| 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−Panyukovversions) 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 relativeto 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), thestrain-dependent predictions of each model were tested from two different viewpoints, i.e., the dependenceof the reduced stresses on the principal ratio and the Ii dependence of (∂W/∂Ij)/Go (i,j = 1,2), where I1 andI2 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 rangeof deformations, but the model definitely underestimates the magnitude of Go because it does not considertrapped entanglements as additional cross-links contributing to Go, in contrast to the tube models andthe slip−link models. The G−D tube model is more successful in reproducing the experimental datarelative to the other two versions of the tube model, but the G−D model obviously underestimates thestresses at large deformations. Among the five molecular theories tested here, the E−V slip−link modelshows the most successful reproducibility over large portions of the experimental results. The agreementsin reduced stress−strain relations are satisfactory over the entire deformation range, although considerabledisagreement is recognized in the Ii dependence of ∂W/∂I2. Also, the fitted parameter values in the E−Vslip−link model are fairly well explained using the molecular considerations based on the structuralcharacteristics of the network sample employed here.
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