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Cited by 384Rheology and Fluid Dynamics StudiesElasticity and Material ModelingAdvanced Materials and Mechanics

The tube model theory of rubber elasticity

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Edwards, S F, Vilgis, T A·1988·Reports on Progress in Physics
DOI 10.1088/0034-4885/51/2/003
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Abstract

Rubbers are highly elastic solids formed by the random permanent linkages between long chain polymers. Their elasticity is largely entropic in origin, so that the molecular theory is largely a matter of counting the configurations available to the polymers and how this number changes under deformation. To do this one needs to know the way in which the crosslinks are formed, which need not be related to any equilibrium process, and to know the restriction placed on the chains by one another's presence, i.e. their entanglements. Recent theoretical developments suggest that the problem is by no means as intractable as it might at first sight appear, and simple models of tube confinement seem to give very good agreement with experiment.

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Crossref · 10.1088/0034-4885/51/2/003

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  • Edwards and Vilgis established the contributions of entanglements and crosslinks to the elastic response of a crosslinked network following an external applied force, and the obtained results compared well with extensive experimental results.

    “Later on, through rigorous statistical mechanic formulations, upon employing the affine deformation assumption, Edwards and Vilgis established the contributions of entanglements and crosslinks to the elastic response of a crosslinked network following an external applied force [21].The obtained results compared well with the extensive experimental results.”

    From Challenges in Multiscale Modeling of Polymer Dynamics (2013) · cites this paper as [21]

  • Since about 90% of the free energy of polymeric materials is entropy, the elasticity of these materials is dominated by entropic forces whose strength is inversely proportional to kBT.

    “Since about 90% of the free energy of polymeric materials is entropy [21], the elasticity of these materials is dominated by entropic forces whose strength is inversely proportional to k B T”

    From Challenges in Multiscale Modeling of Polymer Dynamics (2013) · cites this paper as [21]

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Research works printed but not linked: 28

  1. Allen G, Kirkham M J, Padget J and Price C 1971 Trans. Faraday Soc. 67 1728
  2. Bastide J 1985 Physics ofFinely Divided Matter ed N Boccara and M Daoud (Berlin: Springer) pp 148-53
  3. Baxandall L G 1985 PhD thesis University of Cambridge
  4. Deam R T and Edwards S F 1976 Phil. Trans. R. Soc. A 280 317
  5. ~ 1972 Phys. Lett. 38A 339 -1979 Scaling Conceprs in Polymer Physics (Ithaca, NY: Cornell University Press)
  6. des Cloizeaux J and Jannink G 1987 Les Polymeres en Solution: Modelisation et leurstructures (Paris: Edition
  7. Doi M and Edwards S F 1978 J. Chem. Soc. Faraday Trans. 2 74 1789, 1812, 1818 -1986 Theory of Polymer Dynamics (Oxford: Oxford University Press)
  8. Edwards S F 1965 Proc. Phys. Soc. 85 613 -1966 Proc. Phys. Soc. 88 265 _ . 1967 Proc. Phys. Soc. 91 513 -1968 J. Phys. A : Gen. Phys. 1 15 -1971 Polymer Networks ed A J Chrompff and S Newman (New York: Plenum) pp 85-103 -1977 Br. Polym. J. 9 140 -1987 to be published
  9. Edwards S F and Evans K E 1981 J. Chem. Soc. Faraday Trans. 2 77 1913
  10. Edwards S F and Stockmayer W H 1973 Proc. R. Soc. A 332 439
  11. Ferry J D 1980 Viscoelastic Properties ofPolymers (New York: Wiley)
  12. Fetter A L and Walecka J D 1971 Quantum Theory ofMany-Particle Systems (New York: McGraw-Hill)
  13. Feynman R P and Hibbs A R 1965 Path Integrals and Quanfum Mechanics (New York: McGraw-Hill)
  14. Flory P J 1959 Principles in Polymer Chemistry (Ithaca, NY: Cornell University Press) _ . 1960 Trans. Faraday Soc. 56 722 -1969 Statistical Mechanics of Chain Molecules (New York: Interscience) -1976 Proc.
  15. Fricker H S 1973 Proc. R. Soc. A 335 269
  16. Gee G 1954 Trans. Faraday Soc. 50 881
  17. Gottlieb M, Macosco C W and Lepsch T C E981 J. Polym. Sci. (Phys. Ed.) 19 1603
  18. Gordon M 1962 Proc. R. Soc. A 268 240
  19. Gumbrell S M, Mullins L and Rivlin R S 1953 Trans. Faraday Soc. 49 1495
  20. Helfand E and Pearson D S 1985 J. Polym. Sci., Polym. Symp. 73 71
  21. Lovesey S W 1985 Theory of Neutron Scattering (Oxford: Oxford University Press)
  22. Ogden R W 1972 Proc. R. Soc. A326 565
  23. Pak H and Flory P J 1979 J. Polym. Sci. (Phys. Ed.) 17 1845
  24. Pearson D S 1977 Macromol. 10 698
  25. Pearson D S and Graessley W W 1980 Macromol. 13 372
  26. Pearson D S and Helfand E 1983 Faraday Symp. Chem. Soc. 18 189
  27. Rivlin R S 1948 Phil. Trans. R. Soc. A241 379 -1949 Phil. Trans. R. Soc. A242 173
  28. Tobolsky A V and MacKnight W J 1966 Polymeric Sulphur and Related Polymers (New York: Wiley)

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Authors
Edwards, S. F., & Vilgis, T. A.
Affiliations
University of Cambridge (GB)
ORCID
Venue
Reports on Progress in Physics
Publisher
IOP Publishing
Published
1988-02-01
Volume
51
Issue
2
Pages
243-297
ISSN
  • 0034-4885 (ISSN-L)
  • 1361-6633
DOI
10.1088/0034-4885/51/2/003
OpenAlex
W1967388322
Cited by
384
References
109
Citations by year
2026: 19 · 2025: 15 · 2024: 12 · 2023: 18 · 2022: 13 · 2021: 13 · 2020: 14 · 2019: 12 · 2018: 8 · 2017: 12 · 2016: 11 · 2015: 13 · 2014: 12 · 2013: 13 · 2012: 10
FWCI
10.09
Type
journal article
Language
en
Open access
Locations
Reports on Progress in Physics (publishedVersion)
Topics
  • Physical Sciences › Chemical Engineering › Fluid Flow and Transfer Processes › Rheology and Fluid Dynamics Studies
  • Physical Sciences › Engineering › Biomedical Engineering › Elasticity and Material Modeling
  • Physical Sciences › Engineering › Mechanical Engineering › Advanced Materials and Mechanics
Keywords
rubber elasticity, tube model, entropic elasticity, chain conformation, crosslinking, chain entanglement, polymer networks

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