Crossover from the Rouse to the Entangled Polymer Melt Regime:  Signals from Long, Detailed Atomistic Molecular Dynamics Simulations, Supported by Rheological Experiments

Harmandaris, Vagelis; Mavrantzas, Vlasis G.; Theodorou, Doros N.; Kröger, Martin; Ramı́rez, Jorge; Öttinger, Hans Christian; Vlassopoulos, D.

doi:10.1021/ma020009g

Cited by 214 publications

(313 citation statements)

References 52 publications

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“…Large spatial and temporal scales can rather easily be approached by these generic methods, compared with all-atomistic MD simulations. Scaling laws characterizing the effect of molecular weight on the dynamics or rheology can be obtained and compared with the prediction from the Rouse or tube model, as well as with experiments [76]. However, since these methods neglect chemical details, the obtained results are usually difficult to compare with specific polymers.…”

Section: Overview Of Multiscale Modeling Techniquesmentioning

confidence: 99%

“…Since the rheological properties of entangled polymer melts are dominated by entanglements, many computational works have been undertaken to extract the underlying primitive path (PP) and entanglement characteristics predicted by the tube model directly from the atomistic simulations [76,79,97,119,178,198,223,242,[275][276][277][278][279][280][281][282][283][284][285]. All of the studies are based on the tube concept developed by Doi and Edwards [6] in which the PP is considered to be the shortest entanglement-preserving path between two ends of the polymer chain, as they are fixed in space.…”

Section: Dynamic Mapping Onto Tube Modelmentioning

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: Overview Of Multiscale Modeling Techniquesmentioning

confidence: 99%

Section: Dynamic Mapping Onto Tube Modelmentioning

confidence: 99%

Challenges in Multiscale Modeling of Polymer Dynamics

et al. 2013

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“…Figure 9 compares the zero shear rate viscosities obtained from our PP analysis with reported experimental data [33][34][35][36][37] for a number of model PE ͓Fig. 9͑a͔͒ and PB ͓Fig.…”

Section: -8mentioning

confidence: 99%

Quantifying chain reptation in entangled polymer melts: Topological and dynamical mapping of atomistic simulation results onto the tube model

Stephanou

Baig

Tsolou

et al. 2010

The Journal of Chemical Physics

106

153

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Articles you may be interested inTemperature dependent micro-rheology of a glass-forming polymer melt studied by molecular dynamics simulation J. Chem. Phys. 141, 124907 (2014) The topological state of entangled polymers has been analyzed recently in terms of primitive paths which allowed obtaining reliable predictions of the static ͑statistical͒ properties of the underlying entanglement network for a number of polymer melts. Through a systematic methodology that first maps atomistic molecular dynamics ͑MD͒ trajectories onto time trajectories of primitive chains and then documents primitive chain motion in terms of a curvilinear diffusion in a tubelike region around the coarse-grained chain contour, we are extending these static approaches here even further by computing the most fundamental function of the reptation theory, namely, the probability ͑s , t͒ that a segment s of the primitive chain remains inside the initial tube after time t, accounting directly for contour length fluctuations and constraint release. The effective diameter of the tube is independently evaluated by observing tube constraints either on atomistic displacements or on the displacement of primitive chain segments orthogonal to the initial primitive path. Having computed the tube diameter, the tube itself around each primitive path is constructed by visiting each entanglement strand along the primitive path one after the other and approximating it by the space of a small cylinder having the same axis as the entanglement strand itself and a diameter equal to the estimated effective tube diameter. Reptation of the primitive chain longitudinally inside the effective constraining tube as well as local transverse fluctuations of the chain driven mainly from constraint release and regeneration mechanisms are evident in the simulation results; the latter causes parts of the chains to venture outside their average tube surface for certain periods of time. The computed ͑s , t͒ curves account directly for both of these phenomena, as well as for contour length fluctuations, since all of them are automatically captured in the atomistic simulations. Linear viscoelastic properties such as the zero shear rate viscosity and the spectra of storage and loss moduli obtained on the basis of the obtained ͑s , t͒ curves for three different polymer melts ͑polyethylene, cis-1,4-polybutadiene, and trans-1,4-polybutadiene͒ are consistent with experimental rheological data and in qualitative agreement with the double reptation and dual constraint models. The new methodology is general and can be routinely applied to analyze primitive path dynamics and chain reptation in atomistic trajectories ͑accumulated through long MD simulations͒ of other model polymers or polymeric systems ͑e.g., bidisperse, branched, grafted, etc.͒; it is thus believed to be particularly useful in the future in evaluating proposed tube models and developing more accurate theories for entangled systems.

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“…A power exponent Ϸ 2 for the D ϰ N − dependence has been found experimentally [3][4][5][6][7] and in computer simulations. [8][9][10][11] This diffusional reptation is a long time process influenced by the chain length and ensemble density. It is directly reflected in the bulk macroscopic properties and experimental measurements of viscosity, birefringence, 2 and light or neutron scattering 12 have also been reported to support the theory.…”

Section: Introductionmentioning

confidence: 99%

Forced reptation revealed by chain pull-out simulations

Bulacu

Giessen

2009

The Journal of Chemical Physics

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We report computation results obtained from extensive molecular dynamics simulations of tensile disentanglement of connector chains placed at the interface between two polymer bulks. Each polymer chain (either belonging to the bulks or being a connector) is treated as a sequence of beads interconnected by springs, using a coarse-grained representation based on the Kremer–Grest model, extended to account for stiffness along the chain backbone. Forced reptation of the connectors was observed during their disentanglement from the bulk chains. The extracted chains are clearly seen following an imaginary “tube” inside the bulks as they are pulled out. The entropic and energetic responses to the external deformation are investigated by monitoring the connector conformation tensor and the modifications of the internal parameters (bonds, bending, and torsion angles along the connectors). The work needed to separate the two bulks is computed from the tensile force induced during debonding in the connector chains. The value of the work reached at total separation is considered as the debonding energy G. The most important parameters controlling G are the length (n) of the chains placed at the interface and their areal density. Our in silico experiments are performed at relatively low areal density and are disregarded if chain scission occurs during disentanglement. As predicted by the reptation theory, for this pure pull-out regime, the power exponent from the scaling G∝na is a≈2, irrespective of chain stiffness. Small variations are found when the connectors form different number of stitches at the interface, or when their length is randomly distributed in between the two bulks. Our results show that the effects of the number of stitches and of the randomness of the block lengths have to be considered together, especially when comparing with experiments where they cannot be controlled rigorously. These results may be significant for industrial applications, such reinforcement of polymer-polymer adhesion by connector chains, when incorporated as constitutive laws at higher time/length scales in finite element calculations.

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Crossover from the Rouse to the Entangled Polymer Melt Regime: Signals from Long, Detailed Atomistic Molecular Dynamics Simulations, Supported by Rheological Experiments

Cited by 214 publications

References 52 publications

Challenges in Multiscale Modeling of Polymer Dynamics

Challenges in Multiscale Modeling of Polymer Dynamics

Quantifying chain reptation in entangled polymer melts: Topological and dynamical mapping of atomistic simulation results onto the tube model

Forced reptation revealed by chain pull-out simulations

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