A topologically driven glass in ring polymers

Abstract

The static and dynamic properties of ring polymers in concentrated solutions remains one of the last deep unsolved questions in polymer physics. At the same time, the nature of the glass transition in polymeric systems is also not well understood. In this work, we study a novel glass transition in systems made of circular polymers by exploiting the topological constraints that are conjectured to populate concentrated solutions of rings. We show that such rings strongly interpenetrate through one another, generating an extensive network of topological interactions that dramatically affects their dynamics. We show that a kinetically arrested state can be induced by randomly pinning a small fraction of the rings. This occurs well above the classical glass transition temperature at which microscopic mobility is lost. Our work both demonstrates the existence of long-lived inter-ring penetrations and realizes a novel, topologically induced, glass transition.glass transition | ring polymers | topology | topological glass | molecular dynamics T he physics of ring polymers remains one of the last big mysteries in polymer physics (1). Concentrated systems of ring polymers have been observed, in both simulations and experiments, to display unique features that are not easily reconciled with the standard reptation theory of linear polymers (2-6). The main reason for this is that ring polymers do not possess free terminal segments, or ends, essential for end-directed curvilinear diffusion. In contrast, ring polymers possess a closed contour, which leads to markedly different relaxation and diffusion mechanisms. Recently, there has been much improvement in the production of purified systems of rings (6-8), with the consequent result that more and more experimental puzzling evidence requires a deeper understanding of their motion in concentrated solutions and melts from a theoretical point of view.Recently, it has been conjectured that ring polymers assume crumpled, segregated conformations in concentrated solution or the melt (5). 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 (9-12). Because of this, there have been many recent attempts to rigorously characterize these interchains' interactions (13-16), 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.In the case of concentrated solutions of rings embedded in a gel, a method to identify these interpenetrating threadings has recently been proposed (13). Here it was shown that the number of threadings scales extensively in the polymer length (or mass) and can therefore be numerous for long rings, creating a hierarchical sequence of constraints that can span the entire system. It has also been con...

On the tree-like structure of rings in dense solutions

“…with this finding, several very recent works from different groups 12,[16][17][18] reported that rings in dense solutions display largely inter-penetrating configurations: segments of rings double-fold and thread through the contour of their neighbours, eventually leading to strongly overlapping configurations, perhaps best mimicked by the behaviour of ultra-soft colloids 19 rather than by that of polymers in poor solvents.…”

“…The self-avoiding limit of the same system (randomly branched polymers) was instead shown 30 to display ν = 1/2 in 3D. Numerical 8,12,13 and experimental 31 evidence seem to suggest that the self-avoiding regime (ν = 1/2) in fact holds only for short rings, whereas the ideal behaviour (ν = 1/3) takes over in the limit of large polymerisation index through a broad crossover where 22 ν = 2/5. These arguments seem to lead to a picture of "crumpled lattice animals" where globally collapsed polymers display local tree-like structures.…”

“…This value of the metric exponent ν is usually associated with collapsed polymers in poor solvents, which tightly fold onto themselves expelling other chains and solvent from their interior volume. On the other hand, recent works [12][13][14][15] pointed out that the fraction of a ring's contour length that is in contact with any other ring in solution does not scale as M 2/3 , as the smooth surface of a compact sphere would, but rather as ∼ M 1 , indicating a very "rough" surface and a low degree of segregation. In agreement a School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, Scotland, United Kingdom.…”

“…While the global structure of the rings can be directly inferred from the metric exponent in simulations 10,12 (or neutron scattering in experiments 31 ), their local structure is more difficult to probe. Although the existence of local tree-like conformations has been conjectured, there is only circumstantial evidence for their existence in the literature.…”

“…Here, I will be using the data obtained from large-scale Brownian Dynamics simulations of rings in dense solutions (from Ref. 12 ) to identify tree-like structures at the local scale of the rings' segments (see Fig. 1 for a snapshot of the system and Appendix A for details on the Brownian Dynamics simulations).…”