Thermodynamics of clathrate hydrate at low and high pressures with application to the outer solar system

Abstract

The thermodynamic stability of clathrate hydrate is calculated under a wide range of temperature and pressure conditions applicable to solar system problems, using a statistical mechanical theory developed by van der Waals and Platteeuw (1959) and existing experimental data on properties of clathrate hydrates and their components. At low pressure, dissociation pressures and partition functions (Langmuir constants) for CO clathrate (hydrate) have been predicted, using the properties of clathrate containing, as guests, molecules similar to CO. The comparable or higher propensity of CO to incorporate in clathrate relative to N_2 is used to argue for high CO-to-N_2 ratios in primordial Titan if N_2 was accreted as clathrate. The relative incorporation of noble gases in clathrate from a solar composition gas at low temperatures is calculated and applied to the case of giant-planet atmospheres and icy satellites. It is argued that nonsolar but well-constrained noble gas abundances will be measured by Galileo in the Jovian atmosphere if the observed carbon enhancement is due to bombardment of the atmosphere by clathrate-bearing planetesimals sometime after planetary formation. The noble gas abundances in Titan's atmosphere are also predicted under the hypothesis that much of the satellite's methane accreted as clathrate. Double occupancy of clathrate cages by H_2 and CH_4 in contact with a solar composition gas is examined, and it is concluded that potentially important amounts of H_2 may have incorporated in satellites as clathrate. The kinetics of clathrate formation is also examined, and it is suggested that, under thermodynamically appropriate conditions, essentially complete clathration of water ice could have occurred in high-pressure nebulae around giant planets but probably not in the outer solar nebula; comets probably did not aggregate as clathrate. At moderate pressures, the phase diagram for methane clathrate hydrate in the presence of 15% ammonia (relative to water) is constructed, and application to the early Titan atmospheric composition is described. The high-pressure stability of CH_4, N_2, and mixed CH_4-N_2 clathrate hydrate is calculated; conversion back to water and CH_4 and/ or N_2 fluids or solids is predicted for pressures ≳ 12 kilobars (independent of temperature) and temperatures ≳ 320 K (independent of pressure). The effect of ammonia is to shrink the T-P stability field of clathrate with increasing ammonia concentration. These results imply that (1) clathrate is stable throughout the interior of Oberon- and Rhea-sized icy satellites, and (2) clathrate incorporated in the innermost icy regions of Titan would have decomposed, perhaps allowing buoyant methane to rise. Brief speculation on the implications of this conclusion for the origin of surficial methane on Titan is given. A list of suggested experiments and observations to test the theory and its predictions is presented.