1
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Micheletti C, Chubak I, Orlandini E, Smrek J. Topology-Based Detection and Tracking of Deadlocks Reveal Aging of Active Ring Melts. ACS Macro Lett 2024:124-129. [PMID: 38198592 PMCID: PMC10883035 DOI: 10.1021/acsmacrolett.3c00567] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2024]
Abstract
Connecting the viscoelastic behavior of stressed ring melts to the various forms of entanglement that can emerge in such systems is still an open challenge. Here, we consider active ring melts, where stress is generated internally, and introduce a topology-based method to detect and track consequential forms of ring entanglements, namely, deadlocks. We demonstrate that, as stress accumulates, more and more rings are co-opted in a growing web of deadlocks that entrap many other rings by threading, bringing the system to a standstill. The method ought to help the study of topological aging in more general polymer contexts.
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Affiliation(s)
- Cristian Micheletti
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, I-34136 Trieste, Italy
| | - Iurii Chubak
- Sorbonne Université CNRS, Physico-Chimie des électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - Enzo Orlandini
- Università degli studi di Padova, Dipartimento di Fisica "G. Galilei", Via Marzolo 8, I-35100 Padova, Italy
| | - Jan Smrek
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
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2
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Zheng Y, Tsige M, Wang SQ. Molecular Dynamics Simulation of Entangled Melts at High Rates: Identifying Entanglement Lockup Mechanism Leading to True Strain Hardening. Macromol Rapid Commun 2023; 44:e2200159. [PMID: 35881534 DOI: 10.1002/marc.202200159] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2022] [Revised: 06/20/2022] [Indexed: 01/11/2023]
Abstract
In the present work, molecular dynamics simulations are carried out based on the bead-spring model to indicate how the entanglement lockup manifests in the late stage of fast Rouse-Weissnberg number (WiR >>1) uniaxial melt stretching of entangled polymer melts. At high strains, distinct features show up to reveal the emergence of an increasingly tightened entanglement network. Chain tension can build up, peaking at the middle of the chain, to a level for chain scission, through accumulated interchain interactions, as if there is a tug-of-war ongoing for each load-bearing chain. Thanks to the interchain uncrossability, network junctions form by the pairing of two or more hairpins. It is hypothesized that the interchain entanglement at junctions can lockup through prevailing twist-like interchain couplings as long as WiR > 9. In this limit, a significant fraction of chains act like cyclic chains to form a network held by interchain uncrossability, and appreciable chain tension emerges.
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Affiliation(s)
- Yexin Zheng
- School of Polymer Science and Polymer Engineering, University of Akron, Akron, OH, 44325, USA
| | - Mesfin Tsige
- School of Polymer Science and Polymer Engineering, University of Akron, Akron, OH, 44325, USA
| | - Shi-Qing Wang
- School of Polymer Science and Polymer Engineering, University of Akron, Akron, OH, 44325, USA
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3
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Shen Z, Carrillo JMY, Sumpter BG, Wang Y. Fingerprinting Brownian Motions of Polymers under Flow. PHYSICAL REVIEW LETTERS 2022; 129:057801. [PMID: 35960564 DOI: 10.1103/physrevlett.129.057801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Accepted: 07/08/2022] [Indexed: 06/15/2023]
Abstract
We present a quantitative approach to the self-dynamics of polymers under steady flow by employing a set of complementary reference frames and extending the spherical harmonic expansion technique to dynamic density correlations. Application of this method to nonequilibrium molecular dynamics simulations of polymer melts reveals a number of universal features. For both unentangled and entangled melts, the center-of-mass motions in the flow frame are described by superdiffusive, anisotropic Gaussian distributions, whereas the isotropic component of monomer self-dynamics in the center-of-mass frame is strongly suppressed. Spatial correlation analysis shows that the heterogeneity of monomer self-dynamics increases significantly under flow.
