Topological free volume and quasi-glassy dynamics in melt of ring polymers

TL;DR

This paper introduces a topological free volume model to explain the glass-like dynamics of dense ring polymer solutions, emphasizing cooperative motion and topological crowding effects.

Contribution

It presents a novel free energy framework based on topological volume to quantify crowding and predicts molecular weight dependence of static and dynamic properties.

Findings

Predicted relaxation times match numerical simulations.

Identified cooperative dynamics as key to anomalous diffusion.

Unified description using the entanglement length $N_e$.

Abstract

Motivated by recent observations that non-concatenated ring polymers in their dense solution exhibit a glass-like dynamics, we propose a free volume description of the motion of such rings based on the notion of topological volume. We first construct a phenomenological free energy which enables one to qnaitify the degree of topological crowding measured by the coordination number. Then we pinpoint a key role of the cooperative dynamics of neighboring rings, which is responsible for an anomalous dependence of the global structural relaxation (diffusion) time on ring length. Predictions on molecular weight dependence of both static (ring size, coordination number) and dynamic (relaxation time, diffusion coefficient) quantities are in very good agreement with reported numerical simulations. Throughout the discussion, the entanglement length $N_e$ is assumed to be a unique characteristic length for the topological constraint, hence, all the physical quantities are universally described in terms of the rescaled chain length $N/N_e$. Finally, we discuss how the dense solution of rings is analogous yet different from ordinary glassy systems.