Elasticity of Randomly Cross-Linked Networks in Primitive Chain Network Simulations

Primitive chain network simulations for randomly cross-linked slip-link networks were performed. For the percolated networks, the stress- strain relationship was compared to the theories by Ball et al. [Polymer, 22, 1010 (1981)] and Rubinstein and Panyukov [Macromolecules, 35, 6670 (2002)]. The simulation results are reasonably reproduced by both theories when the contributions from cross-links and slip-links are determined irrespective of the network structure. The fraction of slip-links contained in the network thus obtained is model dependent, and it does not coincide with the number of active slip-links in the actual networks. This discrepancy between the theories and the simulation results is due to the network inhomogeneity.