Elementary reactions lateral interactions

In considering elementary steps it is usually assumed that the kinetics of each step follows a mass action law for example, the forward reaction of two surface species may be represented by r = k i 2, where k is a function of temperature only and 0i and 2 are coverages (0 < 1) of two reactants 1 and 2. Until now, identifying the most abundant surface interaiediates and the rate parameters for the forward and backward rate constants for the steps that influence the overall reaction rate has been a sufficiently arduous task. However, it is known that k must often be a function of j and/or 2 because of lateral interactions among the adsorbed species. Also, it is known that the above surface reaction may take place only at the perimeters of islands of 1 and 2 so that the appropriate concentration measure may be or more generally ( y)", and n may vary with... 

The elementary reaction steps of the hydrocarbons considered in this section are summarized in Fig. 8. Tlie occurrence of monomolecular reactions with linear hydrocarbons that produce hydrogen and alkane fragments was first demonstrated by Haag and Dessau [94], For convenience, the zeolite lattice to which the proton is attached is not explicitly shown in the scheme. However, it will become clear later that proton activation cannot be understood properly without explicitly taking into account the interaction of the carbonium and carbenium ion intermediates with the negatively charged zeolite wall. 

The most complete mathematical model of a nonuniform adsorbed layer is the distributed model, which takes into account interactions of adsorbed species, their mobility, and a possibility of phase transitions under the action of adsorbed species. The layer of adsorbed species corresponds to the two-dimensional model of the lattice gas, which is a characteristic model of statistical mechanics. Currently, it is widely used in the modeling of elementary processes on the catalyst surface. The energies of the lateral interaction between species localized in different lattice cells are the main parameters of the model. In the case of the chemisorption of simple species, each species occupies one unit cell. The catalytic process consists of a set of elementary steps of adsorption, desorption, and diffusion and an elementary act of reaction, which occurs on some set of cells (nodes) of the lattice. 

Similar to adsorption on real surfaces, kinetic models based on involvement of lateral interactions and more specifically lattice gas models have been developed in literature. In the widely used lattice gas model the relationships between the rate of an elementary reaction and coverage is complex and cannot be written in a closed form when this model is used. 

Theoretical investigations of this model (A. G. Makeev, B. E. Nieuwenhuys, Mathematical modeling of the NO + H2/Pt(100) reaction "Surface explosion," kinetic oscillations, and chaos, Journal of Chemical Physics, 108 (1998) 3740-3749) with 11 reversible and irreversible elementary steps included lateral interactions for only two steps in the forward direction and two steps in the reverse direction, leading to the following rate expressions... 

The derivation above considered a two-step sequence on biographically nonuniform surfaces and followed the treatment first developed by Temkin. For induced nonuniform surfaces the reaction rates of elementary reactions are described by eq. 3.103-3.105. These general equations which take into account all the possible lateral interactions between all the surface adsorbed species on the surface can be applied to treat the same two-step sequence. 

If we consider the same mechanism and take into account lateral interactions the rate of the elementary reactions of step 1) in mechanism (7.156) can be written... 

In this book, we demonstrate the use of transition-state theory to describe catalytic reactions on surfaces. In order to do this we start by treating the kinetics of catalytic reactions (Chapter 2) and provide some background information on important catalytic processes (Chapter 3). In Chapter 4 we introduce the statistical mechanical basis of transition-state theory and apply it to elementary surface reactions. Chapter 5 deals with the physical justification of the transition-state theory. We also discuss the consequences of media effects and of lateral interactions between adsorbates on surfaces for the kinetics. In the final chapter we present the principles of catalytic kinetics, based on the application of material given in earlier chapters. 

From these and later studies has come a better understanding of how different chain transfer and radical interaction processes compete, how these competitions change with reaction conditions, structure and temperature and how rate parameters (Arrhenius parameters) for elementary oxidation reactions may be predicted from the structures of the reactants and products. 

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