Dissociation Line and Driving Force for Nucleation of the Multiple Occupied Hydrogen Hydrate from Computer Simulation

In this work, we determine the dissociation temperature of the hydrogen (H$_2$) hydrate by computer simulation using two different methods. In both cases, the molecules of water and H$_2$ are modeled using the TIP4P/Ice and a modified version of the Silvera and Goldman models respectively, and the Berthelot combining rule for the cross water-H$_2$ interactions has been modified. The first method used in this work is the solubility method which consists in determining the solubility of H$_2$ in an aqueous phase when in contact with a H$_2$ hydrate (H--L$_{\text{w}}$) phase and when in contact with a pure H$_2$ phase (L$_{\text{w}}$--L$_{\text{H}_2}$) at different temperatures. At a given pressure value, both solubility curves intersect at the temperature ($T_3$) at which the three phases coexist in equilibrium. Following this approach, we determine the dissociation temperature of the H$_2$ hydrate at $185\,\text{MPa}$ finding a good agreement with the data previously reported in the literature. We also analyze the effect of the multiple occupancy of the D, or small, and H, or large, cages of the sII hydrate structure. We conclude that the $T_3$ value is barely affected by the occupancy of the H$_2$ hydrate at $185\,\text{MPa}$. From the analysis of the solubility curves and performing extra bulk simulations of the three phases involved in the equilibrium, we also determine the driving force for nucleation ($Δμ^{\text{EC}}_{N}$) at $185\,\text{MPa}$ as a function of the supercooling degree and the H$_2$ hydrate occupancy. We determine that, thermodynamically, the most favored occupancy of the H$_2$ hydrate consists of 1 H$_2$ molecule in the D cages and 3 in the H cages (named as 1-3 occupancy).