Stress-Strain Isotherm for Polymer Networks

According to the molecular theory of rubber elasticity, the stress τ is related to the relative length a 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=(2C1+2C2/α)(α−1/α2) which contains the additional parameter C2. 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 C2 term offers improved agreement over the extension phase of an elongation cycle, but not for the subsequent retraction phase; (2) apparent values of C2 (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 crosslinking; (4) C2 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 crosslinking with gamma radiation likewise lowers C2, the value characteristic of the unswollen polymer being restored upon removal of the diluent. The results demonstrate that the controversial C2 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 rubber elasticity is thus refuted.