Understanding the dynamics of rings in the melt in terms of the annealed tree model

Smrek, Jan; Grosberg, Alexander Y.

doi:10.1088/0953-8984/27/6/064117

Cited by 67 publications

(123 citation statements)

References 57 publications

(155 reference statements)

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“…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.…”

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confidence: 99%

A topologically driven glass in ring polymers

Michieletto

Turner

2016

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

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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confidence: 99%

A topologically driven glass in ring polymers

Michieletto

Turner

2016

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

108

185

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“…Smrek and Grosberg [Smrek and Grosberg, 2015] based on the novel description of a ring as an annealed tree made of crumpled branches decorating a self-avoiding path on a Cayley tree, i.e. R ∼ σM 1/3 and R ∼ σ 2/5 L 3/5 with L ∼ σM 5/9 (or ν = 1/3, ρ = 5/9 and ν/ρ = 3/5), advanced an alternative picture for the dynamics of rings in the melt.…”

Section: Dynamics 221 Diffusion Coefficient and Relaxation Timementioning

confidence: 99%

“…More recently, Milner, Iyer and then Grosberg [Iyer andArya, 2012, Smrek andGrosberg, 2015] advanced several other theories for the diffusion of a ring polymers among other chains, or "fixed obstacles". Milner and Newhall [Milner and Newhall, 2010] proposed an approach based on the "centrality" of a node in the lattice animal representation of the ring defined as…”

Section: Dynamics 221 Diffusion Coefficient and Relaxation Timementioning

confidence: 99%

“…Recently there have been quite a few attempts to quantify the stress relaxation of rings in a background of obstacles [Milner and Newhall, 2010] and in the melt [Kapnistos et al, 2008, Pasquino et al, 2013, Smrek and Grosberg, 2015. All the theoretical effort has been focused on describing rings as amoebae [Rubinstein, 1986] moving through obstacles situated around the ring double-folded configuration, i.e.…”

Section: How Rings Relax Stressmentioning

confidence: 99%

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Topological Interactions in Ring Polymers

Michieletto¹

2016

Springer Theses

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“…Moving higher in the hierarchy, two studies are devoted to diffusion inside the crowded nuclear environment [17,18]. Finally, a wide range of approaches is applied to study chromatin organization on large scales [19][20][21][22]. Now, as our understanding of the different levels of chromatin has progressed so much, the future challenge will be to combine the different insights into a more coherent view of all the levels.…”

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confidence: 99%