Random fragmentation

Lonally, the templates were chosen by trial and error or exhaustive enumeration. A itafional method named ZEBEDDE (ZEolites By Evolutionary De novo DEsign) en developed to try to introduce some rationale into the selection of templates et al. 1996 Willock et al. 1997]. The templates are grown within the zeolite by an iterative inside-out approach, starting from a seed molecule. At each jn an action is randomly selected from a list that includes the addition of new (from a library of fragments), random translation or rotation, random bond rota-ing formation or energy minimisation of the template. A cost function based on erlap of van der Waals spheres is used to control the growth of the template ale ... 

PDI extraction requires synchronisation of the oxidative process in neighbouring methylene chains, separated by a polymellitimide fragment. Random chain initiation and transmission would cause the occurrence of a series of oligomers in products of solid-phase oxidation. 

Theoretical efforts a step beyond simply fitting standard statistical curves to fragment size distribution data have involved applications of geometric statistical concepts, i.e., the random partitioning of lines, areas, or volumes into the most probable distribution of sizes. The one-dimensional problem is reasonably straightforward and has been discussed by numerous authors... 

Figure 8.19. Random one-dimensional fragmentation—a Poisson process.

The more common approach is the actual positioning of random lines on a surface to create a statistical distribution of fragment sizes. One example of this, suggested by Mott and Linfoot (1943), is a construction of randomly positioned and oriented infinite lines as illustrated in Fig. 8.23. If the random lines are restricted to horizontal or vertical orientation an analytic solution can be obtained for the cumulative fragment number (Mott and Linfoot,... 

Figure 8.23. Geometric fragmentation with randomly positioned and oriented infinite lines.

Unfortunately, fragmentation by construction does not appear to be independent of the random construction algorithm. An alternative method of successive segmentation (Grady and Kipp, 1985) of the surface, as illustrated in Fig. 8.24 leads to a fragment distribution which agrees well with a linear exponential distribution ((8.59)) and differs significantly from the Mott distribution ((8.58)). 

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