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Phillies GDJ. Simulational Tests of the Rouse Model. Polymers (Basel) 2023; 15:2615. [PMID: 37376261 DOI: 10.3390/polym15122615] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Revised: 05/24/2023] [Accepted: 06/03/2023] [Indexed: 06/29/2023] Open
Abstract
An extensive review of literature simulations of quiescent polymer melts is given, considering results that test aspects of the Rouse model in the melt. We focus on Rouse model predictions for the mean-square amplitudes ⟨(Xp(0))2⟩ and time correlation functions ⟨Xp(0)Xp(t)⟩ of the Rouse mode Xp(t). The simulations conclusively demonstrate that the Rouse model is invalid in polymer melts. In particular, and contrary to the Rouse model, (i) mean-square Rouse mode amplitudes ⟨(Xp(0))2⟩ do not scale as sin-2(pπ/2N), N being the number of beads in the polymer. For small p (say, p≤3) ⟨(Xp(0))2⟩ scales with p as p-2; for larger p, it scales as p-3. (ii) Rouse mode time correlation functions ⟨Xp(t)Xp(0)⟩ do not decay with time as exponentials; they instead decay as stretched exponentials exp(-αtβ). β depends on p, typically with a minimum near N/2 or N/4. (iii) Polymer bead displacements are not described by independent Gaussian random processes. (iv) For p≠q, ⟨Xp(t)Xq(0)⟩ is sometimes non-zero. (v) The response of a polymer coil to a shear flow is a rotation, not the affine deformation predicted by Rouse. We also briefly consider the Kirkwood-Riseman polymer model.
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Arbe A, Alvarez F, Colmenero J. Insight into the Structure and Dynamics of Polymers by Neutron Scattering Combined with Atomistic Molecular Dynamics Simulations. Polymers (Basel) 2020; 12:E3067. [PMID: 33371357 PMCID: PMC7767341 DOI: 10.3390/polym12123067] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2020] [Revised: 12/04/2020] [Accepted: 12/11/2020] [Indexed: 11/23/2022] Open
Abstract
Combining neutron scattering and fully atomistic molecular dynamics simulations allows unraveling structural and dynamical features of polymer melts at different length scales, mainly in the intermolecular and monomeric range. Here we present the methodology developed by us and the results of its application during the last years in a variety of polymers. This methodology is based on two pillars: (i) both techniques cover approximately the same length and time scales and (ii) the classical van Hove formalism allows easily calculating the magnitudes measured by neutron scattering from the simulated atomic trajectories. By direct comparison with experimental results, the simulated cell is validated. Thereafter, the information of the simulations can be exploited, calculating magnitudes that are experimentally inaccessible or extending the parameters range beyond the experimental capabilities. We show how detailed microscopic insight on structural features and dynamical processes of various kinds has been gained in polymeric systems with different degrees of complexity, and how intriguing questions as the collective behavior at intermediate length scales have been faced.
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Affiliation(s)
- 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; (A.A.); (F.A.)
| | - Fernando Alvarez
- Centro de Física de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain; (A.A.); (F.A.)
- Departamento de Polímeros y Materiales Avanzados, Física, Química y Tecnología (UPV/EHU), Apartado 1072, E-20080 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; (A.A.); (F.A.)
- Departamento de Polímeros y Materiales Avanzados, Física, Química y Tecnología (UPV/EHU), Apartado 1072, E-20080 San Sebastián, Spain
- Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, E-20018 San Sebastián, Spain
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Mohorič A, Lahajnar G, Stepišnik J. Diffusion Spectrum of Polymer Melt Measured by Varying Magnetic Field Gradient Pulse Width in PGSE NMR. Molecules 2020; 25:molecules25245813. [PMID: 33317155 PMCID: PMC7762995 DOI: 10.3390/molecules25245813] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/03/2020] [Revised: 12/04/2020] [Accepted: 12/07/2020] [Indexed: 12/03/2022]
Abstract
The translational motion of polymers is a complex process and has a big impact on polymer structure and chemical reactivity. The process can be described by the segment velocity autocorrelation function or its diffusion spectrum, which exhibit several characteristic features depending on the observational time scale—from the Brownian delta function on a large time scale, to complex details in a very short range. Several stepwise, more-complex models of translational dynamics thus exist—from the Rouse regime over reptation motion to a combination of reptation and tube-Rouse motion. Accordingly, different methods of measurement are applicable, from neutron scattering for very short times to optical methods for very long times. In the intermediate regime, nuclear magnetic resonance (NMR) is applicable—for microseconds, relaxometry, and for milliseconds, diffusometry. We used a variation of the established diffusometric method of pulsed gradient spin-echo NMR to measure the diffusion spectrum of a linear polyethylene melt by varying the gradient pulse width. We were able to determine the characteristic relaxation time of the first mode of the tube-Rouse motion. This result is a deviation from a Rouse model of polymer chain displacement at the crossover from a square-root to linear time dependence, indicating a new long-term diffusion regime in which the dynamics of the tube are also described by the Rouse model.
