1
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Entanglement on Nucleation Barrier of Polymer Crystal. CHINESE JOURNAL OF POLYMER SCIENCE 2022. [DOI: 10.1007/s10118-022-2780-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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2
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Wu Z, Müller-Plathe F. Slip-Spring Hybrid Particle-Field Molecular Dynamics for Coarse-Graining Branched Polymer Melts: Polystyrene Melts as an Example. J Chem Theory Comput 2022; 18:3814-3828. [PMID: 35617016 DOI: 10.1021/acs.jctc.2c00107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The topology of chains significantly modifies the dynamical properties of polymer melts. Here, we extend a recently developed efficient simulation method, namely the slip-spring hybrid particle-field (SS-hPF) model, to study the structural and dynamical properties of branched polymer melts over large spatial-temporal scales. In the coarse-grained SS-hPF simulation of polymers, the bonded potentials are derived by iterative Boltzmann inversion from the underlying fine-grained model. The nonbonded potentials are computed from a density functional field instead of pairwise interactions used in standard molecular dynamics simulations, which increases the computational efficiency by a factor of 10-20. The entangled dynamics is lost due to the soft-core nature of density functional field interactions. It is recovered by a multichain slip-spring model that is rigorously parametrized from existing experimental or simulation data. To quantitatively predict the relaxation and diffusion of branched polymers, which are dominated by arm retraction rather than chain reptation, the slip-spring algorithm is augmented to improve the polymer dynamics near the branch point. Multiple dynamical observables, e.g., diffusion coefficients, arm relaxations, and tube survival probabilities, are characterized in an example coarse-grained model of symmetric and asymmetric star-shaped polystyrene melts. Consistent dynamical behaviors are identified and compared with theoretical predictions. With a single rescaling factor, the prediction of diffusion coefficients agrees well with the available experimental measurements. In this work, an efficient approach is provided to build chemistry-specific coarse-grained models for predicting the dynamics of branched polymers.
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Affiliation(s)
- Zhenghao Wu
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Strasse 8, 64287 Darmstadt, Germany
| | - Florian Müller-Plathe
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Strasse 8, 64287 Darmstadt, Germany
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3
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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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4
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Shanbhag S. How Many Monodisperse Fractions are Required to Discretize Polydisperse Polymers? MACROMOL THEOR SIMUL 2020. [DOI: 10.1002/mats.202000020] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Sachin Shanbhag
- Department of Scientific Computing Florida State University Tallahassee FL 32306 USA
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5
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Shanbhag S. Mathematical foundations of an ultra coarse-grained slip link model. J Chem Phys 2019; 151:044903. [PMID: 31370523 DOI: 10.1063/1.5111032] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The master equation underlying ecoSLM, an ultra-coarse-grained slip link model, is presented. In the absence of constraint release, the equilibrium and dynamic properties of the discrete master equation for large chains are found to be virtually identical to the continuous Fokker-Planck equation for Brownian particles diffusing in a potential. A single-chain microscopic model with repulsion between adjacent slip links is described. It is approximately consistent with the quadratic fluctuation potential used in ecoSLM. Mapping ecoSLM with fine-grained slip link models or experiments requires specification of an effective friction as a function of molecular weight. Methods to accomplish this are discussed. Collectively, the mathematical framework described provides an interface for fine-grained slip link models to potentially use ecoSLM for extreme coarse-graining.
