Multiscale entanglement in ring polymers under spherical confinement

TL;DR

This study explores how geometrical and topological entanglement in semiflexible knotted ring polymers confined in spherical cavities varies with confinement strength, revealing a transition from weak to complete knot delocalization and multiscale entanglement.

Contribution

It introduces a scaling framework based on deflection theory to describe knot localization and multiscale entanglement in confined ring polymers.

Findings

Weak knot localization in no confinement

Complete knot delocalization under strong confinement

Multiscale entanglement emerges with increased confinement

Abstract

The interplay of geometrical and topological entanglement in semiflexible knotted polymer rings confined inside a spherical cavity is investigated using advanced numerical methods. By using stringent and robust algorithms for locating knots, we characterize how the knot length lk depends on the ring contour length, Lc and the radius of the confining sphere, Rc . In the no- and strong- confinement cases we observe weak knot localization and complete knot delocalization, respectively. We show that the complex interplay of lk, Lc and Rc that seamlessly bridges these two limits can be encompassed by a simple scaling argument based on deflection theory. The same argument is used to rationalize the multiscale character of the entanglement that emerges with increasing confinement.