| Based on the two-generator nonequilibrium thermodynamics framework, the relevant GENERIC time evolution equation for the system state variables is derived in a generalized canonical (as opposed to microcanonical) ensemble. The derivation makes use of the so called conjugate variables, introduced as proper Lagrange multipliers when projecting the system atomistic coordinates onto 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. By analyzing the structure of the canonical GENERIC equation for spatially homogeneous, time-independent flows, a kinematic interpretation is attributed to the conjugate variables in terms of the components of the velocity gradient tensor. This sets the framework for designing realistic atomistic Monte Carlo simulations, guided by the thermodynamically admissible macroscopic models derived from GENERIC, in order to obtain the potential of mean force of the system away from equilibrium, without going through the full dynamical problem. As a result, the two generator functions, the energy E and the entropy S, on which GENERIC is built can be obtained directly, from first principles, also for nonequilibrium systems. The formulation is outlined for three different viscoelastic fluid models in accord of which the system can be excited away from equilibrium: the single and multiple conformation tensor viscoelastic models for unentangled polymers, and the pompon model for long-chain branched polymers. This generalizes the original work of Mavrantzas and Theodorou (1998) valid only for unentangled polymer melts that are excited through a single-conformation tensor viscoelastic model. Atomistic Monte Carlo simulation results with the new method (termed also GENERIC MC) are presented for the elasticity of linear, unentangled polyethylene (PE) melts in a steady-state uniaxial elongational flow, obtained by employing a 4-mode conformation tensor viscoelastic model. The dependence of the free energy of elasticity of the unentangled melt on chain orientation and/or deformation due to applied flow field is reported and compared against the prediction of simple analytic models, commonly used in polymer flow calculations, such as the Hookean dumbbell and the FENE-P models. The latter, which accounts for the finite extensibility of the polymer, is seen to be more representative of the actual melt response than the former.
for LaTeX users @article{VGMavrantzas2002-35,
author = {V. G. Mavrantzas and H. C. \"Ottinger},
title = {Atomistic Monte Carlo simulations of polymer melt elasticity: Their nonequilibrium thermodynamics GENERIC formulation in a generalized canonical ensemble},
journal = {Macromolecules},
volume = {35},
pages = {960-975},
year = {2002}
}
\bibitem{VGMavrantzas2002-35} V.G. Mavrantzas, H.C. \"Ottinger,
Atomistic Monte Carlo simulations of polymer melt elasticity: Their nonequilibrium thermodynamics GENERIC formulation in a generalized canonical ensemble,
Macromolecules {\bf 35} (2002) 960-975.VGMavrantzas2002-35
V.G. Mavrantzas, H.C. \"Ottinger
Atomistic Monte Carlo simulations of polymer melt elasticity: Their nonequilibrium thermodynamics GENERIC formulation in a generalized canonical ensemble
Macromolecules,35,2002,960-975 |
mk@mat.ethz.ch
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