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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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2
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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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3
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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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4
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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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5
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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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6
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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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7
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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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8
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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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9
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Everaers R, Rosa A. Multi-scale modeling of diffusion-controlled reactions in polymers: Renormalisation of reactivity parameters. J Chem Phys 2012; 136:014902. [DOI: 10.1063/1.3673444] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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10
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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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11
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Puscasu RM, Todd BD, Daivis PJ, Hansen JS. Nonlocal viscosity of polymer melts approaching their glassy state. J Chem Phys 2010; 133:144907. [DOI: 10.1063/1.3499745] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Khaliullin RN, Schieber JD. Self-Consistent Modeling of Constraint Release in a Single-Chain Mean-Field Slip-Link Model. Macromolecules 2009. [DOI: 10.1021/ma900533s] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Renat N. Khaliullin
- Center for molecular study of condensed soft matter and Department of Chemical and Biological Engineering, Illinois Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois 60616
| | - Jay D. Schieber
- Center for molecular study of condensed soft matter and Department of Chemical and Biological Engineering, Illinois Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois 60616
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13
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Sukumaran SK, Likhtman AE. Modeling Entangled Dynamics: Comparison between Stochastic Single-Chain and Multichain Models. Macromolecules 2009. [DOI: 10.1021/ma802059p] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.8] [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
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14
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Ramos J, Vega JF, Theodorou DN, Martinez-Salazar J. Entanglement Relaxation Time in Polyethylene: Simulation versus Experimental Data. Macromolecules 2008. [DOI: 10.1021/ma702445e] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Javier Ramos
- Departamento de Física Macromolecular, Instituto de Estructura de la Materia, CSIC, Serrano 113 bis, 28006 Madrid, Spain, and Department of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou Campus, 15780 Athens, Greece
| | - Juan F. Vega
- Departamento de Física Macromolecular, Instituto de Estructura de la Materia, CSIC, Serrano 113 bis, 28006 Madrid, Spain, and Department of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou Campus, 15780 Athens, Greece
| | - Doros N. Theodorou
- Departamento de Física Macromolecular, Instituto de Estructura de la Materia, CSIC, Serrano 113 bis, 28006 Madrid, Spain, and Department of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou Campus, 15780 Athens, Greece
| | - Javier Martinez-Salazar
- Departamento de Física Macromolecular, Instituto de Estructura de la Materia, CSIC, Serrano 113 bis, 28006 Madrid, Spain, and Department of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou Campus, 15780 Athens, Greece
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