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Affiliation(s)
- Zhiqiang Shen
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Jan-Michael Y Carrillo
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Bobby G Sumpter
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Yangyang Wang
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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4
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Sleiman JL, Burton RH, Caraglio M, Gutierrez Fosado YA, Michieletto D. Geometric Predictors of Knotted and Linked Arcs. ACS POLYMERS AU 2022; 2:341-350. [PMID: 36254317 PMCID: PMC9562465 DOI: 10.1021/acspolymersau.2c00021] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
Inspired by how certain proteins “sense”
knots and
entanglements in DNA molecules, here, we ask if local geometric features
that may be used as a readout of the underlying topology of generic
polymers exist. We perform molecular simulations of knotted and linked
semiflexible polymers and study four geometric measures to predict
topological entanglements: local curvature, local density, local 1D
writhe, and nonlocal 3D writhe. We discover that local curvature is
a poor predictor of entanglements. In contrast, segments with maximum
local density or writhe correlate as much as 90% of the time with
the shortest knotted and linked arcs. We find that this accuracy is
preserved across different knot types and also under significant spherical
confinement, which is known to delocalize essential crossings in knotted
polymers. We further discover that nonlocal 3D writhe is the best
geometric readout of the knot location. Finally, we discuss how these
geometric features may be used to computationally analyze entanglements
in generic polymer melts and gels.
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Affiliation(s)
- Joseph L. Sleiman
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Robin H. Burton
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Michele Caraglio
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Yair Augusto Gutierrez Fosado
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
- MRC Human Genetics Unit, Institute of Genetics and Cancer, University of Edinburgh, Edinburgh EH4 2XU, United Kingdom
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5
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Dietz JD, Hoy RS. Facile equilibration of well-entangled semiflexible bead-spring polymer melts. J Chem Phys 2022; 156:014103. [PMID: 34998323 DOI: 10.1063/5.0072386] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
The widely used double-bridging hybrid (DBH) method for equilibrating simulated entangled polymer melts [Auhl et al., J. Chem. Phys. 119, 12718-12728 (2003)] loses its effectiveness as chain stiffness increases into the semiflexible regime because the energy barriers associated with double-bridging Monte Carlo moves become prohibitively high. Here we overcome this issue by combining DBH with the use of core-softened pair potentials. This reduces the energy barriers substantially, allowing us to equilibrate melts with N ≃ 40Ne and chain stiffnesses all the way up to the isotropic-nematic transition using simulations of no more than 100 × 106 time steps. For semiflexible chains, our method is several times faster than the standard DBH; we exploit this speedup to develop improved expressions for Kremer-Grest melts' chain-stiffness-dependent Kuhn length ℓK and entanglement length Ne.
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Affiliation(s)
- Joseph D Dietz
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
| | - Robert S Hoy
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
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6
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Affiliation(s)
- Liang Dai
- Department of Physics, City University of Hong Kong, Hong Kong 999077, China
- Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
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7
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Ma J, Carrillo JMY, Do C, Chen WR, Falus P, Shen Z, Hong K, Sumpter BG, Wang Y. Spatial correlations of entangled polymer dynamics. Phys Rev E 2021; 104:024503. [PMID: 34525580 DOI: 10.1103/physreve.104.024503] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2021] [Accepted: 08/03/2021] [Indexed: 11/07/2022]
Abstract
The spatial correlations of entangled polymer dynamics are examined by molecular dynamics simulations and neutron spin-echo spectroscopy. Due to the soft nature of topological constraints, the initial spatial decays of intermediate scattering functions of entangled chains are, to the first approximation, surprisingly similar to those of an unentangled system in the functional forms. However, entanglements reveal themselves as a long tail in the reciprocal-space correlations, implying a weak but persistent dynamic localization in real space. Comparison with a number of existing theoretical models of entangled polymers suggests that they cannot fully describe the spatial correlations revealed by simulations and experiments. In particular, the strict one-dimensional diffusion idea of the original tube model is shown to be flawed. The dynamic spatial correlation analysis demonstrated in this work provides a useful tool for interrogating the dynamics of entangled polymers. Lastly, the failure of the investigated models to even qualitatively predict the spatial correlations of collective single-chain density fluctuations points to a possible critical role of incompressibility in polymer melt dynamics.
