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Volatile inventories in clathrate hydrates formed in the primordial nebula

Examination of ambient thermodynamic conditions suggest that clathrate hydrates could exist in the martian permafrost, on the surface and in the interior of Titan, as well as in other icy satellites. Clathrate hydrates probably formed in a significant fraction of planetesimals in the solar system. Thus, these crystalline solids may have been accreted in comets, in the forming giant planets and in their surrounding satellite systems. In this work, we use a statistical thermodynamic model to investigate the composition of clathrate hydrates that may have formed in the primordial nebula. In our approach, we consider the formation sequence of the different ices occurring during the cooling of the nebula, a reasonable idealization of the process by which volatiles are trapped in planetesimals. We then determine the fractional occupancies of guests in each clathrate hydrate formed at given temperature. The major ingredient of our model is the description of the guest-clathrate hydrate interaction by a spherically averaged Kihara potential with a nominal set of parameters, most of which being fitted on experimental equilibrium data. Our model allows us to find that Kr, Ar and N$_2$ can be efficiently encaged in clathrate hydrates formed at temperatures higher than $\sim$ 48.5 K in the primitive nebula, instead of forming pure condensates below 30 K. However, we find at the same time that the determination of the relative abundances of guest species incorporated in these clathrate hydrates strongly depends on the choice of the parameters of the Kihara potential and also on the adopted size of cages. Indeed, testing different potential parameters, we have noted that even minor dispersions between the different existing sets can lead to non-negligible variations in the determination of the volatiles trapped in clathrate hydrates formed in the primordial nebula.