Thermodynamic stability of hydrogen hydrates of ice ${\text{I}}_c$ and II structures

The occupancy of hydrogen inside the voids of ice ${\text{I}}_c$ 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.

Figure 1

Pressure and temperature dependence of chemical potential for hydrogen fluid. The linear line shows the chemical potential of hydrogen treated as ideal fluid.

Figure 2

(Color online) Structures of ${\text{C}}_1$ and ${\text{C}}_2$ in various hydrogen occupancy, obtained from GCMC simulation. On the left side: ${\text{C}}_1$ with maximum hydrogen occupancy $\left(T=273\text{K},p=2100\text{MPa}\right)$ in (a) perspective and (c) orthographic view and (e) ${\text{C}}_1$ with partial hydrogen occupancy $\left(T=273\text{K},p=300\text{MPa}\right)$. On the right side: ${\text{C}}_2$ with maximum hydrogen occupancy $\left(T=273\text{K},p=3500\text{MPa}\right)$ in (b) perspective and (d) orthographic view and (f) ${\text{C}}_2$ with partial hydrogen occupancy $\left(T=273\text{K},p=700\text{MPa}\right)$.

Figure 3

Pressure and temperature dependence of hydrogen-to-water molar ratio in (a) ${\text{C}}_1$ and (b) ${\text{C}}_2$, obtained from GCMC simulation (solid line) and theoretical calculation based on vdWP theory (dashed line). The results from theoretical calculation based on one-dimensional partition function for ${\text{C}}_1$ is shown as dotted line (a).

Figure 4

Density of water in (a) ${\text{C}}_1$ and (b) ${\text{C}}_2$. A discontinuity in the density of ${\text{C}}_2$ suggests for a structure collapse of ice ${\text{I}}_c$ lattice during decompression.

Figure 5

Interaction energy curve of a hydrogen molecule with the surrounding water molecules in an interstitial space of ice ${\text{I}}_c$ as a function of displacement from its stable position: averaged over all orientation (solid line); minimum energy (dashed line). The vertical bars show variance of interaction energy in other interstitial spaces of ice ${\text{I}}_c$.

Figure 6

Isothermal compressibility of (a) ${\text{C}}_2$ and ice VII, (b) ${\text{C}}_1$ and ice II, obtained from free-energy calculation (solid line) and GCMC simulation (dashed line).

Figure 7

Chemical potential of water in ${\text{C}}_1$ (linear) and ${\text{C}}_2$ (curve) at $T=273\text{K}$ (solid line), 250 K (dashed line), and 230 K (dotted line). The chemical-potential shifts suggest a structure transition from ${\text{C}}_1$ to ${\text{C}}_2$ as the compression proceeds.

Figure 8

Phase diagram of ${\text{C}}_1$ and ${\text{C}}_2$ on $p\text{−}{x}_H$ plane at $T=273\text{K}$ (solid line and circle point), 250 K (dashed line and square point), and 230 K (dotted line and triangle point). The horizontal line shows the triple point of ${\text{C}}_1+{\text{C}}_2+{\text{H}}_2$ coexistence and ${\text{C}}_2+{\text{C}}_1+\text{VII}$ coexistence. They also marked the phase boundary between ${\text{C}}_1$, ${\text{C}}_1+{\text{C}}_2$, and ${\text{C}}_2$ on $p\text{−}T$ plane.