1
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Li D, Feng L, Tang Y, Zhu C. Entanglement Characteristic Time from Complex Moduli via i-Rheo GT. Polymers (Basel) 2022; 14:polym14235208. [PMID: 36501603 PMCID: PMC9740520 DOI: 10.3390/polym14235208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2022] [Revised: 11/11/2022] [Accepted: 11/13/2022] [Indexed: 12/03/2022] Open
Abstract
Tassieri et al. have introduced a novel rheological tool called "i-Rheo GT" that allows the evaluation of the frequency-dependent materials' linear viscoelastic properties from a direct Fourier transform of the time-dependent relaxation modulus G(t), without artifacts. They adopted i-Rheo GT to exploit the information embedded in G(t) derived from molecular dynamics simulations of atomistic and quasi-atomistic models, and they estimated the polymers' entanglement characteristic time (τe) from the crossover point of the moduli at intermediate times, which had never been possible before because of the poor fitting performance, at short time scales, of the commonly used generalized Maxwell models. Here, we highlight that the values of τe reported by Tassieri et al. are significantly different (i.e., an order of magnitude smaller) from those reported in the literature, obtained from either experiments or molecular dynamics simulations of different observables. In this work, we demonstrate that consistent values of τe can be achieved if the initial values of G(t), i.e., those governed by the bond-oscillation dynamics, are discarded. These findings have been corroborated by adopting i-Rheo GT to Fourier transform the outcomes of three different molecular dynamics simulations based on the following three models: a dissipative particle dynamics model, a Kremer-Grest model, and an atomistic polyethylene model. Moreover, we have investigated the variations of τe as function of (i) the 'cadence' at which G(t) is evaluated, (ii) the spring constant of the atomic bone, and (iii) the initial value of the shear relaxation modulus G(O). The ensemble of these results confirms the effectiveness of i-Rheo GT and provide new insights into the interpretation of molecular dynamics simulations for a better understanding of polymer dynamics.
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2
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Masubuchi Y, Doi Y, Uneyama T. Effects of Slip-Spring Parameters and Rouse Bead Density on Polymer Dynamics in Multichain Slip-Spring Simulations. J Phys Chem B 2022; 126:2930-2941. [PMID: 35298156 DOI: 10.1021/acs.jpcb.2c00697] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The multichain slip-spring (MCSS) model is one of the coarse-grained models of polymers developed in the niche between bead-spring models and tube type descriptions. In this model, polymers are represented by Rouse chains connected by virtual springs that temporally connect the chains, hop along the chain, and are constructed and annihilated at the chain ends. Earlier studies have shown that MCSS simulations can nicely reproduce entangled and unentangled polymer dynamics. However, the model parameters have been chosen arbitrarily, and their effects have not been reported. In this study, for the first time, we systematically investigated the effects of model parameters: fugacity of virtual springs, its intensity, and the Rouse bead density. We validated the employed simulation code by confirming that the statistics of the system follow the theoretical setup. Namely, the virtual spring density is correctly controlled, and polymer chains exhibit ideal chain statistics irrespective of the chosen parameter values. For diffusion and linear viscoelasticity, simulation results obtained for different parameters can be superposed with each other by conversion factors for the bead number per chain and units of length, time, and modulus. These conversion factors follow scaling laws concerning the number of Rouse segments between two consecutive anchoring points of virtual springs along the polymer chain. Besides, diffusion and viscoelasticity excellently agree with literature data for the standard bead-spring simulation. These results imply that the coarse-graining level for the MCSS model can be arbitrarily chosen and controlled by model parameters.
