(508c) Assessment of Thermodynamic Models Using Brown’s Characteristic Curves

For several applications, thermodynamic properties of fluids need to be modeled at high pressure and temperature, e.g. in rocket propulsion systems, geology, and astronomy. However, in parts, no experiments for determining thermophysical property data are feasible today at such conditions. Using molecular thermodynamics, physically-based models can be used for making predictions of the thermodynamic behavior at such conditions. Their reliability at such regimes is evidently – due to the lack of experimental data – a priori unknown. Hence, thermodynamic consistency tests play an important role for the assessment of the reliability of models at such conditions. An interesting strategy for testing the thermodynamic consistency is based on Brown’s characteristic curves. E.H. Brown proposed four characteristic curves that define lines on the thermodynamic surface where special thermodynamic conditions hold [1]. There is one first-order curve (called Zeno curve) and three second-order characteristic curves (called Amagat, Boyle, and Charles curve), cf. Fig. 1-left. These curves are located within a large pressure and temperature range. For a given molecular fluid, Brown's characteristic curves are known to exhibit certain thermodynamic features [1,2]. The behavior of a given thermodynamic model can be tested regarding these features to assess its consistency. In this work, both molecular simulation and molecular-based equation of state (EOS) models are assessed regarding the thermodynamic consistency of Brown’s criteria. In a first step, a rigorous and generalized simulation method was developed for determining the characteristic curves from a given force field [3].
The method was tested using multiple model fluids and was then applied to complex real fluids such as alkanes, alcohols, and aromatic components. For the model fluids, the classical Lennard-Jones fluid, different Mie fluids, and Stockmayer fluids were studied. For the real substance fluids, methane, ethane, propane, ethanol, and toluene (cf. Fig. 1-right) were studied. In all cases, both classical force fields and molecular-based EOS were applied. If available, also multi-parameter EOS models were used for comparison. For the model fluids, the zero-density limits of the characteristic curves were determined exactly using the virial route.
The results provide a wealth of insights in the thermodynamic consistency of such models at large pressure and temperature: The molecular force field models yield characteristic curves that are conform with Brown’s criteria in all cases. This is interesting as Brown derived the criteria from rational thermodynamics for simple (repulsive-dispersive) particles only. The molecular-based EOS models considered in the evaluation show important differences, i.e. some exhibit artifacts, whereas others yield predictions that are fully conform with Brown’s postulates (and show excellent agreement with the force field predictions, cf. Fig. 1-right). This is astonishing considering the fact that both the force field models and the EOS models were parametrized with respect to vapor-liquid equilibrium data alone. In some cases, also empirical EOS models were used in the evaluation that are found to exhibit artifacts in several cases. This study moreover yields insights into the applicability of the corresponding states principle at high pressure and temperature and reveals that the corresponding states principle fails at such conditions even for simple fluids. In Summary, this work contributes to the question how the quality of models can be rigorously assessed even if no experimental data is available.
References
[1] E.H. Brown: On the thermodynamic properties of fluids, Bulletin de l’Institut International du Froid Annexe 1960–1, 169–178 (1960).
[2] S. Stephan, U. Deiters: Characteristic curves of the Lennard-Jones fluid, International Journal of Thermophysics 41, 147 (2020).
[3] M. Urschel, S. Stephan: Determining Brown’s characteristic curves using molecular simulation, Journal of Chemical Theory and Computation 19, 5 (2023) 1537.