Atomistic Monte Carlo simulations of polymer melt elasticity:: Their nonequilibrium thermodynamics GENERIC formulation in a generalized canonical ensemble

A novel atomistic Monte Carlo (MC) methodology is presented for the simulation of systems with a complex internal microstructure away from equilibrium, directly from first principles. The methodology is based on the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) and proposes MC, and not molecular dynamics (MD), simulations in a generalized canonical ensemble. The new approach, also termed GENERIC MC, is hierarchical and starts with the definition or selection of the set of state variables describing the system at a coarse-grained level. To each state variable, a field or conjugate variable is introduced as a proper Lagrange multiplier when projecting atomistic coordinates onto the macroscopic state variables. Each conjugate variable is formally defined as the partial derivative of the system thermodynamic potential (the entropy) with respect to the corresponding coarse-grained state variable, keeping the rest of the state variables constant. The set of conjugate variables defines the extended canonical ensemble of the atomistic GENERIC MC simulation. By analyzing the structure of the canonical GENERIC equation for spatially homogeneous, time-independent flows, a kinematic interpretation is attributed to the conjugate variables of the structural state variables connecting them to the velocity gradient tensor. This sets the framework for performing realistic atomistic MC simulations, guided by the thermodynamically admissible macroscopic models derived from GENERIC, to calculate the free energy of the nonequilibrium system, without going through the full dynamical problem. The formulation is outlined here for three different viscoelastic fluid models: the single- and multiple-conformation tensor viscoelastic models for unentangled polymers and the pompon model for long-chain branched (LCB) molecules. Results are presented from detailed end-bridging, atomistic MC simulations with the new method for the elasticity of a linear C-156 polyethylene (PE) melt, in a steady-state uniaxial elongational flow. In the simulations, a four-mode conformation tensor viscoelastic model was employed to project atomistic coordinates. The dependence of the melt free energy of elasticity on chain degree of deformation due to applied flow field is reported and compared against the predictions of simple analytic models, commonly used in polymer flow calculations, such as the Hookean dumbbell and the FENE-P. The latter, which accounts for the finite extensibility of the polymer, is soon to be more representative of the actual melt response than the former. It is also seen that, in the regime of small Deborah numbers studied, only the components of the first-mode conformation tensor deviate from their equilibrium values; higher-mode conformation tensors retain their equilibrium, spherical symmetry. This explains the success of the single conformation tensor FENE-P viscoelastic model in fitting rheological data.