1
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Zhao Y, Ma Y, Xiong Y, Qin T, Zhu Y, Deng H, Qin J, Shi X, Zhang G. Chemically crosslinked crystalline thermoplastic polyolefin elastomer with good elasticity and improved thermo-mechanical properties. POLYMER 2022. [DOI: 10.1016/j.polymer.2022.125075] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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2
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Affiliation(s)
- Jiuling Wang
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Ting Ge
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
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3
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Schneider J, Fleck F, Karimi-Varzaneh HA, Müller-Plathe F. Simulation of Elastomers by Slip-Spring Dissipative Particle Dynamics. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00567] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Jurek Schneider
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, D-64287 Darmstadt, Germany
| | - Frank Fleck
- Continental Reifen Deutschland GmbH, D-30419 Hannover, Germany
| | | | - Florian Müller-Plathe
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, D-64287 Darmstadt, Germany
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4
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Steenbakkers RJA, Andreev M, Schieber JD. Thermodynamically consistent incorporation of entanglement spatial fluctuations in the slip-link model. Phys Rev E 2021; 103:022501. [PMID: 33736108 DOI: 10.1103/physreve.103.022501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2020] [Accepted: 12/09/2020] [Indexed: 11/07/2022]
Abstract
We evaluate the thermodynamic consistency of the anisotropic mobile slip-link model for entangled flexible polymers. The level of description is that of a single chain, whose interactions with other chains are coarse grained to discrete entanglements. The dynamics of the model consist of the motion of entanglements through space and of the chain through the entanglements, as well as the creation and destruction of entanglements, which are implemented in a mean-field way. Entanglements are modeled as discrete slip links, whose spatial positions are confined by quadratic potentials. The confinement potentials move with the macroscopic velocity field, hence the entanglements fluctuate around purely affine motion. We allow for anisotropy of these fluctuations, described by a set of shape tensors. By casting the model in the form of the general equation for the nonequilibrium reversible-irreversible coupling from nonequilibrium thermodynamics, we show that (i) since the confinement potentials contribute to the chain free energy, they must also contribute to the stress tensor, (ii) these stress contributions are of two kinds: one related to the virtual springs connecting the slip links to the centers of the confinement potentials and the other related to the shape tensors, and (iii) these two kinds of stress contributions cancel each other if the confinement potentials become anisotropic in flow, according to a lower-convected evolution of the confinement strength or, equivalently, an upper-convected evolution of the shape tensors of the entanglement spatial fluctuations. In previous publications, we have shown that this cancellation is necessary for the model to obey the stress-optical rule and the Green-Kubo relation, and simultaneously to agree with plateau modulus predictions of multichain models and simulations.
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Affiliation(s)
- Rudi J A Steenbakkers
- Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois 60616, USA.,Department of Chemical and Biological Engineering, Illinois Institute of Technology, 10 West 35th Street, Chicago, Illinois 60616, USA
| | - Marat Andreev
- Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois 60616, USA.,Department of Physics, Illinois Institute of Technology, 3101 South Dearborn Street, Chicago, Illinois 60616, USA
| | - Jay D Schieber
- Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois 60616, USA.,Department of Chemical and Biological Engineering, Illinois Institute of Technology, 10 West 35th Street, Chicago, Illinois 60616, USA.,Department of Physics, Illinois Institute of Technology, 3101 South Dearborn Street, Chicago, Illinois 60616, USA.,Department of Applied Mathematics, Illinois Institute of Technology, 10 West 32nd Street, Chicago, Illinois 60616, USA
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5
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Pestryaev EM. Chain Heterogeneity in Simulated Polymer Melts: NMR Free Induction Decay and Absorption Line. POLYMER SCIENCE SERIES A 2020. [DOI: 10.1134/s0965545x20060097] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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6
