Permanent Set of Cross-Linking Networks:  Comparison of Theory with Molecular Dynamics Simulations

The permanent set of cross-linking networks is studied by molecular dynamics. The uniaxial stress for a bead−spring polymer network is investigated as a function of strain and cross-link density history, where cross-links are introduced in unstrained and strained networks. The permanent set is found from the strain of the network after it returns to the state-of-ease where the stress is zero. The permanent set simulations are compared with theory using the independent network hypothesis, together with the various theoretical rubber elasticity theories: affine, phantom, constrained junction, slip-tube, and double-tube models. The slip-tube and double-tube models, which incorporate entanglement effects, are found to be in very good agreement with the simulations.