Desorption kinetics from homogeneous surface

Heterogeneous catalysis has to deal not only with the catalyzed reaction itself but, in addition, with the complexities of surface properties (different crystal surfaces, different catalytic sites), possible segregation of adsorbates (so-called island formation), contamination or deterioration of catalytic sites, and adsorption and desorption equilibria and rates. Moreover, mass transfer to and from the reaction site is a factor more often than in homogeneous catalysis. In practice, these complications may affect behavior more profoundly than does the kinetics of the surface reaction itself. A practical and balanced kinetic treatment therefore uses simplifications and approximations much more generously than was done in the preceding chapters. Excellent textbooks on the subject are available [G1-G7], so coverage here can remain restricted to a critical overview and indications showing when and how concepts and methods developed in the earlier chapters can be useful. 

The possibility of determining the kinetic order of a desorption process having a variation of activation energy with coverage is extremely small since even with a very small value of 8, the exponential term may dominate the kinetics. As an example, we presume a second-order molecular desorption from a homogeneous surface covered with adatoms where there is a small induced heterogeneity that varies with coverage. 

Nonactivated ammonia adsorption is assumed on both sites (/ ads-site-i and ads-site-2) while different rate expressions are used to describe NH3 desorption. Since Site-1 includes different types of Lewis acid sites and also ammonia physisorbed on the catalyst surface, Temkin-type coverage dependent adsorption is adopted in order to take such a site heterogeneity (/ des-site-i) into account. On the contrary, the nature of Br0nsted acid sites is well defined for zeolites, being indeed associated with the so-called bridging hydroxyls, thus it is reasonable to assume that these sites are homogeneous in terms of ammonia adsorption strength. Based on this assumption, simple Arrhenius kinetics are adopted for the NH3 desorption process from Site-2. ... 

A similar kinetic expression was found by Hong et al. [132] for the catalytic, photochemical oxidation of S(IV) on Ti02. In this case, for k < 385 nm, quantum yields in excess of unity (e.g., 0.5 < free-radical chain reactions (i.e., reactions 79 to 84). The observed quantum yields, which ranged between 0.5 and 300, depended on the concentration and nature of free-radical inhibitors present in the heterogeneous suspension. 

Kinetics of heterogeneous catalysis has received much attention. Its mathematical theory is well advanced, largely thanks to extensive work of Boudart, Temkin, and others. On the other hand, heterogeneous catalysis has to deal not only with the same kind of difficulties homogeneous catalysis faces, but with the added complications of surface properties, adsorption/desorption equilibria and rates, and mass transfer to and from catalytic sites, phenomena whose effects often are more important than those of actual kinetics of the reaction on the surface. 

Even from the very beginning it became clear that kinetic methods generally accepted in heterogeneous catalysis, which are based on the analysis of adsorption-desorption equilibria and surface reactions in the steady-state approximation, cannot be applied to the studies of heterogeneous-homogeneous processes. However, on the eve of 1980s no developed methodology applicable... 

At higher partial pressures, the behavior becones nonlinear, and more complex models are required to describe the observed equilibrium data. A frequently used model for monomolecular layer adsorption is the Langmuir isotherm equation. This equation is derived from simple mass-action kinetics. It assumes that the surface of the pores of the adsorbent is homogeneous and that the forces of interaction between the adsorbed molecules are negligible. Let/be the fraction of the surface covered by adsorbed molecules. Therefore, 1 -/ is the fraction of the bare surface. Then, the net rate of adsorption is the difference between the rate of adsorption on the bare surface and desorption from the covered surface ... 

The detailed treatment of the adsorption-desorption process as a chemical reaction reveals a few major concepts that are used in developing the kinetics of heterogeneous reactions from a sequence of several surface reactions such as the one in Eq. 2.1. For the purpose of writing the kinetics of each step, each surface reaction can be treated as an elementary step as in homogeneous reactions. The treatment also shows an individual step as a separate entity independent of the other steps, eventually leading to the concept of a rate-limiting (or rate-controlling) step. 

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