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Sgouros AP, Vogiatzis GG, Megariotis G, Tzoumanekas C, Theodorou DN. Multiscale Simulations of Graphite-Capped Polyethylene Melts: Brownian Dynamics/Kinetic Monte Carlo Compared to Atomistic Calculations and Experiment. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b01379] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Affiliation(s)
- A. P. Sgouros
- School of Chemical Engineering, National Technical University of Athens (NTUA), GR-15780 Athens, Greece
| | - G. G. Vogiatzis
- Department of Mechanical Engineering, Eindhoven University of Technology (TU/e), P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - G. Megariotis
- School of Chemical Engineering, National Technical University of Athens (NTUA), GR-15780 Athens, Greece
| | - C. Tzoumanekas
- School of Chemical Engineering, National Technical University of Athens (NTUA), GR-15780 Athens, Greece
| | - D. N. Theodorou
- School of Chemical Engineering, National Technical University of Athens (NTUA), GR-15780 Athens, Greece
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7
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Cao J, Wang Z, Likhtman AE. Determining Tube Theory Parameters by Slip-Spring Model Simulations of Entangled Star Polymers in Fixed Networks. Polymers (Basel) 2019; 11:E496. [PMID: 30960480 PMCID: PMC6473678 DOI: 10.3390/polym11030496] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2019] [Revised: 03/08/2019] [Accepted: 03/11/2019] [Indexed: 11/26/2022] Open
Abstract
Dynamical properties of branched polymer melts are determined by the polymer molecular weights and architectures containing junction points. Relaxation of entangled symmetric star polymers proceeds via arm-retraction and constraint release (CR). In this work, we investigate arm-retraction dynamics in the framework of a single-chain slip-spring model without CR effect where entanglements are treated as binary contacts, conveniently modeled as virtual "slip-links", each involving two neighboring strands. The model systems are analogous to isolated star polymers confined in a permanent network or a melt of very long linear polymers. We find that the distributions of the effective primitive path lengths are Gaussian, from which the entanglement molecular weight N e , a key tube theory parameter, can be extracted. The procured N e value is in good agreement with that obtained from mapping the middle monomer mean-square displacements of entangled linear chains in slip-spring model to the tube model prediction. Furthermore, the mean first-passage (FP) times of destruction of original tube segments by the retracting arm end are collected in simulations and examined quantitatively using a theory recently developed in our group for describing FP problems of one-dimensional Rouse chains with improbable extensions. The asymptotic values of N e as obtained from the static (primitive path length) and dynamical (FP time) analysis are consistent with each other. Additionally, we manage to determine the tube survival function of star arms μ ( t ) , or equivalently arm end-to-end vector relaxation function ϕ ( t ) , through the mean FP time spectrum τ ( s ) of the tube segments after careful consideration of the inner-most entanglements, which shows reasonably good agreement with experimental data on dielectric relaxation.
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Affiliation(s)
- Jing Cao
- School of Mathematical, Physical and Computational Sciences, University of Reading, Reading RG6 6AX, UK.
| | - Zuowei Wang
- School of Mathematical, Physical and Computational Sciences, University of Reading, Reading RG6 6AX, UK.
| | - Alexei E Likhtman
- School of Mathematical, Physical and Computational Sciences, University of Reading, Reading RG6 6AX, UK
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8
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Panagiotou E, Millett KC, Atzberger PJ. Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and Viscoelasticity. Polymers (Basel) 2019; 11:E437. [PMID: 30960421 PMCID: PMC6473770 DOI: 10.3390/polym11030437] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2019] [Revised: 02/12/2019] [Accepted: 02/26/2019] [Indexed: 12/31/2022] Open
Abstract
We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear chains. We investigate the rheology of polymeric chains entangled into weaves with varying topologies and levels of chain density. To investigate viscoelastic responses, we perform non-equilibrium molecular simulations over a range of frequencies using sheared Lees⁻Edwards boundary conditions. We show how our topological characteristics can be used to capture key features of the polymer entanglements related to the viscoelastic responses. We find there is a linear relation over a significant range of frequencies between the mean absolute Writhe W r and the Loss Tangent tan ( δ ) . We also find an approximate inverse linear relationship between the mean absolute Periodic Linking Number L K P and the Loss Tangent tan ( δ ) . Our results show some of the ways topological methods can be used to characterize chain entanglements to better understand the origins of mechanical responses in polymeric materials.
