First-Principles Diffusivity Ratios for Atmospheric Isotope Fractionation on Mars and Titan

Recent work used the kinetic theory of molecular gases, along with state-of-the-art intermolecular potentials, to calculate from first principles the diffusivity ratios necessary for modeling kinetic fractionation of water isotopes in air. Here, we extend that work to the Martian atmosphere, employing potential-energy surfaces for the interaction of water with carbon dioxide and with nitrogen. We also derive diffusivity ratios for methane isotopes in the atmosphere of Titan by using a high-quality potential for the methane-nitrogen pair. The Mars calculations cover 100 K to 400 K, while the Titan calculations cover 50 K to 200 K. Surprisingly, the simple hard-sphere theory that is inaccurate for Earth's atmosphere is in good agreement with the rigorous results for the diffusion of water isotopes in the Martian atmosphere. A modest disagreement with the hard-sphere results is observed for the diffusivity ratio of CH₃D in the atmosphere of Titan. We present temperature-dependent correlations, as well as estimates of uncertainty, for the diffusivity ratios involving HDO, H₂ ¹⁷O, and H₂ ¹⁸O in the Martian atmosphere, and for CH₃D and ¹³CH₄ in the atmosphere of Titan, providing for the first time the necessary data to be able to model kinetic isotope fractionation in these environments.