Volatile inventories in clathrate hydrates formed in the primordial nebula.

The examination of ambient thermodynamic conditions suggests 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 are 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 a 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 are fitted to experimental equilibrium data. Our model allows us to find that Kr, Ar and N2 can be efficiently encaged in clathrate hydrates formed at temperatures higher than approximately 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, by 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. However, these variations are not found to be strong enough to reverse the relative abundances between the different volatiles in the clathrate hydrates themselves. On the other hand, if contraction or expansion of the cages due to temperature variations are imposed in our model, the Ar and Kr mole fractions can be modified up to several orders of magnitude in clathrate hydrates. Moreover, mole fractions of other molecules such as N2 or CO are also subject to strong changes with the variation of the size of the cages. Our results may affect the predictions of the composition of the planetesimals formed in the outer solar system. In particular, the volatile abundances calculated in the giant planets' atmospheres should be altered because these quantities are proportional to the mass of accreted and vaporized icy planetesimals. For similar reasons, the estimates of the volatile budgets accreted by icy satellites and comets may also be altered by our calculations. For instance, under some conditions, our calculations predict that the abundance of argon in the atmosphere of Titan should be higher than the value measured by Huygens. Moreover, the Ar abundance in comets could be higher than the value predicted by models invoking the incorporation of volatiles in the form of clathrate hydrates in these bodies.