1
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Becerra D, Córdoba A, Schieber JD. Examination of Nonuniversalities in Entangled Polymer Melts during the Start-Up of Steady Shear Flow. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00156] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Diego Becerra
- Department of Chemical Engineering, Universidad de Concepción, Concepción 4030000, Chile
| | - Andrés Córdoba
- Department of Chemical Engineering, Universidad de Concepción, Concepción 4030000, Chile
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, United States
| | - Jay D. Schieber
- Department of Chemical and Biological Engineering, Department of Physics, Department of Applied Mathematics, and Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois 60616, United States
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2
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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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3
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Ma T, Lin G, Tan H. Slip-spring simulations of different constraint release environments for linear polymer chains. ROYAL SOCIETY OPEN SCIENCE 2020; 7:191046. [PMID: 32269780 PMCID: PMC7137961 DOI: 10.1098/rsos.191046] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/21/2019] [Accepted: 02/10/2020] [Indexed: 06/11/2023]
Abstract
The constraint release (CR) mechanism has important effects on polymer relaxation and the chains will show different relaxation behaviour in conditions of monodisperse, bidisperse and other topological environments. By comparing relaxation data of linear polyisoprene (PI) chains dissolved in very long matrix and monodisperse melts, Matsumiya et al. showed that CR mechanism accelerates both dielectric and viscoelastic relaxation (Matsumiya et al. 2013 Macromolecules 46, 6067. (doi:10.1021/ma400606n)). In this work, the experimental data reported by Matsumiya et al. are reproduced using the single slip-spring (SSp) model and the CR accelerating effects on both dielectric and viscoelastic relaxation are validated by simulations. This effect on viscoelastic relaxation is more pronounced. The coincidence for end-to-end relaxation and the viscoelastic relaxation has also been checked using probe version SSp model. A variant of SSp with each entanglement assigning a characteristic lifetime is also proposed to simulate various CR environment flexibly. Using this lifetime version SSp model, the correct relaxation function can be obtained with equal numbers of entanglement destructions by CR and reptation/contour length fluctuation (CLF) for monodisperse melts. Good agreement with published experiment data is also obtained for bidisperse melts, which validates the ability to correctly describe the CR environment of the lifetime version model.
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Affiliation(s)
- Teng Ma
- Centre for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, People's Republic of China
| | - Guochang Lin
- Centre for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, People's Republic of China
- National Key Laboratory of Science and Technology for National Defence on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150080, People's Republic of China
| | - Huifeng Tan
- Centre for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, People's Republic of China
- National Key Laboratory of Science and Technology for National Defence on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150080, People's Republic of China
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4
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Andreev M, Nicholson D, Kotula A, Moore J, den Doelder J, Rutledge GC. Rheology of Crystallizing LLDPE. JOURNAL OF RHEOLOGY 2020; 64:10.1122/8.0000110. [PMID: 34131354 PMCID: PMC8200930 DOI: 10.1122/8.0000110] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Accepted: 09/18/2020] [Indexed: 06/12/2023]
Abstract
Polymer crystallization occurs in many plastic manufacturing processes, from injection molding to film blowing. Linear low-density polyethylene (LLDPE) is one of the most commonly processed polymers, wherein the type and extent of short-chain branching (SCB) may be varied to influence crystallization. In this work, we report simultaneous measurements of the rheology and Raman spectra, using a Rheo-Raman microscope, for two industrial-grade LLDPEs undergoing crystallization. These polymers are characterized by broad polydispersity, SCB and the presence of polymer chain entanglements. The rheological behavior of these entangled LLDPE melts is modeled as a function of crystallinity using a slip-link model. The partially crystallized melt is represented by a blend of linear chains with either free or crosslinked ends, wherein the crosslinks represent attachment to growing crystallites, and a modulus shift factor that increases with degree of crystallinity. In contrast to our previous application of the slip-link model to isotactic polypropylene (iPP), in which the introduction of only bridging segments with crosslinks at both ends was sufficient to describe the available data, for these LLDPEs we find it necessary to introduce dangling segments, with crosslinks at only one end. The model captures quantitatively the evolution of viscosity and elasticity with crystallization over the whole range of frequencies in the linear regime for two LLDPE grades.