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Affiliation(s)
- Sachin Shanbhag
- Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306, USA
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6
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Affiliation(s)
- Sachin Shanbhag
- Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306-4120, United States
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7
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Shanbhag S. pyReSpect: A Computer Program to Extract Discrete and Continuous Spectra from Stress Relaxation Experiments. MACROMOL THEOR SIMUL 2019. [DOI: 10.1002/mats.201900005] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Sachin Shanbhag
- Department of Scientific Computing Florida State University Tallahassee FL 32306 USA
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8
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Shahid T, Clasen C, Oosterlinck F, van Ruymbeke E. Diluting Entangled Polymers Affects Transient Hardening but Not Their Steady Elongational Viscosity. Macromolecules 2019. [DOI: 10.1021/acs.macromol.8b02701] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Taisir Shahid
- Bio and Soft Matter, Institute on Condensed Matter and Nano-science, Université catholique de Louvain, Louvain-la-Neuve, Belgium
- Department of Chemical Engineering, KU Leuven, Celestijnenlaan 200f, 3001 Leuven, Belgium
| | - Christian Clasen
- Department of Chemical Engineering, KU Leuven, Celestijnenlaan 200f, 3001 Leuven, Belgium
| | - Filip Oosterlinck
- DSM Materials
Science Center, P.O. Box 18, NL-6160 MD Geleen, The Netherlands
| | - Evelyne van Ruymbeke
- Bio and Soft Matter, Institute on Condensed Matter and Nano-science, Université catholique de Louvain, Louvain-la-Neuve, Belgium
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9
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Sato T, Harada K, Taniguchi T. Multiscale Simulations of Flows of a Well-Entangled Polymer Melt in a Contraction–Expansion Channel. Macromolecules 2019. [DOI: 10.1021/acs.macromol.8b00649] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- Takeshi Sato
- Department of Chemical Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan
| | - Kohei Harada
- Department of Chemical Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan
| | - Takashi Taniguchi
- Department of Chemical Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan
- Department of Physics, Tohoku University, Sendai, Miyagi 980-8578, Japan
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10
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Affiliation(s)
- Yuichi Masubuchi
- Department of Materials Physics, Nagoya University, Nagoya, Japan
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11
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Shahid T, Huang Q, Oosterlinck F, Clasen C, van Ruymbeke E. Dynamic dilution exponent in monodisperse entangled polymer solutions. SOFT MATTER 2016; 13:269-282. [PMID: 27546279 DOI: 10.1039/c6sm01083k] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We study and model the linear viscoelastic properties of several entangled semi-dilute and concentrated solutions of linear chains of different molar masses and at different concentrations dissolved in their oligomers. We discuss the dilution effect of the oligomers on the entangled long chains. In particular, we investigate the influence of both concentration and molar mass on the value of the effective dynamic dilution exponent determined from the level of the storage plateau at low and intermediate frequencies. We show that the experimental results can be quantitatively explained by considering the tension re-equilibration process along the chains, in agreement with van Ruymbeke et al. (Macromol., 2014), i.e. by considering that the real dilution exponent α is always equal to 1, while larger values of the dilution exponent (1 < α < 1.3) found experimentally are attributed to the enhanced relaxation of the long chain extremities. Then we discuss the influence of the polymer concentration on the terminal relaxation time of the solutions and how this can be modelled by the enhanced contour length fluctuation process (CR-CLF). We point out that this larger dilution effect is not only a function of concentration but also depends on the molar mass of the chains. While the proposed approach successfully explains the viscoelastic properties of a large number of semi-dilute solutions of polymers in their own oligomers, important discrepancies are found for semi-dilute entangled polymers in small-molecule theta or good solvents. Possible explanations for the differences between these sample sets are proposed, based on the comparison of their viscoelastic behavior.
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Affiliation(s)
- T Shahid
- Department of Chemical Engineering, KU Leuven, 3001 Heverlee, Belgium and Bio and Soft Matter, Institute of Condensed Matter and Nano-science (IMCN), Universite Catholique de Louvain, 1348 Louvain-La-Neuve, Belgium.
| | - Q Huang
- Department of Chemical and Biochemical Engineering, The Danish Polymer Centre, 2800 Kgs. Lyngby, Denmark
| | - F Oosterlinck
- Material Science Center, DSM Research Geleen, The Netherlands
| | - C Clasen
- Department of Chemical Engineering, KU Leuven, 3001 Heverlee, Belgium
| | - E van Ruymbeke
- Bio and Soft Matter, Institute of Condensed Matter and Nano-science (IMCN), Universite Catholique de Louvain, 1348 Louvain-La-Neuve, Belgium.