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Affiliation(s)
- Eleni Panagiotou
- Department of Mathematics and SimCenter, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA.
| | - Kenneth C Millett
- Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA 93106-3080, USA.
| | - Paul J Atzberger
- Department of Mathematics and Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, CA 93106-3080, USA.
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9
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Megariotis G, Vogiatzis GG, Sgouros AP, Theodorou DN. Slip Spring-Based Mesoscopic Simulations of Polymer Networks: Methodology and the Corresponding Computational Code. Polymers (Basel) 2018; 10:E1156. [PMID: 30961081 PMCID: PMC6404024 DOI: 10.3390/polym10101156] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2018] [Revised: 10/10/2018] [Accepted: 10/12/2018] [Indexed: 11/16/2022] Open
Abstract
In previous work by the authors, a new methodology was developed for Brownian dynamics/kinetic Monte Carlo (BD/kMC) simulations of polymer melts. In this study, this methodology is extended for dynamical simulations of crosslinked polymer networks in a coarse-grained representation, wherein chains are modeled as sequences of beads, each bead encompassing a few Kuhn segments. In addition, the C++ code embodying these simulations, entitled Engine for Mesoscopic Simulations for Polymer Networks (EMSIPON) is described in detail. A crosslinked network of cis-1,4-polyisoprene is chosen as a test system. From the thermodynamic point of view, the system is fully described by a Helmholtz energy consisting of three explicit contributions: entropic springs, slip springs and non-bonded interactions. Entanglements between subchains in the network are represented by slip springs. The ends of the slip springs undergo thermally activated hops between adjacent beads along the chain backbones, which are tracked by kinetic Monte Carlo simulation. In addition, creation/destruction processes are included for the slip springs at dangling subchain ends. The Helmholtz energy of non-bonded interactions is derived from the Sanchez⁻Lacombe equation of state. The isothermal compressibility of the polymer network is predicted from equilibrium density fluctuations in very good agreement with the underlying equation of state and with experiment. Moreover, the methodology and the corresponding C++ code are applied to simulate elongational deformations of polymer rubbers. The shear stress relaxation modulus is predicted from equilibrium simulations of several microseconds of physical time in the undeformed state, as well as from stress-strain curves of the crosslinked polymer networks under deformation.
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Affiliation(s)
- Grigorios Megariotis
- School of Chemical Engineering, National Technical University of Athens (NTUA), 9 Heroon Polytechniou Street, Zografou Campus, GR-15780 Athens, Greece.
| | - Georgios G Vogiatzis
- Polymer Technology, Department of Mechanical Engineering, Eindhoven University of Technology, PO BOX 513, 5600MB Eindhoven, The Netherlands.
| | - Aristotelis P Sgouros
- School of Chemical Engineering, National Technical University of Athens (NTUA), 9 Heroon Polytechniou Street, Zografou Campus, GR-15780 Athens, Greece.
| | - Doros N Theodorou
- School of Chemical Engineering, National Technical University of Athens (NTUA), 9 Heroon Polytechniou Street, Zografou Campus, GR-15780 Athens, Greece.
