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Phillies GDJ. Simulational Tests of the Rouse Model. Polymers (Basel) 2023; 15:2615. [PMID: 37376261 DOI: 10.3390/polym15122615] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Revised: 05/24/2023] [Accepted: 06/03/2023] [Indexed: 06/29/2023] Open
Abstract
An extensive review of literature simulations of quiescent polymer melts is given, considering results that test aspects of the Rouse model in the melt. We focus on Rouse model predictions for the mean-square amplitudes ⟨(Xp(0))2⟩ and time correlation functions ⟨Xp(0)Xp(t)⟩ of the Rouse mode Xp(t). The simulations conclusively demonstrate that the Rouse model is invalid in polymer melts. In particular, and contrary to the Rouse model, (i) mean-square Rouse mode amplitudes ⟨(Xp(0))2⟩ do not scale as sin-2(pπ/2N), N being the number of beads in the polymer. For small p (say, p≤3) ⟨(Xp(0))2⟩ scales with p as p-2; for larger p, it scales as p-3. (ii) Rouse mode time correlation functions ⟨Xp(t)Xp(0)⟩ do not decay with time as exponentials; they instead decay as stretched exponentials exp(-αtβ). β depends on p, typically with a minimum near N/2 or N/4. (iii) Polymer bead displacements are not described by independent Gaussian random processes. (iv) For p≠q, ⟨Xp(t)Xq(0)⟩ is sometimes non-zero. (v) The response of a polymer coil to a shear flow is a rotation, not the affine deformation predicted by Rouse. We also briefly consider the Kirkwood-Riseman polymer model.
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2
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Wang LM, Cao L, Ji WH, Du R, Tang M, Chen SL, Yan LL, Xiao Y, Zhang JR. Application of Neutron Scattering in Organic Photovoltaic Materials. CHINESE JOURNAL OF STRUCTURAL CHEMISTRY 2023. [DOI: 10.1016/j.cjsc.2023.100023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
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3
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Zhang X, Wei W, Xiong H. Hierarchical Dynamics of Nonsticky Molecular Nanoparticle-Tethered Polymers: End and Topology Effects. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00232] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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4
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Arbe A, Alvarez F, Colmenero J. Insight into the Structure and Dynamics of Polymers by Neutron Scattering Combined with Atomistic Molecular Dynamics Simulations. Polymers (Basel) 2020; 12:E3067. [PMID: 33371357 PMCID: PMC7767341 DOI: 10.3390/polym12123067] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2020] [Revised: 12/04/2020] [Accepted: 12/11/2020] [Indexed: 11/23/2022] Open
Abstract
Combining neutron scattering and fully atomistic molecular dynamics simulations allows unraveling structural and dynamical features of polymer melts at different length scales, mainly in the intermolecular and monomeric range. Here we present the methodology developed by us and the results of its application during the last years in a variety of polymers. This methodology is based on two pillars: (i) both techniques cover approximately the same length and time scales and (ii) the classical van Hove formalism allows easily calculating the magnitudes measured by neutron scattering from the simulated atomic trajectories. By direct comparison with experimental results, the simulated cell is validated. Thereafter, the information of the simulations can be exploited, calculating magnitudes that are experimentally inaccessible or extending the parameters range beyond the experimental capabilities. We show how detailed microscopic insight on structural features and dynamical processes of various kinds has been gained in polymeric systems with different degrees of complexity, and how intriguing questions as the collective behavior at intermediate length scales have been faced.
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Affiliation(s)
- Arantxa Arbe
- Centro de Física de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain; (A.A.); (F.A.)
| | - Fernando Alvarez
- Centro de Física de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain; (A.A.); (F.A.)
- Departamento de Polímeros y Materiales Avanzados, Física, Química y Tecnología (UPV/EHU), Apartado 1072, E-20080 San Sebastián, Spain
| | - Juan Colmenero
- Centro de Física de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain; (A.A.); (F.A.)
