Topological interactions in model polymer networks

We numerically analyze mesh entanglements in model polymer networks. We find G-${\mathit{G}}_{\mathit{ph}}$≊0.85${\mathrm{\rho }}_{\mathit{ent}}$ ${\mathit{k}}_{\mathit{BT}}$, where ${\mathrm{\rho }}_{\mathit{ent}}$ is the entanglement density, G the shear modulus which was measured in extensive molecular dynamics simulations of stretched samples, and ${\mathit{G}}_{\mathit{ph}}$ the phantom model prediction for the equivalent system without topological constraints. A simple model calculation of the prefactor is in close agreement with the observed value. © 1996 The American Physical Society.