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Affiliation(s)
- Yuichi Masubuchi
- Department of Materials Physics, Nagoya University, Nagoya 4648603, Japan
| | - Yuya Doi
- Department of Materials Physics, Nagoya University, Nagoya 4648603, Japan
| | - Takashi Uneyama
- Department of Materials Physics, Nagoya University, Nagoya 4648603, Japan
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3
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Behbahani AF, Schneider L, Rissanou A, Chazirakis A, Bačová P, Jana PK, Li W, Doxastakis M, Polińska P, Burkhart C, Müller M, Harmandaris VA. Dynamics and Rheology of Polymer Melts via Hierarchical Atomistic, Coarse-Grained, and Slip-Spring Simulations. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02583] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Alireza F. Behbahani
- Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, Heraklion GR-71110, Greece
| | - Ludwig Schneider
- Institute for Theoretical Physics, Georg-August University Göttingen, Goettingen 37077, Germany
| | - Anastassia Rissanou
- Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, Heraklion GR-71110, Greece
| | - Anthony Chazirakis
- Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, Heraklion GR-71110, Greece
| | - Petra Bačová
- Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, Heraklion GR-71110, Greece
| | - Pritam Kumar Jana
- Institute for Theoretical Physics, Georg-August University Göttingen, Goettingen 37077, Germany
| | - Wei Li
- Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Manolis Doxastakis
- Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States
| | | | - Craig Burkhart
- The Goodyear Tire and Rubber Company, 142 Goodyear Blvd., Akron, Ohio 44305, United States
| | - Marcus Müller
- Institute for Theoretical Physics, Georg-August University Göttingen, Goettingen 37077, Germany
| | - 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
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4
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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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5
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Wu Z, Kalogirou A, De Nicola A, Milano G, Müller‐Plathe F. Atomistic hybrid
particle‐field
molecular dynamics combined with
slip‐springs
: Restoring entangled dynamics to simulations of polymer melts. J Comput Chem 2020; 42:6-18. [DOI: 10.1002/jcc.26428] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Revised: 09/07/2020] [Accepted: 09/11/2020] [Indexed: 02/03/2023]
Affiliation(s)
- Zhenghao Wu
- Eduard‐Zintl‐Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt Darmstadt Germany
| | - Andreas Kalogirou
- Eduard‐Zintl‐Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt Darmstadt Germany
| | - Antonio De Nicola
- Department of Organic Materials Science Yamagata University Yamagata‐ken Japan
| | - Giuseppe Milano
- Department of Organic Materials Science Yamagata University Yamagata‐ken Japan
| | - Florian Müller‐Plathe
- Eduard‐Zintl‐Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt Darmstadt Germany
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6
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Shanbhag S, Wang Z. Molecular Simulation of Tracer Diffusion and Self-Diffusion in Entangled Polymers. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c00680] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sachin Shanbhag
- Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306, United States
| | - Zuowei Wang
- Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, U.K
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7
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Nafar Sefiddashti MH, Boudaghi-Khajehnobar M, Edwards BJ, Khomami B. High-fidelity scaling relationships for determining dissipative particle dynamics parameters from atomistic molecular dynamics simulations of polymeric liquids. Sci Rep 2020; 10:4458. [PMID: 32157144 PMCID: PMC7064535 DOI: 10.1038/s41598-020-61374-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2019] [Accepted: 02/20/2020] [Indexed: 12/03/2022] Open
Abstract
An optimized Dissipative Particle Dynamics (DPD) model with simple scaling rules was developed for simulating entangled linear polyethylene melts. The scaling method, which can be used for mapping dimensionless (reduced units) DPD simulation data to physical units, was based on scaling factors for three fundamental physical units; namely, length, time, and viscosity. The scaling factors were obtained as ratios of equilibrium Molecular Dynamics (MD) simulation data in physical units and equivalent DPD simulation data for relevant quantities. Specifically, the time scaling factor was determined as the ratio of longest relaxation times, the length scaling factor was obtained as the ratio of the equilibrium end-to-end distances, and the viscosity scaling factor was calculated as the ratio of zero-shear viscosities, each as obtained from the MD (in physical units) and DPD (reduced units) simulations. The scaling method was verified for three MD/DPD model liquid pairs under several different nonequilibrium conditions, including transient and steady-state simple shear and planar elongational flows. Comparison of the MD simulation results with those of the scaled DPD simulations revealed that the optimized DPD model, expressed in terms of the proposed scaling method, successfully reproduced the computationally expensive MD results using relatively cheaper DPD simulations.
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Affiliation(s)
- M H Nafar Sefiddashti
- Materials Research and Innovation Laboratory, Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, 37996, USA
| | - M Boudaghi-Khajehnobar
- Materials Research and Innovation Laboratory, Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, 37996, USA
| | - B J Edwards
- Materials Research and Innovation Laboratory, Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, 37996, USA.
| | - B Khomami
- Materials Research and Innovation Laboratory, Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, 37996, USA.
