Heterogeneous catalysis kinetic model

In heterogeneous catalysis these models are generally referred to as the Langmuir-Hinshelwood-Hougen-Watson (LHHW) models. The term Michaelis-Menten kinetics is often used in homogeneous catalysis, enzyme reactions and reactions of microbial systems. 

M. Kolb, Y. Boudeville. Kinetic model for heterogeneous catalysis Cluster and percolation properties. J Chem Phys 92 3935-3945, 1990. 

In cases of spillover in heterogeneous catalysis the usual kinetic models can no longer be applied in a direct way. The creation of new surface sites or... 

D.A. Rudd, L.A. Apuvicio, J.E. Bekoske and A.A. Trevino, The Microkinetics of Heterogeneous Catalysis (1993), American Chemical Society, Washington DC]. Ideally, as many parameters as can be determined by surface science studies of adsorption and of elementary steps, as well as results from computational studies, are used as the input in a kinetic model, so that fitting of parameters, as employed in Section 7.2, can be avoided. We shall use the synthesis of ammonia as a worked example [P. Stoltze and J.K. Norskov, Phys. Rev. Lett. 55 (1985) 2502 J. Catal. 110 (1988) Ij. 

The examples of the model studies presented show how the meshing of modern surface techniques with reaction kinetics can provide valuable Insights Into the mechanisms of surface reactions and serve as a useful complement to the more traditional techniques. Close correlations between these two areas holds great promise for a better understanding of the many subtleties of heterogeneous catalysis. 

Nevertheless, the kinetic approach to heterogeneous catalysis can be rewarding if relative data for two or more structurally related reactants or catalysts are acquired and interpreted. Instead of applying several assumptions that simplify the reaction scheme and the model of the surface, which are necessary for absolute kinetic description, it is accepted that, under certain conditions, the same reaction scheme holds for all members of the series of reactants or catalysts and that all of the unknown but identical simplifications in the relative data cancel out. However, it is much safer to select a series of reactants in which the structural change from one member to another will be small enough to uphold the basic features of the mechanism than to assume the same for a set of catalysts that are not minor variations of a basic preparation. 

While many techniques have evolved to evaluate surface intermediates, as will be discussed below, it is equally important to also obtain information on gas phase intermediates, as well. While the surface reactions are interesting because they demonstrate heterogeneous kinetic mechanisms, it is the overall product yield that is finally obtained. As presented in a text by Dumesic et al. one must approach heterogeneous catalysis in the way it has been done for gas phase systems, which means using elementary reaction expressions to develop a detailed chemical kinetic mechanism (DCKM). DCKMs develop mechanisms in which only one bond is broken or formed at each step in the reaction scheme. The DCKM concept was promoted and used by numerous researchers to make great advances in the field of gas phase model predictions. 

Most standard chemical engineering tests on kinetics [see those of Car-berry (50), Smith (57), Froment and Bischoff (19), and Hill (52)], omitting such considerations, proceed directly to comprehensive treatment of the subject of parameter estimation in heterogeneous catalysis in terms of rate equations based on LHHW models for simple overall reactions, as discussed earlier. The data used consist of overall reaction velocities obtained under varying conditions of temperature, pressure, and concentrations of reacting species. There seems to be no presentation of a systematic method for initial consideration of the possible mechanisms to be modeled. Details of the methodology for discrimination and parameter estimation among models chosen have been discussed by Bart (55) from a mathematical standpoint. 

However, simple kinetic models, especially of the Langmuir—Hinshel-wood type, can serve with advantage for correlation of experimental data in spite of simplifying assumptions which are necessary for their derivation. Experience shows that heterogeneous acid—base catalysis is the very field where they fit best. Their most frequent general form... 

