Multiaxial Deformations of End-linked Poly(dimethylsiloxane) Networks. 2. Experimental Tests of Molecular Entanglement Models of Rubber Elasticity

Abstract

Five molecular models of rubber elasticity which employ different treatments of entanglement effects (the Kloczkowski−Mark−Erman diffused-constraint model, the Edwards−Vilgis (E−V) slip−link model, the tube models of Gaylord−Douglas (G−D), Kaliske−Heinrich, Rubinstein−Panyukov versions) are assessed using biaxial deformation data for an entanglement-dominated network of end-linked poly(dimethylsiloxane) (PDMS) in which trapped entanglements are dominant in number relative to chemical cross-links. The theoretical stress−strain relations were calculated from the elastic free energy (W) of each model. Using the reduced stress (the nominal stress divided by equilibrium modulus Go), the strain-dependent predictions of each model were tested from two different viewpoints, i.e., the dependence of the reduced stresses on the principal ratio and the Ii dependence of (∂W/∂Ij)/Go (i,j = 1,2), where I1 and I2 are the first and second invariants of deformation tensor (the Rivlin−Saunders method). The diffused-constraint model is relatively successful in reproducing the reduced stress−strain data over a wide range of deformations, but the model definitely underestimates the magnitude of Go because it does not consider trapped entanglements as additional cross-links contributing to Go, in contrast to the tube models and the slip−link models. The G−D tube model is more successful in reproducing the experimental data relative to the other two versions of the tube model, but the G−D model obviously underestimates the stresses at large deformations. Among the five molecular theories tested here, the E−V slip−link model shows the most successful reproducibility over large portions of the experimental results. The agreements in reduced stress−strain relations are satisfactory over the entire deformation range, although considerable disagreement is recognized in the Ii dependence of ∂W/∂I2. Also, the fitted parameter values in the E−V slip−link model are fairly well explained using the molecular considerations based on the structural characteristics of the network sample employed here.