A single particle model to simulate the dynamics of entangled polymer melts

Kindt, Peter; Briels, Willem J.

doi:10.1063/1.2780151

Cited by 68 publications

(97 citation statements)

References 41 publications

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“…More recently, the method has been extended to chains of Gaussian blobs by Pierleoni and his co-workers [253,254] and Kremer and his co-workers [255,256], allowing for much more efficient implementations. Kindt and Briels [86] developed a single-particle model to study entangled polymer chain dynamics. In this model, the entanglement number, n ij , is introduced between particle pairs, i and j, which accounts for the deviation of the the ignored degrees of freedom from the equilibrium state.…”

Section: Super Coarse-graining Methodsmentioning

confidence: 99%

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Challenges in Multiscale Modeling of Polymer Dynamics

et al. 2013

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The mechanical and physical properties of polymeric materials originate from the interplay of phenomena at different spatial and temporal scales. As such, it is necessary to adopt multiscale techniques when modeling polymeric materials in order to account for all important mechanisms. Over the past two decades, a number of different multiscale computational techniques have been developed that can be divided into three categories: (i) coarse-graining methods for generic polymers; (ii) systematic coarse-graining methods and (iii) multiple-scale-bridging methods. In this work, we discuss and compare eleven different multiscale computational techniques falling under these categories and assess them critically according to their ability to provide a rigorous link between polymer chemistry and rheological material properties. For each technique, the fundamental ideas and equations are introduced, and the most important results or predictions are shown and discussed. On the one hand, this review provides a comprehensive tutorial on multiscale computational techniques, which will be of interest to readers newly entering this field; on the other, it presents a critical discussion of the future opportunities and key challenges in the multiscale geometric mapping matrix between all-atomistic and coarse-grained models N number of monomers per chain N e entanglement length, which is the number of monomers between two entanglements n v number of polymer chains per unit volume n ij (n 0 (r ij )) entanglement number (at equilibrium) between particle pairs i and j p r , P R configurational probability distributions in all-atomistic and coarse-grained models, respectively R ee end-to-end distance of polymer chain R G radius of gyration of polymer chain s segment index/contour length variable along primitive chain S(q) single chain coherent dynamic scattering function Z number of entanglements per chain, defined as Z = N/N e α exponent in standard Mittag-Leffler function σ

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Section: Super Coarse-graining Methodsmentioning

confidence: 99%

“…The displacements of the centers of mass of polymer chains are governed by these transient forces and the conservative forces originating from the potential of mean force. The equilibrium entanglement number, n 0 (r ij ), is set as [86]:…”

Section: Super Coarse-graining Methodsmentioning

confidence: 99%

Challenges in Multiscale Modeling of Polymer Dynamics

et al. 2013

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“…It is shown that strong links have the property that they are sampled at least once within this time interval. By following the space-time trajectories of selected links, under equilibrium, deformation, or flow, we could obtain useful mesoscopic information for the development of hierarchical sliplink, or single particle [93][94][95] simulation schemes. The mean square displacement of selected links is presented in the appendices.…”

Section: Introductionmentioning

confidence: 99%

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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“…Then a choice has to be made: either to coarsegrain further but somehow maintain the information about entanglements, or to switch to one-chain models. The …rst method has been most successfully pursued by the group of Wim Briels, who suggested either preventing chain crossing geometrically [9], or maintaining information about entanglements by re-introducing slow variables such as the number of entanglements between two coils [10]. On the other hand, a one chain model can eventually lead to the tube model, which can be simpli…ed to a constitutive equation [11].…”

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confidence: 99%

Whither tube theory: From believing to measuring

Likhtman

2009

Journal of Non-Newtonian Fluid Mechanics

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A single particle model to simulate the dynamics of entangled polymer melts

Cited by 68 publications

References 41 publications

Challenges in Multiscale Modeling of Polymer Dynamics

Challenges in Multiscale Modeling of Polymer Dynamics

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

Whither tube theory: From believing to measuring

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