Thermodynamic stability of hydrogen hydrates of ice I_c and II structures

The occupancy of hydrogen inside the voids of ice I_c and ice II, which gives two stable hydrogen hydrate compounds at high pressure and temperature, has been examined using a hybrid grand-canonical Monte Carlo simulation in wide ranges of pressure and temperature. The simulation reproduces the maximum hydrogen-to-water molar ratio and gives a detailed description on the hydrogen influence toward the stability of ice structures. A simple theoretical model, which reproduces the simulation results, provides a global phase diagram of two-component system in which the phase transitions between various phases can be predicted as a function of pressure, temperature, and chemical composition. A relevant thermodynamic potential and statistical-mechanical ensemble to describe the filled-ice compounds are discussed, from which one can derive two important properties of hydrogen hydrate compounds: the isothermal compressibility and the quantification of thermodynamic stability in term of the chemical potential.