# Glassiness and Heterogeneous Dynamics in Dense Solutions of Ring Polymers

## TL;DR

This study investigates how topological constraints influence the dynamics of dense ring polymer solutions, revealing glassy behaviors, universal scaling laws, and the impact of architecture-specific constraints on heterogeneity and vitrification.

## Contribution

It provides the first systematic analysis of topological effects in ring polymer solutions, including scaling relations and the connection between dynamics and spatial organization.

## Key findings

- Random pinning induces non-Gaussian, heterogeneous, and glassy dynamics.
- Universal scaling relations for density and polymer length at vitrification.
- Heterogeneous dynamics are linked to spatial organization and topological constraints.

## Abstract

Understanding how topological constraints affect the dynamics of polymers in solution is at the basis of any polymer theory and it is particularly needed for melts of rings. These polymers fold as crumpled and space-filling objects and, yet, they display a large number of topological constraints. To understand their role, here we systematically probe the response of solutions of rings at various densities to "random pinning" perturbations. We show that these perturbations trigger non-Gaussian and heterogeneous dynamics, eventually leading to non-ergodic and glassy behaviours. We then derive universal scaling relations for the values of solution density and polymer length marking the onset of vitrification in unperturbed solutions. Finally, we directly connect the heterogeneous dynamics of the rings with their spatial organisation and mutual interpenetration. Our results suggest that deviations from the typical behaviours observed in systems of linear polymers may originate from architecture-specific (threading) topological constraints.