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10
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Pestryaev EM. Oscillating Free Induction Decay in Polymer Systems: Theoretical Analysis. POLYMER SCIENCE SERIES A 2018. [DOI: 10.1134/s0965545x18040090] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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11
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Sgouros AP, Megariotis G, Theodorou DN. Slip-Spring Model for the Linear and Nonlinear Viscoelastic Properties of Molten Polyethylene Derived from Atomistic Simulations. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b00694] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- A. P. Sgouros
- School of Chemical Engineering, National Technical University of Athens (NTUA),GR-15780 Athens, Greece
| | - G. Megariotis
- School of Chemical Engineering, National Technical University of Athens (NTUA),GR-15780 Athens, Greece
| | - D. N. Theodorou
- School of Chemical Engineering, National Technical University of Athens (NTUA),GR-15780 Athens, Greece
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12
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Dell ZE, Schweizer KS. Segment-scale, force-level theory of mesoscopic dynamic localization and entropic elasticity in entangled chain polymer liquids. J Chem Phys 2017; 146:134901. [PMID: 28390385 DOI: 10.1063/1.4978774] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We develop a segment-scale, force-based theory for the breakdown of the unentangled Rouse model and subsequent emergence of isotropic mesoscopic localization and entropic elasticity in chain polymer liquids in the absence of ergodicity-restoring anisotropic reptation or activated hopping motion. The theory is formulated in terms of a conformational N-dynamic-order-parameter generalized Langevin equation approach. It is implemented using a universal field-theoretic Gaussian thread model of polymer structure and closed at the level of the chain dynamic second moment matrix. The physical idea is that the isotropic Rouse model fails due to the dynamical emergence, with increasing chain length, of time-persistent intermolecular contacts determined by the combined influence of local uncrossability, long range polymer connectivity, and a self-consistent treatment of chain motion and the dynamic forces that hinder it. For long chain melts, the mesoscopic localization length (identified as the tube diameter) and emergent entropic elasticity predictions are in near quantitative agreement with experiment. Moreover, the onset chain length scales with the semi-dilute crossover concentration with a realistic numerical prefactor. Distinctive novel predictions are made for various off-diagonal correlation functions that quantify the full spatial structure of the dynamically localized polymer conformation. As the local excluded volume constraint and/or intrachain bonding spring are softened to allow chain crossability, the tube diameter is predicted to swell until it reaches the radius-of-gyration at which point mesoscopic localization vanishes in a discontinuous manner. A dynamic phase diagram for such a delocalization transition is constructed, which is qualitatively consistent with simulations and the classical concept of a critical entanglement degree of polymerization.
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Affiliation(s)
- Zachary E Dell
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
| | - Kenneth S Schweizer
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA
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13
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Vogiatzis GG, Megariotis G, Theodorou DN. Equation of State Based Slip Spring Model for Entangled Polymer Dynamics. Macromolecules 2017. [DOI: 10.1021/acs.macromol.6b01705] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Georgios G. Vogiatzis
- School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou
Campus, GR-15780 Athens, Greece
| | - Grigorios Megariotis
- School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou
Campus, GR-15780 Athens, Greece
| | - Doros N. Theodorou
- School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou
Campus, GR-15780 Athens, Greece
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14
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Vogiatzis GG, Theodorou DN. Multiscale Molecular Simulations of Polymer-Matrix Nanocomposites: or What Molecular Simulations Have Taught us About the Fascinating Nanoworld. ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING : STATE OF THE ART REVIEWS 2017; 25:591-645. [PMID: 29962833 PMCID: PMC6003436 DOI: 10.1007/s11831-016-9207-y] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/08/2016] [Accepted: 12/20/2016] [Indexed: 06/08/2023]
Abstract
Following the substantial progress in molecular simulations of polymer-matrix nanocomposites, now is the time to reconsider this topic from a critical point of view. A comprehensive survey is reported herein providing an overview of classical molecular simulations, reviewing their major achievements in modeling polymer matrix nanocomposites, and identifying several open challenges. Molecular simulations at multiple length and time scales, working hand-in-hand with sensitive experiments, have enhanced our understanding of how nanofillers alter the structure, dynamics, thermodynamics, rheology and mechanical properties of the surrounding polymer matrices.
