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Konstantinou PC, Stephanou PS. Predicting High-Density Polyethylene Melt Rheology Using a Multimode Tube Model Derived Using Non-Equilibrium Thermodynamics. Polymers (Basel) 2023; 15:3322. [PMID: 37571216 PMCID: PMC10422373 DOI: 10.3390/polym15153322] [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: 07/18/2023] [Revised: 07/31/2023] [Accepted: 08/03/2023] [Indexed: 08/13/2023] Open
Abstract
Based on the Generalized bracket, or Beris-Edwards, formalism of non-equilibrium thermodynamics, we recently proposed a new differential constitutive model for the rheological study of entangled polymer melts and solutions. It amended the shortcomings of a previous model that was too strict regarding the values of the convective constraint release parameter for the model not to violate the second law of thermodynamics, and it has been shown capable of predicting a transient stress undershoot (following the overshoot) at high shear rates. In this study, we wish to further examine this model's capability to predict the rheological response of industrial polymer systems by extending it to its multiple-mode version. The comparison with industrial rheological data (High-Density Polyethylene resins), which was based on comparison with experimental data available in (a) Small Amplitude Oscillatory shear, (b) start-up shear, and (c) start-up uniaxial elongation, was noted to be good.
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Affiliation(s)
| | - Pavlos S. Stephanou
- Department of Chemical Engineering, Cyprus University of Technology, P.O. Box 50329, 3603 Limassol, Cyprus;
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2
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Tannoury L, Solar M, Paul W. Structure and dynamics of a 1,4-polybutadiene melt in an alumina nanopore: A molecular dynamics simulation. J Chem Phys 2022; 157:124901. [DOI: 10.1063/5.0105313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present results of Molecular Dynamics simulations of a chemically realistic model of 1,4-polybutadiene (PBD)confined in a cylindrical alumina nanopore of diameter 10 nm. The simulations are done at three different temperaturesabove the glass transition temperature T g . We investigate the density layering across the nanopore as well as theorientational ordering in the polymer melt, brought about by the confinement, on both the segmental and chain scales.For the chain scale ordering, the magnitude and orientation of the axes of the gyration tensor ellipsoid of single chainsare studied and are found to prefer to align parallel to the pore axis. Even though double bonds near the wall arepreferentially oriented along the pore walls, studying the nematic order parameter indicates that there is no nematicordering at the melt-wall interface. As for the dynamics in the melt, we focus here on the mean-square-displacement ofthe monomers for several layers across the nanopore as well as the movement of the chain center of mass which bothdisplay a slowing down of the dynamics in the layer at the wall. We also show the strong adsorption of the monomersto the pore wall at lower temperatures.
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Affiliation(s)
- Lama Tannoury
- Institute of Physics, Martin Luther University Halle Wittenberg, Germany
| | - Mathieu Solar
- Institut f. Physik, Institut National des Sciences Appliques, France
| | - Wolfgang Paul
- Institut f. Physik, Martin-Luther-Universität Halle-Wittenberg, Germany
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3
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Li W, Jana PK, Behbahani AF, Kritikos G, Schneider L, Polińska P, Burkhart C, Harmandaris VA, Müller M, Doxastakis M. Dynamics of Long Entangled Polyisoprene Melts via Multiscale Modeling. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c01376] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Wei Li
- Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Pritam K. Jana
- Institute for Theoretical Physics, Georg-August University, 37077 Göttingen, Germany
| | - Alireza F. Behbahani
- Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, Heraklion GR-71110, Greece
| | - Georgios Kritikos
- Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Ludwig Schneider
- Institute for Theoretical Physics, Georg-August University, 37077 Göttingen, Germany
| | | | - Craig Burkhart
- The Goodyear Tire & Rubber Company, Akron, Ohio 44305, United States
| | - Vagelis A. Harmandaris
- Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, Heraklion GR-71110, Greece
- Department of Mathematics and Applied Mathematics, University of Crete, Heraklion GR-71110, Greece
- Computation-based Science and Technology Research Center, The Cyprus Institute, Nicosia 2121, Cyprus
| | - Marcus Müller
- Institute for Theoretical Physics, Georg-August University, 37077 Göttingen, Germany
| | - Manolis Doxastakis
- Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States
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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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Masubuchi Y, Doi Y, Uneyama T. Primitive chain network simulations for the interrupted shear response of entangled polymeric liquids. SOFT MATTER 2020; 16:6654-6661. [PMID: 32618991 DOI: 10.1039/d0sm00654h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The non-linear viscoelastic response under interrupted shear flows is one of the interesting characteristics of entangled polymers. In particular, the stress overshoot in the resumed shear has been discussed concerning the recovery of the entanglement network in some studies. In this study, we performed multichain slip-link simulations to observe the molecular structure of an entangled polymer melt. After confirming the reasonable reproducibility of our simulation with the literature data, we analyzed the molecular characteristics following the decoupling approximation. We reasonably found that the segment orientation dominates the stress overshoot even under the resumed shear with minor contributions from the segment stretch and entanglement density. We defined the mitigation function for the recovery of the stress overshoot as a function of the rest time and compared it with the relaxation of the molecular quantities after the initial shear. As a result, we have found that the mitigation of the stress overshoot coincides with the relaxation of entanglement density.