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8
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Karatrantos A, Composto RJ, Winey KI, Kröger M, Clarke N. Modeling of Entangled Polymer Diffusion in Melts and Nanocomposites: A Review. Polymers (Basel) 2019; 11:E876. [PMID: 31091725 PMCID: PMC6571671 DOI: 10.3390/polym11050876] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2019] [Revised: 05/06/2019] [Accepted: 05/09/2019] [Indexed: 11/29/2022] Open
Abstract
This review concerns modeling studies of the fundamental problem of entangled (reptational) homopolymer diffusion in melts and nanocomposite materials in comparison to experiments. In polymer melts, the developed united atom and multibead spring models predict an exponent of the molecular weight dependence to the polymer diffusion very similar to experiments and the tube reptation model. There are rather unexplored parameters that can influence polymer diffusion such as polymer semiflexibility or polydispersity, leading to a different exponent. Models with soft potentials or slip-springs can estimate accurately the tube model predictions in polymer melts enabling us to reach larger length scales and simulate well entangled polymers. However, in polymer nanocomposites, reptational polymer diffusion is more complicated due to nanoparticle fillers size, loading, geometry and polymer-nanoparticle interactions.
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Affiliation(s)
- Argyrios Karatrantos
- Materials Research and Technology, Luxembourg Institute of Science and Technology, 5, Avenue des Hauts-Fourneaux, L-4362 Esch-sur-Alzette, Luxembourg.
| | - Russell J Composto
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA.
| | - Karen I Winey
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA.
| | - Martin Kröger
- Polymer Physics, Department of Materials, ETH Zurich, Leopold-Ruzicka-Weg 4, CH-8093 Zurich, Switzerland.
| | - Nigel Clarke
- Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK.
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9
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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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10
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Moghadam S, Saha Dalal I, Larson RG. Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids. Polymers (Basel) 2019; 11:E465. [PMID: 30960449 PMCID: PMC6473671 DOI: 10.3390/polym11030465] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2019] [Revised: 03/02/2019] [Accepted: 03/05/2019] [Indexed: 11/20/2022] Open
Abstract
We combine a slip-spring model with an 'entangled kink dynamics' (EKD) model for strong uniaxial extensional flows (with Rouse Weissenberg number W i R ≫ 1 ) of long ( M w > 1 Mkg / mol for polystyrene) entangled polymers in solutions and melts. The slip-spring model captures the dynamics up to the formation of a 'kinked' or folded state, while the kink dynamics simulation tracks the dynamics from that point forward to complete extension. We show that a single-chain slip-spring model using affine motion of the slip-spring anchor points produces unrealistically high tension near the center of the chain once the Hencky strain exceeds around unity or so, exceeding the maximum tension that a chain entangled with a second chain is able to support. This unrealistic tension is alleviated by pairing the slip links on one chain with those on a second chain, and allowing some of the large tension on one of the two to be transferred to the second chain, producing non-affine motion of each. This explicit pairing of entanglements mimics the entanglement pairing also used in the EKD model, and allows the slip spring simulations to be carried out to strains high enough for the EKD model to become valid. We show that results nearly equivalent to those from paired chains are obtained in a single-chain slip-spring simulation by simply specifying that the tension in a slip spring cannot exceed the theoretical maximum value of ζ ' ϵ ˙ L 2 / 8 where ζ ' , ϵ ˙ and L are the friction per unit length, strain rate and contour length of the chain, respectively. The effects of constraint release (CR) and regeneration of entanglements is also studied and found to have little effect on the chain statistics up to the formation of the kinked state. The resulting hybrid model provides a fast, simple, simulation method to study the response of high molecular weight ( M w > 1 Mkg / mol ) polymers in fast flows ( W i R ≫ 1 ), where conventional simulation techniques are less applicable due to computational cost.
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Affiliation(s)
- Soroush Moghadam
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA.
| | - Indranil Saha Dalal
- Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India.
| | - Ronald G Larson
- Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA.
