Three-dimensional frameworks

Grangeat P. Mathematical framework of cone beam three-dimensional reconstruction via the first derivative of the Radon transform.. Math. Methods in Tomography, V.1947 of Springer Lecturre Notes in Math-cs, Springer-Verlag, Berlin, 1991, p.66-97. 

Zeolites (section C2.13) are unique because they have regular pores as part of their crystalline stmctures. The pores are so small (about 1 nm in diameter) that zeolites are molecular sieves, allowing small molecules to enter the pores, whereas larger ones are sieved out. The stmctures are built up of linked SiO and AlO tetrahedra that share O ions. The faujasites (zeolite X and zeolite Y) and ZSM-5 are important industrial catalysts. The stmcture of faujasite is represented in figure C2.7.11 and that of ZSM-5 in figure C2.7.12. The points of intersection of the lines represent Si or A1 ions oxygen is present at the centre of each line. This depiction emphasizes the zeolite framework stmcture and shows the presence of the intracrystalline pore stmcture. In the centre of the faujasite stmcture is an open space (supercage) with a diameter of about 1.2 nm. The pore stmcture is three dimensional. 

Aluminosilicates. These silicates consist of frameworks of silica and alumina tetrahedra linked at all corners to form three-dimensional networks familiar examples are the common rock-forming minerals quartz and feldspar. Framework silicates generally form blocky crystals, more isotropic... 

MJ Sutcliffe, I Haneef, D Carney, TL Blundell. Knowledge based modelling of homologous proteins. Part I Three dimensional frameworks derived from the simultaneous superposition of multiple structures. Protein Eng 1 377-384, 1987. 

Serine proteinases such as chymotrypsin and subtilisin catalyze the cleavage of peptide bonds. Four features essential for catalysis are present in the three-dimensional structures of all serine proteinases a catalytic triad, an oxyanion binding site, a substrate specificity pocket, and a nonspecific binding site for polypeptide substrates. These four features, in a very similar arrangement, are present in both chymotrypsin and subtilisin even though they are achieved in the two enzymes in completely different ways by quite different three-dimensional structures. Chymotrypsin is built up from two p-barrel domains, whereas the subtilisin structure is of the a/p type. These two enzymes provide an example of convergent evolution where completely different loop regions, attached to different framework structures, form similar active sites. 

There are examples of each of these mechanisms, and a three-dimensional potential energy diagram can provide a useful general framework within which to consider specific addition reactions. The breakdown of a tetrahedral intermediate involves the same processes but operates in the opposite direction, so the principles that are developed will apply equally well to the reactions of the tetrahedral intermediates. Let us examine the three general mechanistic cases in relation to the energy diagram in Fig. 8.3. 

The optimised interlayer distance of a concentric bilayered CNT by density-functional theory treatment was calculated to be 3.39 A [23] compared with the experimental value of 3.4 A [24]. Modification of the electronic structure (especially metallic state) due to the inner tube has been examined for two kinds of models of concentric bilayered CNT, (5, 5)-(10, 10) and (9, 0)-(18, 0), in the framework of the Huckel-type treatment [25]. The stacked layer patterns considered are illustrated in Fig. 8. It has been predicted that metallic property would not change within this stacking mode due to symmetry reason, which is almost similar to the case in the interlayer interaction of two graphene sheets [26]. Moreover, in the three-dimensional graphite, the interlayer distance of which is 3.35 A [27], there is only a slight overlapping (0.03-0.04 eV) of the HO and the LU bands at the Fermi level of a sheet of graphite plane [28,29],... 

In a very similar fashion we ean treat the problem of adsorption within the framework of the three-dimensional model of adsorption [42]. 

Silicon never occurs free it invariably occurs combined with oxygen and, with trivial exceptions, is always 4-coordinate in nature. The Si04 unit may occur as an individual group or be linked into chains, ribbons, rings, sheets or three-dimensional frameworks (pp. 347-59). 

Figure 11. The [B2]X4 framework of an v4[B 2X4 spinel, e.g. A - MnO, with three dimensional pathways for lithium-ion transport. (The direction of transport perpendicular to the plane of the paper has not been marked by an arrow).

A variety of other structures are possible with silicate minerals, including sheets and three-dimensional frameworks. In all cases, the structure includes bonds that are predominantly covalent and directional. They can therefore be viewed as being based on increasingly crosslinked inorganic polymers. 

The framework structures and pore cross-sections of two types of zeolites are shown. (Top) A Faujasite-type zeolite has a three-dimensional channel system with pores of at least 7.4 A in diameter. A pore is formed by 12 oxygen atoms in a ring. (Bottom) ZSM-5 zeolite has interconnected channels running in one direction, with pores 5.6 A in diameter. ZSM-5 pores are formed by 10 oxygen atoms in a ring. Reprinted with permission from Chemical Engineering Progress, 84(2), February 1988, 32. 

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