Reaction in pores

Figure C2.7.13. Schematic representation of diffusion and reaction in pores of HZSM-5 zeolite-catalysed toluene disproportionation the numbers are approximate relative diffusion coefficients in the pores 1131.

Zero Order Reaction in Pores. Zero order reactions are encountered in catalysis whenever the catalyst surface is covered more or less completely with adsorbed reactant. Under these conditions the rate of reaction will be independent of reactant concentration, and hence reaction will be zero order. Diffusion into a pore accompanied by reaction on the pore wall is ruled by eq. (31) with n = 0 ... 

Reactants must diffuse through the network of pores of a catalyst particle to reach the internal area, and the products must diffuse back. The optimum porosity of a catalyst particle is deterrnined by tradeoffs making the pores smaller increases the surface area and thereby increases the activity of the catalyst, but this gain is offset by the increased resistance to transport in the smaller pores increasing the pore volume to create larger pores for faster transport is compensated by a loss of physical strength. A simple quantitative development (46—48) follows for a first-order, isothermal, irreversible catalytic reaction in a spherical, porous catalyst particle. 

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

The design approach is particularly feasible for those reactions in which chemical and pore diffusion rates are most important. For flow related phenomena semi-empirical, dimensionless correlations must be relied on. Therefore in this book scale-up will be used in the more general sense with the airri of using methods that are fundamentally based wherever feasible. 

For the effective diffusivity in pores, De = (0/t)D, the void fraction 0 can be measured by a static method to be between 0.2 and 0.7 (Satterfield 1970). The tortuosity factor is more difficult to measure and its value is usually between 3 and 8. Although a preliminary estimate for pore diffusion limitations is always worthwhile, the final check must be made experimentally. Major results of the mathematical treatment involved in pore diffusion limitations with reaction is briefly reviewed next. 

For the simplest one-dimensional or flat-plate geometry, a simple statement of the material balance for diffusion and catalytic reactions in the pore at steady-state can be made that which diffuses in and does not come out has been converted. The depth of the pore for a flat plate is the half width L, for long, cylindrical pellets is L = dp/2 and for spherical particles L = dp/3. The varying coordinate along the pore length is x ... 

In most cases of interest, shock-induced chemical reactions in solids are studied in mixtures of powders of the potential reactants. In the earlier description of conceptual models it was emphasized that the pores provide space in which the potential reactants can be more intimately mixed in order... 

Fig. 7.80 A schematic thermodynamic phase stability diagram for the A-C-O system, showing three reaction paths. Paths 2 and 3 are only possible if gaseous diffusion in pores in the oxide product results in a carbon activity increase through the scale, as shown in Fig. 7.81 (after...

The oxidation reactions in different carbons are thus very different at low temperatures, but this is less true as the oxidation temperature increases. In porous samples the rapid reaction essentially suppresses the diffusion of gas within the pores and oxidation takes place only on the surface. The Oxidation rate then becomes independent of the type of carbon and is determined by the flow of oxidising gases. This condition is reached at about SOO C in pure materials. 

Many chemical reactions, especially those involving the combination of two molecules, pass through bulky transition states on their way from reactants to products. Carrying out such reactions in the confines of the small tubular pores of zeolites can markedly influence their reaction pathways. This is called transition-state selectivity. Transition-state selectivity is the critical phenomenon in the enhanced selectivity observed for ZSM-5 catalysts in xylene isomerization, a process practiced commercially on a large scale. 

Another SBU with open metal sites is the tri-p-oxo carboxylate cluster (see Section 4.2.2 and Figure 4.2). The tri-p-oxo Fe " clusters in MIL-100 are able to catalyze Friedel-Crafts benzylation reactions [44]. The tri-p-oxo Cr " clusters of MIL-101 are active for the cyanosilylation of benzaldehyde. This reaction is a popular test reaction in the MOF Hterature as a probe for catalytic activity an example has already been given above for [Cu3(BTC)2] [15]. In fact, the very first demonstration of the catalytic potential of MOFs had aheady been given in 1994 for a two-dimensional Cd bipyridine lattice that catalyzes the cyanosilylation of aldehydes [56]. A continuation of this work in 2004 for reactions with imines showed that the hydrophobic surroundings of the framework enhance the reaction in comparison with homogeneous Cd(pyridine) complexes [57]. The activity of MIL-lOl(Cr) is much higher than that of the Cd lattices, but in subsequent reaction rans the activity decreases [58]. A MOF with two different types of open Mn sites with pores of 7 and 10 A catalyzes the cyanosilylation of aromatic aldehydes and ketones with a remarkable reactant shape selectivity. This MOF also catalyzes the more demanding Mukaiyama-aldol reaction [59]. 

Since their development in 1974 ZSM-5 zeolites have had considerable commercial success. ZSM-5 has a 10-membered ring-pore aperture of 0.55 nm (hence the 5 in ZSM-5), which is an ideal dimension for carrying out selective transformations on small aromatic substrates. Being the feedstock for PET, / -xylene is the most useful of the xylene isomers. The Bronsted acid form of ZSM-5, H-ZSM-5, is used to produce p-xylene selectively through toluene alkylation with methanol, xylene isomerization and toluene disproportionation (Figure 4.4). This is an example of a product selective reaction in which the reactant (toluene) is small enough to enter the pore but some of the initial products formed (o and w-xylene) are too large to diffuse rapidly out of the pore. /7-Xylene can, however. 

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