Polyhedral cavities

Clathrasils, which have polyhedral cavities, but with windows that are too small to allow the passage of other molecules, so that enclosed ions or foreign molecules cannot escape. Examples are ultramarines and melanophlogite (Si02)46-8(N2, C02, CH4). 

Zeolites with polyhedral cavities which are connected by wide windows or channels that permit the diffusion of foreign ions or molecules. 

A general conclusion from these DPT studies on M Eio clusters of various types is that the Wade-Mingos rules [13-16] are most applicable when the Eio unit has as large a cavity as possible, i.e., when E is a relatively heavy element such as bismuth or lead. Plowever, if the Eio cavity is too small, particularly when E is arsenic or germanium, then maximizing the internal volume of the polyhedral cavity can override any electronic considerations from the Wade-Mingos rules. 

In certain 3D nets there are well-defined polyhedral cavities, and the links of the net may alternatively be described as the edges of a space-filling assembly of polyhedra. At least four links must meet at every point of such a net, and the most important nets of this kind are, in fact, 4-connected nets. Space-filling arrangements of polyhedra leading to such nets are therefore described after we have dealt with the simpler 4-connected nets. 

We shall conclude our remarks on nets by describing briefly two types of structure which are of particular interest in structural chemistry, namely, those in which there are well-defined polyhedral cavities or infinite tunnels. The Bg groups in CaB are preferably not describeu as polyhedral cavities because they are... 

Class (d). These hydrates are distinguished on the grounds that there are no well defined polyhedral cavities, the nets being 3- or (3 + 4)-connected. The 3-connected framework in N4(CH2)g. 6 H2O (m.p. 13-5°C) is that of Fig. 3.31 (p. 97), the same as one of the two identical interpenetrating frameworks in /3-quinol clathrates. Since a framework of this kind built of H2O molecules has only 9 links (0—H—0 bonds) for every 6 H2O there are 3 H atoms available to form hydrogen bonds to the guest molecules. The latter are suspended bat-like in the cavities halfway between the 6-rings (Fig. 15.8), that is, they occupy the... 

A characteristic feature of zeolites is the existence of tunnels (or systems of interconnected polyhedral cavities) through the structures, and we may therefore expect three main types in which the tunnels are parallel to (a) one line, giving the crystals a fibrous character, (b) two lines and arranged in planes, so that the crystals have a lamellar nature, or (c) three non-coplanar lines, such as cubic axes, when the crystals have no pronounced fibrous or lamellar structure. The most symmetrical... 

As a rule, gas hydrates obtained under the P-T conditions close to those in the nearsurface have one of the three following structures cubic structure 1 (si), cubic structure II (sll) or hexagonal structure H (sH). Each of these structures has its own set of polyhedral cavities of different sizes. The better that the size and molecular shape of the guest... 

The basic idea is that the channels and polyhedral cavities of a zeolite crystal can be placed in correspondence with the bonds and vertices of a d — 3 dimensional, finite Cartesian lattice. Hence, the problem of determining the trajectories of guest molecules through zeolite crystals of finite extent is modeled by studying the random walk problem on, here, finite lattices of two different topologies. 

In obtaining the above estimates of the maximum sorption time, it was assumed that sorption occurred at one cavity only, viz., the one farthest removed from the surface of the zeolite crystal. The question arises whether and to what extent the above picture changes if sorption is permitted in any of the polyhedral cavities defining the assembly. Let si be the probability of sorption of the diffusing species in cavity i. In the case, all St = s > 0, the consequences of sorption at the satellite sites i are displayed in tables 3 and 5 of ref. 14 for faujasite-type structures for both ambient conditions noted earlier, and in table VI of ref. 9 for zeolite A-type structures. It is plain from these results that distinctions between different zeolite channel patterns or between different boundary conditions become inconsequential once the satellite sorption probability 5 > 0.10. 

Consider now the effect of presorbed polar molecules on the diffusivity of nonpolar molecules in host zeolites. Blockage of polyhedral cavities by strongly sorbed polar molecules is found experimentally to lead to a... 

Kitazawa, T. Nishikiori. S. Iwamoto, T. Three-dimensional framework structures built of heptacyanotricad-mate(II) units providing polyhedral cavities for guests Classification of the zeolite-like structures. J. Chem. Soc., Dalton Trans. 1994. 3695-3710. 

In ice, hydrogen-bonding between molecules leads to the formation of a five-molecule structural unit, which is approximately tetrahedral (Fig. 3.4b). Each oxygen atom is surrounded by four others at a distance of 2.75 A three of them are in the same layer (forming, with other water molecules, puckered six-membered rings) and the fourth is in an adjacent layer. Large polyhedral cavities lie between these layers. 

Figure 19. (a) Two views of the partitioning of the 12 vertices of a regular icosahedron into six rhombohedral vertices (R) and six equatorial vertices (E) upon reduction from It, to symmetry, (b) The Samson complex derived from a truncated icosahedron, which is found in the /3-rhombohedral boron structure, (c) The 28-vertex polyhedral cavities formed by overlap of the equatorial pentagonal pyramidal cavities of three Samson complexes in the -rhombohedral boron structure. 

X-ray [41] studies of 13c showed a intriguing structure in which four Vt-cone clefts (Fig. 7.13) were present with seven calixarene oxygen atoms converging toward the central polyhedral cavity, while the bridged oxygens at the 1,3,5,7 positions adopted a tetrahedral arrangement. 

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