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12
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Stadler FJ, Chun YS, Han JH, Lee E, Park SH, Yang CB, Choi C. Deriving comprehensive structural information on long-chain branched polyethylenes from analysis of thermo-rheological complexity. POLYMER 2016. [DOI: 10.1016/j.polymer.2016.07.084] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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13
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Affiliation(s)
- Vaidyanathan Sethuraman
- Department
of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, United States
| | - Dylan Kipp
- Department
of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, United States
| | - Venkat Ganesan
- Department
of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, United States
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14
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Zhao Y, Su B, Zhong L, Chen F, Fu Q. Largely Improved Mechanical Properties of a Poly(styrene-b-isoprene-b-styrene) Thermoplastic Elastomer Prepared under Dynamic-Packing Injection Molding. Ind Eng Chem Res 2014. [DOI: 10.1021/ie5022514] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yongsheng Zhao
- State Key Laboratory of Polymer Materials Engineering, College of Polymer Science & Engineering, Sichuan University, Chengdu 610065, People’s Republic of China
| | - Bin Su
- State Key Laboratory of Polymer Materials Engineering, College of Polymer Science & Engineering, Sichuan University, Chengdu 610065, People’s Republic of China
| | - Licai Zhong
- Department of Electrical and Mechanical Engineering, Lanzhou Resources & Environment Voc-Tech College, Lanzhou 730021, People’s Republic of China
| | - Feng Chen
- State Key Laboratory of Polymer Materials Engineering, College of Polymer Science & Engineering, Sichuan University, Chengdu 610065, People’s Republic of China
| | - Qiang Fu
- State Key Laboratory of Polymer Materials Engineering, College of Polymer Science & Engineering, Sichuan University, Chengdu 610065, People’s Republic of China
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15
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van Ruymbeke E, Lee H, Chang T, Nikopoulou A, Hadjichristidis N, Snijkers F, Vlassopoulos D. Molecular rheology of branched polymers: decoding and exploring the role of architectural dispersity through a synergy of anionic synthesis, interaction chromatography, rheometry and modeling. SOFT MATTER 2014; 10:4762-4777. [PMID: 24705637 DOI: 10.1039/c4sm00105b] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
An emerging challenge in polymer physics is the quantitative understanding of the influence of a macromolecular architecture (i.e., branching) on the rheological response of entangled complex polymers. Recent investigations of the rheology of well-defined architecturally complex polymers have determined the composition in the molecular structure and identified the role of side-products in the measured samples. The combination of different characterization techniques, experimental and/or theoretical, represents the current state-of-the-art. Here we review this interdisciplinary approach to molecular rheology of complex polymers, and show the importance of confronting these different tools for ensuring an accurate characterization of a given polymeric sample. We use statistical tools in order to relate the information available from the synthesis protocols of a sample and its experimental molar mass distribution (typically obtained from size exclusion chromatography), and hence obtain precise information about its structural composition, i.e. enhance the existing sensitivity limit. We critically discuss the use of linear rheology as a reliable quantitative characterization tool, along with the recently developed temperature gradient interaction chromatography. The latter, which has emerged as an indispensable characterization tool for branched architectures, offers unprecedented sensitivity in detecting the presence of different molecular structures in a sample. Combining these techniques is imperative in order to quantify the molecular composition of a polymer and its consequences on the macroscopic properties. We validate this approach by means of a new model asymmetric comb polymer which was synthesized anionically. It was thoroughly characterized and its rheology was carefully analyzed. The main result is that the rheological signal reveals fine molecular details, which must be taken into account to fully elucidate the viscoelastic response of entangled branched polymers. It is important to appreciate that, even optimal model systems, i.e., those synthesized with high-vacuum anionic methods, need thorough characterization via a combination of techniques. Besides helping to improve synthetic techniques, this methodology will be significant in fine-tuning mesoscopic tube-based models and addressing outstanding issues such as the quantitative description of the constraint release mechanism.