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Affiliation(s)
- Georgios G. Vogiatzis
- School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou Campus, 15780 Athens, Greece
- Present Address: Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600MB Eindhoven, The Netherlands
| | - Doros N. Theodorou
- School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou Campus, 15780 Athens, Greece
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15
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Ge T, Tzoumanekas C, Anogiannakis SD, Hoy RS, Robbins MO. Entanglements in Glassy Polymer Crazing: Cross-Links or Tubes? Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b02125] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ting Ge
- Department
of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599, United States
| | - Christos Tzoumanekas
- Department
of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, Athens 15780, Greece
| | - Stefanos D. Anogiannakis
- Department
of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, Athens 15780, Greece
| | - Robert S. Hoy
- Department
of Physics, University of South Florida, Tampa, Florida 33620, United States
| | - Mark O. Robbins
- Department
of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, United States
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16
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Schweizer KS, Sussman DM. A force-level theory of the rheology of entangled rod and chain polymer liquids. I. Tube deformation, microscopic yielding, and the nonlinear elastic limit. J Chem Phys 2016; 145:214903. [DOI: 10.1063/1.4968516] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kenneth S. Schweizer
- Department of Materials Science and Department of Chemistry, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801, USA
| | - Daniel M. Sussman
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA
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17
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Megariotis G, Vogiatzis GG, Schneider L, Müller M, Theodorou DN. Mesoscopic Simulations of Crosslinked Polymer Networks. ACTA ACUST UNITED AC 2016. [DOI: 10.1088/1742-6596/738/1/012063] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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18
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Cao J, Wang Z. Microscopic Picture of Constraint Release Effects in Entangled Star Polymer Melts. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b00554] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Jing Cao
- Department of Mathematics
and Statistics, University of Reading, Whiteknights, PO Box 220, Reading RG6 6AX, U.K
| | - Zuowei Wang
- Department of Mathematics
and Statistics, University of Reading, Whiteknights, PO Box 220, Reading RG6 6AX, U.K
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19
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Ramos J, Vega JF, Martínez-Salazar J. A new insight into the conformation and melt dynamics of hydrogenated polybutadiene as revealed by computer simulations. SOFT MATTER 2016; 12:3929-3936. [PMID: 27003544 DOI: 10.1039/c5sm03080c] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Extensive molecular dynamics simulations of the macromolecular conformation and the melt dynamics for model polymers of different molecular weights have been carried out. The selected models are hydrogenated polybutadienes with a 2% content of ethyl branches and linear polyethylene. It will be shown that the density and chain stiffness are clearly affected by both the molecular weight and the presence of ethyl branches. Furthermore, the results obtained from the simulations on the molecular size and, more remarkably, chain dynamics, perfectly match the neutron scattering experiments performed by Zamponi et al. in hydrogenated polybutadienes. We observe a clear chain contraction and a slow dynamics for the hydrogenated polybutadiene with respect to the linear chain of the same molecular length. Using the Likhtman-McLeish definitions, the obtained values of the entanglement relaxation time (τe) and the tube diameter (a) are found to be in agreement with the available experimental data (by rheology and neutron spin echo) as well as with those obtained by the simulations. Finally, a very good agreement of diffusion coefficients as a function of the molecular weight between simulations and experiments is observed. Therefore, there exists a clear difference between the results obtained for branched and linear polyethylene, accounting for a definitive effect of the short chain branching on the conformational properties and the melt dynamics of polyolefins.
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Affiliation(s)
- Javier Ramos
- Biophym, Departamento de Física Macromolecular, Instituto de Estructura de la Materia, CSIC, c/Serrano 113 bis, 28006 Madrid, Spain.
