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

Abstract

On Earth, the fractionation of stable water isotopes such as HDO and 18 2 H O is important for understanding the hydrologic cycle (Gat, 1996). In addition to the equilibrium fractionation that occurs between water vapor and ice or liquid water, in some cases a significant role is played by kinetic fractionation that depends on the ratio of the atmospheric diffusivity of the isotopologue of interest to that of H 2 O. Recently, we reported temperature-dependent diffusivity ratios in air calculated from the kinetic theory of molecular gases applied to state-of-the-art intermolecular potentials based on ab initio calculations for the interaction between water and molecular nitrogen and oxygen (Hellmann & Harvey, 2020). We found that, especially for HDO, the often-assumed constant diffusivity ratios from simple hard-sphere kinetic theory were in error, and that the temperature dependence of the diffusivity ratios was not negligible. We supplied recommended diffusivity ratios and their uncertainties from 190 to 500 K, greatly exceeding the range in which the (scattered) experimental data exist.Earth is not the only place in our solar system with a hydrologic cycle. The distribution and seasonal variation of isotopic water species (especially HDO) has been used to study the climate of Mars (Encrenaz Abstract 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 highquality potential for the methane-nitrogen pair. The Mars calculations cover 100-400 K, while the Titan calculations cover 50-200 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 CH 3 D in the atmosphere of Titan. We present temperature-dependent correlations, as well as estimates of uncertainty, for the diffusivity ratios involving HDO, H 2 17 O, and H 2 18 O in the Martian atmosphere, and for CH 3 D and 13 CH 4 in the atmosphere of Titan, providing for the first time the necessary data to be able to model kinetic isotope fractionation in these environments.Plain Language Summary Different isotopes distribute unevenly between the vapor phase and liquid or solid phases during precipitation and evaporation, and the resulting changes in isotope ratios are used in the study of climate and other geophysical processes. While equilibrium aspects of this fractionation are fairly well understood, in some circumstances there is also a kinetic component that depends on the relative diffusivities of diffe...

Improved Modeling of Mars' HDO Cycle Using a Mars' Global Climate Model

“…Once taken into account, this correction makes it possible to obtain a valid relation under real conditions, where the kinetic fractionation coefficient α c is expressed in function of the fractionation coefficient of the isotopic equilibrium, obtained with Equation (), and the ratio of saturation of water vapor S : $$${\alpha }_{c}=\frac{\alpha S}{\alpha \left({D}_{{H}_{2}O}/{D}_{\mathit{HDO}}\right)(S-1)+1}$$$ where $${D}_{{H}_{2}O}$$ and D HDO are the coefficients of diffusion of respectively H 2 O and HDO. The calculation of the ratio $${D}_{\mathit{HDO}}/{D}_{{H}_{2}O}$$ is detailed in Merlivat (1978), and confirmed by the recent studies of Hellmann and Harvey (2021). The HDO flux is then calculated as in Equation with α c instead of α .…”

“…where 𝐴𝐴 𝐴𝐴𝐻𝐻 2 𝑂𝑂 and D HDO are the coefficients of diffusion of respectively H 2 O and HDO. The calculation of the ratio 𝐴𝐴 𝐴𝐴𝐻𝐻𝐴𝐴𝐻𝐻∕𝐴𝐴𝐻𝐻 2 𝐻𝐻 is detailed in Merlivat (1978), and confirmed by the recent studies of Hellmann and Harvey (2021). The HDO flux is then calculated as in Equation 2 with α c instead of α.…”

Mutual Intersection Points of Reduced Collision Integrals for Lennard–Jones (n-m), Hulburt–Hirschfelder, and Tang–Toennies Potential Energy Functions

“…There is still a vivid interest in the transport properties of neat gases and gas mixtures. In particular, the calculation of transport properties such as diffusion and viscosity from binary potential energy functions U(r) becomes more and more relevant and also accurate, see, e.g., [1][2][3][4][5][6][7][8][9][10][11] and references therein. In many of these theoretical investigations, it is required to explicitly calculate the collision integrals [12,13].…”