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11
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Kirk J, Wang Z, Ilg P. Entanglement dynamics at flat surfaces: Investigations using multi-chain molecular dynamics and a single-chain slip-spring model. J Chem Phys 2019; 150:094906. [PMID: 30849883 DOI: 10.1063/1.5045301] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The dynamics of an entangled polymer melt confined in a channel by parallel plates is investigated by Molecular Dynamics (MD) simulations of a detailed, multi-chain model. A primitive path analysis predicts that the density of entanglements remains approximately constant throughout the gap and drops to lower values only in the immediate vicinity of the surface. Based on these observations, we propose a coarse-grained, single-chain slip-spring model with a uniform density of slip-spring anchors and slip-links. The slip-spring model is compared to the Kremer-Grest MD bead-spring model via equilibrium correlation functions of chain orientations. Reasonably good agreement between the single-chain model and the detailed multi-chain model is obtained for chain relaxation dynamics, both away from the surface and for chains whose center of mass positions are at a distance from the surface that is less than the bulk chain radius of gyration, without introducing any additional model parameters. Our results suggest that there is no considerable drop in topological interactions for chains in the vicinity of a single flat surface. We infer from the slip-spring model that the experimental plateau modulus of a confined polymer melt may be different to a corresponding unconfined system even if there is no drop in topological interactions for the confined case.
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Affiliation(s)
- Jack Kirk
- School of Mathematical, Physical and Computational Sciences, University of Reading, Reading RG6 6AX, United Kingdom
| | - Zuowei Wang
- School of Mathematical, Physical and Computational Sciences, University of Reading, Reading RG6 6AX, United Kingdom
| | - Patrick Ilg
- School of Mathematical, Physical and Computational Sciences, University of Reading, Reading RG6 6AX, United Kingdom
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12
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Masubuchi Y, Uneyama T. Comparison among multi-chain models for entangled polymer dynamics. SOFT MATTER 2018; 14:5986-5994. [PMID: 29926890 DOI: 10.1039/c8sm00948a] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Although lots of coarse-grained models have been proposed to trace the long-term behaviors of entangled polymers, compatibility among the different models has not been frequently discussed. In this study, some dynamical and static quantities, such as diffusion, relaxation modulus, chain dimension, and entanglement density, were examined for the multi-chain slip-link model (primitive chain network model) and the multi-chain slip-spring model, and the results were compared with those reported for the standard bead-spring model. For the diffusion, three models are compatible with scale-conversion parameters for units of length, time and bead (segment) number (or the molecular weight). The relaxation modulus is also compatible given that the model dependence can be accommodated by the entanglement density and the additional scale-conversion for the unit of modulus. The chain dimension is reasonably coincident with small deviations due to the weak non-Gaussianity of the models. Apart from these plausible compatibilities, significant discrepancies have been found for the inter-chain cross-correlations in the relaxation modulus.
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13
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Tassieri M, Ramírez J, Karayiannis NC, Sukumaran SK, Masubuchi Y. i-Rheo GT: Transforming from Time to Frequency Domain without Artifacts. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b00447] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Manlio Tassieri
- Division of Biomedical Engineering, School of Engineering, University of Glasgow, Glasgow G12 8LT, U.K
| | | | - Nikos Ch. Karayiannis
- Institute for Optoelectronics and Microsystems (ISOM), Universidad Politécnica de Madrid, José Gutiérrez Abascal 2, 28006 Madrid, Spain
| | - Sathish K. Sukumaran
- Graduate School of Organic Materials Science, Yamagata University, Yonezawa 992-8510, Japan
| | - Yuichi Masubuchi
- Department of Materials Physics, Nagoya University, Nagoya 464-8603, Japan
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14
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Zhu J, Likhtman AE, Wang Z. Arm retraction dynamics of entangled star polymers: A forward flux sampling method study. J Chem Phys 2017; 147:044907. [DOI: 10.1063/1.4995422] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Affiliation(s)
- Jian Zhu
- Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, United Kingdom
| | - Alexei E. Likhtman
- Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, United Kingdom
| | - Zuowei Wang
- Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, United Kingdom
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15
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Masubuchi Y, Amamoto Y. Orientational Cross-Correlation in Entangled Binary Blends in Primitive Chain Network Simulations. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b01642] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Yuichi Masubuchi
- National Composite Center, Nagoya University, Furo-cho,
Chikusa-ku, Nagoya 464-8603, Japan
| | - Yoshifumi Amamoto
- National Composite Center, Nagoya University, Furo-cho,
Chikusa-ku, Nagoya 464-8603, Japan
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16
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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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17
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Cheng S, Lu Y, Liu G, Wang SQ. Finite cohesion due to chain entanglement in polymer melts. SOFT MATTER 2016; 12:3340-3351. [PMID: 26931322 DOI: 10.1039/c6sm00142d] [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
