Stress-Strain Isotherm for Polymer Networks

Abstract

According to the molecular theory of rubberelasticity, the stress τ is related to the relative length α in simple extension according to τ=kT(ν/V)<α>2(α−1/α2), where (ν/V)<α>2 is a parameter of the network structure. Improved agreement with experiment has been claimed through use of the relation τ=(2C 1+2C 2/α) (α−1/α2) which contains the additional parameter C 2. In order to explore factors affecting this theoretically inexplicable term, stress‐elongation measurements were performed on networks prepared from natural rubber, Butyl rubber, poly‐(dimethylsiloxane), poly‐(ethyl acrylate), and poly‐(methyl methacrylate) under a wide range of experimental conditions. Results may be summarized as follows: (1) the C 2 term offers improved agreement over the extension phase of an elongation cycle, but not for the subsequent retraction phase; (2) apparent values of C 2 (determined on extension) vary widely from one polymer to another, increasing with hysteresis and with proximity to the glass transition temperature; (3) they are insensitive to the degree of cross linking; (4) C 2 is markedly reduced by permanently swelling the network with a diluent, or by swelling and deswelling the sample at each tension; (5) incorporation of diluent prior to establishing a network by cross linking with gamma radiation likewise lowers C 2, the value characteristic of the unswollen polymer being restored upon removal of the diluent. The results demonstrate that the controversial C 2 term arises from the difficulty of attaining elastic equilibrium; under ideal experimental conditions the value of this parameter becomes negligible. An alleged limitation of the theory of rubberelasticity is thus refuted.