Statistics and Topology of Fluctuating Ribbons

TL;DR

This paper investigates the statistical mechanics of microscopic fluctuating ribbons, revealing three distinct phases and a universal topological response curve, with implications for biological and chemical ribbon-like structures.

Contribution

It introduces a comprehensive analysis of the phase behavior and topological properties of fluctuating ribbons under force and torque, highlighting phase transitions and symmetry breaking.

Findings

Identification of three phases: HT, HW, and entangled.

Discovery of a universal link response curve similar to phase transitions.

Observation of spontaneous parity symmetry breaking.

Abstract

Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, e.g. it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques. We show that these ribbons exhibit a range of topologically and geometrically complex morphologies exemplified by three phases - a twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and an entangled phase - that arise as the applied torque and force is varied. Furthermore, the transition from HW to HT phases is characterized by the spontaneous breaking of parity symmetry and the disappearance of perversions that characterize chirality reversals. This leads to a universal response curve of a topological quantity, the link, as a function of the applied torque that is similar to magnetization curves in second-order phase transitions.