Heterogeneity, elementary

In siunmary, although the application of detailed chemical kinetic modeling to heterogeneous reactions is possible, the effort needed is considerably more involved than in the gas-phase reactions. The thermochemistry of surfaces, clusters, and adsorbed species can be determined in a manner analogous to those associated with the gas-phase species. Similarly, rate parameters of heterogeneous elementary reactions can be estimated, via the application of the transition state theory, by determining the thermochemistry of saddle points on potential energy surfaces. 

The rate of the heterogeneous elementary reaction, V per unit area of catalyst surface, is given for the case when the surface is nearly vacant, and for the case when the surface is practically occupied by the dominant adsorbed molecule 6 as... 

Fig. 19. Temperature dependence of an heterogeneous elementary reaction rate. Reproduced from Horiuti (11).

It must be admitted that the mass action law has been successfully applied to homogeneous elementary reactions, while the statistical independence of the system underlying it is premised in the absolute reaction rate theory of Eyring et al. (1) and in the transition state method of Evans and Polanyi 2). The statistical independence is not however insured in the treatment, especially of heterogeneous elementary reactions constituting heterogeneous catalyses as exemplified below this constitutes the second limitation of the kinetics. 

The rate equation is now developed for a particular heterogeneous elementary reaction. Let cr be a site of the critical complex on a boundary interface. We have from Eq. (11.15), p = q d 0)ld X)] is the special case of defined in Section II,B,2, where S is the critical system J. The 0 (J) of the critical system is now the reciprocal of the number of sites a in the assembly, provided that aU of them are physically identical hence... 

We might now deal with the rate of heterogeneous elementary reactions directly rather than in terms of the appropriate rate constant, which is, not being a constant at a constant temperature, hardly useful... 

The set of reactions shown in Table 5.1 accounts for the formation of the main oxidation products methanol, formaldehyde, and water, but does not provide for their further transformation, since only the initial stage of the process is considered. Nevertheless, its analysis can explain the main qualitative features of the DMTM process, although its quantitative modeling requires much more complex, open-type models that would take into account the totality of homogeneous and heterogeneous elementary steps important in this range of conditions. This means that the model includes all the relevant elementary steps and, if required, it can be readily extended and that all the kinetic parameters are taken from independent databases. Thus, these parameters can and should be modified based only on the subsequent recommendations of these databases. 

The key to this chapter is the consideration of the kinetics of a heterogeneous elementary step... 

ErtI G 1990 Elementary steps in heterogeneous catalysis Agnew. Chem., Int. Ed. Engl. 29 1219... 

Fast transient studies are largely focused on elementary kinetic processes in atoms and molecules, i.e., on unimolecular and bimolecular reactions with first and second order kinetics, respectively (although confonnational heterogeneity in macromolecules may lead to the observation of more complicated unimolecular kinetics). Examples of fast thennally activated unimolecular processes include dissociation reactions in molecules as simple as diatomics, and isomerization and tautomerization reactions in polyatomic molecules. A very rough estimate of the minimum time scale required for an elementary unimolecular reaction may be obtained from the Arrhenius expression for the reaction rate constant, k = A. The quantity /cg T//i from transition state theory provides... 

Despite their simplicity, certainly compared to the all-atom potentials used in molecular dynamics studies, these contact energy functions enable the exploration of different interaction scenarios. This diversity is achieved by changing the heterogeneity of the sequence, by altering the number N of different types of residues that are being used. The most elementary lattice model involves only two types of monomers hydrophobic... 

Heterogeneous reaetions involve two or more phases. Examples are gas-liquid reaetions, solid eatalyst-gas phase reaetions and produets, and reaetions between two immiseible liquids. Catalytie reaetions as illustrated in Chapter 1 involve a eomponent or speeies that par-tieipates in various elementary reaetion steps, but does not appear in the overall reaetion. In heterogeneous systems, mass is transferred aeross the phase. 