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Affiliation(s)
- Jihong Ma
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Jan-Michael Y Carrillo
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Changwoo Do
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Wei-Ren Chen
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Péter Falus
- Institut Laue-Langevin, B.P. 156, F-38042 Grenoble CEDEX 9, France
| | - Zhiqiang Shen
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Kunlun Hong
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Bobby G Sumpter
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Yangyang Wang
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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8
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Smrek J, Garamella J, Robertson-Anderson R, Michieletto D. Topological tuning of DNA mobility in entangled solutions of supercoiled plasmids. SCIENCE ADVANCES 2021; 7:eabf9260. [PMID: 33980492 PMCID: PMC8115916 DOI: 10.1126/sciadv.abf9260] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2020] [Accepted: 03/26/2021] [Indexed: 05/04/2023]
Abstract
Ring polymers in dense solutions are among the most intriguing problems in polymer physics. Because of its natural occurrence in circular form, DNA has been extensively used as a proxy to study the fundamental physics of ring polymers in different topological states. Yet, torsionally constrained-such as supercoiled-topologies have been largely neglected so far. The applicability of existing theoretical models to dense supercoiled DNA is thus unknown. Here, we address this gap by coupling large-scale molecular dynamics simulations with differential dynamic microscopy of entangled supercoiled DNA plasmids. We find that, unexpectedly, larger supercoiling increases the size of entangled plasmids and concomitantly induces an enhancement in DNA mobility. These findings are reconciled as due to supercoiling-driven asymmetric and double-folded plasmid conformations that reduce interplasmid entanglements and threadings. Our results suggest a way to topologically tune DNA mobility via supercoiling, thus enabling topological control over the (micro)rheology of DNA-based complex fluids.
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Affiliation(s)
- Jan Smrek
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Jonathan Garamella
- Department of Physics and Biophysics, University of San Diego, San Diego, CA 92110, USA
| | | | - Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK.
- MRC Human Genetics Unit, Institute of Genetics and Molecular Medicine University of Edinburgh, Edinburgh EH4 2XU, UK
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9
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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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10
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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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11
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Lu L, Zhu H, Yuyuan Lu, An L, Dai L. Application of the Tube Model to Explain the Unexpected Decrease in Polymer Bending Energy Induced by Knot Formation. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01436] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Luwei Lu
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P.R. China
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P.R. China
- University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, P.R. China
| | - Haoqi Zhu
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P.R. China
- Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Yuyuan Lu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P.R. China
| | - Lijia An
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P.R. China
- University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, P.R. China
| | - Liang Dai
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P.R. China
- Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
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12
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Bobbili SV, Milner ST. Simulation Study of Entanglement in Semiflexible Polymer Melts and Solutions. Macromolecules 2020. [DOI: 10.1021/acs.macromol.9b02681] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Sai Vineeth Bobbili
- Pennsylvania State University, University Park 16801, Pennsylvania, United States
| | - Scott T. Milner
- Pennsylvania State University, University Park 16801, Pennsylvania, United States
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13
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Abstract
We review recent neutron scattering work and related results from simulation and complementary techniques focusing on the microscopic dynamics of polymers under confinement. Confinement is either realized in model porous materials or in polymer nanocomposites (PNC). The dynamics of such confined polymers is affected on the local segmental level, the level of entanglements as well as on global levels: (i) at the segmental level the interaction with the surface is of key importance. At locally repulsive surfaces compared to the bulk the segmental dynamics is not altered. Attractive surfaces slow down the segmental dynamics in their neighborhood but do not give rise to dead, glassy layers. (ii) Confinement generally has little effect on the inter-chain entanglements: both for weakly as well as for marginally confined polymers the reptation tube size is not changed. Only for strongly confined polymers disentanglement takes place. Similarly, in PNC at higher NP loading disentanglement phenomena are observed; in addition, at very high loading a transition from polymer caused topological constraints to purely geometrical constraints is observed. (iii) On the more global scale NSE experiments revealed important information on the nature of the interphase between adsorbed layer and bulk polymer. (iv) Polymer grafts at NP mutually confine each other, an effect that is most pronounced for one component NP. (v) Global diffusion of entangled polymers both in weakly and strongly attractive PNC is governed by the ratio of bottle-neck to chain size that characterizes the 'entropic barrier' for global diffusion.