- Departamento de Polímeros y Materiales Avanzados, Física, Química y Tecnología (UPV/EHU), Apartado 1072, E-20080 San Sebastián, Spain
- Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, E-20018 San Sebastián, Spain
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5
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Wu Z, Milano G, Müller-Plathe F. Combination of Hybrid Particle-Field Molecular Dynamics and Slip-Springs for the Efficient Simulation of Coarse-Grained Polymer Models: Static and Dynamic Properties of Polystyrene Melts. J Chem Theory Comput 2020; 17:474-487. [PMID: 33275441 DOI: 10.1021/acs.jctc.0c00954] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
A quantitative prediction of polymer-entangled dynamics based on molecular simulation is a grand challenge in contemporary computational material science. The drastic increase of relaxation time and viscosity in high-molecular-weight polymeric fluids essentially limits the usage of classic molecular dynamics simulation. Here, we demonstrate a systematic coarse-graining approach for modeling entangled polymers under the slip-spring particle-field scheme. Specifically, a frequency-controlled slip-spring model, a hybrid particle-field model, and a coarse-grained model of polystyrene melts are combined into a hybrid simulation technique. Via a rigorous parameterization strategy to determine the parameters in slip-springs from existing experimental or simulation data, we show that the reptation behavior is clearly observed in multiple characteristics of polymer dynamics, mean-square displacements, diffusion coefficients, reorientational relaxation, and Rouse mode analysis, consistent with the predictions of the tube theory. All dynamical properties of the slip-spring particle-field models are in good agreement with classic molecular dynamics models. Our work provides an efficient and practical approach to establish chemical-specific coarse-grained models for predicting polymer-entangled dynamics.
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Affiliation(s)
- Zhenghao Wu
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, 64287 Darmstadt, Germany
| | - Giuseppe Milano
- Department of Organic Materials Science, Yamagata University, 4-3-16 Jonan, Yonezawa, 992-8510 Yamagata-ken, Japan
| | - Florian Müller-Plathe
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, 64287 Darmstadt, Germany
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6
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Rauscher PM, Rowan SJ, de Pablo JJ. Topological Effects in Isolated Poly[ n]catenanes: Molecular Dynamics Simulations and Rouse Mode Analysis. ACS Macro Lett 2018; 7:938-943. [PMID: 35650969 DOI: 10.1021/acsmacrolett.8b00393] [Citation(s) in RCA: 42] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Poly[n]catenanes are mechanically interlocked polymers consisting of interlocking ring molecules. Over the years, researchers have speculated that the permanent topological interactions within the poly[n]catenane backbone could lead to unique dynamical behaviors. To investigate these unusual polymers, molecular dynamics simulations of isolated poly[n]catenanes have been conducted, along with a Rouse mode analysis. Owing to the mechanical bonds within the molecule, the dynamics of poly[n]catenanes at short length scales are significantly slowed and the distribution of relaxation times is broadened; these same behaviors have been observed in melts of linear polymers and are associated with entanglement. Despite these entanglement-like effects, at large length scales poly[n]catenanes do not relax much slower than isolated linear polymers and are less strongly impacted by increased segmental stiffness.
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7
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Deng B, Huang L, Shi Y. Solvent Effect on the Diffusion of Unentangled Linear Polymer Melts. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2017; 33:11845-11850. [PMID: 28930634 DOI: 10.1021/acs.langmuir.7b02901] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We conducted molecular dynamics (MD) simulations to study how solvent chains affect the diffusion of linear polymers in the unentangled regime. For monodisperse solvent chains, the self-diffusivity of a tagged chain scales with its chain length. The solvent chain length affects both the prefactor and the exponent, the latter of which ranges from -0.79 to -0.85. The scaling exponent here deviates from -1 as predicted by the Rouse model, which may suggest that the friction coefficient increases with the solvent chain length. In addition, we carried out diffusion simulations on two polydisperse melts, one with the Flory-Schulz distribution and the other with the Gaussian distribution. The measured diffusivity as a function of the tagged chain length agrees with a simple proposed model accounting for the heterogeneous medium.
