Slowing Down of Ring Polymer Diffusion Caused by Inter‐Ring Threading

Abstract

Diffusion of long ring polymers in a melt is much slower than the reorganization of their internal structures. While direct evidences for entanglements have not been observed in the long ring polymers unlike linear polymer melts, threading between the rings is suspected to be the main reason for slowing down of ring polymer diffusion. It is, however, difficult to define the threading configuration between two rings because the rings have no chain end. In this work, evidences for threading dynamics of ring polymers are presented by using molecular dynamics simulation and applying a novel analysis method. The simulation results are analyzed in terms of the statistics of persistence and exchange times that have proved useful in studying heterogeneous dynamics of glassy systems. We find that the threading time of ring polymer melts increases more rapidly with the degree of polymerization than that of linear polymer melts. This indicates that threaded ring polymers cannot diffuse until unthreading event occurs, which results in the slowing down of ring polymer diffusion.

A topologically driven glass in ring polymers

“…These findings are a strong signature that rings display longlasting intercoil correlations that are present even after they have traveled beyond their own size, in agreement with previous numerical and experimental findings (5,8). In addition, this is clear evidence that the exchange dynamics of the rings becomes slower, more glass-like (16,36), as the polymerization M increases. The increasingly stretched decay of φ nc also implies that the relaxation dynamics of the chains becomes more heterogeneous, i.e., some parts of the chains are much slower to separate from one another than other parts.…”

“…These interchain interactions may include threadings that have been conjectured to be intimately related to the slow overall diffusion of the rings' center of mass (5,8,13,16) (see also SI Appendix, Fig. S4), an observation that is in apparent contrast with the very fast stress relaxation (6, 7), characterized by a power-law decay of the relaxation modulus GðtÞ and by a remarkable absence of the entanglement plateau that characterizes concentrated solutions of linear polymers.…”

“…On the other hand, numerical and experimental findings (5,6) suggest that rings exhibit strong intercoil correlations, which have proved difficult to address in simplified theoretical models (9)(10)(11)(12). Because of this, there have been many recent attempts to rigorously characterize these interchains' interactions (13)(14)(15)(16), although a precise definition and unambiguous identification of these "threadings" in concentrated solutions of rings remains elusive. The primary reason for this is that the rings are assumed to remain strictly topologically unlinked from one another throughout if synthesized in this state.…”

On the tree-like structure of rings in dense solutions

“…10). Such large threadings may eventually generate topological constraints which can leave a signature in the long-time relaxation of the rings 3,13,16,18,70,72 and allow one to gen-erate topologically frozen states by randomly pinning a small fraction of the rings 12 . In summary, I have shown that the conformations of rings in dense solutions contain local tree-like structures that are not necessarily described by the classical tightly double-folded lattice animal picture.…”

“…In these cases, the topological constraints that they generate on the configurations of the threaded neighbours (or of itself, in the case of self-threading 25 ) lead to long-lived correlations that are strong candidates for explaining the "slowing down" in the rings' dynamics observed by several groups 14,[16][17][18]70,71 . The arguments presented here, together with several previous observations 16,18,70 also support the conjecture that in the limit of very large rings, long threadings will populate the system, and may eventually lead to spontaneous topological vitrification 72 . Compelling numerical evidence 12 indeed suggest that a "topological glass" state can be achieved by randomly pinning even a small fraction of rings in dense solutions when these are long enough.…”