Intracrystalline effectiveness factor

The analysis of the literature data shows that zeolites modified with nobel metals are among perspective catalysts for this process. The main drawbacks related to these catalysts are rather low efficiency and selectivity. The low efficiency is connected with intracrystalline diffusion limitations in zeolitic porous system. Thus, the effectiveness factor for transformation of n-alkanes over mordenite calculated basing on Thiele model pointed that only 30% of zeolitic pore system are involved in the catalytic reaction [1], On the other hand, lower selectivity in the case of longer alkanes is due to their easier cracking in comparison to shorter alkanes. 

The development of composite micro/mesoporous materials opens new perspectives for the improvement of zeolytic catalysts. These materials combine the advantages of both zeolites and mesoporous molecular sieves, in particular, strong acidity, high thermal and hydrothermal stability and improved diffusivity of bulky molecules due to reduction of the intracrystalline diffusion path length, resulting from creation of secondary mesoporous structure. It can be expected that the creation of secondary mesoporous structure in zeolitic crystals, on the one hand, will result in the improvement of the effectiveness factor in hydroisomerization process and, on the other hand, will lead to the decrease of the residence time of products and minimization of secondary reactions, such as cracking. This will result in an increase of both the conversion and the selectivity to isomerization products. 

The shape of this relation is found to be rather insensitive to the given geometry of the crystallites []]. In particular, the effectiveness factor is found to be equal to 1 for intracrystalline diffusion in zeolites under stationary conditions [4,5]. 

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]. 

It is seen that the intracrystalline MgO induces pore blockage in a fraction of the pore system and alters the porosity as well as D0, and/or r with the latter factors contributing most to the reduced diffusivity. In contrast, the coke modifier appears to affect mainly the surface-to-volume ratio and suggests that the effective surface area, number of available entrance ports, is reduced by two orders of magnitude. 

Although the systems investigated here exhibited predominantly macropore control (at least those with pellet diameters exceeding 1/8" or 0.32 cm), there is no reason to believe that surface diffusion effects would not be exhibited in systems in which micropore (intracrystalline) resistances are important as well. In fact, this apparent surface diffusion effect may be responsible for the differences in zeolitic diffusion coefficients obtained by different methods of analysis (13). However, due to the complex interaction of various factors in the anlaysis of mass transport in zeolitic media, including instabilities due to heat effects, the presence of multimodal pore size distribution in pelleted media, and the uncertainties involved in the measurement of diffusion coefficients in multi-component systems, further research is necessary to effect a resolution of these discrepancies. 

The site preferences shown by cations in the spinel structure demonstrate that transition metal ions prefer coordination sites that bestow on them greatest electronic stability. In addition, certain cations deform their surrounding in order to attain enhanced stability by the Jahn-Teller effect. These two features suggest that similar factors may operate and cause enrichments of cations in specific sites in silicate structures, leading to cation ordering or intersite (intracrystalline ) partitioning within individual minerals which, in turn, may influence distribution coefficients of cations between coexisting phases. 

Effective mean free path in the intercrystalline space Tortuosity factor Intracrystalline mean life time... 

For the acid catalysed conversion of hydrocarbons, the reaction mechanisms in absence of sterical hinderance are rather well understood, so that molecular shape-selective effects exerted by constrained environments can be isolated [8,9]. Shape-selective catalysis is also possible when other than acid functions are confined to the intracrystalline void volumes of zeolite crystals, e.g. metal [10,11], bifunctional [12] and basic functions [13]. Nowadays, catalysis on zeolites with organic substrates containing heteroatoms receives much attention. Molecular shape-selectivity seems to be superimposed on electronic factors determining the selectivities [14,15]. 

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