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Affiliation(s)
- Aleš Mohorič
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia;
- Institute Josef Stefan, 1000 Ljubljana, Slovenia;
- Correspondence: ; Tel.: +386-1-4766500
| | | | - Janez Stepišnik
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia;
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Miwatani R, Takahashi KZ, Arai N. Performance of Coarse Graining in Estimating Polymer Properties: Comparison with the Atomistic Model. Polymers (Basel) 2020; 12:polym12020382. [PMID: 32046337 PMCID: PMC7077424 DOI: 10.3390/polym12020382] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2019] [Revised: 01/20/2020] [Accepted: 01/26/2020] [Indexed: 01/23/2023] Open
Abstract
Combining atomistic and coarse-grained (CG) models is a promising approach for quantitative prediction of polymer properties. However, the gaps between the length and time scales of atomistic and CG models still need to be bridged. Here, the scale gaps of the atomistic model of polyethylene melts, the bead–spring Kremer–Grest model, and dissipative particle dynamics with the slip-spring model were investigated. A single set of spatial and temporal scaling factors was determined between the atomistic model and each CG model. The results of the CG models were rescaled using the set of scaling factors and compared with those of the atomistic model. For each polymer property, a threshold value indicating the onset of static or dynamic universality of polymers was obtained. The scaling factors also revealed the computational efficiency of each CG model with respect to the atomistic model. The performance of the CG models of polymers was systematically evaluated in terms of both the accuracy and computational efficiency.
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Affiliation(s)
- Ryota Miwatani
- Department of Mechanical Engineering, Kindai University, 3-4-1 Kowakae, Higashiosaka, Osaka 577-8522, Japan;
| | - Kazuaki Z. Takahashi
- Research Center for Computational Design of Advanced Functional Materials, National Institute of Advanced Industrial Science and Technology (AIST), Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
- Correspondence: ; Tel.: +81-29-861-2972; Fax: +81-29-861-5375
| | - Noriyoshi Arai
- Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Yokohama, Kanagawa 223-8522, Japan;
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Liu L, den Otter WK, Briels WJ. Coarse-Grained Simulations of Three-Armed Star Polymer Melts and Comparison with Linear Chains. J Phys Chem B 2018; 122:10210-10218. [DOI: 10.1021/acs.jpcb.8b03104] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Li Liu
- Department of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China
| | | | - Wim J. Briels
- Forschungszentrum Jülich, ICS 3, D-52425 Jülich, Germany
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Takahashi KZ, Nishimura R, Yamato N, Yasuoka K, Masubuchi Y. Onset of static and dynamic universality among molecular models of polymers. Sci Rep 2017; 7:12379. [PMID: 28959052 PMCID: PMC5620073 DOI: 10.1038/s41598-017-08501-0] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2017] [Accepted: 07/12/2017] [Indexed: 12/03/2022] Open
Abstract
A quantitatively accurate prediction of properties for entangled polymers is a long-standing challenge that must be addressed to enable efficient development of these materials. The complex nature of polymers is the fundamental origin of this challenge. Specifically, the chemistry, structure, and dynamics at the atomistic scale affect properties at the meso and macro scales. Therefore, quantitative predictions must start from atomistic molecular dynamics (AMD) simulations. Combined use of atomistic and coarse-grained (CG) models is a promising approach to estimate long-timescale behavior of entangled polymers. However, a systematic coarse-graining is still to be done for bridging the gap of length and time scales while retaining atomistic characteristics. Here we examine the gaps among models, using a generic mapping scheme based on power laws that are closely related to universality in polymer structure and dynamics. The scheme reveals the characteristic length and time for the onset of universality between the vastly different scales of an atomistic model of polyethylene and the bead-spring Kremer-Grest (KG) model. The mapping between CG model of polystyrene and the KG model demonstrates the fast onset of universality, and polymer dynamics up to the subsecond time scale are observed. Thus, quantitatively traceable timescales of polymer MD simulations can be significantly increased.
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Affiliation(s)
- Kazuaki Z Takahashi
- Multi-scale Soft-matter Simulation Team, Research Center for Computational Design of Advanced Functional Materials, National Institute of Advanced Industrial Science and Technology (AIST), Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan.
- Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan.
| | - Ryuto Nishimura
- Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan
| | - Nobuyoshi Yamato
- Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan
| | - Kenji Yasuoka
- Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan
| | - Yuichi Masubuchi
- National Composite Center, Nagoya University, Furocho, Chikusa, Nagoya, 464-8630, Japan
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Gooneie A, Schuschnigg S, Holzer C. A Review of Multiscale Computational Methods in Polymeric Materials. Polymers (Basel) 2017; 9:E16. [PMID: 30970697 PMCID: PMC6432151 DOI: 10.3390/polym9010016] [Citation(s) in RCA: 113] [Impact Index Per Article: 16.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2016] [Revised: 12/07/2016] [Accepted: 12/22/2016] [Indexed: 11/17/2022] Open
Abstract
Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.
