Cage occupancies of CH4, CO2, and Xe hydrates: Mean field theory and grandcanonical Monte Carlo simulations.

We propose a statistical mechanical theory for the thermodynamic stability of clathrate hydrates, considering the influence of the guest-guest interaction on the occupancies of the cages. A mean field approximation is developed to examine the magnitude of the influence. Our new method works remarkably well, which is manifested by two sorts of grandcanonical Monte Carlo (GCMC) simulations. One is full GCMC, and the other is designed in the present study for clathrate hydrates, called lattice-GCMC, in which each guest can be adsorbed at one of the centers of the cage. In the latter simulation, only the guest-guest interaction is explicitly treated, incorporating the host-guest interaction into the free energy of the cage occupation without other guests. Critical phenomena for guest species, such as large density fluctuations, are observed when the temperature is low or the guest-guest interaction is strong.