Summary
A scaling analysis of the rubber-like elastic behavior of a cross-linked polymer network is presented which incorporates the two most salient contributions to the free energy of deformation: the chain connectivity of the segments and the restrictions on the chain configurations due to entanglements. The affine deformation of the junction points is assumed and a tube model is used to discuss the deformation dependence of the entanglement constraint parameter.
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References
Edwards, S. F., Proc. Phys. Soc., 92, 9 (1967). It should be noted that eq. 3.4 should obviously be d ∼ α, so that eq. 3.6 should be α ∼ ϱ−1.
de Gennes, P.-G., J. de Phys.-Lettres, 35, L-133 (1974). This paper complains that the Edwards harmonic potential model in ref. 1 gives E ∼ ϱ3/2 This criticism is invalid. It appears to result from using the miswritten eq. 3.4, d ∼ α, in the expressions ɛ0 ∼ α−1, F ∼ Nɛ0, d ∼ ϱ−1/2, E ∼ ϱɛ0. Using the correct d2 ∼ α relation brings the Edwards and deGennes models into agreement in obtaining E ∼ ϱ2.
Heinrich, G., Straube, E. and Helmis, G., Z. Phys. Chemie, Leipzig, 258, 361 (1977); 260, 737 (1979).
Kunne, U., Ph.D., Thesis, Technischen Universität, Hannover, Germany (1972).
DiMarzio, E. A., Am. Chem. Soc. Polymer Prepr., 9(1), 256 (1968).
Thomas, F., Straube, E. and Helmis, G., Plaste und Kautschuk, 22, 411 (1975).
Gaylord, R. J., Polymer Eng. and Sci., 19, 263 (1979).
Gaylord, R. J., Polymer Bull., 8, 325 (1982); 9, 181 (1983).
Kovac, J. and Crabb, C. C., Macromolecules, 19, 1744 (1986).
Marrucci, G., Macromolecules, 14, 434 (1981). This paper uses the same constant tube volume deformation assumption as ref. 8 but otherwise differs considerably, e.g., in its use of a single straight tube (which results in a non-separable free energy expression) and its prediction that the equilibrium modulus is independent of the number of network chains (which follows from using the primitive path as the center line of that tube).
Tschoegl, N. W. and Gurer, C., Macromolecules, 18, 680 (1985).
Doi, M., J. Phys. A, 8, 959 (1975).
Gottlieb, M. and Gaylord, R. J., Polymer, 24, 1644 (1983).
Gottlieb, M. and Gaylord, R. J., Macromolecules, 20, 130 (1987).
Gaylord, R. J., DiMarzio, E. A., Lee, A. and Weiss, G. H., Polymer Comm., 26, 337 (1985).
Gaylord, R. J., Weiss, G. H. and DiMarzio, E. A., Macromolecules, 19, 927 (1986).
Heinrich, G., Straube, E. and Helmis, G., Adv. Polym. Sci., in press.
Edwards, S. F. and Vilgis, T. A., Rep. Prog. Phys., to appear.
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Gaylord, R.J., Douglas, J.F. Rubber elasticity: a scaling approach. Polymer Bulletin 18, 347–354 (1987). https://doi.org/10.1007/BF00256236
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DOI: https://doi.org/10.1007/BF00256236