Elasticity and Fluctuations of Frustrated Nano-Ribbons

TL;DR

This paper develops a reduced theoretical model for frustrated nano-ribbons, capturing their elastic behavior and thermal fluctuations, and reveals unique fluctuation effects and phase transitions not seen in non-frustrated filaments.

Contribution

It introduces a geometric, scale-independent theory for frustrated ribbons, enabling analysis of their equilibrium states and fluctuations, including a novel twisted-to-helical transition.

Findings

Persistence length varies non-monotonically with width.

Fluctuation effects alter critical exponents at the transition.

Statistical properties differ from non-frustrated filaments.

Abstract

We derive a reduced quasi-one-dimensional theory of geometrically frustrated elastic ribbons. Expressed in terms of geometric properties alone, it applies to ribbons over a wide range of scales, allowing the study of their elastic equilibrium, as well as thermal fluctuations. We use the theory to account for the twisted-to-helical transition of ribbons with spontaneous negative curvature, and the effect of fluctuations on the corresponding critical exponents. The persistence length of such ribbons changes non-monotonically with the ribbon's width, dropping to zero at the transition. This and other statistical properties qualitatively differ from those of non-frustrated fluctuating filaments.