Résumé
The elastic modulus G of a polymer network depends notably on parameters such as the initial concentration of the monomers before the synthesis (rho 0), the density of the cross-linker, or the topology of the network. Understanding how these factors influence the stiffness of the sample is hampered by the fact that, in experiments, it is difficult to tune them individually. Here, we use coarse-grained molecular dynamics simulations to study how these quantities, as well as excluded volume interactions, affect the elastic modulus of the network. We find that, for a regular diamond network, G is independent of the initial monomer concentration, while for disordered networks (monodisperse or polydisperse), the modulus increases with rho 0, at odds with the classical predictions for rubber elasticity. Analysis of the network structure reveals that, for the disordered networks, defects contribute only weakly to the observed increase, and that instead the rho 0-dependence of G can be rationalized by the presence of a prestrain in the sample. This prestrain can be quantified by the topological factor introduced in the affine network theory (ANT). Comparison of the disordered networks with their phantom counterparts reveals that weakly cross-linked systems show a stronger rho 0-dependence of G due to an increase in entanglements at higher rho 0, and that the polydisperse networks contain more entanglements than the monodisperse ones with the same average strand length. Finally, we discuss the quantitative application of ANT to the simulated real networks and their phantom counterparts and conclude that the presence of excluded volume effects must be comprehensively taken into account to achieve a qualitative understanding of the mechanical modulus of the disordered networks.