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20
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Affiliation(s)
- Vaidyanathan Sethuraman
- Department
of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, United States
| | - Dylan Kipp
- Department
of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, United States
| | - Venkat Ganesan
- Department
of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, United States
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21
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Ramos J, Vega JF, Martínez-Salazar J. Molecular Dynamics Simulations for the Description of Experimental Molecular Conformation, Melt Dynamics, and Phase Transitions in Polyethylene. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b00823] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Javier Ramos
- Biophym, Departamento de
Física Macromolecular, Instituto de Estructura de la Materia, IEM-CSIC, C/Serrano 113 bis, 28006 Madrid, Spain
| | - Juan F. Vega
- Biophym, Departamento de
Física Macromolecular, Instituto de Estructura de la Materia, IEM-CSIC, C/Serrano 113 bis, 28006 Madrid, Spain
| | - Javier Martínez-Salazar
- Biophym, Departamento de
Física Macromolecular, Instituto de Estructura de la Materia, IEM-CSIC, C/Serrano 113 bis, 28006 Madrid, Spain
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22
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Moreira LA, Zhang G, Müller F, Stuehn T, Kremer K. Direct Equilibration and Characterization of Polymer Melts for Computer Simulations. MACROMOL THEOR SIMUL 2015. [DOI: 10.1002/mats.201500013] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Livia A. Moreira
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
| | - Guojie Zhang
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
| | - Franziska Müller
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
| | - Torsten Stuehn
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
| | - Kurt Kremer
- Max-Planck-Institut für Polymerforschung; Ackermannweg 10 55128 Mainz Germany
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23
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Foteinopoulou K, Karayiannis NC, Laso M. Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement. Chem Eng Sci 2015. [DOI: 10.1016/j.ces.2014.08.021] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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24
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De Nicola A, Kawakatsu T, Milano G. Generation of Well-Relaxed All-Atom Models of Large Molecular Weight Polymer Melts: A Hybrid Particle-Continuum Approach Based on Particle-Field Molecular Dynamics Simulations. J Chem Theory Comput 2014; 10:5651-67. [PMID: 26583248 DOI: 10.1021/ct500492h] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
A procedure based on Molecular Dynamics (MD) simulations employing soft potentials derived from self-consistent field (SCF) theory (named MD-SCF) able to generate well-relaxed all-atom structures of polymer melts is proposed. All-atom structures having structural correlations indistinguishable from ones obtained by long MD relaxations have been obtained for poly(methyl methacrylate) (PMMA) and poly(ethylene oxide) (PEO) melts. The proposed procedure leads to computational costs mainly related on system size rather than to the chain length. Several advantages of the proposed procedure over current coarse-graining/reverse mapping strategies are apparent. No parametrization is needed to generate relaxed structures of different polymers at different scales or resolutions. There is no need for special algorithms or back-mapping schemes to change the resolution of the models. This characteristic makes the procedure general and its extension to other polymer architectures straightforward. A similar procedure can be easily extended to the generation of all-atom structures of block copolymer melts and polymer nanocomposites.
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Affiliation(s)
- Antonio De Nicola
- Dipartimento di Chimica e Biologia, Università degli Studi di Salerno , via Ponte don Melillo, Fisciano, Salerno I-84085, Italy.,IMAST Scarl-Technological District in Polymer and Composite Engineering, Piazza Bovio 22, Napoli, Napoli I-80133, Italy
| | - Toshihiro Kawakatsu
- Department of Physics, Tohoku University , Aoba, Aramaki, Aoba-ku, Sendai, Miyagi 980-8578, Japan
| | - Giuseppe Milano
- Dipartimento di Chimica e Biologia, Università degli Studi di Salerno , via Ponte don Melillo, Fisciano, Salerno I-84085, Italy.,IMAST Scarl-Technological District in Polymer and Composite Engineering, Piazza Bovio 22, Napoli, Napoli I-80133, Italy
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25
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Liu L, den Otter WK, Briels WJ. Coarse grain forces in star polymer melts. SOFT MATTER 2014; 10:7874-7886. [PMID: 25158294 DOI: 10.1039/c4sm00767k] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
An analysis is presented of forces acting on the centers of mass of three-armed star polymers in the molten state. The arms consist of 35 Kremer-Grest beads, which is slightly larger than needed for one entanglement mass. For a given configuration of the centers of mass, instantaneous forces fluctuate wildly around averages which are two orders of magnitude smaller than their root mean square deviations. Average forces are well described by an implicit many-body potential, while pair models fail completely. The fluctuating forces are modelled by means of dynamical variables quantifying the degree of mixing of the various polymer pairs. All functions and parameters in a coarse grain model based on these concepts are obtained from the underlying small scale simulation. The coarse model reproduces both the diffusion coefficient and the shear relaxation modulus. Ways to improve the model suggest themselves on the basis of our findings.
