Structure Selectivity of Mixed Gas Hydrates and Group 14 Clathrates

The structure selectivity of mixed gas hydrates and group 14 clathrates is examined on the basis of statistical mechanical theories and the empirical rule on the topological constraint of the Frank-Kasper phases. The most stable structure is revealed by the generalized phase diagram, where the chemical potential differences in the three canonical forms of clathrates are independent variables. The most stable structure incorporating individual guest species is evaluated by the locus of the chemical potential differences on this generalized phase diagram. We show that the method developed here is simple but powerful to estimate roughly phase behaviors of clathrate compounds in a wide range of thermodynamic conditions, which is demonstrated by two applications: the generalized phase diagram of group 14 element clathrates and the phase behavior of mixed gas hydrates. The present theory leads to proposals of phase change agents, of which the addition sensitively influences the structure selectivity, encompassing even minor structures.