A Study of the Entanglement in Systems with Periodic Boundary Conditions

Panagiotou, Eleni; Tzoumanekas, Christos; Lambropoulou, Sofia; Millett, Kenneth C.; Theodorou, Doros N.

doi:10.1143/ptps.191.172

Cited by 28 publications

(27 citation statements)

References 15 publications

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“…The knots were defined at the real chain level by using as topological criterion a local form of the Gauss linking number. For open chains this criterion is not more rigorous 54,55,122 than the one defined here, while it is computationally more complex.…”

Section: Appendix Ii: Mean Square Displacement and Characteristic Relmentioning

confidence: 95%

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

2012

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Abstract:We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, or as certain pairwise uncrossability interactions, as in slip-link models.A pairwise parameter, which varies between these limiting cases, shows that, for the systems studied, the character of the entanglement environment is more pairwise than collective. We employ a novel methodology, which analyzes entanglement constraints into a complete set of pairwise interactions, similar to slip links. Entanglement confinement is assembled by a plethora of links, with a spectrum of confinement strengths, from strong to weak. The strength of interactions is quantified through a link 'persistence', which is the fraction of time for which the links are active. By weighting links according to their strength, we show that confinement is imposed mainly by the strong ones, and that the weak, trapped, uncrossability interactions cannot contribute to the low frequency modulus of an elastomer, or the plateau modulus of a melt. A selfconsistent scheme for mapping topological constraints to specific, strong binary links, according to a given entanglement density, is proposed and validated. Our results demonstrate that slip links can be viewed as the strongest pairwise interactions of a collective entanglement environment. The methodology developed provides a basis for bridging the gap between atomistic simulations and mesoscopic slip link models.

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Section: Appendix Ii: Mean Square Displacement and Characteristic Relmentioning

confidence: 95%

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

2012

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“…The properties of LK were studied in [57]. We stress the following: (i) LK is independent of the choice of the image I u of the free chain I in the periodic system.…”

Section: The Local Periodic Linking Numbermentioning

confidence: 99%

“…In [57], by using the local periodic linking number LK, we examined the extent to which the CReTA method preserves that linking measure of entanglement in PE melts, or if critical entanglement information is lost in the reduction process. To do this, we computed the normalized probability distribution of LK for pairs of PE chains in a frame and compared it to the LK for the corresponding reduced pairs.…”

Section: The Creta Algorithm and The Local Periodic Linking Numbermentioning

confidence: 99%

“…In [57], the basis for the study of entanglement in systems employing PBC was introduced, and the local periodic linking number was defined and applied to samples of polyethylene (PE) melts. In this paper the periodic linking number is defined and its properties for closed, open or infinite chains, and its relation to the Gauss linking number and the local periodic linking number are studied.…”

Section: Introductionmentioning

confidence: 99%

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The linking number in systems with Periodic Boundary Conditions

Panagiotou

2015

Journal of Computational Physics

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“…Simulations of polymer melts typically use periodic boundary conditions and generate complex periodic weavings that have been studied using topological constraint graphs and generalized definitions of linking numbers [70,71]. These linking numbers may be correlated to our periodic ropelength as is the case for finite knots and average crossing number [20].…”

Section: Introductionmentioning

confidence: 99%

Ideal geometry of periodic entanglements

2015

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Three-dimensional entanglements, including knots, knotted graphs, periodic arrays of woven filaments and interpenetrating nets, form an integral part of structure analysis because they influence various physical properties. Ideal embeddings of these entanglements give insight into identification and classification of the geometry and physically relevant configurations in vivo. This paper introduces an algorithm for the tightening of finite, periodic and branched entanglements to a least energy form. Our algorithm draws inspiration from the ShrinkOn-No-Overlaps (SONO) (Pieranski 1998 In Ideal knots (eds A Stasiak, V Katritch, LH Kauffman), vol. 19, pp. 20-41.) algorithm for the tightening of knots and links: we call it Periodic-Branched Shrink-On-No-Overlaps (PB-SONO). We reproduce published results for ideal configurations of knots using PB-SONO. We then examine ideal geometry for finite entangled graphs, including θ-graphs and entangled tetrahedron-and cube-graphs. Finally, we compute ideal conformations of periodic weavings and entangled nets. The resulting ideal geometry is intriguing: we see spontaneous symmetrisation in some cases, breaking of symmetry in others, as well as configurations reminiscent of biological and chemical structures in nature.

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A Study of the Entanglement in Systems with Periodic Boundary Conditions

Cited by 28 publications

References 15 publications

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

The linking number in systems with Periodic Boundary Conditions

Ideal geometry of periodic entanglements

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