Three different types of experiments, quiescent stress relaxation, delayed rate-switching during stress relaxation, and elastic recovery after step strain, are carried out in this work to elucidate the existence of a finite cohesion barrier against free chain retraction in entangled polymers. Our experiments show that there is little hastened stress relaxation from step-wise shear up to γ = 0.7 and step-wise extension up to the stretching ratio λ = 1.5 at any time before or after the Rouse time. In contrast, a noticeable stress drop stemming from the built-in barrier-free chain retraction is predicted using the GLaMM model. In other words, the experiment reveals a threshold magnitude of step-wise deformation below which the stress relaxation follows identical dynamics whereas the GLaMM or Doi-Edwards model indicates a monotonic acceleration of the stress relaxation dynamics as a function of the magnitude of the step-wise deformation. Furthermore, a sudden application of startup extension during different stages of stress relaxation after a step-wise extension, i.e. the delayed rate-switching experiment, shows that the geometric condensation of entanglement strands in the cross-sectional area survives beyond the reptation time τd that is over 100 times the Rouse time τR. Our results point to the existence of a cohesion barrier that can prevent free chain retraction upon moderate deformation in well-entangled polymer melts.
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Affiliation(s)
- Shiwang Cheng
- Department of Polymer Science, University of Akron, Akron, Ohio 44325-3909, USA.
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18
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Wang M, Likhtman AE, Olsen BD. Crossover between activated reptation and arm retraction mechanisms in entangled rod-coil block copolymers. J Chem Phys 2015; 143:184904. [PMID: 26567681 DOI: 10.1063/1.4933427] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Using a coarse-grained slip-spring model, the dynamics of rod-coil block copolymers is explored over a wide parameter space to fully capture the crossover between the short rod (activated reptation) and long rod (arm retraction) limits. An analytical, closed-form expression for curvilinear diffusion by activated reptation was derived by separating the drag into individual components for the rod and coil block. Curvilinear diffusion in the intermediate rod regime, where both mechanisms are important, was then found to be faster than predicted when both mechanisms are independently combined. The discrepancy in the crossover regime arises because the rod-coil copolymer's exploration of space is not accurately described by either a coil homopolymer (assumed by activated reptation) or a rod homopolymer (assumed by arm retraction). This effect is explored by tracking the rod orientation as the polymer reptates, confirming that the polymer reptates along a path that becomes more rodlike as the rod fraction is increased. Thus, activated reptation under-predicts diffusion because the rod can choose reptation paths that are more extended than the coil homopolymer by renewal of the entanglement tube from the ends. Arm retraction under-predicts diffusion because minor rotations of the rod allow some motion before full retractions of the coil block. Finally, more familiar 3-dimensional center-of-mass diffusion measurements are related to the curvilinear diffusion analysis because the ratio of these two quantities varies smoothly between the coil and rod homopolymer limits as the reptation path becomes more extended.
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Affiliation(s)
- Muzhou Wang
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Alexei E Likhtman
- School of Mathematical and Physical Sciences, University of Reading, Reading RG6 6AX, United Kingdom
| | - Bradley D Olsen
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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19
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Lu Y, An L, Wang SQ, Wang ZG. Molecular Mechanisms for Conformational and Rheological Responses of Entangled Polymer Melts to Startup Shear. Macromolecules 2015. [DOI: 10.1021/ma502236m] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Yuyuan Lu
- State
Key Laboratory of Polymer Physics and Chemistry, Changchun Institute
of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Lijia An
- State
Key Laboratory of Polymer Physics and Chemistry, Changchun Institute
of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Shi-Qing Wang
- Department
of Polymer Science, University of Akron, Akron, Ohio 44325-3909, United States
| | - Zhen-Gang Wang
- State
Key Laboratory of Polymer Physics and Chemistry, Changchun Institute
of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
- Division
of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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20
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Wang M, Likhtman AE, Olsen BD. Tube Curvature Slows the Motion of Rod-Coil Block Copolymers through Activated Reptation. ACS Macro Lett 2015; 4:242-246. [PMID: 35596415 DOI: 10.1021/mz5007377] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Understanding the dynamics of molecules with complex shapes is important as researchers develop advanced materials using hybrid molecules. This study applies a slip-spring model to visualize and quantify the entangled dynamics of rod-coil block copolymers. The parameters of the model are determined by matching with molecular dynamics simulation results. By monitoring the positions of polymers along the entanglement tube, rod-coil copolymers are shown to disfavor configurations where the rod occupies curved portions of the tube of randomly varying curvature created by the coil ends. This confirms that reptation of copolymers occurs by an activated mechanism and is the first demonstration of the activation barriers that have been previously inferred through diffusion measurements by simulation and experiment. The barriers to diffusion are further quantified by considering the curvilinear motion of ring polymers, and their effect on diffusion is quantitatively captured by considering one-dimensional motion along an entanglement tube with a rough free energy potential.
