Primitive-chain Brownian simulations of entangled rubbers

We present a new multi-chain Brownian dynamics simulation of a polymeric network containing both crosslinks and slip-links (entanglements). We coarse-grain at the level of chain segments connecting consecutive nodes (cross- or slip-links). Affine displacement of nodes is not imposed; rather, their displacement as well as sliding of monomers through slip-links is governed by force balances. The stress-strain response in uniaxial extension is compared with the slip-link theories of Ball et al. (Polymer, 22 (1981) 1010) and Edwards and Vilgis (Polymer, 27 (1986) 483), and with the molecular-dynamics simulations of Grest et al. (J. Non-Cryst. Solids, 274 (2000) 139). Qualitative agreement both with the Mooney-Rivlin expression and with the stress upturn at large strains confirms the role of entanglements in explaining departure from the classical theory of phantom chain networks. However, quantitative agreement with data is satisfactory at low strains only, and the observed discrepancy at larger strains suggests possible refinements of the model. Additivity of free energy contributions of crosslinks and entanglements used in several molecular theories of rubber elasticity is confirmed by the simulation results.