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Affiliation(s)
- E van Ruymbeke
- Bio and Soft Matter, Institute on Condensed Matter and Nano-science, Université catholique de Louvain, Louvain-la-Neuve 1348, Belgium.
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16
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17
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Bačová P, Lentzakis H, Read DJ, Moreno AJ, Vlassopoulos D, Das C. Branch-Point Motion in Architecturally Complex Polymers: Estimation of Hopping Parameters from Computer Simulations and Experiments. Macromolecules 2014. [DOI: 10.1021/ma5003936] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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
| | - Helen Lentzakis
- Institute of Electronic Structure & Laser, Foundation for Research and Technology Hellas (FORTH), Heraklion, Crete 71110, Greece
- Department
of Materials Science and Technology, Univerisity of Crete, Heraklion, Crete 71300, Greece
| | - Daniel J. Read
- Department
of Applied Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - 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, Paseo Manuel de Lardizabal 4, E-20018 San Sebastián, Spain
| | - Dimitris Vlassopoulos
- Institute of Electronic Structure & Laser, Foundation for Research and Technology Hellas (FORTH), Heraklion, Crete 71110, Greece
- Department
of Materials Science and Technology, Univerisity of Crete, Heraklion, Crete 71300, Greece
| | - Chinmay Das
- School of
Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
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18
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Milchev A, Müller M, Klushin L. Arm Retraction Dynamics and Bistability of a Three-Arm Star Polymer in a Nanopore. Macromolecules 2014. [DOI: 10.1021/ma500053n] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- A. Milchev
- Institute
for Physical Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
- Institut für Theoretische Physik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - M. Müller
- Institut für Theoretische Physik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - L. Klushin
- Department
of Physics, American University of Beirut, Beirut, Lebanon
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19
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Abstract
The extreme sensitivity of rheology to the microstructure of polymer melts has prompted the development of “analytical rheology,” which seeks inferring the structure and composition of an unknown sample based on rheological measurements. Typically, this involves the inversion of a model, which may be mathematical, computational, or completely empirical. Despite the imperfect state of existing models, analytical rheology remains a practically useful enterprise. I review its successes and failures in inferring the molecular weight distribution of linear polymers and the branching content in branched polymers.
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Affiliation(s)
- Sachin Shanbhag
- Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA
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20
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Howard MP, Milner ST. Numerical simulation methods for the Rouse model in flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:051804. [PMID: 22181436 DOI: 10.1103/physreve.84.051804] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2011] [Revised: 11/03/2011] [Indexed: 05/31/2023]
Abstract
Simulation of the Rouse model in flow underlies a great variety of numerical investigations of polymer dynamics, in both entangled melts and solutions and in dilute solution. Typically a simple explicit stochastic Euler method is used to evolve the Rouse model. Here we compare this approach to an operator splitting method, which splits the evolution operator into stochastic linear and deterministic nonlinear parts and takes advantage of an analytical solution for the linear Rouse model in terms of the noise history. We show that this splitting method has second-order weak convergence, whereas the Euler method has only first-order weak convergence. Furthermore, the splitting method is unconditionally stable, in contrast to the limited stability range of the Euler method. Similar splitting methods are applicable to a broad class of problems in stochastic dynamics in which noise competes with ordering and flow to determine steady-state order parameter structures.