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Affiliation(s)
- Marat Andreev
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA
| | - David Nicholson
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA
| | - Anthony Kotula
- National Institute of Standards and Technology, Gaithersburg, MD
| | | | - Jaap den Doelder
- Dow Benelux BV, Terneuzen, The Netherlands
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology. Eindhoven, The Netherlands
| | - Gregory C Rutledge
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA
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5
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Hall R, Desai PS, Kang BG, Huang Q, Lee S, Chang T, Venerus DC, Mays J, Ntetsikas K, Polymeropoulos G, Hadjichristidis N, Larson RG. Assessing the Range of Validity of Current Tube Models through Analysis of a Comprehensive Set of Star–Linear 1,4-Polybutadiene Polymer Blends. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b00642] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | | | - Beom-Goo Kang
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| | | | - Sanghoon Lee
- Department of Chemistry and Division of Advanced Materials Science, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | - Taihyun Chang
- Department of Chemistry and Division of Advanced Materials Science, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | - David C. Venerus
- Department of Chemical and Biological Engineering and Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, Chicago, Illinois 60616, United States
| | - Jimmy Mays
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Konstantinos Ntetsikas
- Physical Sciences and Engineering Division, KAUST Catalysis Center, Polymer Synthesis Laboratory, King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia
| | - George Polymeropoulos
- Physical Sciences and Engineering Division, KAUST Catalysis Center, Polymer Synthesis Laboratory, King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia
| | - Nikos Hadjichristidis
- Physical Sciences and Engineering Division, KAUST Catalysis Center, Polymer Synthesis Laboratory, King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia
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6
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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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7
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Xi L. Molecular simulation for predicting the rheological properties of polymer melts. MOLECULAR SIMULATION 2019. [DOI: 10.1080/08927022.2019.1605600] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Li Xi
- Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada
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8
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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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9
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Affiliation(s)
- Rakwoo Chang
- Department of Chemistry, Kwangwoon University, Seoul 01897, Republic of Korea
| | - Arun Yethiraj
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, United States
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10
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Hall R, Kang BG, Lee S, Chang T, Venerus DC, Hadjichristidis N, Mays J, Larson RG. Determining the Dilution Exponent for Entangled 1,4-Polybutadienes Using Blends of Near-Monodisperse Star with Unentangled, Low Molecular Weight Linear Polymers. Macromolecules 2019. [DOI: 10.1021/acs.macromol.8b01828] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | - Beom-Goo Kang
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Sanghoon Lee
- Department of Chemistry and Division of Advanced Materials Science, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | - Taihyun Chang
- Department of Chemistry and Division of Advanced Materials Science, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | - David C. Venerus
- Department of Chemical and Materials Engineering, New Jersey Institute of Technology, Newark, New Jersey 07102, United States
- Department of Chemical and Biological Engineering, and Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, Chicago, Illinois 60616, United States
| | - Nikos Hadjichristidis
- Polymer Synthesis Laboratory, Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
| | - Jimmy Mays
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
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11
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Uneyama T. A transient bond model for dynamic constraints in meso-scale coarse-grained systems. J Chem Phys 2019; 150:024901. [DOI: 10.1063/1.5062495] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Takashi Uneyama
- Center for Computational Science, Graduate School of Engineering, Nagoya University, Nagoya, Japan
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12
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Efficient Determination of Slip-Link Parameters from Broadly Polydisperse Linear Melts. Polymers (Basel) 2018; 10:polym10080908. [PMID: 30960833 PMCID: PMC6403776 DOI: 10.3390/polym10080908] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2018] [Revised: 08/04/2018] [Accepted: 08/07/2018] [Indexed: 11/17/2022] Open
Abstract
We investigate the ability of a coarse-grained slip-link model and a simple double reptation model to describe the linear rheology of polydisperse linear polymer melts. Our slip-link model is a well-defined mathematical object that can describe the equilibrium dynamics and non-linear rheology of flexible polymer melts with arbitrary polydispersity and architecture with a minimum of inputs: the molecular weight of a Kuhn step, the entanglement activity, and Kuhn step friction. However, this detailed model is computationally expensive, so we also examine predictions of the cheaper double reptation model, which is restricted to only linear rheology near the terminal zone. We report the storage and loss moduli for polydisperse polymer melts and compare with experimental measurements from small amplitude oscillatory shear. We examine three chemistries: polybutadiene, polypropylene and polyethylene. We also use a simple double reptation model to estimate parameters for the slip-link model and examine under which circumstances this simplified model works. The computational implementation of the slip-link model is accelerated with the help of graphics processing units, which allow us to simulate in parallel large ensembles made of up to 50,000 chains. We show that our simulation can predict the dynamic moduli for highly entangled polymer melts over nine decades of frequency. Although the double reptation model performs well only near the terminal zone, it does provide a convenient and inexpensive way to estimate the entanglement parameter for the slip-link model from polydisperse data.
