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The statistical mechanics of polymerized material
Open accessAbstract
It is argued that a solid consisting of fully entangled long chain molecules will show elastic properties similar to those of cross linked, i.e. vulcanized material, provided that elastic moduli are studied in periods short compared with creep times. An appropriate formula for the free energy is deduced, and calculated for a model in which each chain is confined to an environment formed by the others. Under deformation this environment changes and the elastic energy can be deduced. If 1 , 2 , 3 are the principal strains, that part of the free energy due to the polymer entanglements is shown to be Δ F = - B κ T ( 1 2 + 2 2 + 3 2 ) L (σ l/m ) 1/2 for small strains, where B is a numerical constant, L is the total length of polymer present, σ the density of polymer, and l, m the effective length and mass of one of the submolecules from which the polymer is made. An expression is also given for the case of a strain of arbitrary size.
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Cites
The Physics of Rubber Elasticity
Treloar, L. R. G., & Montgomery, D. J. (1959) · Physics Today · doi:10.1063/1.3060678 · Cited by 3,787
Statistical mechanics with topological constraints: I
Edwards, S. F. (1967) · Proceedings of the Physical Society · doi:10.1088/0370-1328/91/3/301 · Cited by 454
Self-citation
Cited by
Dynamics of entangled linear polymer melts: A molecular-dynamics simulation
Kremer, K., & Grest, G. S. (1990) · The Journal of Chemical Physics · doi:10.1063/1.458541 · Cited by 4,023
A review of polymer dissolution
Miller-Chou, B. A., & Koenig, J. L. (2003) · Progress in Polymer Science · doi:10.1016/s0079-6700(03)00045-5 · Cited by 1,115
A theory crack healing in polymers
Wool, R. P., & O’Connor, K. M. (1981) · Journal of Applied Physics · doi:10.1063/1.328526 · Cited by 1,093
Rheology and microscopic topology of entangled polymeric liquids
Everaers, R., Sukumaran, S. K., Grest, G. S., Svaneborg, C., Sivasubramanian, A., & Kremer, K. (2004) · Science · doi:10.1126/science.1091215 · Cited by 832
Elasticity of polymer networks
Rubinstein, M., & Panyukov, S. (2002) · Macromolecules · doi:10.1021/ma0203849 · Cited by 566
Metadata
- Authors
- Edwards, S. F.
- Venue
- Proceedings of the Physical Society
- Publisher
- IOP Publishing
- Published
- 1967-09
- Volume
- 92
- Issue
- 1
- Pages
- 9-16
- ISSN
- 0370-1328 (ISSN-L)
- OpenAlex
- W2120086325
- Cited by
- 578
- References
- 2
- FWCI
- 2.31
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
