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

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

1995-07-20

arxiv.org/abs/cond-mat/9507080v1

Phys. Rev. E 53 (1996) 650

Physics

Condensed Matter

plain TeX, (33 pages), 17 figures, some uufiled and included, the remaining available at ftp://ftp.sns.ias.edu/pub/kamien/ or

Scientific paper

10.1103/PhysRevE.53.650

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.

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