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13
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Masubuchi Y, Pandey A, Amamoto Y, Uneyama T. Orientational cross correlations between entangled branch polymers in primitive chain network simulations. J Chem Phys 2017; 147:184903. [DOI: 10.1063/1.5001960] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Affiliation(s)
- Yuichi Masubuchi
- Department of Materials Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
| | - Ankita Pandey
- Department of Materials Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
| | - Yoshifumi Amamoto
- Department of Materials Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
| | - Takashi Uneyama
- Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192, 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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Ramírez-Hernández A, Peters BL, Schneider L, Andreev M, Schieber JD, Müller M, de Pablo JJ. A multi-chain polymer slip-spring model with fluctuating number of entanglements: Density fluctuations, confinement, and phase separation. J Chem Phys 2017; 146:014903. [PMID: 28063448 DOI: 10.1063/1.4972582] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Coarse grained simulation approaches provide powerful tools for the prediction of the equilibrium properties of polymeric systems. Recent efforts have sought to develop coarse-graining strategies capable of predicting the non-equilibrium behavior of entangled polymeric materials. Slip-link and slip-spring models, in particular, have been shown to be capable of reproducing several key aspects of the linear response and rheology of polymer melts. In this work, we extend a previously proposed multi-chain slip-spring model in a way that correctly incorporates the effects of the fluctuating environment in which polymer segments are immersed. The model is used to obtain the equation of state associated with the slip-springs, and the results are compared to those of related numerical approaches and an approximate analytical expression. The model is also used to examine a polymer melt confined into a thin film, where an inhomogeneous distribution of polymer segments is observed, and the corresponding inhomogeneities associated with density fluctuations are reflected on the spatial slip-spring distribution.
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Affiliation(s)
- Abelardo Ramírez-Hernández
- Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA
| | - Brandon L Peters
- Institute for Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Ludwig Schneider
- Institut für Theoretische Physik, Georg-August-Universität, 37077 Göttingen, Germany
| | - Marat Andreev
- Institute for Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Jay D Schieber
- Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, Chicago, Illinois 60616, USA
| | - Marcus Müller
- Institut für Theoretische Physik, Georg-August-Universität, 37077 Göttingen, Germany
| | - Juan J de Pablo
- Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA
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16
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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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17
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Masubuchi Y, Langeloth M, Böhm MC, Inoue T, Müller-Plathe F. A Multichain Slip-Spring Dissipative Particle Dynamics Simulation Method for Entangled Polymer Solutions. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b01971] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Affiliation(s)
- Yuichi Masubuchi
- National
Composite Center, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8603, Japan
| | - Michael Langeloth
- Eduard-Zintl-Institut
für Anorganische und Physikalische Chemie and Center of Smart
Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Strasse
8, 64287 Darmstadt, Germany