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Affiliation(s)
- Ali Gooneie
- Chair of Polymer Processing, Montanuniversitaet Leoben, Otto Gloeckel-Strasse 2, 8700 Leoben, Austria.
| | - Stephan Schuschnigg
- Chair of Polymer Processing, Montanuniversitaet Leoben, Otto Gloeckel-Strasse 2, 8700 Leoben, Austria.
| | - Clemens Holzer
- Chair of Polymer Processing, Montanuniversitaet Leoben, Otto Gloeckel-Strasse 2, 8700 Leoben, Austria.
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Gooneie A, Schuschnigg S, Holzer C. Dissipative Particle Dynamics Models of Orientation of Weakly-Interacting Anisometric Silicate Particles in Polymer Melts under Shear Flow: Comparison with the Standard Orientation Models. MACROMOL THEOR SIMUL 2016. [DOI: 10.1002/mats.201500086] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Ali Gooneie
- Chair of Polymer Processing; Department of Polymer Engineering and Science; Montanuniversität Leoben; Otto Glöckel-Straße 2 8700 Leoben Austria
| | - Stephan Schuschnigg
- Chair of Polymer Processing; Department of Polymer Engineering and Science; Montanuniversität Leoben; Otto Glöckel-Straße 2 8700 Leoben Austria
| | - Clemens Holzer
- Chair of Polymer Processing; Department of Polymer Engineering and Science; Montanuniversität Leoben; Otto Glöckel-Straße 2 8700 Leoben Austria
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Gooneie A, Schuschnigg S, Holzer C. Coupled Orientation and Stretching of Chains in Mesoscale Models of Polydisperse Linear Polymers in Startup of Steady Shear Flow Simulations. MACROMOL THEOR SIMUL 2016. [DOI: 10.1002/mats.201500060] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Ali Gooneie
- Department of Polymer Engineering and Science; Montanuniversität Leoben; Otto Glöckel-Straße 2 8700 Leoben Austria
| | - Stephan Schuschnigg
- Department of Polymer Engineering and Science; Montanuniversität Leoben; Otto Glöckel-Straße 2 8700 Leoben Austria
| | - Clemens Holzer
- Department of Polymer Engineering and Science; Montanuniversität Leoben; Otto Glöckel-Straße 2 8700 Leoben Austria
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Stepišnik J, Lahajnar G, Zupančič I, Mohorič A. Study of translational dynamics in molten polymer by variation of gradient pulse-width of PGSE. J Magn Reson 2013; 236:41-46. [PMID: 24051201 DOI: 10.1016/j.jmr.2013.08.003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2013] [Revised: 08/06/2013] [Accepted: 08/11/2013] [Indexed: 06/02/2023]
Abstract
Pulsed gradient spin echo is a method of measuring molecular translation. Changing Δ makes it sensitive to diffusion spectrum. Spin translation effects the buildup of phase structure during the application of gradient pulses as well. The time scale of the self-diffusion measurement shortens if this is taken into account. The method of diffusion spectrometry with variable δ is also less sensitive to artifacts caused by spin relaxation and internal gradient fields. Here the method is demonstrated in the case of diffusion spectrometry of molten polyethylene. The results confirm a model of constraint release in a system of entangled polymer chains as a sort of tube Rouse motion.
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Affiliation(s)
- Janez Stepišnik
- University of Ljubljana, Faculty of Mathematics and Physics, Physics Department, Jadranska 19, 1000 Ljubljana, Slovenia; Institute Jožef Stefan, Jamova 39, 1000 Ljubljana, Slovenia.
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11
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Colmenero J. A Generalized Rouse Incoherent Scattering Function for Chain Dynamics of Unentangled Polymers in Dynamically Asymmetric Blends. Macromolecules 2013. [DOI: 10.1021/ma400309c] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- J. Colmenero
- Centro de Física de Materiales (CSIC-UPV/EHU) and Donostia International Physics Center, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain
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Padding JT, Briels WJ. Systematic coarse-graining of the dynamics of entangled polymer melts: the road from chemistry to rheology. J Phys Condens Matter 2011; 23:233101. [PMID: 21613700 DOI: 10.1088/0953-8984/23/23/233101] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, thus automatically preventing bond crossing. This also implies an upper limit on the number of atoms that can be lumped together (up to five backbone carbon atoms) and therefore on the longest chain lengths that can be studied. To reach a higher degree of coarse-graining, in CGSD many more atoms are lumped together (more than ten backbone carbon atoms), leading to relatively soft beads. In that case friction and stochastic forces dominate the interactions, and action must be undertaken to prevent bond crossing. We also review alternative methods that make use of the tube model of polymer dynamics, by obtaining the entanglement characteristics through a primitive path analysis and by simulation of a primitive chain network. We finally review super-coarse-grained methods in which an entire polymer is represented by a single particle, and comment on ways to include memory effects and transient forces.
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Affiliation(s)
- J T Padding
- Institut de la Matière Condensée et des Nanosciences, Université Catholique de Louvain, Croix du Sud 1, B-1348 Louvain-la-Neuve, Belgium.
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