Microkinetic Model Analysis

Determine the values of the descriptors from step 1 that yield optimal catalytic activity. This determination can, again, be made empirically, via microkinetic modeling, or via Sabatier analysis. 

A simple tool is described, which provides a conceptual framework for analyzing microkinetic models of heterogeneous reactions. We refer to this tool as the Sabatier Analysis . The Sabatier Analysis of the microkinetic models developed in this section suggests that the clustering of good catalysts can be explained by the combination of the universal BEP-relation and activated re-adsorption of synthesis products onto the catalyst. 

In a follow-up paper, Linic and Barteau constructed a reaction coordinate and a microkinetic model for ethylene epoxidation on silver from DFT calculations [1]. The calculations were based on an Agis cluster to represent the silver surface. The reaction coordinate produced had TSl as the species formed by the initial interaction of ethylene with an adsorbed oxygen atom. This is in agreement with species proposed by Grant and Lambert [24], by Force and Bell [36] and by the analysis presented earlier in this chapter for the initial interaction of ethylene with an oxidised silver surface. 

Now that the basic principles of the reaction network analysis have been enumerated, we proceed to analyze in detail the water-gas shift reaction (WGSR) microkinetic model. Due to its industrial significance, the catalysis and kinetics of the WGSR has been a key example in microkinetic modeling [17-26]. In the meantime, we have shown [13,14] that reliable microkinetic models for the WGSR on Cu(lll) may be developed based on rather rudimentary kinetic considerations. 

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... 

The error in the conversion of CO provided by this overall rate equation is virtually zero as compared with the exact microkinetic model, which points to the robustness of the reaction network analysis approach presented here. 

In the following section, we will discuss the kinetic implications of the dynamical changes in catalyst morphology during methanol synthesis. First, we will present an analysis of steady state kinetic experiments using a static, microkinetic model where it is assumed that the number of sites are constant. Then, we will introduce the dynamic aspect into the microkinetic modeling and also discuss some recent transient experiments. 

Analysis of steady state results using a static microkinetic model... 

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. 

The previous sections described techniques employed for parameter estimation. These thermodynamic and kinetic parameters are input to a microkinetic model that is solved numerically to describe material balances in a chemical reactor (e.g., a PFR). This section describes tools for the subsequent model analysis, which can be used in multiple ways. Initially during mechanism development, they can be used to assess which reactions and reactive intermediates are important in the model, which helps the modeler to focus on important features of the surface reaction mechanism. During this process, simulated macroscopic observables, for example, global reaction orders and apparent activation energies can be compared directly to experimental data. Then, once the model describes experimental data reasonably well, analytical tools can be used to develop further insights into the reaction mechanism, with apphcations that include catalyst design [50]. 

In this chapter, an overview of microkinetic modeling was given. Microkinetic modeling aims at understanding how surface structure and adsorbate properties at the molecular level affect thermodynamic and kinetic phenomena at the macroscale. Inputs to microkinetic modeling via first-principles and semiempirical methods were discussed, followed by an explanation of several microkinetic analysis tools. The modeling of the WGS reaction on platinum was presented as an example of using these tools in the assessment of the surface reaction mechanism. 

These steps increase the coverage of surface nitrites which rapidly convert to N2. The differential rate data for temperatures below 250 °C presented earlier show clear evidence for multiple reaction pathways The differential rate of NO2 consumption exceeds that of NO at lower temperatures. This points to the formation of NH4NO3 and its inhibition of N2 formation, but also the mitigation of the inhibition by and AN reduction by NO. It can be shown that an overall rate based on the reduction of HNO3 and/or NH4NO3 as the RDS has the functional features to predict the main trends in the experimental data. Further analysis of microkinetic models that include these steps Sl lO and S19-S26 is needed. Later we describe global kinetic models that predict these data as a first step toward this goal. 

Boszo reported the temperature programmed desorption spectroscopy, indicating that the temperature of maximum desorption rate on Fe (111) is at the range of 850 K-890 K. The prediction temperatures by analysis of three microkinetic models are 820 K-870K, 790 K 830 K and 760 K 820K, respectively. The value predicted by model III seems too low, but close to the temperatures with maximmn desorp>-tion rate in the nitrogen temperature programmed desorption experiments carried out by authors on Fe obtained after reduction of Fei xO-basis catalyst. Possibly, it relates to the catalytic activity. 

The microkinetics analysis, as a useful and powerful tool to interpret, harmonize and consolidate the study of catal3dic phenomena, can describe various results obtained at wide experimental conditions. For ammonia synthesis reaction discussed in this section, the microkinetic models are evaluated from the experimental data such as the sticking coefficient of dissociated nitrogen adsorption, the spectrum of programmed-temperature desorption of adsorbed nitrogen as well as the kinetics of ammonia synthesis at industrial conditions and at laboratory conditions are far from equilibrium. 

Two of three microkinetic models could give these data obtained at the range of 11 orders pressure i.e., from ultrahigh vacurnn to 10 MPa, and the third model could represent reasonably the kinetic data obtained at industrial reaction conditions and cannot be extended to describe suitably these data obtained at ultrahigh vacuum conditions. Hence, analysis of microkinetics could provide a frame for quantitative comparison of kinetic information obtained at wide experimental conditions, and this comparison could distinguish the ensembles of kinetic parameters, which seem to be equivalent, obtained in more narrow range of conditions. 

We now introduce a method that provides the simplest possible conceptual framework for analyzing microkinetic models of heterogeneous reactions, the so-called Sabatier analysis. We call it so because it brings out the qualitative reasoning behind the Sabatier principle in a quantitative form. 

Figure 7.6 shows the Sabatier map in comparison to the full solution from the microkinetic model. The Sabatier map gives an excellent description for small approaches to equilibrium (y-> 0). There is some discrepancy at the maximum where the Sabatier analysis predicts too high rates. This can be attributed to a failure of describing coverages that are in between 0 and 1, since these are the limiting cases... 

Comparison of the volcano curves obtained from a Sabatier analysis and full microkinetic models at different approaches to equilibrium y. Reprinted from T. Bligaard, et al., J. Catal., 2004, 224, 206-217 with permission from Elsevier. ... 

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