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We built randomly cross-linked model poly(dimethylsiloxane) (PDMS) networks and used molecular dynamics methods to obtain stress–strain curves. The Mooney–Rivlin (MR) analysis was used to estimate the shear moduli. We applied primitive path analysis (PPA) and its variation, phantom primitive path analysis (3PA), to estimate the entanglement and the cross-link moduli, respectively. The MR moduli estimates are in good agreement with the sum of the entanglement and the cross-link moduli, and we observe that the stress–strain data collapse to a universal form when reduced with the PPA and 3PA moduli. We studied how the MR parameters C1and C2vary from cross-link to entanglement-dominated networks. For the latter, we observed 40% and 60% contributions of 2C1and 2C2to the shear modulus, respectively. Finally, we fitted several theoretical models to our stress-strain data. While all fits are good, the estimates for the entanglement and cross-link moduli vary significantly when compared to our independently obtained PPA and 3PA benchmarks.

The Kremer–Grest (KG) polymer model is a standard model for studying generic polymer properties in molecular dynamics simulations. It owes its popularity to its simplicity and computational efficiency, rather than its ability to represent specific polymers species and conditions. Here we show that by tuning the chain stiffness it is possible to adapt the KG model to model melts of real polymers. In particular, we provide mapping relations from KG to SI units for a wide range of commodity polymers. The connection between the experimental and the KG melts is made at the Kuhn scale, i.e., at the crossover from the chemistry-specific small scale to the universal large scale behavior. We expect Kuhn scale-mapped KG models to faithfully represent universal properties dominated by the large scale conformational statistics and dynamics of flexible polymers. In particular, we observe very good agreement between entanglement moduli of our KG models and the experimental moduli of the target polymers.

The Kremer–Grest (KG) model is a standard for studying generic polymer properties. Here we have equilibrated KG melts up to and beyond 200 entanglements per chain for varying chain stiffness. We present methods for estimating the Kuhn length corrected for incompressibility effects, for estimating the entanglement length corrected for chain stiffness, and for estimating bead frictions and Kuhn times taking into account entanglement effects. These are the key parameters for enabling quantitative, accurate, and parameter free comparisons between theory, experiment, and simulations of KG polymer models with varying stiffness. We demonstrate this for the chain dynamics in moderately to highly entangled melts as well as for the shear relaxation modulus for unentangled melts, which are found to be in excellent agreement with the predictions from standard theories of polymer dynamics.

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.