Keywords

Free Energy, Stress, Thermodynamic Modeling, Thermodynamic Properties, Thermodynamics

Abstract

Phase-field models are relatively inexpensive field-based models capable of capturing the nonequilibrium multiphase behavior of polymers and other soft materials. With their rise in popularity over the past several years, questions have arisen concerning the thermodynamic consistency of some model formulations. In doing so, researchers have employed several different forms of the Gibbs–Duhem equation─a classical thermodynamic relationship used to assess consistency─leading to questions about the correct form of this expression for inhomogeneous mixtures. In this paper, we derive a generalized Gibbs–Duhem relation that is valid for phase-field models. The key to the derivation is the recognition that the functional derivatives used with phase-field models give exchange chemical potentials, in contrast to the classical chemical potentials commonly used in homogeneous thermodynamics. We use this derivation to demonstrate that a phase-field model that generalizes the Flory–Huggins model satisfies the Gibbs–Duhem expression and is therefore thermodynamically consistent. In addition, we find that the Gibbs–Duhem relationship provides some unique insights into the relationship between the traditional chemical potentials, the exchange chemical potentials, and the osmotic stress tensor.

Original Publication Citation

Rami Alhasan and Douglas R. Tree Macromolecules 2022 55 (3), 759-765 DOI: 10.1021/acs.macromol.1c02021