A unifying stress–strain model for physical networks (polymer melts) and for permanent networks (rubbers) is presented. It is based on three assumptions: (1) the uncrossability condition of real chains can be modeled by the tube concept; (2) the tube diameter is a function of the average stretch; and (3) the tube volume is invariant with respect to deformation. The model predicts that stress–strain behavior of dry and swollen rubber networks is completely determined by four material constants: the equilibrium modulus G∞ of the bulk network; the critical entanglement modulus G*e, which is equivalent to the plateau modulus GN of the un‐crosslinked parent melt; a finite extensibility parameter α; and a solvent‐polymer interaction exponent β. Predictions are compared with experimental data in elongation, and agreement is excellent. The Mooney–Rivlin constant C2 of unswollen networks with high crosslink densities is limited to roughly GN/2, and the origin of the C2 term is shown to be due to nonaffine deformation of the entanglement network. Nonaffine deformation of network strands is caused by an increasing lateral restriction due to neighboring chains, while upon swelling, the nonaffine reduction of the microscopic length scale leads to the vanishing C2 value of highly swollen rubbers.
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Research Article|
May 01 1994
The origin of the C2 term in rubber elasticitya)
M. H. Wagner
M. H. Wagner
Institut für Kunststofftechnologie, Universität Stuttgart, Böblingerstr. 70, D‐70199 Stuttgart, Germany
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J. Rheol. 38, 655–679 (1994)
Article history
Received:
October 08 1993
Accepted:
January 15 1994
Citation
M. H. Wagner; The origin of the C2 term in rubber elasticitya). J. Rheol. 1 May 1994; 38 (3): 655–679. https://doi.org/10.1122/1.550480
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