Thermodynamic stability of hydrogen clathrates

Abstract

The stability of the recently characterized type II hydrogen clathrate [Mao, W. L., Mao, H.-K., Goncharov, A. F., Struzhkin, V. V., Guo, Q., et al. (2002) Science 297, 2247-2249] with respect to hydrogen occupancy is examined with a statistical mechanical model in conjunction with first-principles quantum chemistry calculations. It is found that the stability of the clathrate is mainly caused by dispersive interactions between H2 molecules and the water forming the cage walls. Theoretical analysis shows that both individual hydrogen molecules and nH2 guest clusters undergo essentially free rotations inside the clathrate cages. Calculations at the experimental conditions--2,000 bar (1 bar = 100 kPa) and 250 K confirm multiple occupancy of the clathrate cages with average occupations of 2.00 and 3.96 H2 molecules per D-5(12) (small) and H-5(12)6(4) (large) cage, respectively. The H2-H2O interactions also are responsible for the experimentally observed softening of the H[bond]H stretching modes. The clathrate is found to be thermodynamically stable at 25 bar and 150 K.

Fig. 1.

Structure of the S (D-5¹²) and L (H-5¹²6⁴) cages of the type II ice clathrate. Positions of the hydrogen atoms are omitted for clarity. The coordinate axes correspond to the orientation of the model cages used in the calculations.

Fig. 2.

Translational potential energy curve for rigid H₂ inside an L (H-5¹²6⁴) cage (a)andS(D-5¹²) cage (b).The H₂ molecules are displaced from the center of the cage (R = 0) along the (1, 1, 1) direction (Fig. 1). Calculated average occupancies of the S (H-5¹²6⁴) and L (H-5¹²6⁴) cages at 250 K (c) and 150 K (d).

Fig. 3.

Calculated dynamical contributions to enthalpy (Upper) and enthropy (Lower) per mole of clathrated H₂ at 150 K. The extreme left point corresponds to H₂ in ideal gas. Open and filled symbols denote the results obtained in harmonic and “improved” approximations, respectively. Qualitatively similar dependence (not shown) is found at 250 K.