Nucleation Rate of N₂ and O₂ in Cryogenic H₂ and He

The homogeneous nucleation of N₂ and O₂ in cryogenic H₂ and He is investigated by using classical molecular dynamics (MD) simulations. The nucleation kinetics of N₂ and O₂ clusters, including nucleation rate, critical cluster size, and cluster energy, are elucidated in H₂ and He carrier gas at thermalization temperatures of 30-80 K and initial gas densities of 5.65 × 10²⁴-2 × 10²⁷ m^-3. The energy released from the clusters during nucleation increases the system temperature by 77-138%, consistent with N₂ nucleation experiments in supersonic nozzles and the mean-field kinetic nucleation theory. The nucleation rate derived by MD, J_sim, spans across 2.14 × 10²⁹-5.25 × 10³⁶ m^-3 s^-1 for both N₂ and O₂ under all conditions. The MD-obtained homogeneous nucleation rate is in agreement with predictions from the self-consistent classical nucleation theory (CNT) at low temperature (<70 K) but is 3-7 orders of magnitude faster than the CNT when temperature exceeds 70 K, consistent with the literature. Increasing temperature and decreasing concentration of the nucleating vapors leads to larger critical cluster sizes. The CNT underpredicts the critical cluster size at cryogenic temperatures below 60 K by 200-700%. The present MD methodology can be used for the direct determination of the nucleation rate and critical cluster size of N₂ and O₂ under cryogenic conditions, circumventing the assumptions inherent in CNT.