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Affiliation(s)
- Yuichi Masubuchi
- Center of Computational Science, Nagoya University, Nagoya 4648603, Japan. and Department of Materials Physics, Nagoya University, Nagoya 4648603, Japan
| | - Yuya Doi
- Department of Materials Physics, Nagoya University, Nagoya 4648603, Japan
| | - Takashi Uneyama
- Center of Computational Science, Nagoya University, Nagoya 4648603, Japan. and Department of Materials Physics, Nagoya University, Nagoya 4648603, Japan
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7
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Feng L, Gao P, Guo H. Retardation on Blending in the Entangled Binary Blends of Linear Polyethylene: A Molecular Dynamics Simulation Study. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b00047] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Lukun Feng
- Beijing National Laboratory for Molecular Sciences, Joint Laboratory of Polymer Sciences and Materials, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of
Chinese Academy of Sciences, Beijing 100049, China
| | - Peiyuan Gao
- Beijing National Laboratory for Molecular Sciences, Joint Laboratory of Polymer Sciences and Materials, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of
Chinese Academy of Sciences, Beijing 100049, China
| | - Hongxia Guo
- Beijing National Laboratory for Molecular Sciences, Joint Laboratory of Polymer Sciences and Materials, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of
Chinese Academy of Sciences, Beijing 100049, China
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8
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Li S, Chen Q, Ding M, Shi T. Effect of Bidispersity on Dynamics of Confined Polymer Films. Polymers (Basel) 2018; 10:E1327. [PMID: 30961252 PMCID: PMC6402039 DOI: 10.3390/polym10121327] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2018] [Revised: 11/26/2018] [Accepted: 11/28/2018] [Indexed: 11/20/2022] Open
Abstract
Using Monte Carlo simulations, we studied the effect of bidispersity on the dynamics of polymer films capped between two neutral walls, where we chose three representative compositions for bidispersed polymer films. Our results demonstrate that the characteristic entanglement length is an important parameter to clarify the effect of the bidispersity on the dynamics of polymer films. For the short chains, shorter than the characteristic entanglement length, the average number of near-neighboring particles increases with the decrease of the film thickness and limits the diffusivity of the short chains, which is independent of the film compositions. However, the dynamics of the long chains, of which is above the characteristic entanglement length, is determined by the film's composition. In our previous paper, we inferred from the structures and entanglements of the bidisperse system with short and long chains that the constraint release contributes significantly to the relaxation mechanism of long chains. By calculating the self-diffusion coefficient of long chains, we confirmed this prediction that, with a lower weight fraction of long chains, the self-diffusion coefficient of long chains decreases slowly with the decrease of the film thickness, which is similar to that of short chains. With a higher weight fraction of long chains, the competition between the disentanglement and the increased in the local degree of confinement which resulted in the self-diffusion coefficient of long chains varying non-monotonically with the film thickness. Furthermore, for the bidisperse system with long and long chains, the diffusivity of long chains was not affected by the constraint release, which varied nonmonotonically with the decrease of the film thickness due to the competition between the disentanglement and the enhanced confinement. Herein, compared with the previous work, we completely clarified the relationship between the structures and dynamics for three representative compositions of bidisperse polymer films, which contains all possible cases for bidisperse systems. Our work not only establishes a unified understanding of the dependency of dynamics on the bidispersity of polymer films, but also helps to understand the case of polydispersity, which can provide computational supports for various applications for polymer films.
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Affiliation(s)
- Sijia Li
- Department of Fire Command, China People's Police University, Langfang 065000, China.
| | - Qiaoyue Chen
- Xinjiang Laboratory of Phase Transitions and Microstructures in Condensed Matter Physics, College of Physical Science and Technology, Yili Normal University, Yining 835000, China.
| | - Mingming Ding
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Science, Changchun 130022, China.
| | - Tongfei Shi
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Science, Changchun 130022, China.
- School of Applied Chemistry and Engineering, University of Science and Technology of China, Hefei 230026, China.