| | - Michael C. Böhm
- Eduard-Zintl-Institut
für Anorganische und Physikalische Chemie and Center of Smart
Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Strasse
8, 64287 Darmstadt, Germany
| | - Tadashi Inoue
- Department
of Macromolecular Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
| | - Florian Müller-Plathe
- Eduard-Zintl-Institut
für Anorganische und Physikalische Chemie and Center of Smart
Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Strasse
8, 64287 Darmstadt, Germany
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18
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Desai PS, Kang BG, Katzarova M, Hall R, Huang Q, Lee S, Shivokhin M, Chang T, Venerus DC, Mays J, Schieber JD, Larson RG. Challenging Tube and Slip-Link Models: Predicting the Linear Rheology of Blends of Well-Characterized Star and Linear 1,4-Polybutadienes. Macromolecules 2016. [DOI: 10.1021/acs.macromol.5b02641] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
| | - Beom-Goo Kang
- Department
of Chemistry, University of Tennessee, Knoxville, Tennessee 37966, United States
| | | | | | | | - Sanghoon Lee
- Department
of Chemistry and Division of Advanced Materials Science, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | | | - Taihyun Chang
- Department
of Chemistry and Division of Advanced Materials Science, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | | | - Jimmy Mays
- Department
of Chemistry, University of Tennessee, Knoxville, Tennessee 37966, United States
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19
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Karim M, Indei T, Schieber JD, Khare R. Determination of linear viscoelastic properties of an entangled polymer melt by probe rheology simulations. Phys Rev E 2016; 93:012501. [PMID: 26871112 DOI: 10.1103/physreve.93.012501] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2015] [Indexed: 11/07/2022]
Abstract
Particle rheology is used to extract the linear viscoelastic properties of an entangled polymer melt from molecular dynamics simulations. The motion of a stiff, approximately spherical particle is tracked in both passive and active modes. We demonstrate that the dynamic modulus of the melt can be extracted under certain limitations using this technique. As shown before for unentangled chains [Karim et al., Phys. Rev. E 86, 051501 (2012)PLEEE81539-375510.1103/PhysRevE.86.051501], the frequency range of applicability is substantially expanded when both particle and medium inertia are properly accounted for by using our inertial version of the generalized Stokes-Einstein relation (IGSER). The system used here introduces an entanglement length d_{T}, in addition to those length scales already relevant: monomer bead size d, probe size R, polymer radius of gyration R_{g}, simulation box size L, shear wave penetration length Δ, and wave period Λ. Previously, we demonstrated a number of restrictions necessary to obtain the relevant fluid properties: continuum approximation breaks down when d≳Λ; medium inertia is important and IGSER is required when R≳Λ; and the probe should not experience hydrodynamic interaction with its periodic images, L≳Δ. These restrictions are also observed here. A simple scaling argument for entangled polymers shows that the simulation box size must scale with polymer molecular weight as M_{w}^{3}. Continuum analysis requires the existence of an added mass to the probe particle from the entrained medium but was not observed in the earlier work for unentangled chains. We confirm here that this added mass is necessary only when the thickness L_{S} of the shell around the particle that contains the added mass, L_{S}>d. We also demonstrate that the IGSER can be used to predict particle displacement over a given timescale from knowledge of medium viscoelasticity; such ability will be of interest for designing nanoparticle-based drug delivery.
