Fluctuating semiflexible polymer ribbon constrained to a ring

TL;DR

This paper models the behavior of a thermally fluctuating elastic ribbon constrained to a ring, revealing bend-bend coupling, increased effective stiffness, and proposing a new measurable parameter for experimental analysis.

Contribution

It introduces a comprehensive elastic ribbon model capturing twist and asymmetric bending stiffness effects in ring geometries, including analytical and simulation validation.

Findings

Ring geometry induces bend-bend coupling.

Effective bending stiffness increases due to constraints.

Mean square diameter of the ring is analytically determined.

Abstract

Twist stiffness and an asymmetric bending stiffness of a polymer or a polymer bundle is captured by the elastic ribbon model. We investigate the effects a ring geometry induces to a thermally fluctuating ribbon, finding bend-bend coupling in addition to twist-bend coupling. Furthermore, due to the geometric constraint the polymer's effective bending stiffness increases. A new parameter for experimental investigations of polymer bundles is proposed: the mean square diameter of a ribbonlike ring, which is determined analytically in the semiflexible limit. Monte Carlo simulations are performed which affirm the model's prediction up to high flexibility.