(670f) On the Thermodynamic Consistency of Phase-Field Models of Polymeric Solutions

Phase-field models have become increasingly important for simulations of the dynamics of phase separation and the microstructural evolution of polymeric materials. Recently, several researchers have raised questions regarding the thermodynamic consistency of various phase-field models of polymeric mixtures. These consistency checks of the free-energy models are based on the Gibbs–Duhem equation, a traditional thermodynamic equation that portrays the relation among changes in temperature, pressure, and chemical potential. Differing expressions of the Gibbs–Duhem equation can be found in the literature leading to confusion about the correct form of the equation and highlighting the need for a well-founded understanding of such consistency approaches. In order to resolve this controversy, we derive the Gibbs–Duhem equation for phase-field models from first principles. In our derivation, we highlight the importance of differentiating between exchange chemical potentials and traditional chemical potentials, and we clarify the connection between the two potentials and the osmotic stress tensor. Finally, we validate our derivation by a thermodynamic consistency assessment for a Flory–Huggins phase-field model, and we use simulations to highlight the effect of breaking thermodynamic consistency.

*We acknowledge the financial support from the BYU Board of Trustees and the computational resources from the BYU Office of Research Computing.