Polymer networks undergoing cross-linking reactions are studied using molecular dynamics simulations to investigate how the stress is influenced by the coupling between cross-linking and deformation. For networks cross-linked in the undeformed state, the modulus increases linearly with the cross-link density as expected from rubber elasticity theory. When cross-links are added to a network that was uniaxially deformed, the stress remains constant in accordance with the independent network hypothesis of Tobolsky. When the deformed network is subsequently released, permanent set is observed. Using the independent network hypothesis, together with the affine theory of rubber elasticity, a constitutive model is developed that accounts for the effect of the coupling between the cross-link density and strain histories of the network. The permanent set predictions from the affine model are higher than found from MD simulations.

The effects of sequential cross-linking and scission of polymer networks formed in two states of strain are investigated using molecular dynamics simulations. Two-stage networks are studied in which a network formed in the unstrained state (stage 1) undergoes additional cross-linking in a uniaxially strained state (stage 2). The equilibrium stress is measured before and after removing some or all of the original (stage 1) cross-links. The results are interpreted in terms of a generalized independent network hypothesis. In networks where the first-stage cross-links are subsequently removed, a fraction (quantified by the stress transfer function Φ) of the second-stage cross-links contribute to the effective first-stage cross-link density. The stress transfer functions extracted from the MD simulations of the reacting networks are found to be in very good agreement with the predictions of Flory and Fricker. It was found that the fractional stress reduction upon removal of the first-stage cross-links could be accurately calculated from the slip tube model of Rubinstein and Panyukov modified to use the theoretical transfer functions of Fricker.

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 doubletube models, which incorporate entanglement effects, are found to be in very good agreement with the simulations.