Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models
We present a method to map the full equilibrium distribution of the primitive-path (PP) length, obtained from multi-chain simulations of polymer melts, onto a single-chain mean-field ‘target’ model. Most previous works used the Doi–Edwards tube model as a target. However, the average number of monom...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2014-01-01
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| Series: | New Journal of Physics |
| Online Access: | https://doi.org/10.1088/1367-2630/16/1/015027 |
| _version_ | 1797751511100424192 |
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| author | Rudi J A Steenbakkers Christos Tzoumanekas Ying Li Wing Kam Liu Martin Kröger Jay D Schieber |
| author_facet | Rudi J A Steenbakkers Christos Tzoumanekas Ying Li Wing Kam Liu Martin Kröger Jay D Schieber |
| author_sort | Rudi J A Steenbakkers |
| collection | DOAJ |
| description | We present a method to map the full equilibrium distribution of the primitive-path (PP) length, obtained from multi-chain simulations of polymer melts, onto a single-chain mean-field ‘target’ model. Most previous works used the Doi–Edwards tube model as a target. However, the average number of monomers per PP segment, obtained from multi-chain PP networks, has consistently shown a discrepancy of a factor of two with respect to tube-model estimates. Part of the problem is that the tube model neglects fluctuations in the lengths of PP segments, the number of entanglements per chain and the distribution of monomers among PP segments, while all these fluctuations are observed in multi-chain simulations. Here we use a recently proposed slip-link model, which includes fluctuations in all these variables as well as in the spatial positions of the entanglements. This turns out to be essential to obtain qualitative and quantitative agreement with the equilibrium PP-length distribution obtained from multi-chain simulations. By fitting this distribution, we are able to determine two of the three parameters of the model, which govern its equilibrium properties. This mapping is executed for four different linear polymers and for different molecular weights. The two parameters are found to depend on chemistry, but not on molecular weight. The model predicts a constant plateau modulus minus a correction inversely proportional to molecular weight. The value for well-entangled chains, with the parameters determined ab initio , lies in the range of experimental data for the materials investigated. |
| first_indexed | 2024-03-12T16:50:34Z |
| format | Article |
| id | doaj.art-5b4469808a1f48ec98cd491b27af4c95 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:50:34Z |
| publishDate | 2014-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-5b4469808a1f48ec98cd491b27af4c952023-08-08T11:21:42ZengIOP PublishingNew Journal of Physics1367-26302014-01-0116101502710.1088/1367-2630/16/1/015027Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field modelsRudi J A Steenbakkers0Christos Tzoumanekas1Ying Li2Wing Kam Liu3Martin Kröger4Jay D Schieber5https://orcid.org/0000-0002-9644-5236Department of Chemical and Biological Engineering, Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology , 3440 South Dearborn Street, Chicago, IL 60616, USASchool of Chemical Engineering, National Technical University of Athens , GR-15780 Athens, Greece; Dutch Polymer Institute , PO Box 902, 5600-AX Eindhoven, The NetherlandsDepartment of Mechanical Engineering, Northwestern University , 2145 Sheridan Road, Evanston, IL 60208, USADepartment of Mechanical Engineering, Northwestern University , 2145 Sheridan Road, Evanston, IL 60208, USADepartment of Materials, Polymer Physics, ETH Zürich, CH-8093 Zürich, SwitzerlandDepartment of Chemical and Biological Engineering, Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology , 3440 South Dearborn Street, Chicago, IL 60616, USA; Department of Physics, Illinois Institute of Technology , 3101 South Dearborn Street, Chicago, IL 60616, USAWe present a method to map the full equilibrium distribution of the primitive-path (PP) length, obtained from multi-chain simulations of polymer melts, onto a single-chain mean-field ‘target’ model. Most previous works used the Doi–Edwards tube model as a target. However, the average number of monomers per PP segment, obtained from multi-chain PP networks, has consistently shown a discrepancy of a factor of two with respect to tube-model estimates. Part of the problem is that the tube model neglects fluctuations in the lengths of PP segments, the number of entanglements per chain and the distribution of monomers among PP segments, while all these fluctuations are observed in multi-chain simulations. Here we use a recently proposed slip-link model, which includes fluctuations in all these variables as well as in the spatial positions of the entanglements. This turns out to be essential to obtain qualitative and quantitative agreement with the equilibrium PP-length distribution obtained from multi-chain simulations. By fitting this distribution, we are able to determine two of the three parameters of the model, which govern its equilibrium properties. This mapping is executed for four different linear polymers and for different molecular weights. The two parameters are found to depend on chemistry, but not on molecular weight. The model predicts a constant plateau modulus minus a correction inversely proportional to molecular weight. The value for well-entangled chains, with the parameters determined ab initio , lies in the range of experimental data for the materials investigated.https://doi.org/10.1088/1367-2630/16/1/015027 |
| spellingShingle | Rudi J A Steenbakkers Christos Tzoumanekas Ying Li Wing Kam Liu Martin Kröger Jay D Schieber Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models New Journal of Physics |
| title | Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models |
| title_full | Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models |
| title_fullStr | Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models |
| title_full_unstemmed | Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models |
| title_short | Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models |
| title_sort | primitive path statistics of entangled polymers mapping multi chain simulations onto single chain mean field models |
| url | https://doi.org/10.1088/1367-2630/16/1/015027 |
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