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Affiliation(s)
- L Liu
- Computational Biophysics, MESA+, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands.
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26
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Theodorou DN, Vogiatzis GG, Kritikos G. Self-Consistent-Field Study of Adsorption and Desorption Kinetics of Polyethylene Melts on Graphite and Comparison with Atomistic Simulations. Macromolecules 2014. [DOI: 10.1021/ma501454t] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Affiliation(s)
- Doros N. Theodorou
- School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou
Campus, GR-15780 Athens, Greece
| | - Georgios G. Vogiatzis
- School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou
Campus, GR-15780 Athens, Greece
| | - Georgios Kritikos
- School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou
Campus, GR-15780 Athens, Greece
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27
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Panagiotou E, Kröger M. Pulling-force-induced elongation and alignment effects on entanglement and knotting characteristics of linear polymers in a melt. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042602. [PMID: 25375516 DOI: 10.1103/physreve.90.042602] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2014] [Indexed: 06/04/2023]
Abstract
We employ a primitive path (PP) algorithm and the Gauss linking integral to study the degree of entanglement and knotting characteristics of linear polymer model chains in a melt under the action of a constant pulling force applied to selected chain ends. Our results for the amount of entanglement, the linking number, the average crossing number, the writhe of the chains and their PPs and the writhe of the entanglement strands all suggest a different response at the length scale of entanglement strands than that of the chains themselves and of the corresponding PPs. Our findings indicate that the chains first stretch at the level of entanglement strands and next the PP (tube) gets oriented with the "flow." These two phases of the extension and alignment of the chains coincide with two phases related to the disentanglement of the chains. Soon after the onset of external force the PPs attain a more entangled conformation, and the number of nontrivially linked end-to-end closed chains increases. Next, the chains disentangle continuously to attain an almost unentangled conformation. Using the linking matrix of the chains in the melt, we furthermore show that these phases are accompanied by a different scaling of the homogeneity of the global entanglement in the system. The homogeneity of the end-to-end closed chains first increases to a maximum and then decreases slowly to a value characterizing a completely unlinked system.
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Affiliation(s)
- E Panagiotou
- Department of Mathematics, University of California, Santa Barbara, California 93106, USA
| | - M Kröger
- Polymer Physics, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland
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28
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Ge T, Grest GS, Robbins MO. Tensile Fracture of Welded Polymer Interfaces: Miscibility, Entanglements, and Crazing. Macromolecules 2014. [DOI: 10.1021/ma501473q] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ting Ge
- Department
of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, United States
- Department
of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, United States
| | - Gary S. Grest
- Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Mark O. Robbins
- Department
of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, United States
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29
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Abstract
To optimize automation for polymer processing, attempts have been made to simulate the flow of entangled polymers. In industry, fluid dynamics simulations with phenomenological constitutive equations have been practically established. However, to account for molecular characteristics, a method to obtain the constitutive relationship from the molecular structure is required. Molecular dynamics simulations with atomic description are not practical for this purpose; accordingly, coarse-grained models with reduced degrees of freedom have been developed. Although the modeling of entanglement is still a challenge, mesoscopic models with a priori settings to reproduce entangled polymer dynamics, such as tube models, have achieved remarkable success. To use the mesoscopic models as staging posts between atomistic and fluid dynamics simulations, studies have been undertaken to establish links from the coarse-grained model to the atomistic and macroscopic simulations. Consequently, integrated simulations from materials chemistry to predict the macroscopic flow in polymer processing are forthcoming.