In the case of coupled heterogeneous catalytic reactions the form of the concentration curves of analytically determined gaseous or liquid components in the course of the reaction strongly depends on the relation between the rates of adsorption-desorption steps and the rates of surface chemical reactions. This is associated with the fact that even in the case of the simplest consecutive or parallel catalytic reaction the elementary steps (adsorption, surface reaction, and desorption) always constitute a system of both consecutive and parallel processes. If the slowest, i.e. ratedetermining steps, are surface reactions of adsorbed compounds, the concentration curves of the compounds in bulk phase will be qualitatively of the same form as the curves typical for noncatalytic consecutive (cf. Fig. 3b) or parallel reactions. However, anomalies in the course of bulk concentration curves may occur if the rate of one or more steps of adsorption-desorption character becomes comparable or even significantly lower then the rates of surface reactions, i.e. when surface and bulk concentration are not in equilibrium. 

The study of catalytic polymerization of olefins performed up to the present time is certain to hold a particular influence over the progress of the concepts of the coordination mechanism of heterogeneous catalysis. With such an approach the elementary acts of catalytic reaction are considered to proceed in the coordination sphere of one ion of the transition element and, to a first approximation, the collective features of solids are not taken into account. It is not surprising that polymerization by Ziegler-Natta catalysts is often considered together with the processes of homogeneous catalysis. 

The most complex type of gas-liquid-particle process is one in which gaseous components participate in a heterogeneous catalytic reaction, with the formation of gaseous products. The following elementary steps must occur in a process of this type ... 

Volume 18 Selected Elementary Reactions Section 8. HETEROGENEOUS REACTIONS (4 volumes)... 

A heterogeneous catalyst is a catalyst present in a phase different from that of the reactants. The most common heterogeneous catalysts are finely divided or porous solids used in gas-phase or liquid-phase reactions. They are finely divided or porous so that they will provide a large surface area for the elementary reactions that provide the catalytic pathway. One example is the iron catalyst used in the... 

Equation (1.20) is frequently used to correlate data from complex reactions. Complex reactions can give rise to rate expressions that have the form of Equation (1.20), but with fractional or even negative exponents. Complex reactions with observed orders of 1/2 or 3/2 can be explained theoretically based on mechanisms discussed in Chapter 2. Negative orders arise when a compound retards a reaction—say, by competing for active sites in a heterogeneously catalyzed reaction—or when the reaction is reversible. Observed reaction orders above 3 are occasionally reported. An example is the reaction of styrene with nitric acid, where an overall order of 4 has been observed. The likely explanation is that the acid serves both as a catalyst and as a reactant. The reaction is far from elementary. 

In particular, reactions in heterogeneous catalysis are always a series of steps, including adsorption on the surface, reaction, and desorption back into the gas phase. In the course of this chapter we will see how the rate equations of overall reactions can be constructed from those of the elementary steps. 

Computational chemistry has reached a level in which adsorption, dissociation and formation of new bonds can be described with reasonable accuracy. Consequently trends in reactivity patterns can be very well predicted nowadays. Such theoretical studies have had a strong impact in the field of heterogeneous catalysis, particularly because many experimental data are available for comparison from surface science studies (e.g. heats of adsorption, adsorption geometries, vibrational frequencies, activation energies of elementary reaction steps) to validate theoretical predictions. 

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. 

In the following we shall study a model system for the synthesis of hydrogen peroxide (H2O2) over a heterogeneous catalyst containing a hypothetical metal M. It is proposed to split the reaction into the following elementary steps, which are all assumed to be in quasi-equilibrium except for step 3, which is assumed to be the rate-limiting step ... 

Section 3 deals with reactions in which at least one of the reactants is an inorganic compound. Many of the processes considered also involve organic compounds, but autocatalytic oxidations and flames, polymerisation and reactions of metals themselves and of certain unstable ionic species, e.g. the solvated electron, are discussed in later sections. Where appropriate, the effects of low and high energy radiation are considered, as are gas and condensed phase systems but not fully heterogeneous processes or solid reactions. Rate parameters of individual elementary steps, as well as of overall reactions, are given if available. 

Keywords Elementary steps Homogeneous and heterogeneous catalysis ... 

It is clear that a molecular imderstanding of phenomena on surfaces, elementary steps, help to imderstand how to improve catalytic systems through a structure-activity relationship. While there is still room for improvement, it should lead, in the near future, to a more rational design of heterogeneous catalysts and to the apphcation of metals modified by surface organometalhc chemistry to a larger number of reactions. 

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