Correlation intracrystalline diffusion

The control of reaction rates by a bulk difiusion process is not usually demonstrable by microscopic observations, but support may be obtained from measurements of diffusion coefficients of appropriate species within the structure concerned. This approach has been invaluable in formulating the mechanisms of oxidation of metals, where rates of reaction have been correlated with rates of transportation of ions across barrier layers of product. Sometimes the paths by which such movements occur correspond to regions of high difi isivity, involving imperfect zones within the barrier layer, compared with normal rates of intracrystalline diffusion across more perfect regions of material [63]. Difiusion measurements have been made for ions in nickel sulfide and it was concluded that the decomposition of NiS is diffiision controlled [50]. 

Fig. 56 Correlation between the actual boundary concentration (Csurf) and the relative uptake (m) at the corresponding instant of time. Three different cases are shown the mass transport is essentially limited by intracrystalline diffusion (la/D = 100), by surface barriers la/D = 0.01), and both by intracrystalline diffusion and surface resistance la/D = 1)...

Surface diffusion is an activated process which is in some ways analogous to micropore or intracrystalline diffusion. The temperature dependence may be correlated by an Eyring equation ... 

The best correlation of the observed isomerization selectivities was found in terms of the diameter of the intracrystalline cavity, determined from the known crystal structure (9) of these zeolites, as shown in Figure 2. While faujasite, mordenite and ZSM-4 all have 12-membered ring ports and hence should be similar in their diffusion properties, they differ considerably in the size of their largest intracrystalline cavity both mordenite and ZSM-4 have essentially straight channels, whereas faujasite has a large cavity at the intersection of the three-dimensional channel system. 

The correlation between selectivity and intracrystalline free space can be readily accounted for in terms of the mechanisms of the reactions involved. The acid-catalyzed xylene isomerization occurs via 1,2-methyl shifts in protonated xylenes (Figure 3). A mechanism via two transalkylation steps as proposed for synthetic faujasite (8) can be ruled out in view of the strictly consecutive nature of the isomerization sequence o m p and the low activity for disproportionation. Disproportionation involves a large diphenylmethane-type intermediate (Figure 4). It is suggested that this intermediate can form readily in the large intracrystalline cavity (diameter. 1.3 nm) of faujasite, but is sterically inhibited in the smaller pores of mordenite and ZSM-4 (d -0.8 nm) and especially of ZSM-5 (d -0.6 nm). Thus, transition state selectivity rather than shape selective diffusion are responsible for the high xylene isomerization selectivity of ZSM-5. 

It has been demonstrated by numerical simulations [9] that, with this definition, eq. 2 provides a reasonable order-of-magnitude estimate of the effectiveness factor also in the case of single-file diffusion. While in the case of ordinary diffnsion the intracrystalline mean life time may be easily correlated with the crystal size and the internal mobility [11], similar analytical expressions for single-file diffusion have not been established. The rule-of-thumb given in Ref. [10] on the basis of a few first numerical simulations turned out to be of rather limited validity in recent more refined considerations [12]. 

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