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Affiliation(s)
- Yuichi Masubuchi
- Institute for Chemical Research, Kyoto University, Gokasho Uji-City, Japan 611-0011
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30
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Gavrilov AA, Chertovich AV. Computer simulation of random polymer networks: Structure and properties. POLYMER SCIENCE SERIES A 2014. [DOI: 10.1134/s0965545x14010027] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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31
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Sussman DM, Schweizer KS. Entangled polymer chain melts: Orientation and deformation dependent tube confinement and interchain entanglement elasticity. J Chem Phys 2013; 139:234904. [DOI: 10.1063/1.4847895] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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32
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Panagiotou E, Kröger M, Millett KC. Writhe and mutual entanglement combine to give the entanglement length. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062604. [PMID: 24483478 DOI: 10.1103/physreve.88.062604] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2013] [Revised: 09/25/2013] [Indexed: 06/03/2023]
Abstract
We propose a method to estimate N(e), the entanglement length, that incorporates both local and global topological characteristics of chains in a melt under equilibrium conditions. This estimate uses the writhe of the chains, the writhe of the primitive paths, and the number of kinks in the chains in a melt. An advantage of this method is that it works for both linear and ring chains, works under all periodic boundary conditions, does not require knowing the contour length of the primitive paths, and does not rely on a smooth set of data. We apply this method to linear finitely extendable nonlinear elastic chains and we observe that our estimates are consistent with those from other studies.
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Affiliation(s)
- E Panagiotou
- Department of Mathematics, University of California, Santa Barbara, California 93106, USA
| | - M Kröger
- Polymer Physics, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland
| | - K C Millett
- Department of Mathematics, University of California, Santa Barbara, California 93106, USA
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33
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Ramírez-Hernández A, Detcheverry FA, Peters BL, Chappa VC, Schweizer KS, Müller M, de Pablo JJ. Dynamical Simulations of Coarse Grain Polymeric Systems: Rouse and Entangled Dynamics. Macromolecules 2013. [DOI: 10.1021/ma400526v] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Abelardo Ramírez-Hernández
- Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne,
Illinois 60439, United States
- Institute for Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States
| | - François A. Detcheverry
- Institut Lumière Matière, UMR5306 Université
Lyon 1-CNRS, Université de Lyon,
69622 Villeurbanne, France
| | - Brandon L. Peters
- Institute for Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States
| | - Verónica C. Chappa
- Institut für Theoretische
Physik, Georg-August-Universität, 37077 Göttingen, Germany
| | - Kenneth S. Schweizer
- Department of Materials Science
and Engineering, University of Illinois, Urbana, Illinois 61801, United
States
| | - Marcus Müller
- Institut für Theoretische
Physik, Georg-August-Universität, 37077 Göttingen, Germany
| | - Juan J. de Pablo
- Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne,
Illinois 60439, United States
- Institute for Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States
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34
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35
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Bačová P, Hawke LGD, Read DJ, Moreno AJ. Dynamics of Branched Polymers: A Combined Study by Molecular Dynamics Simulations and Tube Theory. Macromolecules 2013. [DOI: 10.1021/ma4005988] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Petra Bačová
- Departamento de Física de Materiales, Universidad del País Vasco (UPV/EHU), Apartado
1072, 20080 San Sebastián, Spain
| | | | - Daniel J. Read
- Department of Applied Mathematics, University of Leeds, LS2 9JT Leeds, U.K
| | - Angel J. Moreno
- Centro de Física de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo
Manuel de Lardizabal 5, 20018 San Sebastián, Spain
- Donostia International Physics Center, Paseo Manuel de Lardizabal 4, 20018
San Sebastián, Spain
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