Curvature ring size

The hydrogen bond interaction of OH groups at the surface is determined by the Si-O-Si ring size, and its opening degree, the number of hydroxyls per silicon site, and the surface curvature. The concentration of OH groups at the surface is approximately 2-5 x 1018 OH/m2, and it is found to be almost independent of the synthesis conditions of porous silica [162],... 

Figure 2.12 Plot of the area per T-atom vertex SI) versus the average ring size, n, for a variety of zeolites, silica clathrasils and dense silicates. (All zeolites have a silicon aluminium ratio exceeding three, so that the approximate stoichiometry of all these frameworks is Si02). Zeolite and clathrasil frameworks are labelled by the code adopted by the International Zeolite Association [18]). The shaded domain indicates the window of geometrically accessible values of as a function of the ring size. Despite the allowed geometric variability, the value of D is close to 12.2A2 for all these "silicates", regardless of the ring size and consequent intrinsic curvature.

In all the cases analysed here, those frameworks realised in the laboratory (or in nature) do lie near to the dotted curves deduced from reasonable bond lengths and angles. Remarkably though, the variation in bulk density follows the locus of the curves assuming constant area. The intersection of the two curves determines the preferred intrinsic curvature, characterised by the ring size. 

How do these unconventional ideas link with the standard view of a solid as a close packed array of atoms Evidently most of the frameworks discussed above cannot be so characterised. The two-dimensional hyperbolic picture does break down for very dense structures. Thus the densest four-coordinated silicate, coesite, violates this universality (see Fig. 2.12). (Its ring size is less than that of trid5m[ ite, cristobalite, keatite or quartz, in spite of its higher density.) This polymorph is too dense for a two-dimensional description to be useful and the Aree-dimensional description takes over. The notion of intrinsic curvature is less rigid for silicates than for the other frameworks, because the Si-O-Si angle usually differs from 180 . 

Figure 5.27 Model representing the structure of a diamond particle about 2nm in size with a partly graphitized surface. A part of this shell is highlighted for better visibility. At the corners of this section the five-membered rings inducing curvature can be seen ( Springer 2005).

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