Diffusion surface reaction, and

Surface diffusion and reaction at widely separated sites J. Catal. 22, 282-284 (1971). 

Coupling between surface diffusion and reaction. If this mode is dominating [such as with the CO oxidation on Pt(100)], chemical waves propagating across the surface will give rise to spatiotemporal pattern formation. 

The role of the adsorptive surface characteristics in many processes of practical importance is a topic of increasing interest in surfiice science. Adsorption, surface diffusion, and reactions on catalysts are some of the phenomena that are strongly dependent upon surface structure. Most materials have heterogeneous surfaces that, when interacting with gas molecules, present a complex spatial dependence of the adsorptive energy. This is specially the case for activated carbons, where many defects and impurity atoms and molecules are incorporated... 

Surface diffusion and reactions volatile reaction products... 

Kinetic theories of adsorption, desorption, surface diffusion, and surface reactions can be grouped into three categories. (/) At the macroscopic level one proceeds to write down kinetic equations for macroscopic variables, in particular rate equations for the (local) coverage or for partial coverages. This can be done in a heuristic manner, much akin to procedures in gas-phase kinetics or, in a rigorous approach, using the framework of nonequihbrium thermodynamics. Such an approach can be used as long as... 

Phase transition occurs at a state of thermodynamic equilibrium, inducing a change in the microstructure of atoms. However, corrosion is a typical nonequilibrium phenomenon accompanied by diffusion and reaction processes. We can also observe that this phenomenon is characterized by much larger scales of length than an atomic order (i.e., masses of a lot of atoms), which is obvious if we can see the morphological change in the pitted surface. 

Figure 3.3. Schematic representation of the adsorption, surface diffusion, and surface reaction steps identified by surface-science experiments on model supported-palladium catalysts [28]. Important conclusions from this work include the preferential dissociation of NO at the edges and defects of the Pd particles, the limited mobility of the resulting Nads and Oads species at low temperatures, and the enhancement in NO dissociation promoted by strongly-bonded nitrogen atoms in the vicinity of edge and defect sites at high adsorbate coverages. (Figure provided by Professor Libuda and reproduced with permission from the American Chemical Society, Copyright 2004).

Figure 14. Simple model demonstrating how adsorption and surface diffusion can co-Urnit overall reaction kinetics, as explained in the text, (a) A semi-infinite surface establishes a uniform surface coverage Cao of adsorbate A via equilibrium of surface diffusion and adsorption/desorption of A from/to the surrounding gas. (b) Concentration profile of adsorbed species following a step (drop) in surface coverage at the origin, (c) Surface flux of species at the origin (A 4i(t)) as a function of time. Points marked with a solid circle ( ) correspond to the concentration profiles in b. (d) Surface flux of species at the origin (A 4i(ft>)) resulting from a steady periodic sinusoidal oscillation at frequency 0) of the concentration at the origin.

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. 

The study of the intra-phase mass transfer in SCR reactors has been addressed by combining the equations for the external field with the differential equations for diffusion and reaction of NO and N H 3 in the intra-porous region and by adopting the Wakao-Smith random pore model to describe the diffusion of NO and NH3 inside the pores [30, 44]. The solution of the model equations confirmed that steep reactant concentration gradients are present near the external catalyst surface under typical industrial conditions so that the internal catalyst effectiveness factor is low [27]. 

As mentioned earlier, if the rate of a catalytic reaction is proportional to the surface area, then a catalyst with the highest possible area is most desirable and that is generally achieved by its porous structure. However, the reactants have to diffuse into the pores within the catalyst particle, and as a result a concentration gradient appears between the pore mouth and the interior of the catalyst. Consequently, the concentration at the exterior surface of the catalyst particle does not apply to die whole surface area and the pore diffusion limits the overall rate of reaction. The effectiveness factor tjs is used to account for diffusion and reaction in porous catalysts and is defined as... 

In the literature, one can find other empirical or semi-empirical equations representing the kinetics of powder reactions. One can certainly take into account grain size distribution, contact probability, deviations from the spherical shape, etc. in a better way than Carter has done. Even more important are parameters such as evaporation rate, gas transport, surface diffusion, and interface transport in this context. As long as these parameters are neglected in quantitative work, the kinetic equations are inadequate. Nevertheless, considering its technological relevance, a particular type of powder reaction will be discussed in the next section. 

In order to get a more realistic description of surface reactions energetic interactions must be taken into account. We introduced in Section 9.2.1 a general model which is able to handle systems which include mono- and bimolecular steps like adsorption, desorption, diffusion and reaction [38]. Here we apply this model to an extended version of the ZGB-model which incorporates particle diffusion and desorption [41]. 

The effects of phase transitions, surface diffusions, and defects on surface catalyzed reactions Fluctuations and oscillations (with D.G. Vlachos and L.D. Schmidt). J. Chem. Phys. 93, 8306-8313 (1990). 

Aspects of the distribution of species on surfaces have been reviewed (35) and our understanding of the disposition, composition, and properties of the adsorbed phase is increasing through applications of recently developed high-vacuum techniques, for example, LEED (60, 61). Some information about the mobility of adsorbed material is available (62a-e) and the significance of surface diffusivity in reaction kinetics has been discussed (63). The behavior of supported metal catalysts may be influenced by the transfer of material between the two phases (metal and support) by diffusion (64-66). 

The tools needed to analyze adsorption, surface diffusion, and surface reaction to form a product are the same as those used to analyze reactions on catalytic surfaces, the only difference being that in catalytic systems the product leaves the surface and desorbs into the fluid phase. In the processing of electronic materials, the product is the thin film that is formed on the surface. 

For most CVD reactions, the supersaturation is so high that calculated values of r are of atomic dimensions. For such reactions, the classical theory is not appropriate, and detailed atomic treatments must be considered. Because of the interesting fundamental questions underlying nucleation and the important applications of thin films, interest in modeling adsorption, surface diffusion, and nucleation has been considerable. These efforts are described in several, well-documented reviews (61, 75-78). 

The catalyst packing of the reactor consists of an iron oxide Fe20s, promoted with potassium carbonate K COo, and chromium oxide Cr O-s,. The catalyst pellets are extrudates of a cylindrical shape. Since at steady state the problem of simultaneous diffusion and reaction are independent of the particle shape, an equivalent slab geometry is used for the catalyst pellet, with a characteristic length making the surface to volume ratio of the slab equal to that of the original shape of the pellet. 

Analysis of structure formation processes by using Monte Carlo methods. Monte Carlo methods will he used extensively for the calculation of processes during which new phases are formed. In particular, these are adsorption-desorption, diffusion, and reactions on the surfaces of solids. The results of this modelling will be used to decode structures formed on catalyst surfaces. 

Once the thermodynamic parameters of stable structures and TSs are determined from quantum-chemical calculations, the next step is to find theoretically the rate constants of all elementary reactions or elementary physical processes (say, diffusion) relevant to a particular overall process (film growth, deposition, etc.). Processes that proceed at a surface active site are most important for modeling various epitaxial processes. Quantum-chemical calculations show that many gas-surface reactions proceed via a surface complex (precursor) between an incident gas-phase molecule and a surface active site. Such precursors mostly have a substantial adsorption energy and play an important role in the processes of dielectric film growth. They give rise to competition among subsequent processes of desorption, stabilization, surface diffusion, and chemical transformations of the surface complex. 

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