Thermodynamic Properties and Equations of State

Thermodynamic properties describe the relationships between pressure, temperature, volume and composition in fluid and solid phases, underpinning the design, optimisation and operation of chemical processes, energy systems and advanced materials. Central to this endeavour are equations of state, mathematical models that relate state variables and capture phase behaviour from vapour–liquid equilibria to near-critical phenomena. From the ideal gas law and van der Waals equation to cubic formulations such as Peng–Robinson and sophisticated statistical associating fluid theory (SAFT) variants, equations of state integrate empirical data, perturbation theory and molecular interaction potentials to predict density, enthalpy, heat capacity and compressibility with increasing fidelity. Recent developments address challenges in complex mixtures, interfacial phenomena and nanoscale confinement by uniting molecular simulation, density gradient theories and data-driven techniques. Such advances extend predictive capability to hydrogen solubility in hydrocarbons, capillary condensation at curved interfaces and the thermophysical behaviour of chain molecules, with direct impact on carbon capture, enhanced oil recovery, materials synthesis and sustainable chemical production.

Research from Nature Portfolio

Recent studies have harnessed advanced computational approaches to refine the prediction of fluid thermodynamics under challenging conditions. One investigation applied a suite of machine learning algorithms—among them extreme gradient boosting and gradient-boosted support vector regression—to estimate hydrogen solubility in diverse hydrocarbons across wide ranges of pressure and temperature. This approach outperformed traditional equations of state, reducing average absolute errors and offering rapid estimators for industrial applications. Another work employed molecular dynamics simulations coupled with a density gradient framework and the Peng–Robinson equation to explore bulk and interfacial properties of methane–decane–carbon dioxide mixtures under geological conditions. Key findings include the pressure and temperature dependence of interfacial tension, preferential adsorption of carbon dioxide and implications for carbon capture and storage and enhanced oil recovery processes.

Thermodynamic Properties and Equations of State publication trend

The graph below shows the total number of articles in thermodynamic properties and equations of state across all publications each year (not limited to Nature Index journals).

Technical terms

Equation of state (EOS): A mathematical model relating thermodynamic variables such as pressure, volume and temperature to predict phase behaviour and properties.

Statistical associating fluid theory (SAFT): A molecular-based EOS that uses perturbation theory and association models to describe intermolecular interactions in complex fluids.

Mie potential: A generalised Lennard–Jones form that describes variable-range attractive and repulsive interactions between molecular segments.

Flash calculation: A computational procedure to determine phase splits and compositions for given overall conditions in multi-component systems.

Density gradient theory: A theoretical framework for modelling inhomogeneous systems, particularly interfacial properties, by incorporating spatial variations in density.

Extreme gradient boosting (XGBoost): A machine learning algorithm that builds an ensemble of decision trees to optimise predictive accuracy for regression or classification tasks.

References

1. ML-SAFT: A machine learning framework for PCP-SAFT parameter prediction. Chemical Engineering Journal (2024).
2. Modeling hydrogen solubility in hydrocarbons using extreme gradient boosting and equations of state. Scientific Reports (2021).
3. Thermodynamics-Informed Neural Network (TINN) for Phase Equilibrium Calculations Considering Capillary Pressure. Energies (2021).
4. Bulk and interfacial properties of decane in the presence of carbon dioxide, methane, and their mixture. Scientific Reports (2019).