Polymer Braids and Iterated Moire Maps

TL;DR

This paper explores how strong chirality in dense polymer packings leads to complex twisted structures described by iterated moiré maps, revealing new phases and intricate dynamical behaviors.

Contribution

It introduces the concept of a 'moire state' in chiral polymer packings and links it to complex iterated moiré maps, advancing understanding of chiral polymer organization.

Findings

Weak chirality favors triangular lattice of rigid rods.

Strong chirality induces screw dislocations and new phases.

Polymer trajectories exhibit complex dynamical behavior similar to dynamical systems.

Abstract

Crystalline order in dense packings of long polymers with a definite handedness is difficult to reconcile with the tendency of these chiral objects to twist and braid about each other. If the chirality is weak, the state of lowest energy is a triangular lattice of rigid rods. When the chirality is strong, however, screw dislocations proliferate, leading to either a tilt grain boundary phase or a new "moire state" with twisted bond order. In the latter case, polymer trajectories in the plane perpendicular to their average direction are described by iterated moir\'e maps of remarkable complexity, reminiscent of dynamical systems.