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Affiliation(s)
- Binghui Deng
- Department of Materials Science and Engineering, Rensselaer Polytechnic Institute , Troy, New York 12180, United States
| | - Liping Huang
- Department of Materials Science and Engineering, Rensselaer Polytechnic Institute , Troy, New York 12180, United States
| | - Yunfeng Shi
- Department of Materials Science and Engineering, Rensselaer Polytechnic Institute , Troy, New York 12180, United States
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8
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Hofmann M, Kresse B, Heymann L, Privalov AF, Willner L, Fatkullin N, Aksel N, Fujara F, Rössler EA. Dynamics of a Paradigmatic Linear Polymer: A Proton Field-Cycling NMR Relaxometry Study on Poly(ethylene–propylene). Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b01906] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- M. Hofmann
- Experimentalphysik
II, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - B. Kresse
- Institut
für Festkörperphysik, TU Darmstadt, D-64289 Darmstadt, Germany
| | - L. Heymann
- Technische
Mechanik und Strömungsmechanik, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - A. F. Privalov
- Institut
für Festkörperphysik, TU Darmstadt, D-64289 Darmstadt, Germany
| | - L. Willner
- Institute
of Complex Systems, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - N. Fatkullin
- Institute
of Physics, Kazan Federal University, Kazan 420008, Tatarstan Russia
| | - N. Aksel
- Technische
Mechanik und Strömungsmechanik, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - F. Fujara
- Institut
für Festkörperphysik, TU Darmstadt, D-64289 Darmstadt, Germany
| | - E. A. Rössler
- Experimentalphysik
II, Universität Bayreuth, D-95440 Bayreuth, Germany
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9
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Hofmann M, Kresse B, Privalov AF, Heymann L, Willner L, Aksel N, Fatkullin N, Fujara F, Rössler EA. Segmental Mean Square Displacement: Field-Cycling 1H Relaxometry vs Neutron Scattering. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b01860] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- M. Hofmann
- Experimentalphysik
II, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - B. Kresse
- Institut
für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, D-64289 Darmstadt, Germany
| | - A. F. Privalov
- Institut
für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, D-64289 Darmstadt, Germany
| | - L. Heymann
- Technische
Mechanik und Strömungsmechanik, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - L. Willner
- Institute
of Complex Systems, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - N. Aksel
- Technische
Mechanik und Strömungsmechanik, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - N. Fatkullin
- Institute
of Physics, Kazan Federal University, Kazan 420008, Tatarstan Russia
| | - F. Fujara
- Institut
für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, D-64289 Darmstadt, Germany
| | - E. A. Rössler
- Experimentalphysik
II, Universität Bayreuth, D-95440 Bayreuth, Germany
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10
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Arbe A, Moreno AJ, Allgaier J, Ivanova O, Fouquet P, Colmenero J, Richter D. Role of Dynamic Asymmetry on the Collective Dynamics of Comblike Polymers: Insights from Neutron Spin-Echo Experiments and Coarse-Grained Molecular Dynamics Simulations. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b00931] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Arantxa Arbe
- Materials Physics Center (MPC), Centro de Física de Materiales (CFM), CSIC−UPV/EHU, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain
- Jülich Centre for Neutron Science and Institut for Complex Systems, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
- Jülich Centre for Neutron Science, Forschungszentrum Jülich GmbH, Outstation at Heinz
Maier-Leibnitz Zentrum, Lichtenbergstr.1, 85747 Garching, Germany
- Institut Laue−Langevin, CS 20156, 38042 Grenoble, Cedex 9, France
- Departamento de Física de Materiales, UPV/EHU, Apartado 1072, 20080 San Sebastián, Spain
| | - Angel J. Moreno
- Materials Physics Center (MPC), Centro de Física de Materiales (CFM), CSIC−UPV/EHU, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain
- Jülich Centre for Neutron Science and Institut for Complex Systems, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
- Jülich Centre for Neutron Science, Forschungszentrum Jülich GmbH, Outstation at Heinz
Maier-Leibnitz Zentrum, Lichtenbergstr.1, 85747 Garching, Germany
- Institut Laue−Langevin, CS 20156, 38042 Grenoble, Cedex 9, France