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Affiliation(s)
- Mir Karim
- Department of Chemical Engineering, Texas Tech University, Box 43121, Lubbock, Texas 79409, USA
| | - Tsutomu Indei
- Center for Molecular Study of Condensed Soft Matter, and Department of Chemical and Biological Engineering, Illinois Institute of Technology, 3440 S. Dearborn Street, Chicago, Illinois 60616, USA
| | - Jay D Schieber
- Center for Molecular Study of Condensed Soft Matter, and Department of Chemical and Biological Engineering, Illinois Institute of Technology, 3440 S. Dearborn 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
| | - Rajesh Khare
- Department of Chemical Engineering, Texas Tech University, Box 43121, Lubbock, Texas 79409, USA
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Ramírez-Hernández A, Peters BL, Andreev M, Schieber JD, de Pablo JJ. A multichain polymer slip-spring model with fluctuating number of entanglements for linear and nonlinear rheology. J Chem Phys 2015; 143:243147. [DOI: 10.1063/1.4936878] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Abelardo Ramírez-Hernández
- Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA
- Institute for Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Brandon L. Peters
- Institute for Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Marat Andreev
- Institute for Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Jay D. Schieber
- Institute for Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Juan J. de Pablo
- Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA
- Institute for Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
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Unidad HJ, Goad MA, Bras AR, Zamponi M, Faust R, Allgaier J, Pyckhout-Hintzen W, Wischnewski A, Richter D, Fetters LJ. Consequences of Increasing Packing Length on the Dynamics of Polymer Melts. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b00341] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Herwin Jerome Unidad
- Jülich
Centre for Neutron Science, Outstation at Heinz Maier-Leibnitz Zentrum, Forschungszentrum Jülich GmbH, Lichtenbergstraße 1, 85747 Garching, Germany
| | - Mahmoud Abdel Goad
- Jülich
Centre for Neutron Science-1 and Institute of Complex Systems-1, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
| | - Ana Rita Bras
- Jülich
Centre for Neutron Science-1 and Institute of Complex Systems-1, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
| | - Michaela Zamponi
- Jülich
Centre for Neutron Science, Outstation at Heinz Maier-Leibnitz Zentrum, Forschungszentrum Jülich GmbH, Lichtenbergstraße 1, 85747 Garching, Germany
| | - Rudolf Faust
- Chemistry
Department, University of Massachusetts Lowell, Lowell, Massachusetts 01854, United States
| | - Jürgen Allgaier
- Jülich
Centre for Neutron Science-1 and Institute of Complex Systems-1, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
| | - Wim Pyckhout-Hintzen
- Jülich
Centre for Neutron Science-1 and Institute of Complex Systems-1, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
| | - Andreas Wischnewski
- Jülich
Centre for Neutron Science-1 and Institute of Complex Systems-1, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
| | - Dieter Richter
- Jülich
Centre for Neutron Science-1 and Institute of Complex Systems-1, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
| | - Lewis J. Fetters
- Department
of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14850, United States
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Andreev M, Schieber JD. Accessible and Quantitative Entangled Polymer Rheology Predictions, Suitable for Complex Flow Calculations. Macromolecules 2015. [DOI: 10.1021/ma502525x] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Marat Andreev
- Department of Physics, ‡Center for Molecular
Study of Condensed Soft Matter, and §Department of
Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, Illinois 60616, United States
| | - Jay D. Schieber
- Department of Physics, ‡Center for Molecular
Study of Condensed Soft Matter, and §Department of
Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, Illinois 60616, United States
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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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Schieber JD, Andreev M. Entangled Polymer Dynamics in Equilibrium and Flow Modeled Through Slip Links. Annu Rev Chem Biomol Eng 2014; 5:367-81. [DOI: 10.1146/annurev-chembioeng-060713-040252] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
The idea that the dynamics of concentrated, high–molecular weight polymers are largely governed by entanglements is now widely accepted and typically understood through the tube model. Here we review alternative approaches, slip-link models, that share some similarities to and offer some advantages over tube models. Although slip links were proposed at the same time as tubes, only recently have detailed, quantitative mathematical models arisen based on this picture. In this review, we focus on these models, with most discussion limited to mathematically well-defined objects that conform to state-of-the-art beyond-equilibrium thermodynamics. These models are connected to each other through successive coarse graining, using nonequilibrium thermodynamics along the way, and with a minimal parameter set. In particular, the most detailed level of description has four parameters, three of which can be determined directly from atomistic simulations. Once the remaining parameter is determined for any system, all parameters for all members of the hierarchy are determined. We show how, using this hierarchy of slip-link models combined with atomistic simulations, we can make predictions about the nonlinear rheology of monodisperse homopolymer melts, polydisperse melts, or blends of different architectures. Mathematical details are given elsewhere, so these are limited here, and physical ideas are emphasized. We conclude with an outlook on remaining challenges that might be tackled successfully using this approach, including complex flow fields and polymer blends.
