Persistent Homology Reveals the Role of Stiffness in Forming Topological Glasses in Dense Solutions of Ring Polymers

TL;DR

This study uses persistent homology to analyze how chain stiffness influences the formation of topological glasses in dense solutions of ring polymers, revealing that stiffness affects the size and prevalence of threading loops.

Contribution

It introduces a novel application of persistent homology to quantify topological structures in ring polymers, highlighting the role of stiffness in topological glass formation.

Findings

Stiff ring polymers form larger loops and more threading structures.

Flexible rings do not generate sufficiently large loops for threading.

Chain stiffness significantly influences topological glass formation.

Abstract

Ring polymers are characterized by topology-specific entanglements called threadings. In the limit of large rings, it is conjectured that a "topological glass" should emerge due to the proliferation of threadings. In this study, we used persistent homology to quantify threading structures of ring polymers with different chain stiffness and elucidate mechanisms behind topological glasses. Using coordination data from coarse-grained molecular dynamics simulations, we analyzed the topology of the union of virtual spheres centered on each monomer or center of mass. As the radius of each sphere increases, the corresponding points connect, giving rise to topological entities such as edges, loops, and facets. We then analyzed how the number of loops per ring chain and penetrated loops varies with sphere radius, focusing on the effects of chain stiffness and density. The results reveal that loops are larger in stiff ring chains, whereas flexible ring chains do not generate sufficiently large loops to establish a threading structure. The stiffness of ring polymer plays a significant role in the formation of topological glasses in ring polymers.