The topological glass in ring polymers

Lo, Wei-Chang; Turner, Matthew S.

doi:10.1209/0295-5075/102/58005

Cited by 39 publications

(47 citation statements)

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“…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.…”

Section: Return Probability On a Finite-size Surfacesupporting

confidence: 86%

“…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.…”

Section: Discussionmentioning

confidence: 99%

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On the tree-like structure of rings in dense solutions

Michieletto

2016

Soft Matter

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One of the most challenging problems in polymer physics is providing a theoretical description for the behaviour of rings in dense solutions and melts. Although it is nowadays well established that the overall size of a ring in these conditions scales like that of a collapsed globule, there is compelling evidence that rings may exhibit ramified and tree-like conformations. In this work I show how to characterise these local tree-like structures by measuring the local writhing of the rings' segments and by identifying the patterns of intra-chain contacts. These quantities reveal two major topological structures: loops and terminal branches which strongly suggest that the strictly double-folded "lattice animal" picture for rings in the melt may be replaced by a more relaxed tree-like structure accommodating loops. In particular, I show that one can identify hierarchically looped structures whose degree increases linearly with the size of a ring, and that terminal branches are found to store about 30% of the whole ring mass, irrespectively of its length. Finally, I draw an analogy between rings in the melt and slip-linked chains, where contact points are enforced by mobile slip-links and for which a field-theoretic treatment can be employed to get some insight into their typical conformations. These findings are ultimately discussed in the light of recent works on the static structure of rings and on the existence of inter-ring threadings.

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Section: Return Probability On a Finite-size Surfacesupporting

confidence: 86%

Section: Discussionmentioning

confidence: 99%

On the tree-like structure of rings in dense solutions

Michieletto

2016

Soft Matter

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“…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 conjectured that a kinetically frozen state, or a "topological glass" (17) can emerge, because such an extensive network of constraints can eventually suppress the translational degrees of freedom of the rings. However, the molten, or highly concentrated, state does differ from that of polymers embedded in a gel and so whether a similar jamming transition occurs for long enough polymers or even whether threadings are present in the absence of a gel remain open problems and are the main questions addressed in this study.…”

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confidence: 99%

A topologically driven glass in ring polymers

Michieletto

Turner

2016

Proc. Natl. Acad. Sci. U.S.A.

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108

185

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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...

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“…Are there upper and lower critical dimensions for which random coil melts lose entanglement localization at any value of N ? Is our prediction of a mesoscopic "topological glass transition" relevant to dense liquids of ring polymers and biological analogs [9,10]? More generally, if macromolecules are not ideal random walks but still interpenetrating fractals, how does the breakdown of the isotropic Rouse model and entanglement localization evolve as a function of mass fractal and spatial dimensions?…”

Section: Discussionmentioning

confidence: 99%

“…The relevant wide range of length and times scales results in distinctive viscoelastic behavior, the first principles understanding of which is a complex task. A fundamental understanding impacts diverse problems that range from plastics processing [4,5] to biophysical phenomena such as protein folding, chromosome dynamics, and cytoskeleton mechanics [6][7][8][9][10][11].…”

Section: Introduction a General Background And Entanglement Phenomentioning

confidence: 99%

Segment-scale, force-level theory of mesoscopic dynamic localization and entropic elasticity in entangled chain polymer liquids

Dell

Schweizer

2017

The Journal of Chemical Physics

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We develop a segment-scale, force-based theory for the breakdown of the unentangled Rouse model and subsequent emergence of isotropic mesoscopic localization and entropic elasticity in chain polymer liquids in the absence of ergodicity-restoring anisotropic reptation motion. The theory is formulated in terms of a conformational N -dynamic-order-parameter Generalized Langevin Equation approach. It is implemented using a field-theoretic Gaussian thread model of polymer structure and closed in a universal manner at the level of the chain dynamic second moment matrix. The physical idea is that the isotropic Rouse model fails due to the dynamical emergence of time-persistent intermolecular contacts determined by the combined influence of local chain uncrossability, long range polymer connectivity and a self-consistent treatment of chain motion and the dynamic forces that hinder it. For long chain melts, the mesoscopic localization length (tube diameter) and emergent elasticity predictions are in near quantitative agreement with experiment. Moreover, the onset chain length scales with the semi-dilute crossover concentration with a realistic numerical prefactor. Distinctive predictions are made for various off-diagonal correlation functions that quantify the full spatial structure of the dynamically localized polymer conformation. As the local uncrossability constraint and/or intrachain bonding spring are softened, the tube diameter is predicted to swell until it reaches the chain radius-of-gyration at which point entanglement localization vanishes in a discontinuous manner. A full dynamic phase diagram for the destruction of mesoscopic localization is constructed, which is qualitatively consistent with simulations and the classical concept of an entanglement degree of polymerization.

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The topological glass in ring polymers

Abstract: Systematic coarse-graining of the dynamics of entangled polymer melts: the road fromchemistry to rheology J T Padding and W J Briels -

Cited by 39 publications

References 28 publications

On the tree-like structure of rings in dense solutions

On the tree-like structure of rings in dense solutions

A topologically driven glass in ring polymers

Segment-scale, force-level theory of mesoscopic dynamic localization and entropic elasticity in entangled chain polymer liquids

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