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Affiliation(s)
- Jay D. Schieber
- Center for Molecular Study of Condensed Soft Matter, Department of Chemical and Biological Engineering and Department of Physics, Illinois Institute of Technology, Chicago, Illinois 60616
| | - Marat Andreev
- Center for Molecular Study of Condensed Soft Matter, Department of Chemical and Biological Engineering and Department of Physics, Illinois Institute of Technology, Chicago, Illinois 60616
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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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Katzarova M, Andreev M, Sliozberg YR, Mrozek RA, Lenhart JL, Andzelm JW, Schieber JD. Rheological predictions of network systems swollen with entangled solvent. AIChE J 2014. [DOI: 10.1002/aic.14370] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Maria Katzarova
- Dept. of Chemical and Biological Engineering, and Center for Molecular Study of Condensed Soft Matter; Illinois Institute of Technology; Chicago IL 60616
| | - Marat Andreev
- Dept. of Physics; Illinois Institute of Technology; Chicago IL 60616
| | - Yelena R. Sliozberg
- U.S. Army Research Laboratory; Aberdeen Proving Ground; Aberdeen MD 21005
- Bowhead Science and Technology; King George VA 22485
| | - Randy A. Mrozek
- U.S. Army Research Laboratory; Aberdeen Proving Ground; Aberdeen MD 21005
| | - Joseph L. Lenhart
- U.S. Army Research Laboratory; Aberdeen Proving Ground; Aberdeen MD 21005
| | - Jan W. Andzelm
- U.S. Army Research Laboratory; Aberdeen Proving Ground; Aberdeen MD 21005
| | - Jay D. Schieber
- Dept. of Chemical and Biological Engineering, Dept. of Physics, and Center for Molecular Study of Condensed Soft Matter; Illinois Institute of Technology; Chicago IL 60616
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Lang M. Monomer Fluctuations and the Distribution of Residual Bond Orientations in Polymer Networks. Macromolecules 2013. [DOI: 10.1021/ma402013b] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Michael Lang
- Leibniz Institute of Polymer Research, Hohe Straße 6, 01069 Dresden, Germany
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29
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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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Uneyama T, Masubuchi Y. Multi-chain slip-spring model for entangled polymer dynamics. J Chem Phys 2012; 137:154902. [DOI: 10.1063/1.4758320] [Citation(s) in RCA: 90] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Steenbakkers RJA, Schieber JD. Derivation of free energy expressions for tube models from coarse-grained slip-link models. J Chem Phys 2012; 137:034901. [DOI: 10.1063/1.4730170] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Pilyugina E, Andreev M, Schieber JD. Dielectric Relaxation as an Independent Examination of Relaxation Mechanisms in Entangled Polymers Using the Discrete Slip-Link Model. Macromolecules 2012. [DOI: 10.1021/ma202658h] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Ekaterina Pilyugina
- Department of Chemical and Biological
Engineering,
and Center for Molecular Study of Condensed Soft Matter, Illinois
Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois,
United States
| | - Marat Andreev
- Department of Chemical and Biological
Engineering,
and Center for Molecular Study of Condensed Soft Matter, Illinois
Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois,
United States
| | - Jay D. Schieber
- Department of Chemical and Biological
Engineering,
and Center for Molecular Study of Condensed Soft Matter, Illinois
Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois,
United States
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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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34
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Khaliullin RN, Schieber JD. Calculation of the Helmholtz potential of an elastic strand in an external electric field. J Chem Phys 2011; 134:065105. [DOI: 10.1063/1.3532830] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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35
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Khaliullin RN, Schieber JD. Application of the Slip-Link Model to Bidisperse Systems. Macromolecules 2010. [DOI: 10.1021/ma902823k] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Renat N. Khaliullin
- Center for Molecular Study of Condensed Soft Matter, Department of Chemical and Biological Engineering, and Department of Biological, Chemical, and Physical Sciences, Illinois Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois
| | - Jay D. Schieber
- Center for Molecular Study of Condensed Soft Matter, Department of Chemical and Biological Engineering, and Department of Biological, Chemical, and Physical Sciences, Illinois Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois
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36
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Schieber JD, Horio K. Fluctuation in entanglement positions via elastic slip-links. J Chem Phys 2010; 132:074905. [DOI: 10.1063/1.3314727] [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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