- Departamento de Física de Materiales, UPV/EHU, Apartado 1072, 20080 San Sebastián, Spain
| | - Jürgen Allgaier
- Materials Physics Center (MPC), Centro de Física de Materiales (CFM), CSIC−UPV/EHU, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain
- Jülich Centre for Neutron Science and Institut for Complex Systems, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
- Jülich Centre for Neutron Science, Forschungszentrum Jülich GmbH, Outstation at Heinz
Maier-Leibnitz Zentrum, Lichtenbergstr.1, 85747 Garching, Germany
- Institut Laue−Langevin, CS 20156, 38042 Grenoble, Cedex 9, France
- Departamento de Física de Materiales, UPV/EHU, Apartado 1072, 20080 San Sebastián, Spain
| | - Oxana Ivanova
- Materials Physics Center (MPC), Centro de Física de Materiales (CFM), CSIC−UPV/EHU, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain
- Jülich Centre for Neutron Science and Institut for Complex Systems, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
- Jülich Centre for Neutron Science, Forschungszentrum Jülich GmbH, Outstation at Heinz
Maier-Leibnitz Zentrum, Lichtenbergstr.1, 85747 Garching, Germany
- Institut Laue−Langevin, CS 20156, 38042 Grenoble, Cedex 9, France
- Departamento de Física de Materiales, UPV/EHU, Apartado 1072, 20080 San Sebastián, Spain
| | - Peter Fouquet
- Materials Physics Center (MPC), Centro de Física de Materiales (CFM), CSIC−UPV/EHU, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain
- Jülich Centre for Neutron Science and Institut for Complex Systems, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
- Jülich Centre for Neutron Science, Forschungszentrum Jülich GmbH, Outstation at Heinz
Maier-Leibnitz Zentrum, Lichtenbergstr.1, 85747 Garching, Germany
- Institut Laue−Langevin, CS 20156, 38042 Grenoble, Cedex 9, France
- Departamento de Física de Materiales, UPV/EHU, Apartado 1072, 20080 San Sebastián, Spain
| | - Juan Colmenero
- Materials Physics Center (MPC), Centro de Física de Materiales (CFM), CSIC−UPV/EHU, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain
- Jülich Centre for Neutron Science and Institut for Complex Systems, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
- Jülich Centre for Neutron Science, Forschungszentrum Jülich GmbH, Outstation at Heinz
Maier-Leibnitz Zentrum, Lichtenbergstr.1, 85747 Garching, Germany
- Institut Laue−Langevin, CS 20156, 38042 Grenoble, Cedex 9, France
- Departamento de Física de Materiales, UPV/EHU, Apartado 1072, 20080 San Sebastián, Spain
| | - Dieter Richter
- Materials Physics Center (MPC), Centro de Física de Materiales (CFM), CSIC−UPV/EHU, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain
- Jülich Centre for Neutron Science and Institut for Complex Systems, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
- Jülich Centre for Neutron Science, Forschungszentrum Jülich GmbH, Outstation at Heinz
Maier-Leibnitz Zentrum, Lichtenbergstr.1, 85747 Garching, Germany
- Institut Laue−Langevin, CS 20156, 38042 Grenoble, Cedex 9, France
- Departamento de Física de Materiales, UPV/EHU, Apartado 1072, 20080 San Sebastián, Spain
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11
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Kalathi JT, Kumar SK, Rubinstein M, Grest GS. Rouse mode analysis of chain relaxation in polymer nanocomposites. SOFT MATTER 2015; 11:4123-32. [PMID: 25939276 PMCID: PMC4840937 DOI: 10.1039/c5sm00754b] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Large-scale molecular dynamics simulations are used to study the internal relaxations of chains in nanoparticle (NP)/polymer composites. We examine the Rouse modes of the chains, a quantity that is closest in spirit to the self-intermediate scattering function, typically determined in an (incoherent) inelastic neutron scattering experiment. Our simulations show that for weakly interacting mixtures of NPs and polymers, the effective monomeric relaxation rates are faster than in a neat melt when the NPs are smaller than the entanglement mesh size. In this case, the NPs serve to reduce both the monomeric friction and the entanglements in the polymer melt, as in the case of a polymer-solvent system. However, for NPs larger than half the entanglement mesh size, the effective monomer relaxation is essentially unaffected for low NP concentrations. Even in this case, we observe a strong reduction in chain entanglements for larger NP loadings. Thus, the role of NPs is to always reduce the number of entanglements, with this effect only becoming pronounced for small NPs or for high concentrations of large NPs. Our studies of the relaxation of single chains resonate with recent neutron spin echo (NSE) experiments, which deduce a similar entanglement dilution effect.
