Elasticity of Polymer Networks

We develop and solve a new molecular model for nonlinear elasticity of entangled polymer networks. This model combines and generalizes several succeseful ideas introduced over the years in the field of the rubber elasticity. The topological constraints imposed by the neighboring network chains on a given network are represented by the confining potential that changes upon network deformation. This topological potential restricts fluctuations of the network chain to the nonaffinely deformed confining tube. Network chains are allowed to fluctuate and redistribute their length along the contour of their confining tubes. The dependence of the stress σ on the elongation coefficient λ for the uniaxially deformed network is usially represented in the form of the Mooney stress, f*(1/λ) = σ/(λ − 1/λ2). We find a simple expression for the Mooney stress, f*(1/λ) = Gc + Ge/(0.74λ + 0.61λ-1/2 − 0.35), where Gc and Ge are phantom and entangled network moduli. This allows one to analyze the experimental data in the form of the universal plot and to obtain the two moduli Gc and Ge related to the densities of cross-links and entanglements of the individual networks. The predictions of our new model are in good agreement with experimental data for uniaxially deformed polybutadiene, poly(dimethylsiloxane), and natural rubber networks, as well as with recent computer simulations.