The theory of rubber elasticity is reformulated on the basis of a statistical distribution of the end-to-end distance partially accounting for intramolecular ecluded volume. The relationship between the uniaxial stress, $\sigma$, and the elongation ratio, $\alpha$, is: $$\sigma = \frac{5}{3}\, \nu \, kT \Big( \alpha - \frac{1}{\alpha^{2}} \Big) - \nu \, kT \,\Phi (\alpha)$$ where $\nu$ is the number of effective chains per unit volume, and $\Phi(\alpha)$ is a function with a maximum close to $\alpha = 2,5$. The elastic modulus for $\alpha = 1$ turns out to be 1.27 times the value calculated by the classical Gaussian theory.
Referenze Bibliografiche
[1] Vedi per esempio: F. BUECHE (1962) - Physical Properties of Polymers, Wiley (Interscience), New York.
[2] B. MUKHERIJI and W. PRINS (1964) - «J. Polymer Sci.», A 2, 4367.
[3] F. T. WALL and J. J. ERPENBECK (1959) - «J. Chem. Phys.», 30, 634.
[4] C. DOMB (1963) - «J. Chem. Phys.», 38, 2975.
[5] S. WINDWER (1965) - «J. Chem. Phys.», 43, 115.
[6] D. A. MCQUARRIE and M. SHEN (1965) — First Western Regional Meeting, American Chemical Society, Los Angeles; vedi anche M. SHEN, W. F. HALL and R. E. DE WAMES (1968) - «J. Macromol. Sci.», C 2 (2), 183.
[7] S. F. EDWARDS (1965) - «Proc. Phys. Soc.», (London), 83, 613.
[8] H. REISS (1967) - «J. Chem. Phys.», 47, 186.
[9] G. GEE (1966) - «Polymer», 7, 373.
[10] P. J. FLORY (1969) — Statistical Mechanics of Chain Molecules, Wiley (Interscience), New York.
[11] J. MAZUR (1965) - «J. Res. Nat. Bur. Stand.», Sect A, 69, 355.
[12] Z. ALEXANDROWICZ (1967) - «J. Chem. Phys.», 46, 3789.
[13] F. T. WALL and R. A. WHITE (1974) - «Macromolecules», 7, 849.
Con il contributo del Ministero per i Beni e le Attività Culturali