Entanglement networks of 1,2-polybutadiene crosslinked in states of strain. IV. States of ease and stress–strain behavior |
| |
Authors: | Rick L Carpenter Ole Kramer John D Ferry |
| |
Abstract: | Linear 1,2-polybutadiene, glass transition temperature (Tg) ?18°C, is crosslinked at ?10°C, to ?20°C by γ irradiation while strained in simple extension, with extension, ratios (λ0) from 1.2 to 2.7. After release, the sample retracts to a state of ease (λs) at room temperature. From equilibrium stress–strain measurements up to a stretch ratio relative to the state of ease (Λ) of 1.2, together with λ0 and λs, the concentration of network strands terminated by trapped entanglements (νN) is calculated. For this purpose, a three-constant Mooney–Rivlin formulation is used, in which the entanglement network is described by Mooney–Rivlin coefficients C1N and C2N, whereas the crosslink networks is described by the coefficient C1x only. The ratio ψN = C2N/(C1N + C2N) is estimated from parallel studies of nonlinear stress relaxation of the uncrosslinked polymer, taking into account the thermal history before and during irradiation. For substantial degrees of crosslinking, i.e., for R0′ = νx/νN > 0.4 (where νN is the concentration of network strands terminated by crosslinks), and for λ0 < 1.8, C2N agrees rather well with the value obtained from stress relaxation of the uncrosslinked polymer in the range of time scale where it is nearly independent of time (1.87 X 105 pascals). The corresponding value of νN is 2.3 × 10?4 moles/cm3, in good agreement with that obtained from viscoelastic measurements of the uncrosslinked polymer in the plateau zone (2.5 × 10?4). However, for R0′ ? 0.2, smaller values of C2N and νN are obtained, indicating that for low degrees of crosslinking the entanglements are not completely trapped. Also, for higher values of λ0, C2N and νN turn out to be somewhat smaller. Similar, less extensive results were obtained previously on a 1,2-polybutadiene with somewhat higher vinyl content and a higher Tg. Crosslinked samples of both these polymers were subjected to equilibrium stress–strain measurements in simple elongation from the state of ease at higher strains up to Λ = 1.7. The results agreed closely with calculations from the three-constant Mooney–Rivlin theory. |
| |
Keywords: | |
|
|