Nonideal surface reaction

The treatment based on the two-step sequence for nonideal surfaces originates from the complexity of deriving the explicit form of rate equations for other reaction mechanisms on biographical non uniform surfaces. At the same time models based on lateral interactions have no restrictions from this point of view as the implicit form can be and is used for the data fitting. 

We can easily see, that in a certain range of partial pressures the descriptions offered by the two models for ideal and nonideal surfaces, are close to each other, however the deviation is systematic. Moreover, these two models give qualitatively different behavior at boundary values of partial pressures. For instance, according to an ideal surface model, at high partial pressures, the reaction rate obeys zero order kinetics, meanwhile at low pressures, the reaction... 

The paradox of using ideal surfaces to represent surfaces known to be nonideal or nonuniform was addressed in the preceding chapter, and justification was provided for doing so. Thus let us proceed with some of the various approaches for proposing reaction models and deriving rate expressions. Some of the oldest and most straightforward approaches involve the use of L-H-type or H-W-type reaction models, which invoke a RDS [1]. We will start with this family of sequences by examining the simplest surface reactions first, and then reaction models without a RDS will be discussed. 

Real surfaces are known to be nonuniform, so two obvious questions are the following. Can rate expressions for catalytic reactions on nonuniform surfaces be meaningfully and readily derived If so, do these rate laws more accurately describe the experimental results obtained with real catalysts The previous chapter was devoted to modeling reactions occurring on a uniform or ideal surface in the Langmurian sense, and the reasons for the validity and success of this approach were cited. The paradox of this successful application of Langmurian types of rate laws to nonideal surfaces was addressed in Chapter 6.5, and the earliest rationale for this observation is still the best explanation, i.e., the reaction proceeding on the most active sites, which may constitute but a small fraction of the total number of sites, dominates the macroscopic kinetic behavior. 

Fig. 3.15 Dependence of reaction rate on coverage for nonideal surfaces.

In a similar fashion as for the two-step sequence on nonideal surfaces, the reaction rate is obtained by multiplication of Eq. (7.131) by the distribution function with further integration in the region of medium coverage. Here we present only the result of such treatment, which is an extension of Eq. (7.80). 

Summary. The potential of in-situ scanning probe techniques for the local investigation of surface properties and reactions at "nonideal" electrodes is presented in a typical example in the field of metal underpotential deposition, the essential role of the step dislocations for the local progress of adsorbate formation and also for the longterm adsorbate stability is shown and discussed for the adsorption of Pb and TI monolayers at stepped Ag(l 11) electrodes. 

In this chapter, the Navier-Stokes equations have been solved in the actual 3D geometry of the reactor, thereby exploiting the full potential of the new approach, and detailed surface kinetics (Visconti et al., 2013) was implemented in the model with two main implications. On a more fundamental level, it demonstrates the power of the CAT-PP approach proposed here, which allows us to perform simulations of complex catalytic reactors characterized by nonideal flow fields, in which multistep reactions take place. On a more applied level, it allows us to assess the extent of the nonidealities of the simulated operando FTIR reaction cell, which is commercially available and is used by many research groups worldwide. This is extremely relevant especially for researchers who ivant to use the cell to collect quantitative information, since it will allow the verification of whether the cell is an ideal reactor or not. This latter hypothesis has been exploited, for example, by Visconti et al. (2013) to develop the first comprehensive and physically consistent spectrokinetic model for NOx storage... 

The results of the simulation allow us to evaluate the extent of the nonidealities of the simulated operando FTIR reaction cell. A comparison of the simulation results obtained with the CAT-PP and with the ideal PFR model is provided in Figure 3.12, in which the experimental data, the results of the simulation with the ideal reactor mode, and the results of CAT-PP are compared (Corbetta et al, 2014). It is clear that the ideal PFR and the CAT-PP simulations are in good agreement with each other. This proves that the adopted FTIR cell may be described as an ideal reactor or not, thus proving an ex-postvalidation of the hypothesis done by Visconti et al. (2013) to develop a spectrokinetic model for the NOx storage over a representative LNT catalyst on the basis of a set of transient surface and gas-phase experimental data collected in such a cell. 

A number of isotherms that dispense with assumptions (1) and (2) have been proposed (see Doraiswamy, 1991). Some studies (e.g., Kiperman et al., 1989) indicate that it may not be possible to model certain reactions without invoking the role of surface nonideality. Fortuitously, the use of more rigorous isotherms does not materially affect the companion problem of the diffusion-reaction behavior of systems (Shendye et al., 1993)—a topic considered in the next section. 

An interesting feature of LHHW kinetics is worth noting. Many reactions on surfaces known to be nonideal surprisingly follow the ideal LHHW models, a situation that can only be described as the placebo effect or the paradox of heterogeneous kinetics (Boudart et al., 1967 Boudart, 1986). In the same vein but with less justification, it has also been argued for more than four decades—... 

As in ideal reactors, the kinetics and reaction conditions are similar. However, the distribution of products is quite different and to correlate them with the experiments, it requires a more detailed study of the conditions of nonideality, for example, interfacial and surface phenomena, heat and mass transfer, and flows types. These phenomena characterize the axial and radial dispersion, caused by diffusion and convection. 

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