Framework Densities FDs

A zeolitic structure can be described in various crystallographic terms. For many systems it is now possible to specify the following structural features the SBUs, the framework density, the coordination sequences, the unit cell dimensions and composition, the direction of the channels and the aperture (window) dimensions (Atlas of Zeolite Structure Types, 1992 Thomas et al., 1997). The framework density, FD, is defined as the number of T atoms per 1000 A1 (i.e. per 1 nm3) of the structure. 

Wide-pore zeolites must have a low "framework density" (FD), equal to the number of tetrahedral "T" atoms (silicon or aluminium) per lOOOA. Two questions arise naturally in this context. What sets the framework density What is the minimum FD achievable for a hydrophobic zeolite These are difficult questions to answer within the standard three-dimensional Euclidean view of these frameworks. However, within a two-dimensional hyperbolic perspective, they are readily answered. 

Micropore volume of zeolites can be estimated from their framework density, Fd, included in Table 2 [17], These data are obtained from XRD and correspond to the number of T atoms (A1 or Si) per 1000 A. From this information, and the molecular formula of the zeolite, the volume occupied by the framework per gram of sample can be calculated from equation 2. 

Figure 5.6 Enthalpy of transition from quartz vs framework density (FD) for several dense and microporous SiOi polymorphs. Zeolite phases are denoted by their FTC, while minor case codes correspond to the dense phases quartz (q), tridymite (tr), cristobalite (cr), moganite (mo) and coesite (co). The figure suggests the stabilities of silica phases decrease when their densities decrease (except for the high-pressure phase coesite, which is compressed beyond the density of quartz the enthalpy for moganite deviates from the trend, but it was not directly measured and is not as reliable as the rest). The figure also shows pure-silica zeolites are not highly destabilised. Reproduced with permission from P.M. Piccione, C. Laberty, S. Yang, M.A. Camblor, A. Navrotsky and M.E. Davis, /. Phys. Chem. B, 104, 10001. Copyright (2000) American Chemical Society.

Figure 2.13 Meier s plot of the framework density (FD) of tetrahedral frameworks against the size of the smallest ring present in the structure indicates that the most open structures tend to contain small rings, particularly 4MRs and 3MRs. [Reproduced from reference 2 with permission. Copyright 2001, Elsevier.]...

The framework density is dependent only on the average ring size and the area per vertex. From these equations, it can be seen immediately that the formation of wide-pore zeolites (of low FD) requires networks whose average ring size on the surface is as close to four as possible. 

As can be seen from Figure 2.22, a majority of the structure types are in category 4 . + Indicates that T-atoms are associated with larger rings only. One important conclusion derived from this plot is that low-density frameworks are likely to contain 3-rings. This hypothesis has been tested by hypothetical structures and 3-ring structures having FDs below 10. 

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