Extrapolating into no man’s land enables accurate estimation of surface properties with multiparameter equations of state

Abstract

Thermodynamic properties of homogeneous fluids in the metastable and unstable regions are needed to describe confined fluids, interfaces, nucleating embryos and estimate critical mass flow rates. The most accurate equations of state (EoS) called multiparameter EoS, have a second, non-physical Maxwell loop that renders predictions unreliable in these regions. We elaborate how information from the stable region can be used to reconstruct the metastable and unstable regions. For a simple interaction potential, comparison to results from molecular simulations reveals that isochoric expansion of the pressure from stable states reproduces simulation results in the metastable regions. By constructing a dome that extends above the critical point, we obtain an extrapolated pressure from multiparameter EoS that is free of second Maxwell loops. A reconstructed EoS is developed next, by integrating the extrapolated pressure from a stable state to obtain the Helmholtz energy. The consistency of the reconstructed EoS is gauged by computing phase equilibrium densities, pressures, and enthalpies of evaporation, which are in reasonable agreement with experimental values. Combined with density gradient theory, the reconstructed EoS yields surface tensions of water, carbon dioxide, ammonia, hydrogen and propane that deviate, on average, 4.4%, 1.6%, 6.0%, 0.7% and 5.4% from experimental values respectively. The results reveal a potential to develop more accurate extrapolation protocols, which can be leveraged to obtain prediction of metastable properties, surface properties or used as constraints in fitting multiparameter EoS.