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12
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Panja D, Barkema GT, Ball RC. Complex Interactions with the Surroundings Dictate a Tagged Chain’s Dynamics in Unentangled Polymer Melts. Macromolecules 2015. [DOI: 10.1021/ma502523p] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Affiliation(s)
- Debabrata Panja
- Institute
of Physics, Universiteit van Amsterdam, Science Park 904, Postbus 94485, 1090
GL Amsterdam, The Netherlands
| | - Gerard T. Barkema
- Institute
for Theoretical Physics, Universiteit Utrecht, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
- Instituut-Lorentz, Universiteit Leiden,
Niels Bohrweg 2, 2333 CA, Leiden, The Netherlands
| | - Robin C. Ball
- Department
of Physics, University of Warwick, Coventry CV4 7AL, U.K
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13
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Kalathi JT, Kumar SK, Rubinstein M, Grest GS. Rouse Mode Analysis of Chain Relaxation in Homopolymer Melts. Macromolecules 2014; 47:6925-6931. [PMID: 25328247 PMCID: PMC4196748 DOI: 10.1021/ma500900b] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2014] [Revised: 07/31/2014] [Indexed: 11/29/2022]
Abstract
![]()
We use molecular dynamics simulations
of the Kremer–Grest
(KG) bead–spring model of polymer chains of length between
10 and 500, and a closely related analogue that allows for chain crossing,
to clearly delineate the effects of entanglements on the length-scale-dependent
chain relaxation in polymer melts. We analyze the resulting trajectories
using the Rouse modes of the chains and find that entanglements strongly
affect these modes. The relaxation rates of the chains show two limiting
effective monomeric frictions, with the local modes experiencing much
lower effective friction than the longer modes. The monomeric relaxation
rates of longer modes vary approximately inversely with chain length
due to kinetic confinement effects. The time-dependent relaxation
of Rouse modes has a stretched exponential character with a minimum
of stretching exponent in the vicinity of the entanglement chain length.
None of these trends are found in models that allow for chain crossing.
These facts, in combination, argue for the confined motion of chains
for time scales between the entanglement time and their ultimate free
diffusion.
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Affiliation(s)
- Jagannathan T Kalathi
- Department of Chemical Engineering, Columbia University , New York, New York 10027, United States
| | - Sanat K Kumar
- Department of Chemical Engineering, Columbia University , New York, New York 10027, United States
| | - Michael Rubinstein
- Department of Chemistry, University of North Carolina , Chapel Hill, North Carolina 27599, United States
| | - Gary S Grest
- Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
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14
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Colmenero J, Arbe A. Recent progress on polymer dynamics by neutron scattering: From simple polymers to complex materials. ACTA ACUST UNITED AC 2012. [DOI: 10.1002/polb.23178] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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