The cavities in hydrates

Jeffrey noted that the 12-, 14-, and 16-hedra are not stable in a pure water structure. However, some studies have suggested that liquid water is structured as cavities (Sorensen, 1994 Walrafen and Chu, 1995). Pauling (1959) proposed that water was composed of complexes of 512 cavities with a water molecule as 

Cavity Small Large Small Large Small Medium Large 

Asterisks represent the variation in radius taken by dividing the difference between the largest and smallest distances by the largest distance. 

Many hydrate cavities have analogs (1) in the clathrasils in which SiC 2 replaces water as a host molecule (Gerke and Gies, 1984) and (2) in the Buckminsterfullerene (covalently bonded carbon cavities) family (Curl and Smalley, 1991). Even with these analogous structures providing estimates of other cavities, for hydrate unit crystals there is the additional restriction that the cavities must be packed to fill space. 

With the exceptions of cavities containing square faces, all hydrate cavities (as well as clathrasil and Buckyball family cavities) follow Euler s theorem (Lyusternik, 1963) for convex polyhedra, stated as (F + V = E + 2). The number of faces (F) plus the vertices (V) equals the edges (E) plus 2. Euler s theorem is easily fulfilled in cavities having exactly 12 pentagonal faces and any number of hexagonal faces except one. 

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