Applications of a two-network model for crosslinks and trapped entanglements

The dependence of stress and birefringence on strain in uniaxial extension of crosslinked rubbers can accurately be described by a model in which the properties of a network of crosslinks and a network of trapped entanglements are additive. The crosslink network is neo-Hookean and the entanglement network can conveniently be described by the Mooney-Rivlin equation. When the crosslinks are introduced in a state of strain near the glass transition temperature, the two networks have different reference undeformed states; they can be distinguished by appropriate measurements in the state of ease where their associated stresses are equal and opposite and in the state of deformation where the cross-links were introduced and make no contribution to the stress. When partial relaxation is permitted before crosslinking, trapping probabilities can be calculated for both relaxed and unrelaxed entanglements and compared with the Langley theory. The results are consistent with the terminal mechanism of relaxation in the tube theory of Doi and Edwards.