On the continuous modeling of fluid and solid states

For over 150 years, the “holy grail” of thermodynamic modeling has been to express the free energy of matter as a single analytical expression from where all other thermodynamic properties can be derived. This vision was partially achieved with the pioneering suggestion of J. D. van der Waals of modeling the gas and liquid states with a continuous polynomial. van der Waals' work spawned a century of development of equations of state (EoSs) for fluid phases and fluid phase equilibria. However, the extension to include the solid phase has largely been ignored, presumably out of the inherent difficulties in expressing the corresponding thermodynamic surface analytically. In this contribution, we resolve this century-old problem by presenting a procedure where an equation of state based on artificial neural networks is built based on an extensive database of accurate molecular dynamics data. The use of this EoS is exemplified here for the Mie particle, providing a single thermodynamically consistent model that continuously represents the fluid (gas, liquid and supercritical) and crystalline states. Apart from accurately predicting the derivative properties, the equation exhibits metastable regions characterized by van der Waals loops that correctly quantify the existence of vapor-liquid, solid-liquid, and solid-vapor equilibria along with the position of the critical and triple points. This new paradigm in EoS development is a pathway for the rapid deployment of models for complex matter and its interpretation opens doors to studying the transition regions between different aggregation states.