Threading Dynamics of Ring Polymers in a Gel

TL;DR

This study uses large-scale molecular dynamics simulations to investigate how ring polymers move through a gel, revealing that inter-ring threadings grow with chain length and may cause a jammed state.

Contribution

It introduces a new method to identify and quantify inter-ring threadings and links these to the dynamics of ring polymers in a gel environment.

Findings

Number and persistence of threadings increase with chain length

Percolating network of inter-ring penetrations forms for longer chains

Potential emergence of a topological jammed state for very long rings

Abstract

We perform large scale three-dimensional molecular dynamics simulations of unlinked and unknotted ring polymers diffusing through a background gel, here a three-dimensional cubic lattice. Taking advantage of this architecture, we propose a new method to unambiguously identify and quantify inter-ring threadings (penetrations) and to relate these to the dynamics of the ring polymers. We find that both the number and the persistence time of the threadings increase with the length of the chains, ultimately leading to a percolating network of inter-ring penetrations. We discuss the implications of these findings for the possible emergence of a topological jammed state of very long rings.