Pore shape change

The decrease in IT is caused by small shifts of atoms located in a layer of 3 to 5 atomic diameters near the interface. Such shifts can be clearly observed in monociystals (reconstruction and relaxation phenomena) [12], There are mechanisms based on the decrease of A at V = const with the decrease of dispersion A/V. The results of action of these mechanisms are change of particle and pore shape, decrease of the micropore amount and surface roughness, etc. during sintering, coalescence, etc. 

If we consider the microstructural changes to the particles, it is clear that the spherical particles will alter their shape with time to that of a prolate ellipsoid of revolution by tins transfer of material finm the spherical surface to that of the neck. In fact, the distance between the centers of the particles is not affected by vapor phase transport and only the shape of the pores is changed. Without a decrease in the center-to-center distance there is no densification or sintering. Therefore, this is one example of coarsening during the initial stage sintering. 

The increase in isobutene selectivity with time-on-stream is a particular property of the ferrierite. This zeolite has two types of active sites the external sites (on the external surface of the zeolite crystallites) which are non-selective for skeletal isomerization and the internal sites (inside the zeolite pores) which are selective for this reaction (9). The changes observed on the selectivity have been associated with modifications of pore shapes ough coke deposition that favor reactions involving small molecules, such as -butene to isobutene isomerization (8). More recently, it has been reported that a bimolecular mechanism takes place at the non-selective acid sites, while a monomolecular mechanism occurs on the selective sites (10), the coke deposition being necessary in order to poison, block, and modify the non-shape selective acid sites. 

The silica materials with various pore-wall thicknesses are suitable as templates for mesoporous carbons with controlled pore diameters.[252] The carbons exhibit wide varieties of pore shape, connectivity, and pore-wall thickness, depending on the silica templates that are synthesized with various structures and pore diameters. The syntheses of mesoporous carbons are summarized in Table 8.8. Figure 8.49 show the XRD pattern of CMK-3 (keeps original symmetry) [34] and Figure 8.50 shows the changes in powder XRD patterns during synthesis of the CMK-1 with its silica template MCM-48 (creates new symmetry).1321... 

Fig. 8.13. Schematic picture of changes in pore shape during sintering.

The equations and plots presented in the foregoing sections largely pertain to the diffusion of a single component followed by reaction. There are several other situations of industrial importance on which considerable information is available. They include biomolecular reactions in which the diffusion-reaction problem must be extended to two molecular species, reactions in the liquid phase, reactions in zeolites, reactions in immobilized catalysts, and extension to complex reactions (see Aris, 1975 Doraiswamy, 2001). Several factors influence the effectiveness factor, such as pore shape and constriction, particle size distribution, micro-macro pore structure, flow regime (bulk or Knudsen), transverse diffusion, gross external surface area of catalyst (as distinct from the total pore area), and volume change upon reaction. Table 11.8 lists the major effects of all these situations and factors. 

Figure 10.9 Basic atomic mechanisms that can lead to (a) coarsening and change in pore shape and (b) densification. (c) Thought experiment illustrating how removal of material from the area between particles into the pore leads to shrinkage and densification.

We also can use these microscopic models to describe diffusion radially inward, accounting for the changing pore shape and the presence of void or solid as a function of any position (r, 0, mass transfer is solved rigorously in a pellet at the level depicted in Figure 7.1D to give an equation of the form... 

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