The air pressure effect on the homogeneous nucleation of carbon dioxide by molecular simulation

Vapour-liquid equilibria (VLE) and the influence of an inert carrier gas on homogeneous vapour to liquid nucleation are investigated by molecular simulation for quaternary mixtures of carbon dioxide, nitrogen, oxygen, and argon. Canonical ensemble molecular dynamics simulation using the Yasuoka-Matsumoto method is applied to nucleation in supersaturated vapours that contain more carbon dioxide than in the saturated state at the dew line. Established molecular models are employed that are known to accurately reproduce the VLE of the pure fluids as well as their binary and ternary mixtures. On the basis of these models, also the quaternary VLE properties of the bulk fluid are determined with the Grand Equilibrium method. Simulation results for the carrier gas influence on the nucleation rate are compared with the classical nucleation theory (CNT) considering the “pressure effect” [Phys. Rev. Lett. 101: 125703 (2008)]. It is found that the presence of air as a carrier gas decreases the nucleation rate only slightly and, in particular, to a significantly lower extent than predicted by CNT. The nucleation rate of carbon dioxide is generally underestimated by CNT, leading to a deviation between one and two orders of magnitude for pure carbon dioxide in the vicinity of the spinodal line and up to three orders of magnitude in presence of air as a carrier gas. Furthermore, CNT predicts a temperature dependence of the nucleation rate in the spinodal limit, which cannot be confirmed by molecular simulation.

💡 Research Summary

The paper presents a comprehensive molecular‑simulation study of homogeneous nucleation of carbon dioxide (CO₂) in the presence of an inert carrier gas composed of nitrogen, oxygen, and argon. Using well‑validated intermolecular potentials that accurately reproduce vapor‑liquid equilibria (VLE) for the pure components as well as their binary and ternary mixtures, the authors first determine the quaternary VLE properties of the bulk fluid with the Grand Equilibrium method. This step provides reliable saturation pressures and compositions, which are essential for defining supersaturation levels in the subsequent nucleation simulations.

Nucleation is investigated in the canonical ensemble by employing the Yasuoka‑Matsumoto (YM) method. In each simulation a supersaturated vapor is prepared that contains a higher CO₂ mole fraction than at the dew line. The system is then evolved at constant temperature and number of particles while the size distribution of molecular clusters is monitored. By counting the rate at which clusters exceed a chosen critical size, the nucleation rate J is obtained directly from the molecular dynamics trajectories. A series of simulations is performed over a range of temperatures (approximately –20 °C to 30 °C) and carrier‑gas concentrations, from pure CO₂ up to mixtures containing up to 90 % air by mole fraction.

The simulation results are compared with predictions from classical nucleation theory (CNT) that include the so‑called “pressure effect” as formulated in Phys. Rev. Lett. 101, 125703 (2008). According to CNT, the presence of an inert gas raises the total pressure, thereby increasing the free‑energy barrier ΔG* for forming a critical nucleus and consequently reducing J dramatically. The authors find that this theoretical pressure effect is severely overestimated. In pure CO₂, CNT underestimates the nucleation rate by roughly one to two orders of magnitude near the spinodal limit; when air is added, the discrepancy grows to up to three orders of magnitude. In other words, the carrier gas does lower J, but only modestly, contrary to the strong suppression predicted by CNT.

A second key observation concerns the temperature dependence of J in the spinodal regime. CNT predicts that, at a given supersaturation, J should decrease sharply with increasing temperature because ΔG* grows with T. The molecular‑dynamics data, however, show almost no systematic temperature trend; in some cases J even exhibits a slight increase. This indicates that the assumptions of CNT—particularly the use of a temperature‑independent surface tension and a simple additive pressure term—do not hold for the multicomponent, highly supersaturated systems studied here.

The authors discuss the implications of these findings for atmospheric science, carbon‑capture technologies, and any modeling effort that relies on CNT to estimate nucleation rates under realistic conditions. Their work demonstrates that a molecular‑level description, grounded in accurate intermolecular potentials and rigorous statistical‑mechanical methods, is essential for capturing the subtle interplay between carrier‑gas pressure, surface tension, and temperature. The study thus calls for a reassessment of CNT‑based parameterizations in climate‑model nucleation schemes and in the design of industrial processes where CO₂ condensation plays a critical role.