Nonequilibrium Monte Carlo simulations of entangled polymer melts under steady shear flow

We present a nonequilibrium Monte Carlo (MC) methodology based on expanded nonequilibrium thermodynamic formalism to simulate entangled polymeric materials undergoing steady shear flow. Motivated by the standard kinetic theory for entangled polymers, a second-rank symmetric conformation tensor based on the entanglement segment vector was adopted in the expanded statistical-ensemble based MC method as the nonequilibrium structural variable that properly represents the deformed structure of the system by the flow. The corresponding (second-rank symmetric) conjugate thermodynamic force variable was introduced to simulate an external flow field. As a test case, we applied the GENERIC MC to C₄₀₀H₈₀₂ entangled linear polyethylene melts in a wide range of shear rates. Detailed analysis of the GENERIC MC results for various structural and rheological properties (such as chain size, chain orientation, mesoscale chain configuration, topological properties, and material functions) was carried out via direct comparison with the corresponding NEMD results. Overall, the GENERIC MC is shown to predict the general trends of the nonequilibrium properties of polymer systems reasonably for a wide range of flow strengths (i.e., 0.5 ≤ De ≤ 540). In conjunction with NEMD, the present MC method can thus be used to extract fundamental thermodynamic information (nonequilibrium entropy and free energy functions) of entangled polymeric systems under various flow types. Despite the general consistency between the GENERIC MC and NEMD results, some quantitative discrepancies appear in the intermediate-to-strong flow regime. This behavior stems from the inherent mean-field nature of the MC force field which is applied to the individual entanglement segments independently and uniformly along the chain, without accounting for any flow-induced structural or dynamical correlations between segments.