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

TL;DR

This paper explores defects in chiral columnar phases of biomolecules, revealing two distinct states—tilt grain boundaries and a novel moire state—characterized by complex twisted bond order and intricate polymer arrangements.

Contribution

It introduces the concept of a new moire state with twisted bond order and analyzes the complex polymer configurations using iterated moire maps.

Findings

Identification of tilt grain boundary phase in chiral polymers

Discovery of a new moire state with twisted bond order

Polymer trajectories described by complex iterated moire maps

Abstract

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.