Elasticità della gomma e volume escluso intramolecolare

Moraglio, Giovanni ; Pavan, Andrea

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 60 (1976) no. 4, pp. 483-486

Résumé

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.