Statistical Mechanics of Developable Ribbons

TL;DR

This paper explores the statistical mechanics of developable ribbons, revealing their inherent helical structures and longer persistence lengths compared to wormlike chains, with implications for polymer physics and nanoscience.

Contribution

It introduces a novel analysis of developable ribbons, showing their unique coupling of bending and torsion and oscillatory correlation functions, extending beyond classical models.

Findings

Tangent-tangent correlations decay oscillatory at all temperatures.

Persistence length exceeds that of wormlike chains by over three times.

Ribbons exhibit inherent helical structures without zero-temperature twist.

Abstract

We investigate the statistical mechanics of long developable ribbons of finite width and very small thickness. The constraint of isometric deformations in these ribbon-like structures that follows from the geometric separation of scales introduces a coupling between bending and torsional degrees of freedom. Using analytical techniques and Monte Carlo simulations, we find that the tangent-tangent correlation functions always exhibits an oscillatory decay at any finite temperature implying the existence of an underlying helical structure even in absence of a preferential zero-temperature twist. In addition the persistence length is found to be over three times larger than that of a wormlike chain having the same bending rigidity. Our results are applicable to many ribbon-like objects in polymer physics and nanoscience that are not described by the classical worm-like chain model.