Elementary reactions microkinetic modeling

The proposed theoretical methodology has been applied here to study and rationalize a 15 elementary reaction microkinetic mechanism for the WGSR on Cu(lll) for illustrative purposes. A reaction network has been constructed that incorporates all of the 26 direct RRs that have been previously generated using the conventional methods. Using the electrical circuit analogy the reaction network was subsequently simplified and reduced to a reaction network involving only 3 dominant RRs. An overall rate equation has been developed that reproduces the complete microkinetic model precisely. 

In 2001, Mirodatos et al. [89] stressed the importance of transient studies as an alternative to steady continuous reactor operations. A combination of microkinetic analysis together with transient experiments should allow the determination of the global catalytic conversion from elementary reaction steps. Prerequisite for such analysis is the correlation of experimental data with the data of a model. Compliance between the data helps to derive the reaction mechanism. 

Thus, it is adequate to determine the energetic characteristics of the elementary reactions based on the Unity Bond Index-Quadratic Exponential Potential (UBI-QEP) method developed by Shustorovich [2], while the pre-exponential factors may be estimated simply from the transition-state theory [4,26]. Here we employ, for illustrative purposes, a simplified version of a microkinetic WGSR model developed by us earlier [14],... 

Here S represents a vacant site on the surface of the catalyst. The set of elementary reactions generated under these constraints for the WGS reaction is presented in Table 1. To simplify the resulting analysis, in what follows we further disregard two of the elementary reactions from this microkinetic model, namely... 

Microkinetic modeling is a framework for assembling the microscopic information provided by atomistic simulations and electronic structure calculations to obtain macroscopic predictions of physical and chemical phenomena in systems involving chemical transformations. In such an approach the particular catalytic reaction mechanism is expressed in terms of its most elementary steps. In contrast to the Langmuir-Hinshelwood-Hougen-Watson (LHHW) formulations, no rate-determining mechanistic step (RDS) is assumed. 

Microkinetic models are much more widely applicable than LHHW traditional models which assume an RDS, since the RDS can change with reaction conditions. Because all postulated elementary steps are included explicitly, accurate rate parameters for all of the forward and... 

Microkinetic modeling assembles molecular-level information obtained from quantum chemical calculations, atomistic simulations and experiments to quantify the kinetic behavior at given reaction conditions on a particular catalyst surface. In a postulated reaction mechanism the rate parameters are specified for each elementary reaction. For instance adsorption preexponential terms, which are in units of cm3 mol"1 s"1, have been typically assigned the values of the standard collision number (1013 cm3 mol"1 s 1). The pre-exponential term (cm 2 mol s 1) of the bimolecular surface reaction in case of immobile or moble transition state is 1021. The same number holds for the bimolecular surface reaction between one mobile and one immobile adsorbate producing an immobile transition state. However, often parameters must still be fitted to experimental data, and this limits the predictive capability that microkinetic modeling inherently offers. A detailed account of microkinetic modelling is provided by P. Stoltze, Progress in Surface Science, 65 (2000) 65-150. 

The term microkinetic analysis has been applied " to attempts to synthesise information from a variety of sources into a coherent reaction model for the hydrogenation of ethene. The input includes steady-state kinetics (most importantly the temperature-dependence of reaction orders ), isotopic tracing, vibrational spectroscopy and TPD it uses deterministic methods, i.e. the solution of ordinary differential equations, for estimating kinetic parameters. It selects a somewhat eclectic set of elementary reactions, and in particular the model... 

The reaction proceeds along the same elementary steps as with the Fe catalyst, and again successful microkinetic modeling on the basis of experimentally derived parameters could be achieved [46]. Again, dissociative nitrogen adsorption is rate limiting, where the sticking coefficient is markedly affected by the presence of atomic steps [47] whose role as "active sites" had been discussed in Chapter 5. 

In general, a mechanism for any complex reaction (catalytic or non-catalytic) is defined as a sequence of elementary steps involved in the overall transformation. To determine these steps and especially to find their kinetic parameters is very rare if at all possible. It requires sophisticated spectroscopic methods and/or computational tools. Therefore, a common way to construct a microkinetic model describing the overall transformation rate is to assume a simplified reaction mechanism that is based on experimental findings. Once the model is chosen, a rate expression can be obtained and fitted to the kinetics observed. 

Microkinetics as defined by Dumesic, is the examination of catalytic reactions in terms of elementary chemical reactions that occur on the catalytic surface and their relation with each other and with the surface during a catalytic cycle. This definition can easily be expanded into covering non-catalytic systems as well. Microkinetics, for the most part, has focused on analysis or understanding of the reaction mechanism. The approach, however, also holds the promise of being used to aid in the synthesis of new materials. Microkinetic modeling is now an important tool for many of the practicing reaction engineers. This approach enables one to formulate and follow the detailed concentration profile for most if not all of the reaction intermediates. 

There is now a great deal of interest in utilizing the microkinetic approach in modeling rates of catalytic reactions despite the lack so r of reliable rate constants of elementary reactions on different catalytic materials. However, the alternative approaches diat provide a simple means of understanding, explaining and predicting the kinetic behavior of complex heterogeneous catalytic reactions continue to be invaluable. The main approximations that are conventionally used to simpUfy the detailed kinetics are [1] ... 

Figure 8.2 summarizes the methods discussed here. The organization of this chapter is as follows. First, methods for calculating the rate constant of an elementary step are described. Then DFT is briefly introduced for estimation of adsorption properties and barriers, followed by an outline of selected statistical Ihermodynantics. Examples of the thermochemistry on Ni(l 11) and Pt(lll) are presented to address thermodynamic consistency of the DFT-predicted adsorption properties. S iempirical methods for predicting adsorbate thermodynamic properties and kinetic parameters are also presented. With this input, microkinetic models can be solved. Finally, analytical tools are described to develop and analyze a nticrokinetic model, with the water-gas shift (WGS) reaction on Pt-based catalysts taken as an example. 

Microkinetic modeling predicts thermodynamic properties for species and kinetic parameters of elementary steps of a mechanism, as described in subsequent sections. The kinetic parameters, that is, sticking coefficient (5 ) of a species, preexponential factor (Ajp, and activation energy as well as the change in enthalpy (Aff ) and entropy (A5°) in each elementary step at 298 K on Pt(lll) are also presented in Table 8.1. Here, stands for reaction index and f for forward. This mechanism will be used throughout this chapter to illustrate the capabilities of microkinetic modeling tools. 

Stolze et al. analyzed the investigating results for ammonia s3mthesis kinetics at wide experimental conditions which are described by all three microkinetic models, and indicated that all models were established on, in fact, the same chemical reaction mechanisms. The difference between them is only that the estimated values of kinetic parameters used are different for each elementary step. In the special example above, the precise kinetic data on iron single crystal were provided only for adsorption step and for other steps the data were estimated indirectly. Accordingly, the extension of data from single crystal to industrial reactions is valid only for the case that adsorption step is rate determining step and the most abundant surface reaction... 

Nevertheless, these microkinetic models still contain no information about the effect of catalysts on the parameters in rate equations for elementary steps. In addition, there is no verification for important kinetic steps 1 and 2, but they were checked in other cases of elementary reaction steps. 

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