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Affiliation(s)
- Dieter Richter
- Jülich Centre for Neutron Science (JCNS-1) and Institute of Complex Systems (ICS-1), Forschungszentrum Jülich GmbH, Jülich, Germany.
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14
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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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15
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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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16
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Panagiotou E, Millett KC, Atzberger PJ. Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and Viscoelasticity. Polymers (Basel) 2019; 11:E437. [PMID: 30960421 PMCID: PMC6473770 DOI: 10.3390/polym11030437] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2019] [Revised: 02/12/2019] [Accepted: 02/26/2019] [Indexed: 12/31/2022] Open
Abstract
We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear chains. We investigate the rheology of polymeric chains entangled into weaves with varying topologies and levels of chain density. To investigate viscoelastic responses, we perform non-equilibrium molecular simulations over a range of frequencies using sheared Lees⁻Edwards boundary conditions. We show how our topological characteristics can be used to capture key features of the polymer entanglements related to the viscoelastic responses. We find there is a linear relation over a significant range of frequencies between the mean absolute Writhe W r and the Loss Tangent tan ( δ ) . We also find an approximate inverse linear relationship between the mean absolute Periodic Linking Number L K P and the Loss Tangent tan ( δ ) . Our results show some of the ways topological methods can be used to characterize chain entanglements to better understand the origins of mechanical responses in polymeric materials.
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Affiliation(s)
- Eleni Panagiotou
- Department of Mathematics and SimCenter, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA.
| | - Kenneth C Millett
- Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA 93106-3080, USA.
| | - Paul J Atzberger
- Department of Mathematics and Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, CA 93106-3080, USA.
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17
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Thees MF, Roth CB. Unexpected Molecular Weight Dependence to the Physical Aging of Thin Polystyrene Films Present at Ultra‐High Molecular Weights. ACTA ACUST UNITED AC 2019. [DOI: 10.1002/polb.24797] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
| | - Connie B. Roth
- Department of Physics Emory University Atlanta Georgia 30322
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18
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Moreno AJ, Lo Verso F. Computational investigation of microgels: synthesis and effect of the microstructure on the deswelling behavior. SOFT MATTER 2018; 14:7083-7096. [PMID: 30118116 DOI: 10.1039/c8sm01407h] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We present computer simulations of a realistic model of microgels. Unlike the regular network frameworks usually assumed in the simulation literature, we model and simulate a realistic and efficient synthesis route, mimicking cross-linking of functionalized chains inside a cavity. This model is inspired, e.g., by microfluidic fabrication of microgels from macromolecular precursors and is different from standard polymerization routes. The assembly of the chains is mediated by a low fraction of interchain crosslinks. The microgels are polydisperse in size and shape but globally spherical objects. In order to deeply understand the microgel structure and eventually improve the synthesis protocol we characterize their conformational properties and deswelling kinetics, and compare them with the results found for microgels obtained via underlying regular (diamond-like) structures. For the same molecular weight, monomer concentration and effective degree of cross-linking, the specific microstructure of the microgel has no significant effect on the locus of the volume phase transition (VPT). However, it strongly affects the deswelling kinetics, as revealed by a consistent analysis of the domain growth during the microgel collapse. Though both the disordered and the regular networks exhibit a similar early growth of the domains, an acceleration is observed in the regular network at the late stage of the collapse. Similar trends are found for the dynamic correlations coupled to the domain growth. As a consequence, the fast late processes for the domain growth and the dynamic correlations in the regular network are compensated, and the dynamic correlations follow a power-law dependence on the growing length scale that is independent of the microgel microstructure.
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Affiliation(s)
- 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.