Chapter 2 describes the evolution in fundamental concepts of chemical kinetics (in particular, that of heterogeneous catalysis) and the "prehis-tory of the problem, i.e. the period before the construction of the formal kinetics apparatus. Data are presented concerning the ideal adsorbed layer model and the Horiuti-Temkin theory of steady-state reactions. In what follows (Chapter 3), an apparatus for the modern formal kinetics is represented. This is based on the qualitative theory of differential equations, linear algebra and graphs theory. Closed and open systems are discussed separately (as a rule, only for isothermal cases). We will draw the reader s attention to the two results of considerable importance. 

Phase transformations in heterogeneous catalysis have been described recently by topochemical kinetic models [111-115]. These models were taken from solid chemistry, where they had been developed for "gas-solid reactions. The products of such reactions are solids. When gas is in contact with the initial solid, the reaction rate is negligible. But as nucleates of the phase... 

Equation (102) is the non-steady-state kinetic model for the conversion of intermediates (for heterogeneous catalysis, for the conversion of surface substances) assuming that the concentrations of the observed substances are constant. As is known, the solution of eqn. (102) is of the form... 

Any real system is known to suffer constantly from the perturbing effects of its environment. One can hardly build a model accounting for all the perturbations. Besides, as a rule, models account for the internal properties of the system only approximately. It is these two factors that are responsible for the discrepancy between real systems and theoretical models. This discrepancy is different for various objects of modem science. For example, for the objects of planetary mechanics this discrepancy can be very small. On the other hand, in chemical kinetics (particularly in heterogeneous catalysis) it cannot be negligible. Strange as it is, taking into consideration such unpredictable discrepancies between theoretical models and real systems can simplify the situation. Perturbations "smooth out some fine details of dynamics. 

Analysis of the simplest non-linear kinetic models (in particular, of kinetic models for heterogeneous catalysis). The aim is to select the simplest non-linear kinetic models to carry out the most complete investigation of their steady-state and relaxation characteristics. The obtained systems of typical relationships facilitates the interpretation of complex reactions, including simpler "typical units. 

Kinetic analysis of concrete catalytic reactions. In the kinetics of heterogeneous catalysis, such reactions are usually model oxidation reactions (e.g. CO and H2 oxidation) over metals. 

This book has been written by mathematicians and chemists, the collaborators of the Institutes of the Siberian Branch of the U.S.S.R. Academy of Sciences [The Institute of Catalysis (Novosibirsk), the Computing Centre (Krasnoyarsk) and the Tuva Complex Department (Kyzyl)]. It presents the results of 15 years activity of this Siberian team as reported in two earlier monographs (Kinetic Models of Catalytic Reactions, Nauka, Novosibirsk, 1983 and Kinetics for Model Reactions of Heterogeneous Catalysis, Nauka, Novosibirsk, 1984, both published in Russian). Unfortunately, these results are hardly known to English-speaking readers. 

If a chemical reaction is operated in a flow reactor under fixed external conditions (temperature, partial pressures, flow rate etc.), usually also a steady-state (i.e., time-independent) rate of reaction will result. Quite frequently, however, a different response may result The rate varies more or less periodically with time. Oscillatory kinetics have been reported for quite different types of reactions, such as with the famous Belousov-Zha-botinsky reaction in homogeneous solutions (/) or with a series of electrochemical reactions (2). In heterogeneous catalysis, phenomena of this type were observed for the first time about 20 years ago by Wicke and coworkers (3, 4) with the oxidation of carbon monoxide at supported platinum catalysts, and have since then been investigated quite extensively with various reactions and catalysts (5-7). Parallel to these experimental studies, a number of mathematical models were also developed these were intended to describe the kinetics of the underlying elementary processes and their solutions revealed indeed quite often oscillatory behavior. In view of the fact that these models usually consist of a set of coupled nonlinear differential equations, this result is, however, by no means surprising, as will become evident later, and in particular it cannot be considered as a proof for the assumed underlying reaction mechanism. 

Cortright and Dumesic present an update of progress in reaction kinetics, showing how it is providing a broader and sturdier foundation for heterogeneous catalysis. The chapter illustrates how the power of computers and modern theoretical methods, exemplified by density functional theory, allow the incorporation of numerous elementary steps and realistic models of... 

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