps of remarkable complexity, reminiscent of dynamical systems.Comment: plain TeX, (33 pages), 17 figures, some uufiled and included, the remaining available at ftp://ftp.sns.ias.edu/pub/kamien/ or by request to [email protected]