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Affiliation(s)
- Michael P Howard
- Department of Chemical Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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21
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Padding JT, Briels WJ. Systematic coarse-graining of the dynamics of entangled polymer melts: the road from chemistry to rheology. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:233101. [PMID: 21613700 DOI: 10.1088/0953-8984/23/23/233101] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, thus automatically preventing bond crossing. This also implies an upper limit on the number of atoms that can be lumped together (up to five backbone carbon atoms) and therefore on the longest chain lengths that can be studied. To reach a higher degree of coarse-graining, in CGSD many more atoms are lumped together (more than ten backbone carbon atoms), leading to relatively soft beads. In that case friction and stochastic forces dominate the interactions, and action must be undertaken to prevent bond crossing. We also review alternative methods that make use of the tube model of polymer dynamics, by obtaining the entanglement characteristics through a primitive path analysis and by simulation of a primitive chain network. We finally review super-coarse-grained methods in which an entire polymer is represented by a single particle, and comment on ways to include memory effects and transient forces.
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Affiliation(s)
- J T Padding
- Institut de la Matière Condensée et des Nanosciences, Université Catholique de Louvain, Croix du Sud 1, B-1348 Louvain-la-Neuve, Belgium.
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22
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Masubuchi Y, Yaoita T, Matsumiya Y, Watanabe H. Primitive chain network simulations for asymmetric star polymers. J Chem Phys 2011; 134:194905. [PMID: 21599086 DOI: 10.1063/1.3590276] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yuichi Masubuchi
- Institute for Chemical Research, Kyoto University, Gokasyo, Uji, Kyoto 611-0011, Japan.
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23
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Tzoumanekas C, Lahmar F, Rousseau B, Theodorou DN. Onset of Entanglements Revisited. Topological Analysis. Macromolecules 2009. [DOI: 10.1021/ma901131c] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- C. Tzoumanekas
- National Technical University of Athens, School of Chemical Engineering, Zografou Campus, GR-15780 Athens, Greece
- Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands
| | - F. Lahmar
- Laboratoire de Chimie Physique, Université Paris-Sud 11, UMR 8000 CNRS, Orsay, France
| | - B. Rousseau
- Laboratoire de Chimie Physique, Université Paris-Sud 11, UMR 8000 CNRS, Orsay, France
| | - D. N. Theodorou
- National Technical University of Athens, School of Chemical Engineering, Zografou Campus, GR-15780 Athens, Greece
- Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands
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24
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Shanbhag S, Park SJ, Zhou Q, Larson RG. Implications of microscopic simulations of polymer melts for mean-field tube theories. Mol Phys 2007. [DOI: 10.1080/00268970601143333] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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25
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Inkson NJ, Graham RS, McLeish TCB, Groves DJ, Fernyhough CM. Viscoelasticity of Monodisperse Comb Polymer Melts. Macromolecules 2006. [DOI: 10.1021/ma060018f] [Citation(s) in RCA: 97] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- N. J. Inkson
- School of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom; Interdisciplinary Research Centre in Polymer Science and Technology, School of Physics and Astronomy, The University of Leeds, Leeds, LS2 9JT, United Kingdom; and Department of Chemistry, University of Sheffield, Sheffield S3 7HF, UK
| | - R. S. Graham
- School of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom; Interdisciplinary Research Centre in Polymer Science and Technology, School of Physics and Astronomy, The University of Leeds, Leeds, LS2 9JT, United Kingdom; and Department of Chemistry, University of Sheffield, Sheffield S3 7HF, UK
| | - T. C. B. McLeish
- School of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom; Interdisciplinary Research Centre in Polymer Science and Technology, School of Physics and Astronomy, The University of Leeds, Leeds, LS2 9JT, United Kingdom; and Department of Chemistry, University of Sheffield, Sheffield S3 7HF, UK
| | - D. J. Groves
- School of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom; Interdisciplinary Research Centre in Polymer Science and Technology, School of Physics and Astronomy, The University of Leeds, Leeds, LS2 9JT, United Kingdom; and Department of Chemistry, University of Sheffield, Sheffield S3 7HF, UK
| | - C. M. Fernyhough
- School of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom; Interdisciplinary Research Centre in Polymer Science and Technology, School of Physics and Astronomy, The University of Leeds, Leeds, LS2 9JT, United Kingdom; and Department of Chemistry, University of Sheffield, Sheffield S3 7HF, UK
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