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19
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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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20
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Ramos J, Vega J, Martínez-Salazar J. Predicting experimental results for polyethylene by computer simulation. Eur Polym J 2018. [DOI: 10.1016/j.eurpolymj.2017.12.027] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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21
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Xiao H, Luo C, Yan D, Sommer JU. Molecular Dynamics Simulation of Crystallization Cyclic Polymer Melts As Compared to Their Linear Counterparts. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b01570] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Hongyi Xiao
- Department
of Physics, Beijing Normal University, 100875 Beijing, China
- Institute
Theory of Polymers, Leibniz-Institute of Polymer Research Dresden, 01069 Dresden, Germany
| | - Chuanfu Luo
- State
Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, 130022 Changchun, China
| | - Dadong Yan
- Department
of Physics, Beijing Normal University, 100875 Beijing, China
| | - Jens-Uwe Sommer
- Institute
Theory of Polymers, Leibniz-Institute of Polymer Research Dresden, 01069 Dresden, Germany
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22
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Bačová P, Lo Verso F, Arbe A, Colmenero J, Pomposo JA, Moreno AJ. The Role of the Topological Constraints in the Chain Dynamics in All-Polymer Nanocomposites. Macromolecules 2017. [DOI: 10.1021/acs.macromol.6b02340] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Petra Bačová
- Centro de Física
de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain
| | - Federica Lo Verso
- Donostia International
Physics Center (DIPC), Paseo Manuel
de Lardizabal 4, E-20018 San Sebastián, Spain
| | - Arantxa Arbe
- Centro de Física
de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain
| | - Juan Colmenero
- Centro de Física
de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain
- Donostia International
Physics Center (DIPC), Paseo Manuel
de Lardizabal 4, E-20018 San Sebastián, Spain
- Departamento
de Física de Materiales, UPV/EHU, Apartado 1072, E-20080 San Sebastián, Spain
| | - José A. Pomposo
- Centro de Física
de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain
- Departamento
de Física de Materiales, UPV/EHU, Apartado 1072, E-20080 San Sebastián, Spain
- IKERBASQUE - Basque
Foundation for Science, María
Díaz de Haro, E-48013 Bilbao, Spain
| | - Angel J. Moreno
- Centro de Física
de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain
- Donostia International
Physics Center (DIPC), Paseo Manuel
de Lardizabal 4, E-20018 San Sebastián, Spain
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23
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Lee NK, Diddens D, Meyer H, Johner A. Local Chain Segregation and Entanglements in a Confined Polymer Melt. PHYSICAL REVIEW LETTERS 2017; 118:067802. [PMID: 28234517 DOI: 10.1103/physrevlett.118.067802] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2016] [Indexed: 06/06/2023]
Abstract
The reptation mechanism, introduced by de Gennes and Edwards, where a polymer diffuses along a fluffy tube, defined by the constraints imposed by its surroundings, convincingly describes the relaxation of long polymers in concentrated solutions and melts. We propose that the scale for the tube diameter is set by local chain segregation, which we study analytically. We show that the concept of local segregation is especially operational for confined geometries, where segregation extends over mesoscopic domains, drastically reducing binary contacts, and provide an estimate of the entanglement length. Our predictions are quantitatively supported by extensive molecular dynamics simulations on systems consisting of long, entangled chains.
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Affiliation(s)
- Nam-Kyung Lee
- Institute of Fundamental Physics, Department of Physics, Sejong University, Seoul 05006, Korea
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess 67034, Strasbourg cedex 2, France
| | - Diddo Diddens
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess 67034, Strasbourg cedex 2, France
| | - Hendrik Meyer
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess 67034, Strasbourg cedex 2, France
| | - Albert Johner
- Institute of Fundamental Physics, Department of Physics, Sejong University, Seoul 05006, Korea
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess 67034, Strasbourg cedex 2, France
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24
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Ge T, Tzoumanekas C, Anogiannakis SD, Hoy RS, Robbins MO. Entanglements in Glassy Polymer Crazing: Cross-Links or Tubes? Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b02125] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ting Ge
- Department
of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599, United States
| | - Christos Tzoumanekas
- Department
of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, Athens 15780, Greece
| | - Stefanos D. Anogiannakis
- Department
of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, Athens 15780, Greece
| | - Robert S. Hoy
- Department
of Physics, University of South Florida, Tampa, Florida 33620, United States
| | - Mark O. Robbins
- Department
of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, United States
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25
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Sussman DM. Spatial distribution of entanglements in thin free-standing films. Phys Rev E 2016; 94:012503. [PMID: 27575172 DOI: 10.1103/physreve.94.012503] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2016] [Indexed: 11/07/2022]
Abstract
We simulate entangled linear polymers in free-standing thin film geometries where the confining dimension is on the same scale as or smaller than the bulk chain dimensions. We compare both film-averaged and layer-resolved, spatially inhomogeneous measures of the polymer structure and entanglement network with theoretical models. We find that these properties are controlled by the ratio of both chain- and entanglement-strand length scales to the film thickness. While the film-averaged entanglement properties can be accurately predicted, we identify outstanding challenges in understanding the spatially resolved character of the heterogeneities in the entanglement network, particularly when the scale of both the entanglement strand and the chain end-to-end vector is comparable to or smaller than the film thickness.