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Affiliation(s)
- Muzhou Wang
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Alexei E. Likhtman
- School
of Mathematical and Physical Sciences, University of Reading, Reading RG6 6AX, U.K
| | - Bradley D. Olsen
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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21
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Ouyang YT, Guo HX. Phase behavior of amphiphiles at liquid crystals/water interface: A coarse-grained molecular dynamics study. CHINESE JOURNAL OF POLYMER SCIENCE 2014. [DOI: 10.1007/s10118-014-1520-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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22
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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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23
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Abstract
Although the tube theory is very popular and successful, the tube concept remains evasive and ill defined. This paper proposes a simple computer algorithm to construct the tube axis as a center line of the cloud of chain configurations at different moments of time. We test this algorithm on trajectories generated from simulations of concatenated well entangled ring polymers, thus avoiding all disentanglement processes. We find that entanglements are clearly manifested through the curvature of the tube axis, and we can successfully identify binary and ternary entanglements in molecular dynamics simulations. Several quantitative characteristics of entanglements are reported and discussed.
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Affiliation(s)
- Alexei E Likhtman
- School of Mathematical and Physical Sciences, University of Reading, Reading RG6 6AX, UK.
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24
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Affiliation(s)
- Alexei E. Likhtman
- School
of Mathematical and
Physical Sciences, University of Reading, Reading RG6 6AX, U.K
| | - M. Ponmurugan
- School
of Mathematical and
Physical Sciences, University of Reading, Reading RG6 6AX, U.K
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25
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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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26
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Likhtman AE, Talib MS, Vorselaars B, Ramirez J. Determination of Tube Theory Parameters Using a Simple Grid Model as an Example. Macromolecules 2013. [DOI: 10.1021/ma302103p] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Alexei E. Likhtman
- School of Mathematical
and Physical Sciences, University of Reading, Reading RG6 6AX, U.K
| | - Mohamad S. Talib
- School of Mathematical
and Physical Sciences, University of Reading, Reading RG6 6AX, U.K
| | - Bart Vorselaars
- School of Mathematical
and Physical Sciences, University of Reading, Reading RG6 6AX, U.K
| | - Jorge Ramirez
- School of Mathematical
and Physical Sciences, University of Reading, Reading RG6 6AX, U.K
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27
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28
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Uneyama T, Akimoto T, Miyaguchi T. Crossover time in relative fluctuations characterizes the longest relaxation time of entangled polymers. J Chem Phys 2012; 137:114903. [DOI: 10.1063/1.4752768] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Everaers R. Topological versus rheological entanglement length in primitive-path analysis protocols, tube models, and slip-link models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:022801. [PMID: 23005812 DOI: 10.1103/physreve.86.022801] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2011] [Revised: 06/18/2012] [Indexed: 06/01/2023]
Abstract
We show that the front factor appearing in the shear modulus of a phantom network, G(ph) = (1-2/f)(ρk(B)T)/N(s), also controls the ratio of the strand length, N(s), and the number of monomers per Kuhn length of the primitive paths, N(ph)(PPKuhn), characterizing the average network conformation. In particular, N(ph)(PPKuhn) = N(s)/(1-2/f) and G(ph) = (ρk(B)T)/N(ph)(PPKuhn). Neglecting the difference between cross-links and slip-links, these results can be transferred to entangled systems and the interpretation of primitive path analysis data. In agreement with the tube model, the analogy to phantom networks suggest that the rheological entanglement length, N(e)(rheo) = (ρk(B)T)/G(e), should equal N(e)(PPKuhn). Assuming binary entanglements with f = 4 functional junctions, we expect that N(e)(rheo) should be twice as large as the topological entanglement length, N(e)(topo). These results are in good agreement with reported primitive path analysis results for model systems and a wide range of polymeric materials. Implications for tube and slip-link models are discussed.
