Diffusion with catalytic surface reaction

Steady-state mass diffusion with catalytic surface reaction... 

The boundary conditions for equation (29) are that Y is bounded, that Y — Yq at z = 0, and that 7 = 0 at x = 0, x — a, y = 0, and y = b (that is, at the walls of the duct). This last condition follows directly from an analysis in the spirit of Section B.4 in the steady state, as the specific rate constant for the surface reaction approaches infinity, the concentrations of the reactant on the surface and in the gas phase adjacent to the surface both approach zero, and steps 1 and 5 of Section B.4 (the diffusion transport steps) become rate controlling. For recombination processes, the limit of an infinite surface rate constant is usually referred to as the case of a perfectly catalytic wall. Systems with finite surface reaction rates have been studied in [19] and [20], for example. ... 

Diffusion factor y in cylindrical catalyst mass. The case of cylindrical channel filled with catalytic surfaces having one entrance for the reactant leads for a first-order reaction to... 

With the introduction of LT and VT STM, it is now possible to monitor the fundamental steps of chemical reactions, that is, reactant chemisorption, diffusion, and catalytic transformation. A detailed review covering this subject was published by Wintterlin in 2000 [24]. Since then, in situ STM studies have flourished and expanded to the visualization of the reaction pathway and kinetics of surface processes. In the following section, we highlight selected examples of recent progress in using in situ STM for studying fundamental catalytic processes. 

The rate of a catalytic reaction depends on the rate of diffusion of both substrates and products to and from the catalytic sites. Therefore it is of outmost importance that the catalytically active sites are freely accessible for reactions. Only dendrimers of low generation number can possibly be expected to be suitable carriers for catalytically active sites, especially when these are located in the interior. In high-generation dendrimers with crowded surfaces catalytic activity of an internal site would be prevented. On the other hand, a crowded surface will not only hinder access to an interior ligand site but will also cause steric hindrance between groups attached to it and thus prevent high reactivity of sites at the periphery. 

In the case that the chemical reaction proceeds much faster than the diffusion of educts to the surface and into the pore system a starvation with regard to the mass transport of the educt is the result, diffusion through the surface layer and the pore system then become the rate limiting steps for the catalytic conversion. They generally lead to a different result in the activity compared to the catalytic materials measured under non-diffusion-limited conditions. Before solutions for overcoming this phenomenon are presented, two more additional terms shall be introduced the Thiele modulus and the effectiveness factor. 

Attaching the catalyst molecules to the electrode surface presents an obvious advantage for synthetic and sensor applications. Catalysis can then be viewed as a supported molecular catalysis. It is the object of the next section. A distinction is made between monolayer and multilayer coatings. In the former, only chemical catalysis may take place, whereas both types of catalysis are possible with multilayer coatings, thanks to their three-dimensional structure. Besides substrate transport in the bathing solution, the catalytic responses are then under the control of three main phenomena electron hopping conduction, substrate diffusion, and catalytic reaction. While several systems have been described in which electron transport and catalysis are carried out by the same redox centers, particularly interesting systems are those in which these two functions are completed by two different molecular systems. 

The first example cited is one in which the solid is totally consumed, whereas the second and third examples involve the formation of a new solid product which might be either a desired product, as in the second case, or a waste product (the gangue) as in the third example. Despite such fundamental differences from catalytic reactions, there are many similarities. In each case, chemisorption, surface chemical reaction emd diffusion through porous media occurs which is in common with heterogeneous chemical reactions. Hence, models representing the dynamics of these non-catalytic gas—solid processess incoporate the same principles of chemical reaction concomitant with diffusion and reaction in heterogeneous catalysts. 

There are a number of examples of tube waU reactors, the most important being the automotive catalytic converter (ACC), which was described in the previous section. These reactors are made by coating an extruded ceramic monolith with noble metals supported on a thin wash coat of y-alumina. This reactor is used to oxidize hydrocarbons and CO to CO2 and H2O and also reduce NO to N2. The rates of these reactions are very fast after warmup, and the effectiveness factor within the porous wash coat is therefore very smaU. The reactions are also eternal mass transfer limited within the monohth after warmup. We wUl consider three limiting cases of this reactor, surface reaction limiting, external mass transfer limiting, and wash coat diffusion limiting. In each case we wiU assume a first-order irreversible reaction. 

An investigation of the influence of surface area on the activity of the supported catalysts has shown that the activity increases with increase in surface area, but the selectivity is virtually independent of surface area (27). This result is consistent with both mechanisms i and ii. Thus, in mechanism i the reaction takes place in the pores of the catalyst, which are sufficiently large not to impose steric demands on the reactants, so that the activity of the catalyst is dependent on the rates of diffusion of the reactants to the active site. In terms of mechanism ii, in which the supported complex acts only as a precursor of a soluble catalytically active species, the activity of the catalyst will depend on the ease with which this species is abstracted from the polymer support clearly, this will increase with increasing surface area. 

