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Computational study of the cross-link and the entanglement contributions to the elastic properties of model PDMS networks

We built randomly cross-linked model PDMS networks and used Molecular Dynamics Methods to obtain stress-strain curves. 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 $\mathrm{C}_1$, $\mathrm{C}_2$ vary from cross-link to entanglement dominated networks. For the latter, we observed a $40\%$, $60\%$ contribution of $2\,\mathrm{C}_1$, $2\,\mathrm{C}_2$ to the shear modulus, respectively. Finally, we fitted several models to the data. While all fits are good, the estimates for the entanglement and the cross-link moduli vary significantly when compared to our PPA and 3PA benchmarks.