Diffusion in heterogeneous catalysis

Modeling of reaction and diffusion in heterogeneous catalysis begins with a definition of the structure or geometry of the internal porous media. 

The problem of diffusion in electrocatalysts is analogous to that of diffusion in heterogeneous catalysis. The assumptions adopted in the model are as follows... 

Therefore, it is necessary to determine the influence of mass transfer to or from the above-mentioned interfaces on the conversion, which leads to expressions for the flux of a reactant across the interface and for the overall reaction rate. After balancing the disappearance of the components Ai and A2, e. g., at the gas/liquid interface, by analogy with the treatment of the rate of chemical reaction and pore diffusion in heterogeneous catalysis, the overall reaction rate is given by eq. (1) [2] ... 

Ernest W. Thiele A Pioneer in Defining the Role of Diffusion in Heterogeneous Catalysis... 

For gas-phase diffusion in small pores at lowpressure, the molecular mean free path may be larger than the pore diameter, giving rise to Knudsen diffusion. Satterfield (Ma.s.s Tran.sfer in Heterogeneous Catalysis, MIT, Cambridge, MA, 1970, p. 43), gives the following expression for the pore dimisivity ... 

Knudsen diffusion is generally encountered in heterogeneous catalysis. In the smallest pores configurational diffusion takes place with diffusion coefficient ranging from 10 to 10 m /s. 

Inspection of Fig. 15.3 reveals that while for jo 0.1 nAcm , the effectiveness factor is expected to be close to 1, for a faster reaction with Jo 1 p,A cm , it will drop to about 0.2. This is the case of internal diffusion limitation, well known in heterogeneous catalysis, when the reagent concentration at the outer surface of the catalyst grains is equal to its volume concentration, but drops sharply inside the pores of the catalyst. In this context, it should be pointed out that when the pore size is decreased below about 50 nm, the predominant mechanism of mass transport is Knudsen diffusion [Malek and Coppens, 2003], with the diffusion coefficient being less than the Pick diffusion coefficient and dependent on the porosity and pore stmcture. Moreover, the discrete distribution of the catalytic particles in the CL may also affect the measured current owing to overlap of diffusion zones around closely positioned particles [Antoine et ah, 1998]. 

The surface diffusion of defects and adsorbates is of obvious importance in heterogeneous catalysis, as this process brings the reactants together. Understanding the dynamics of molecules on oxide surfaces is also a key step toward the realization of working molecular electronics. We note here that diffusion of Ob-vacs really means diffusion of Ob into the vacancy, which leaves another Ob-vac in the position vacated by the Ob- Similarly, diffusion of OHb occurs by diffusion of the H atom. 

This example treats a diffusion-reaction process in a spherical biocatalyst bead. The original problem stems from a model of oxygen diffusion and reaction in clumps of animal cells by Keller (1991), but the modelling method also applies to bioflocs and biofilms, which are subject to potential oxygen limitation. Of course, the modelling procedure can also be applied generally to problems in heterogeneous catalysis. 

The philosophy used to develop detailed chemical kinetic mechanisms for gas-phase reactions can, in principle, be extended to treat heterogeneous reactions, provided diffusion is also considered in the final analysis. Clearly, the problem in heterogeneous catalysis is considerably more complex because of the close proximity of a large number of atoms and their collective effect on reaction kinetics and mechanisms, and the inevitable variation of catalyst structure with time—for example, as a result of sintering and poisoning. 

Three fundamental processes can limit overall reaction rates in heterogeneous catalysis mass transfer of the reactants from the bulk liquid phase(s) to the surface of the solid catalyst, diffusion of the reactants from the catalyst surface to the active site, and the intrinsic reaction at the active site 61,62). Each of these processes depends on one or more experimental parameters, as shown in Fig. 1. 

If adatom-impurity atom interaction is attractive, then the impurity atom can act as a trapping center. A diffusing adatom may be trapped. In heterogeneous catalysis, the reaction rate may be changed by the trapping effect of impurities as also by lattice defects and lattice steps and so on. 

As discussed earlier, the first step in heterogeneous catalysis is the adsorption of the molecules of the reactants on the surface of the adsorbent or of the catalyst (inner and outer surfaces). Then, molecular dissociation of at least one or two reacting components takes place, usually preceded by surface diffusion. The next step is a surface reaction, which is... 

The fact that ATR-IR spectroscopy uses an evanescent field and therefore probes only the volume very close to the IRE has important consequences for its application in heterogeneous catalysis, in investigations of films of powder catalysts. The catalyst particle size and packing affect the size of the detectable signals from the catalyst and bulk phase. Furthermore, if the catalyst layer is much thicker than the penetration depth of the evanescent field, diffusion of reactants and products may influence the observed signals. In fast reactions, gradients may exist within the catalyst layer, and ATR probes only the slice closest to the IRE. 

Laminar flow reactors are equipped with microstructured reaction chambers that have the desired low Reynolds numbers due to their small dimensions. Mass transport perpendicular to the laminar channel flow is dominated by diffusion, a phenomenon known as dispersion. Without the influence of diffusion, laminar flow reactors could not be used in heterogeneous catalysis. There would be no mass transport from the bulk flow to the walls as laminar flow, in contrast to turbulent flow, cannot mix the flow macroscopically. 

Cradun, R., Miller, D.J., Dulamita, N. and Jackson, J.E. (1996) Diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) applied in heterogeneous catalysis studies. Prog. Catal., 5, 55. 

It plays the same role as the effectiveness factor in heterogeneous catalysis and is a measure of the film thickness uniformity. It represents the ratio of the total reaction rate on each pair of wafers to that we would obtain if the concentration in the cell formed by the two wafers were equal to the bulk concentration everywhere. Thus, if the surface reaction is the rate controlling step, n = 1, whereas if the diffusion between the wafers controls, n < 1. In the limit of strong diffusion resistance the deposition is confined to a narrow outer band of the wafers and a strongly nonuniform film results. 

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