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9
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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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10
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Stephanou PS, Kröger M. Non-constant link tension coefficient in the tumbling-snake model subjected to simple shear. J Chem Phys 2017; 147:174903. [DOI: 10.1063/1.4991935] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pavlos S. Stephanou
- Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
| | - Martin Kröger
- Department of Materials, Polymer Physics, ETH Zürich, CH-8093 Zürich, Switzerland
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11
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Li S, Ding M, Shi T. Effect of Bidispersity on Structure and Entanglement of Confined Polymer Films. J Phys Chem B 2017; 121:7502-7507. [PMID: 28703586 DOI: 10.1021/acs.jpcb.7b04468] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Using Monte Carlo simulations combined with a geometric primitive path analysis method (Z1 algorithm), we investigate the effect of bidispersity on the structure and entanglement of polymer films which consist of short (the molecular length is below the characteristic entanglement molecular length) and long (the molecular length is above the characteristic entanglement molecular length) chains between two neutral walls. Our results demonstrate the length-based migrations of chains in bidisperse films (the longer chains reside away from the walls and the shorter chains are close to the walls), which becomes more obvious with the decrease in the weight fraction of long chains. With decreasing the weight fraction of long chains, the number of short-long entanglements exhibits a dramatic increase, whereas the number of long-long entanglements exhibits a slight decrease, which indicates that short chains can significantly affect the local situations of entanglements of bidisperse polymer films. On the basis of the constraint release mechanism, our simulations imply that for the lower weight fraction of long chains, the local degree of confinement instead of the long-long entanglements has a marked effect on the relaxation of long chains, due to the fast relaxation of short chains dilating the tube diameter of long chains. However, for the higher weight fraction of long chains, after the relaxation of short chains, the long-long entanglements are in sufficient quantities to restrict long chains within a tube, which implies that the relaxation of long chains is hardly affected by the number of short-long entanglements. Our work can be helpful for understanding the microscopic structure and entanglement of bidisperse polymer films, which can provide computational support for their various technological applications.
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Affiliation(s)
- Sijia Li
- Department of Fire Command, Chinese People's Armed Police Force Academy , Langfang 065000, P. R. China
| | - Mingming Ding
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Science , Changchun 130022, P. R. China
| | - Tongfei Shi
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Science , Changchun 130022, P. R. China
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12
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Stephanou PS, Schweizer T, Kröger M. Communication: Appearance of undershoots in start-up shear: Experimental findings captured by tumbling-snake dynamics. J Chem Phys 2017; 146:161101. [DOI: 10.1063/1.4982228] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Stephanou PS, Kröger M. Solution of the complete Curtiss-Bird model for polymeric liquids subjected to simple shear flow. J Chem Phys 2016; 144:124905. [DOI: 10.1063/1.4944674] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pavlos S. Stephanou
- Department of Materials, Polymer Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Martin Kröger
- Department of Materials, Polymer Physics, ETH Zürich, CH-8093 Zürich, Switzerland
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14
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Stephanou PS, Mavrantzas VG. Accurate prediction of the linear viscoelastic properties of highly entangled mono and bidisperse polymer melts. J Chem Phys 2014; 140:214903. [DOI: 10.1063/1.4878500] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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15
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16
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Anogiannakis SD, Tzoumanekas C, Theodorou DN. Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes. Macromolecules 2012. [DOI: 10.1021/ma300912z] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Stefanos D. Anogiannakis
- School of Chemical Engineering, Zografou Campus, National Technical University of Athens, GR-15780 Athens,
Greece
| | - Christos Tzoumanekas
- School of Chemical Engineering, Zografou Campus, National Technical University of Athens, GR-15780 Athens,
Greece
- Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven,
The Netherlands
| | - Doros N. Theodorou
- School of Chemical Engineering, Zografou Campus, National Technical University of Athens, GR-15780 Athens,
Greece
- Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven,
The Netherlands
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Li Y, Tang S, Abberton BC, Kröger M, Burkhart C, Jiang B, Papakonstantopoulos GJ, Poldneff M, Liu WK. A predictive multiscale computational framework for viscoelastic properties of linear polymers. POLYMER 2012. [DOI: 10.1016/j.polymer.2012.09.055] [Citation(s) in RCA: 74] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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18
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Li Y, Kröger M, Liu WK. Nanoparticle Geometrical Effect on Structure, Dynamics and Anisotropic Viscosity of Polyethylene Nanocomposites. Macromolecules 2012. [DOI: 10.1021/ma202289a] [Citation(s) in RCA: 89] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ying Li
- Department of Mechanical
Engineering, Northwestern University, 2145
Sheridan Road, Evanston,
Illinois 60208-0311, United States
| | - Martin Kröger
- Department of Materials, Polymer
Physics, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Wing Kam Liu
- Department of Mechanical
Engineering, Northwestern University, 2145
Sheridan Road, Evanston,
Illinois 60208-0311, United States
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20
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Stephanou PS, Baig C, Mavrantzas VG. Toward an Improved Description of Constraint Release and Contour Length Fluctuations in Tube Models for Entangled Polymer Melts Guided by Atomistic Simulations. MACROMOL THEOR SIMUL 2011. [DOI: 10.1002/mats.201100052] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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21
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Vaca Chávez F, Saalwächter K. Time-Domain NMR Observation of Entangled Polymer Dynamics: Universal Behavior of Flexible Homopolymers and Applicability of the Tube Model. Macromolecules 2011. [DOI: 10.1021/ma1025708] [Citation(s) in RCA: 89] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Fabián Vaca Chávez
- Institut für Physik − NMR, Martin-Luther-Universität Halle-Wittenberg, Betty-Heimann-Str. 7, D-06120 Halle, Germany
| | - Kay Saalwächter
- Institut für Physik − NMR, Martin-Luther-Universität Halle-Wittenberg, Betty-Heimann-Str. 7, D-06120 Halle, Germany
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