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Affiliation(s)
- Daniel M Sussman
- Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA
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26
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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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27
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Qin J, Milner ST. Tube Dynamics Works for Randomly Entangled Rings. PHYSICAL REVIEW LETTERS 2016; 116:068307. [PMID: 26919023 DOI: 10.1103/physrevlett.116.068307] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2015] [Indexed: 06/05/2023]
Abstract
The tube model is the cornerstone of molecular theory for polymer rheology. We test its microscopic assumptions by simulating topologically equilibrated ring polymers, whose dynamics is free from end segment relaxation. We show that a closed-form expression derived from the tube model adapted to ring polymers quantitatively predicts the segmental mean squared displacements over the entire range of time scales from local motion to complete equilibration, with a time-independent local friction factor.
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Affiliation(s)
- Jian Qin
- Department of Chemical Engineering, Stanford University, Stanford, California 94305, USA
| | - Scott T Milner
- Department of Chemical Engineering, Pennsylvania State University, State College, Pennsylvania 16802, USA
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28
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Franz C, Lange F, Golitsyn Y, Hartmann-Azanza B, Steinhart M, Krutyeva M, Saalwächter K. Chain Dynamics and Segmental Orientation in Polymer Melts Confined to Nanochannels. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b02309] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Cornelius Franz
- Institut
für Physik − NMR, Martin-Luther-Universität Halle-Wittenberg, Betty-Heimann-Str.
7, D-06120 Halle, Germany
| | - Frank Lange
- Institut
für Physik − NMR, Martin-Luther-Universität Halle-Wittenberg, Betty-Heimann-Str.
7, D-06120 Halle, Germany
| | - Yury Golitsyn
- Institut
für Physik − NMR, Martin-Luther-Universität Halle-Wittenberg, Betty-Heimann-Str.
7, D-06120 Halle, Germany
| | - Brigitte Hartmann-Azanza
- Institut
für Chemie neuer Materialien, Universität Osnabrück, Barbarastr.
7, D-49069 Osnabrück, Germany
| | - Martin Steinhart
- Institut
für Chemie neuer Materialien, Universität Osnabrück, Barbarastr.
7, D-49069 Osnabrück, Germany
| | - Margarita Krutyeva
- Jülich
Centre for Neutron Science (JCNS) and Institute for Complex Systems
(ICS), Forschungszentrum Jülich GmbH, D-52428 Jülich, Germany
| | - Kay Saalwächter
- Institut
für Physik − NMR, Martin-Luther-Universität Halle-Wittenberg, Betty-Heimann-Str.
