On the thermodynamic stability of clathrate hydrate. I

Abstract

The thermodynamic stability of a clathrate hydrate has been investigated by examining the free energy of formation of clathrate hydrate II encaging propane. The total free energy has been divided into several contributions—the interaction between water and guest propane molecules, the entropic contribution arising from the combinations of cage occupancy, and also the free energy due to intermolecular vibrations. The present method avoids some of the fundamental assumptions in the van der Waals and Platteeuw theory. This enables us to assess separately the factors which have a bearing on the thermodynamic stability of the hydrate. Kinetic stability has also been investigated by calculating molecular dynamics trajectories having initially excited several characteristic vibrational modes. We show, for propane in large cages, that the potential energy surface of the guest molecule in a cage has a single minimum and molecular motions can be approximated accurately to a collection of harmonic oscillators. It is found that the intermolecular vibrational modes for water molecules shift toward the higher frequency regions in the presence of the guest molecules. This shift of the vibrational motions of water molecules gives rise to an increase in the chemical potential of water compared with that evaluated under the fixed lattice sites approximation where only vibrations of the guest molecules are taken into account. The empty clathrate hydrate structures melt into liquid water within a few picoseconds when several of the lowest frequency modes are excited. On the other hand, the guest molecules are found to prevent the clathrate structures from melting even 10 ps after the excitation of the same frequency modes.