Desorption kinetics from heterogeneous surface

This section is devoted to the calculation of the desorption kinetics from a heterogeneous surface characterized by a desorption energy distribution function (peq(E) given by Eq. (9) with E = q, i.e. of the desorption kinetics from a surface which in equilibrium conditions obeys the Freundlich or Temkin isotherm. The local desorption kinetics will be assumed to be of the first order. 

A theory as rigorous and comprehensive as the theory of adsorption equilibrium on heterogeneous surfaces has not been developed yet for the description of adsorption [desorption] kinetics on [from] heterogeneous surfaces. This work aims to fill, at least partially, this gap and new methods are developed for kinetics in strict analogy to what was done... 

In general the desorption kinetics from patchwise heterogeneous surfaces are given by ... 

Since the factor 0(1) becomes o(l) for t close to tu and the correction to the logarithm behaviour vanishes as 0(1)desorption kinetics are expected to be observed on strongly heterogeneous surfaces which in equilibrium conditions obey the Temkin equation. For a simplified demonstration that the Elovich equation is expected to be observed in the desorption from heterogeneous surfaces, see Refs. [22, 52],... 

Cerofolini and Rudzihski [43] have reviewed the theoretical principles of single gas and mixture adsorption on heterogeneous surfaces. Their review is chronologically arranged from the earliest to the latest approaches. In the same book, Tovbin [44] reported the application of lattice-gas models to explain mixed-gas adsorption equilibria on heterogeneous surfaces he also discussed [45] the kinetic aspects of adsorption-desorption on flat heterogeneous surfaces. The book [46] also contains other papers on different aspects of adsorption for the reader interested in surface diffusion processes. 

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. 

Surface heterogeneity has ever been considered to play a major role on adsorption [desorption] kinetics on [from] real surfaces and on heterogeneous catalytic processes. In fact, the most frequently observed kinetics which deviate from the theoretical first- or second-order ones, i.e. the time-logarithm law commonly known as Elovich equation, have in most cases been interpreted as due to surface heterogeneity. 

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. 

In a series of papers, Suvorov et al. investigated heterogeneous catalysis of the cyclization of isolated aldehyde and ketone phenylhydrazones. y-Alumina was typically employed as catalyst in the vapor phase reaction at atmospheric pressure and at temperatures around 300 °C. A maximum yield of 60% was obtained from acetaldehyde phenylhydrazone as a result of thermal decomposition of the hydrazone [7] and the formation of benzene and aniline as by-products [8]. Kinetic studies indicated that the rate-determining step was desorption of product from the surface [9]. 

To calculate thermodynamic equilibrium in multicomponent systems, the so-called optimization method and the non-linear equation method are used, both discussed in [69]. In practice, however, kinetic problems have also to be considered. A heterogeneous process consists of various occurrences such as diffusion of the starting materials to the surface, adsorption of these materials there, chemical reactions at the surface, desorption of the by-products from the surface and their diffusion away. These single occurrences are sequential and the slowest one determines the rate of the whole process. Temperature has to be considered. At lower substrate temperatures surface processes are often rate controlling. According to the Arrhenius equation, the rate is exponentially dependent on temperature ... 

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. ... 

Note 1. From the formal point of view, the equations for the adsorption kinetics on a heterogeneous surface with a given adsorption-time distribution may be modified to have the same expression [Eq. (42)], as the desorption kinetics with the same desorption-time distribution (see, for instance. Refs. [35]). The forms (46) and (47), however, may be apphed only to thermally activated adsorption kinetics chemisorption usually runs in this situation, whereas physisorption is generally a nonactivated process. 

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. 

Heterogeneous catalytic processes begin with the adsorption jof a molecule on the surface, then proceed to diffusion,reaction, and rearrangement on the surface, and end with desorption of products from the surface. With the purpose of being an aid for understanding and characterization of. these p jcesses, the computational approach can provide information in three aspects, (a) electronic or vibrational spectra,. (b) reaction mechanism or reactivity, and (c) kinetic or dynamic aspects based on computed potential energy functions. The current status is summarized by van Santen and cited in Table 2. ... 

Fig. 3.18 Rate of N2 desorption as a function of time during the NO—H2 reaction on Pt(IOO) at Pno = 3 X 10 bar and 7=460 K (A) period-1 osciiiations at Pno/Ph2 = 1 (B) period-2, (C) period-4, and (D) and aperiodic osciiiations at Pno/Ph2 —1-4. (From V.P. Zhdanov, Impact of surface science on the understanding of kinetics of heterogeneous catalytic reactions, Surf. Sci. 500 (2002) 966. Copyright...

The quantitative solution of the problem, i.e. simultaneous determination of both the sequence of surface chemical steps and the ratios of the rate constants of adsorption-desorption processes to the rate constants of surface reactions from experimental kinetic data, is extraordinarily difficult. The attempt made by Smith and Prater 82) in a study of cyclohexane-cyclohexene-benzene interconversion, using elegant mathematic procedures based on the previous theoretical treatment 28), has met with only partial success. Nevertheless, their work is an example of how a sophisticated approach to the quantitative solution of a coupled heterogeneous catalytic system should be employed if the system is studied as a whole. 

Interpretation of the mechanisms of the hydrocarbon desorption reactions mentioned above was considered (31,291) with due regard for the possible role of clay dehydration. While this water evolution process is not regarded as a heterogeneous catalytic reaction, it is at least possible that water loss occurs at an interface (293) so that estimations of preexponential factors per unit area can be made. On this assumption, Arrhenius parameters (in the units used throughout the present review) were calculated from the available observations in the literature and it was found (Fig. 9, Table V, S) that compensation trends were present in the kinetic data for the dehydration reactions of illite (+) (294), kaolinite ( ) (293,295 298), montmorillonite (x) (294) and muscovite (O) (299). If these surface reactions are at least partially reversible,... 

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