Clathrate hydrates Thermodynamic stability

The lattice of the host in the form it takes in the clathrate is usually thermodynamically unstable by itself—that is, with the holes empty. It is stabilized by inclusion of the guest molecules, and it is of obvious interest in connection with the nonstoichiometry of clathrates to consider the extent to which the cavities in the host lattice must be filled before the system achieves thermodynamic stability. The cavities in the host lattice may all be identical in size and environment, as in the hydroquinone clathrates, or they may be of more than one kind. The gas hydrates, for example, have two possible structures, in each of which there are two sorts of cavity, van der Waals and Platteeuw (15) have developed a general statistical theory of clathrates containing more than one type of cavity. 

We treat, in this chapter, mainly solid composed of water molecules such as ices and clathrate hydrates, and show recent significant contribution of simulation studies to our understanding of thermodynamic stability of those crystals in conjunction with structural morphology. Simulation technique adopted here is not limited to molecular dynamics (MD) and Monte Carlo (MC) simulations[l] but does include other method such as lattice dynamics. Electronic state as well as nucleus motion can be solved by the density functional theory[2]. Here we focus, however, our attention on the ambient condition where electronic state and character of the chemical bonds of individual molecules remain intact. Thus, we restrict ourselves to the usual simulation with intermolecular interactions given a priori. 

H. Tanaka and K. Kiyohara, The thermodynamic stability of clathrate hydrate. II. Simultaneous occupation of larger and smaller cages , J. Chem. Phys. 98 (1993) 8110. 

In 1958, van der Waals and Platteenw developed a statistical mechanical theory for predicting the stability region of the clathrate hydrate phase with different guest molecules under different temperature and pressure conditions. The van der Waals-Platteeuw (vdWP) theory is based on the thermodynamic condition of equilibrium between a hydrate phase water/ice ()8) phase and i guest species encapsulated in the hydrate at the phase boundary ... 

STATISTICAL MECHANICAL APPROACH TO THE THERMODYNAMIC STABILITY OF CLATHRATE HYDRATES... 

VII. Application to Thermodynamic Stability of Clathrate Hydrates A. Chemical Potential of Ices and Empty Clathrate Hydrates... 

We may evaluate thermodynamic stability under various conditions where a set of the independent thermodynamic variables is specified. Specification of the independent variables is equivalent to specification of ensemble. In any case, the number of water molecules is fixed to a constant value, and the temperature is also set to the constant one, T. The other mechanical conditions depend on the choice of the variables. The number of water molecules, irrespective of the choice of ensemble, is reserved for the extensive property to indicate the system size. Whatever the other properties are, they can be substituted for the (formal) intensive properties. According to the phase rule, the number of degrees of freedom for clathrate hydrate in equilibrium with the guest fluid consisting of a single component (A = 2,/jp = 2),//f = 2 + / c—r pis2. 

The chemical potential difference is tabulated in Table III [17,18]. There are small but nonmegligible differences depending on both the method and the pair potential. Two distinctive features are noteworthy. CS-II is more stable than CS-I irrelevant as to whether the anharmonic free energy is taken into account for the TIP4P potential (all the properties are calculated for clathrate hydrates with this potential unless otherwise mentioned) [52]. This is also true for most of the other pair potential of water such as SPC/E [53]. The chemical potential difference is negative for most of the potential but it is positive for the CC potential [54] and other potentials with the same functional form, which is favorable to observe a hydration structure around a hydrophobic solute but is inappropriate to evaluate the thermodynamic stability of clathrate hydrates. 

It is highly desirable to establish a relationship between reduction of the dissociation pressure and the efficiency as hydrogen storage in a wide range of pressure with varying composition of a promoter species. To this end, we should find a simple way to evaluate the thermodynamic stability of clathrate hydrates and its cage occupancy from intermolecular interactions currently available under a fixed occupancy of a promoter guest elaborated in Section III.D. Since the chemical potential of water is written as... 

H. Tanaka,/. Chem. Phys., 101, 10833 (1994). The Thermodynamic Stability of Clathrate Hydrate. III. Accommodation of Nonspherical Propane and Ethane Molecules. 

Y. Koyama, H. Tanaka, and K. Koga,/. Chem. Phys., 122, 074503 (2005). On the Thermodynamic Stability and Structural Transition of Clathrate Hydrates. 

H. Tanaka and M. Matsumoto,/. Phys. Chem. B, 115, 14256 (2011). On the Thermodynamic Stability of Clathrate Hydrates V Phase Behaviors Accommodating Large Guest Molecules with New Reference States. 

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