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30
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Wang Z, Likhtman AE, Larson RG. Segmental Dynamics in Entangled Linear Polymer Melts. Macromolecules 2012. [DOI: 10.1021/ma202759v] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Zuowei Wang
- School of Mathematical
and Physical
Sciences, University of Reading, Whiteknights,
Reading RG6 6AX, United Kingdom
| | - Alexei E. Likhtman
- School of Mathematical
and Physical
Sciences, University of Reading, Whiteknights,
Reading RG6 6AX, United Kingdom
| | - Ronald G. Larson
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136,
United States
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31
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Arman B, Reddy AS, Arya G. Viscoelastic Properties and Shock Response of Coarse-Grained Models of Multiblock versus Diblock Copolymers: Insights into Dissipative Properties of Polyurea. Macromolecules 2012. [DOI: 10.1021/ma3001934] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Bedri Arman
- Department
of NanoEngineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0448, La Jolla, California 92093,
United States
| | - A. Srinivas Reddy
- Department
of NanoEngineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0448, La Jolla, California 92093,
United States
| | - Gaurav Arya
- Department
of NanoEngineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0448, La Jolla, California 92093,
United States
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32
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Masubuchi Y, Uneyama T, Saito K. A multiscale simulation of polymer processing using parameter-based bridging in melt rheology. J Appl Polym Sci 2012. [DOI: 10.1002/app.36593] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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33
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Padding JT, Briels WJ. Systematic coarse-graining of the dynamics of entangled polymer melts: the road from chemistry to rheology. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:233101. [PMID: 21613700 DOI: 10.1088/0953-8984/23/23/233101] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, thus automatically preventing bond crossing. This also implies an upper limit on the number of atoms that can be lumped together (up to five backbone carbon atoms) and therefore on the longest chain lengths that can be studied. To reach a higher degree of coarse-graining, in CGSD many more atoms are lumped together (more than ten backbone carbon atoms), leading to relatively soft beads. In that case friction and stochastic forces dominate the interactions, and action must be undertaken to prevent bond crossing. We also review alternative methods that make use of the tube model of polymer dynamics, by obtaining the entanglement characteristics through a primitive path analysis and by simulation of a primitive chain network. We finally review super-coarse-grained methods in which an entire polymer is represented by a single particle, and comment on ways to include memory effects and transient forces.
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Affiliation(s)
- J T Padding
- Institut de la Matière Condensée et des Nanosciences, Université Catholique de Louvain, Croix du Sud 1, B-1348 Louvain-la-Neuve, Belgium.
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34
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Affiliation(s)
- Juan J. de Pablo
- Department of Chemical and Biological Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706;
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35
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Ramírez J, Sukumaran SK, Vorselaars B, Likhtman AE. Efficient on the fly calculation of time correlation functions in computer simulations. J Chem Phys 2010; 133:154103. [DOI: 10.1063/1.3491098] [Citation(s) in RCA: 91] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Lyubimov IY, McCarty J, Clark A, Guenza MG. Analytical rescaling of polymer dynamics from mesoscale simulations. J Chem Phys 2010; 132:224903. [DOI: 10.1063/1.3450301] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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37
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Durand M, Meyer H, Benzerara O, Baschnagel J, Vitrac O. Molecular dynamics simulations of the chain dynamics in monodisperse oligomer melts and of the oligomer tracer diffusion in an entangled polymer matrix. J Chem Phys 2010; 132:194902. [DOI: 10.1063/1.3420646] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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38
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Likhtman AE, Sukumaran SK. Comment on “Entangled Polymer Melts: Relation between Plateau Modulus and Stress Autocorrelation Function”. Macromolecules 2010. [DOI: 10.1021/ma9027849] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Alexei E. Likhtman
- Department of Mathematics, University of Reading, Whiteknights, Reading RG6 6AX, U.K
| | - Sathish K. Sukumaran
- Graduate School of Science and Engineering, Yamagata University, Yonezawa 992-8510, Japan
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