Surface reaction vacant sites involved

Non-linearities arising from non-reactive interactions between adsorbed species will not be our main concern. In this section we return to variations of the Langmuir-Hinshelwood model, so the adsorption and desorption processes are not dependent on the surface coverage. We are now interested in establishing which properties of the chemical reaction step (12.2) may lead to multiplicity of stationary states. In particular we will investigate situations where the reaction step requires the involvement of additional vacant sites. Thus the reaction step can be represented in the general form... 

Fig. 12.3. Stationary-state fractional coverage for adsorption and reaction involving two vacant sites (a) k2/K = 36 showing multiplicity, (b) multiplicity in absence of desorption now one solution corresponding to a fully covered surface exists for all reactant pressures.

In this section we turn to a model where the adsorption and desorption of two reactants occur on similar timescales. The adsorption is competitive, i.e. both reactants are adsorbed on to the same surface sites. Again, a number of vacant sites will be involved in the reaction step. The model is... 

The mechanism by which oscillations occur also involves the vacant site requirement for reaction. For critical values of the partial pressures, the coverage of one of the reactants decreases leading to an increase in the rate of reaction due to the availability of vacant sites. This accelerates the decrease in coverage until the rate of reaction subsides. The large number of vacant sites then increases the rate of adsorption until the surface coverage returns to its previous state to complete the cycle. 

The second-best case to consider is two reactions of the same order differing by one reactant only, for example, Cs + Hs CHS versus CHS + Hs CH2,s. Finally, if a vacant surface site S is treated as a reactant, one can compare dissociation reactions with recombination reactions, e.g., S + COs Cs + Os versus Hs + COs HCOs + S. Here, however, the conclusions based on AE will be the least definitive, because the differences in the nature of surface sites (on-top, bridge, or hollow) and in the effective number of the sites involved in the reaction may strongly affect the value of A. 

The early use of deuterium in place of hydrogen in the study of catalytic hydrogenation led to the recognition that the process was not simply the addition of H2 to the double bond. Horiuti and Polanyi proposed that both H2 and alkene (1) are bound to the catalyst surface and transformed to products by a sequence of elementary steps, which they represented as shown in Scheme 1, where an asterisk ( ) represents a vacant site on the catalyst.The last step, (d), is virtually irreversible under the usual hydrogenation conditions, but can be observed in the exchange reactions of D2 with alkanes. The mechanism accounts for the isomerization of an alkene if the reversal of step (c), which involves the formation of the alkyl intermediate (3), involves the abstraction of a hydrogen atom other than the one first added, and is coupled with the desorption of the alkene, (2) - (1). At present, the bond between the alkene and the metal often is represented as a ir-complex (4), as in equation (7). ... 

This approach has even been used to prepare highly dispersed palladium catalysts supported on low surface area aluminas. 39 EXAFS analyses of the various stages in the interaction of Pd(acac)2 with alumina has shown that the initial reaction involves an octahedral aluminum vacant site. On heating the resulting ionic species was converted to a supported crystalline oxide which was then reduced to the Pd/Al203 catalyst. " ... 

Each term is proportional to the surface coverage by the respective species, scaled so that the leading " 1" is proportional to the vacant surface, and n is the number of sites involved in the molecular reaction. Some reactions require substitutions in eqn 9.7. A tabulation of groups and substitutions is shown on the next two pages. 

The adsorption of oxygen is assumed as irreversible and dissociative with a rate proportional to the fraction of vacant sites [1]. In contrast to Sant et al. [2] adsorption of both ethene and ethyne is also assumed to be first order in the vacant sites. The rate of the surface reactions between adsorbed ethene and adsorbed oxygen, and between adsorbed ethyne and adsorbed oxygen, is considered as proportional to the product of the involved surface coverages. The adsorption rate coefficients are obtained fi om the kinetic gas theory, while Arrhenius-type expressions are used for the rate coefficients of desorption,dissociation and the surface reactions. The kinetic parameter values used in this study are shown in Table 2. 

The chemical steps involved in heterogeneous reactions (adsorption, desorption, surface reaction) are generally treated as elementary reactions. In many cases, one reaction is the slow step and the remaining steps are at equilibrium. For heterogeneous reactions, we add a site balance to account for the vacant and occupied sites that take part in the reaction steps. 

The exponent n on the adsorption term is equal to the number of sites participating in the surface reaction, regardless of whether they hold adsorbed species or participate as vacant sites. If more than one site is involved, we assume... 

Stochastic models are also able to capture complicated pattern formation seen in chemically reacting media and can be used to study the effects of fluctuations on chemical patterns and wave propagation. The mesoscopic dynamics of the FHN model illustrates this point. In order to formulate a microscopically based stochastic model for this system, it is first necessary to provide a mechanism whose mass action law is the FHN kinetic equation. Some features of the FHN kinetics seem to preclude such a mechanistic description for example, the production of u is inhibited by a term linear in V, a contribution not usually encountered in mass action kinetics. However, if each local region of space is assumed to be able to accommodate only a maximum number m of each chemical species, then such a mechanism may be written. We assume that the chemical reactions depend on the local number of molecules of the species as well as the number of vacancies corresponding to each species, in analogy with the dependence of some surface reactions on the number of vacant surface sites or biochemical reactions involving complexes of allosteric enzymes that depend on the number of vacant active sites. 

At first glance, this process does not appear to be simple enough to be elementary. The forward reaction requires that one H-H bond be broken and two H-S bonds be formed. More importantly, the forward reaction appears to be termolecular, since three chemical entities are involved, one H2 molecule and two vacant sites on the surface of the catalyst However, the probability of this disassociative chemisorption process is much higher than the probability of a three-body collision in a fluid, since the two surface sites are adjacent and are not moving with respect to each other. Therefore, in evaluating the likelihood that a given reaction on the surface of a catalyst is elementary, we can be more tolerant of termolecular processes than we would be for homogeneous, fluid-phase reactions. However, only one of the chemical entities involved in an elementary, termolecular surface reaction should be a fluid species. For example, it is unlikely that the reaction... 

There is evidence that certain chemical adsorption processes involve dissociation of the adsorbate to form two bonds with the adsorbent surface. On many metals, hydrogen is adsorbed in atomic form. For such situations the kinetic approach to the derivation of the Langmuir equation requires that the process be regarded as a reaction between the gas molecule and two vacant surface sites. Thus, the adsorption rate is written as... 

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