Multiscale simulation of polymer melt viscoelasticity: Expanded-ensemble Monte Carlo coupled with atomistic nonequilibrium molecular dynamics

Abstract

We present a powerful framework for computing the viscoelastic properties of polymer melts based on an efficient coupling of two different atomistic models: the first is represented by the nonequilibrium molecular dynamics method and is considered as the microscale model. The second is represented by a Monte Carlo (MC) method in an expanded statistical ensemble and is free from any long time scale constraints. Guided by recent developments in nonequilibrium thermodynamics, the expanded ensemble incorporates appropriately defined "field" variables driving the corresponding structural variables to beyond equilibrium steady states. The expanded MC is considered as the macroscale solver for the family of all viscoelastic models built on the given structural variable(s). The explicit form of the macroscopic model is not needed; only its structure in the context of the general equation for the nonequilibrium reversible irreversible coupling or generalized bracket formalisms of nonequilibrium thermodynamics is required. We illustrate the method here for the case of unentangled linear polymer melts, for which the appropriate structural variable to consider is the conformation tensor c□. The corresponding Lagrange multiplier is a tensorial field α. We have been able to compute model-independent values of the tensor α, which for a wide range of strain rates (covering both the linear and the nonlinear viscoelastic regimes) bring results for the overall polymer conformation from the two models (microscale and macroscale) on top of each other. In a second step, by comparing the computed values of α with those suggested by the macroscopic model addressed by the chosen structural variable(s), we can identify shortcomings in the building blocks of the model. How to modify the macroscopic model in order to be consistent with the results of the coupled micro-macro simulations is also discussed. From a theoretical point of view, the present multiscale modeling approach provides a solid framework for the design of improved, more accurate macroscopic models for polymer melts.