7, D-06120 Halle, Germany
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29
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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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30
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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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31
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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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32
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Affiliation(s)
- Jing Cao
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Jian Qin
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Scott T. Milner
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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33
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Sussman DM, Tung WS, Winey KI, Schweizer KS, Riggleman RA. Entanglement Reduction and Anisotropic Chain and Primitive Path Conformations in Polymer Melts under Thin Film and Cylindrical Confinement. Macromolecules 2014. [DOI: 10.1021/ma501193f] [Citation(s) in RCA: 77] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Daniel M. Sussman
- Department of Physics and Astronomy, ‡Department of Materials
Science
and Engineering, and §Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
- Departments of Materials Science, Chemistry, and Chemical & Biomolecular Engineering and ⊥Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | - Wei-Shao Tung
- Department of Physics and Astronomy, ‡Department of Materials
Science
and Engineering, and §Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
- Departments of Materials Science, Chemistry, and Chemical & Biomolecular Engineering and ⊥Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | - Karen I. Winey
- Department of Physics and Astronomy, ‡Department of Materials
Science
and Engineering, and §Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
- Departments of Materials Science, Chemistry, and Chemical & Biomolecular Engineering and ⊥Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | - Kenneth S. Schweizer
- Department of Physics and Astronomy, ‡Department of Materials
Science
and Engineering, and §Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
- Departments of Materials Science, Chemistry, and Chemical & Biomolecular Engineering and ⊥Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
| | - Robert A. Riggleman
- Department of Physics and Astronomy, ‡Department of Materials
Science
and Engineering, and §Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
- Departments of Materials Science, Chemistry, and Chemical & Biomolecular Engineering and ⊥Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
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34
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Affiliation(s)
- Jian Qin
- Institute
for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Scott T. Milner
- Department
of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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35
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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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36
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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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37
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Cao J, Qin J, Milner ST. Simulating Constraint Release by Watching a Ring Cross Itself. Macromolecules 2014. [DOI: 10.1021/ma500325z] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jing Cao
- Department
of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Jian Qin
- Department
of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Scott T. Milner
- Department
of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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38
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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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39
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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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40
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Panagiotou E, Kröger M, Millett KC. Writhe and mutual entanglement combine to give the entanglement length. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062604. [PMID: 24483478 DOI: 10.1103/physreve.88.062604] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2013] [Revised: 09/25/2013] [Indexed: 06/03/2023]
Abstract
We propose a method to estimate N(e), the entanglement length, that incorporates both local and global topological characteristics of chains in a melt under equilibrium conditions. This estimate uses the writhe of the chains, the writhe of the primitive paths, and the number of kinks in the chains in a melt. An advantage of this method is that it works for both linear and ring chains, works under all periodic boundary conditions, does not require knowing the contour length of the primitive paths, and does not rely on a smooth set of data. We apply this method to linear finitely extendable nonlinear elastic chains and we observe that our estimates are consistent with those from other studies.
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Affiliation(s)
- E Panagiotou
- Department of Mathematics, University of California, Santa Barbara, California 93106, USA
| | - M Kröger
- Polymer Physics, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland
| | - K C Millett
- Department of Mathematics, University of California, Santa Barbara, California 93106, USA
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41
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Pestryaev EM. Molecular-dynamics study of chain reptation in a gel. POLYMER SCIENCE SERIES A 2013. [DOI: 10.1134/s0965545x13050052] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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42
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Affiliation(s)
- Jian Qin
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania
16802, United States
| | - Scott T. Milner
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania
16802, United States
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43
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Qin J, So J, Milner ST. Tube Diameter of Stretched and Compressed Permanently Entangled Polymers. Macromolecules 2012. [DOI: 10.1021/ma301830w] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jian Qin
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania
16802, United States
| | - Jungseob So
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania
16802, United States
| | - Scott T. Milner
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania
16802, United States
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44
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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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45
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Li Y, Tang S, Abberton BC, Kröger M, Burkhart C, Jiang B, Papakonstantopoulos GJ, Poldneff M, Liu WK. A predictive multiscale computational framework for viscoelastic properties of linear polymers. POLYMER 2012. [DOI: 10.1016/j.polymer.2012.09.055] [Citation(s) in RCA: 74] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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46
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Sussman DM, Schweizer KS. Microscopic Theory of Quiescent and Deformed Topologically Entangled Rod Solutions: General Formulation and Relaxation after Nonlinear Step Strain. Macromolecules 2012. [DOI: 10.1021/ma300006s] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Daniel M. Sussman
- Department
of Physics, ‡Department of Materials Science, and §Frederick Seitz Materials Research
Laboratory, University of Illinois, 1304 W. Green Street, Urbana, Illinois 61801, United States
| | - Kenneth S. Schweizer
- Department
of Physics, ‡Department of Materials Science, and §Frederick Seitz Materials Research
Laboratory, University of Illinois, 1304 W. Green Street, Urbana, Illinois 61801, United States
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