If monolayers are involved then the substrate probably reacts with catalytic sites directly on the electrode surface. However, when multilayers are involved the substrate is denied access to the surface and movement of electrons is by the previously described process of electrochemical charge transport the substrate also diffuses through the multilayers. Under certain circumstances the presence of multilayers and hence of an increased number of catalytic sites may increase the rate of reaction. 

The results obtained for the stochastic model show that surface reactions are well-suited for a description in terms of the master equations. Since this infinite set of equations cannot be solved analytically, numerical methods must be used for solving it. In previous Sections we have studied the catalytic oxidation of CO over a metal surface with the help of a similar stochastic model. The results are in good agreement with MC and CA simulations. In this Section we have introduced a much more complex system which takes into account the state of catalyst sites and the diffusion of H atoms. Due to this complicated model, MC and in some respect CA simulations cannot be used to study this system in detail because of the tremendous amount of required computer time. However, the stochastic ansatz permits to study very complex systems including the distribution of special surface sites and correlated initial conditions for the surface and the coverages of particles. This model can be easily extended to more realistic models by introducing more aspects of the reaction mechanism. Moreover, other systems can be represented by this ansatz. Therefore, this stochastic model represents an elegant alternative to the simulation of surface reaction systems via MC or CA simulations. 

Catalyst surface activity may be manipulated to alter the ratio of HDM activity to metal compound diffusivity with a predictable impact on optimum pore size (Howell etal., 1985). Lowering the intrinsic surface activity by varying the quantity, chemical composition, or distribution of active catalytic metals will increase the Ni and V penetration into the catalyst. The lower surface activity catalysts may be able to tolerate a smaller pore size (higher total surface area) and still maintain an acceptable performance for the HDM reactions. 

We have used CO oxidation on Pt to illustrate the evolution of models applied to interpret critical effects in catalytic oxidation reactions. All the above models use concepts concerning the complex detailed mechanism. But, as has been shown previously, critical. effects in oxidation reactions were studied as early as the 1930s. For their interpretation primary attention is paid to the interaction of kinetic dependences with the heat-and-mass transfer law [146], It is likely that in these cases there is still more variety in dynamic behaviour than when we deal with purely kinetic factors. A theory for the non-isothermal continuous stirred tank reactor for first-order reactions was suggested in refs. 152-155. The dynamics of CO oxidation in non-isothermal, in particular adiabatic, reactors has been studied [77-80, 155]. A sufficiently complex dynamic behaviour is also observed in isothermal reactors for CO oxidation by taking into account the diffusion both in pores [71, 147-149] and on the surfaces of catalyst [201, 202]. The simplest model accounting for the combination of kinetic and transport processes is an isothermal continuously stirred tank reactor (CSTR). It was Matsuura and Kato [157] who first showed that if the kinetic curve has a maximum peak (this curve is also obtained for CO oxidation [158]), then the isothermal CSTR can have several steady states (see also ref. 203). Recently several authors [3, 76, 118, 156, 159, 160] have applied CSTR models corresponding to the detailed mechanism of catalytic reactions. 

Leitner et al. have synthesized the PEG-modified silica stabilized and immobilized palladium nanoparticles for aerobic alcohol oxidation in combination with scC02 as reaction medium under mild conditions, which show high activity and excellent stability under continuous-flow operation [68], ScC02 could diffuse the substrates and products from the active nanoparticles in a gas-like manner. This allows rapid chemical transformation at the active center, ensures efficient removal of the products from the surface, and minimizes the mobility of solid-supported catalytically active species [69]. In this way, catalysts based on palladium nanoparticles together with PEG as stabilizing matrix could avoid aggregating and forming less active and selective Pd-black [20, 60, 70]. 

Now possibilities of the MC simulation allow to consider complex surface processes that include various stages with adsorption and desorption, surface reaction and diffusion, surface reconstruction, and new phase formation, etc. Such investigations become today as natural analysis of the experimental studying. The following papers [282-285] can be referred to as corresponding examples. Authors consider the application of the lattice models to the analysis of oscillatory and autowave processes in the reaction of carbon monoxide oxidation over platinum and palladium surfaces, the turbulent and stripes wave patterns caused by limited COads diffusion during CO oxidation over Pd(110) surface, catalytic processes over supported nanoparticles as well as crystallization during catalytic processes. 

The trends in carbon number distribution and in a-olefin/paraffin ratio on Ru, Fe, and Co, three very different catalytic surfaces, are remarkably similar. All catalysts show a curved Flory plot and an a-olefin/paraffin ratio that decreases with increasing carbon number until only paraffins are observed at high carbon numbers. In each case, diffusion-enhanced olefin readsorption accounts for such trends. Its contribution depends on the catalytic surface, its physical structure, and reaction conditions. 

If we analyze all the steps taking part in the process, the final result will be very complicated. The diffusion, adsorption, and desorption processes are fast enough in comparison with the chemical reaction. Therefore, the adsorption process is in equilibrium during the catalytic reaction, since it is a fast process, and as a result, we can use an adsorption isotherm, for example, the Langmuir isotherm to calculate the amount of reactant in the surface. 

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