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 ͑MC͒ 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 variable͑s͒. 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 ␣. We have been able to compute modelindependent values of the tensor ␣, which for a wide range of strain rates ͑covering both the linear and the nonlinear viscoelastic regimes͒ bring results for the overall polymer conformation from the two models ͑mi-croscale and macroscale͒ on top of each other. In a second step, by comparing the computed values of ␣ with those suggested by the macroscopic model addressed by the chosen structural variable͑s͒, 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.

Challenges in Multiscale Modeling of Polymer Dynamics

“…Thus, there is no need to have an explicit form of the macroscopic model. The obtained conformation tensors, as well as the chain orientation functions of low-molecular weight PE melts are found to agree with atomistic non-equilibrium simulations [318]. (a) (b)…”

“…In addition, the flow curves for η, Ψ 1 and the second normal stress difference, Ψ 2 = σ yy − σ zz , have been obtained and compare well with the NEMD results [299]. Baig and his co-workers [318,319] adopted a similar concept to study the viscoelasticity of polymer melts. They used an expanded Monte Carlo method as the macroscale solver for a family of viscoelastic models, which are built on the "structural" variable, x.…”

“…With help from recent advances in the field of non-equilibrium statistical mechanics and thermodynamics, the molecularly-derived constitutive equation, shown in Section 5.2, has demonstrated some capabilities in the comprehensive modeling of polymer flow behavior. However, the current results are limited to either generic polymer models (FENE chains [299]) or specific models of very simple polymers (PE chains [318]) with short chain length (smaller than or comparable to the entanglement length). Since the entanglements between different chains have significant effects on the dynamics and shear rheology of polymer melts, it is necessary to extend these methods to study the complex flow behavior of highly entangled polymer chains.…”

Quantifying chain reptation in entangled polymer melts: Topological and dynamical mapping of atomistic simulation results onto the tube model

“…Establishing our concept under nonequilibrium conditions would mark a tremendous achievement, since it could help quantify the effect and role of other mechanisms ͑such as CCR 49,50 ͒ on the linear and nonlinear viscoelastic properties of polymers. In conjunction with the design of thermodynamically consistent coarse-graining methodologies for systems beyond equilibrium, [51][52][53][54][55] this could enable the prediction of the rheological properties of truly long polymers and the development of more accurate constitutive equations based on multiscale constructions ͑involving, e.g., projection operators͒ in the framework of nonequilibrium statistical mechanics and thermodynamics.…”

Analysis of the configurational temperature of polymeric liquids under shear and elongational flows using nonequilibrium molecular dynamics and Monte Carlo simulations

“…16,26,30 In addition to the NEMD simulations, NEMC simulations were performed using a recently developed thermodynamically well-founded MC ͑the so-called GENERIC MC͒ methodology, 17,31 the underlying principles of which are based on a rigorous formulation of nonequilibrium thermodynamics. 23 Since the detailed fundamental aspects of the GENERIC MC method can be found in the literature, 17,31 here we present only some basic equations that are directly involved in the simulations. As a nonequilibrium structural thermodynamic variable, we adopted the second-rank conformation tensor c, which is defined as 22,32,33 …”