Surface reaction kinetics description

Another reason for describing surface reaction kinetics in more detail is that we need to examine the processes on a microscopic scale. While we are interested primarily in the macroscopic description of catalytic reactor behavior, we cannot do this intelligently until we understand these processes at a molecular level. 

Most surface-reaction kinetics involves submonolayer coverages of adsorbed species. However, multilayer adsorption can occur. The standard description of multilayer adsorption is... 

In kinetic analysis of coupled catalytic reactions it is necessary to consider some specific features of their kinetic behavior. These specific features of the kinetics of coupled catalytic reactions will be discussed here from a phenomenological point of view, i.e. we will show which phenomena occur or may occur, and what formal kinetic description they have if the coupling of reactions is taking place. No attention will be paid to details of mechanisms of the processes occurring on the catalyst surface from a molecular point of view. 

A kinetic description of a heterogeneous catalytic reaction will in most cases be different when the reaction proceeds simultaneously with other reactions in a complex system, compared with the case where its kinetics was studied separately. The most important is the effect in the case where the reactions concerned take place on the same sites of the surface of a catalyst. Let us take, for example, the system of competitive reactions... 

The mechanism of the NO -1- CO reaction at realistic pressures is thus very complicated. In addition to the reaction steps considered above, one also has to take into account that intermediates on the surface may organize into islands or periodically ordered structures. Monte Carlo techniques are needed to account for these effects. Consequently, we are still far from a complete kinetic description of the CO -1- NO reaction. For an interesting review of the mechanism and kinetics of this reaction we refer to Zhdanov and Kasemo [V.P. Zhdanov and B. Kasemo, Suif. Sci. Rep. 29 (1997) 31],... 

These assumptions are partially different from those introduced in our previous model.10 In that work, in fact, in order to simplify the kinetic description, we assumed that all the steps involved in the formation of both the chain growth monomer CH2 and water (i.e., Equations 16.3 and 16.4a to 16.4e) were a series of irreversible and consecutive steps. Under this assumption, it was possible to describe the rate of the overall CO conversion process by means of a single rate equation. Nevertheless, from a physical point of view, this hypothesis implies that the surface concentration of the molecular adsorbed CO is nil, with the rate of formation of this species equal to the rate of consumption. However, recent in situ Fourier transform infrared (FT-IR) studies carried out on the same catalyst adopted in this work, at the typical reaction temperature and in an atmosphere composed by H2 and CO, revealed the presence of a significant amount of molecular CO adsorbed on the catalysts surface.17 For these reasons, in the present work, the hypothesis of the irreversible molecular CO adsorption has been removed. 

Nevertheless, the kinetic approach to heterogeneous catalysis can be rewarding if relative data for two or more structurally related reactants or catalysts are acquired and interpreted. Instead of applying several assumptions that simplify the reaction scheme and the model of the surface, which are necessary for absolute kinetic description, it is accepted that, under certain conditions, the same reaction scheme holds for all members of the series of reactants or catalysts and that all of the unknown but identical simplifications in the relative data cancel out. However, it is much safer to select a series of reactants in which the structural change from one member to another will be small enough to uphold the basic features of the mechanism than to assume the same for a set of catalysts that are not minor variations of a basic preparation. 

Specific research subjects have emerged with respect to improved descriptions of specific phenomena. Some time ago, it was speculated that gas-solid interactions and turbulence effects on reaction kinetics would be important areas of advance in the modeling art. Gas-solid interactions include both chemical formation of aerosols and reactions on surfaces of pre-existing suspended particulate matter. Because of differing effects of a material in the gas phase and in some condensed phase, it will be important to characterize transformation processes. The achex (Aerosol Characterization hYperiment) program recently carried out under the direction of Hidy will provide an extensive data base with which to test new ways of treating the gas-solid interaction problem. 

Klupinski et al. (2004) conclude that the reduction of nitroaromatic compounds is a surface-mediated process and suggest that, with lack of an iron mineral, reductive transformation induced only by Fe(II) does not occur. However, when C Cl NO degradation was investigated in reaction media containing Fe(II) with no mineral phase added, a slow reductive transformation of the contaminant was observed. Because the loss of C Cl NO in this case was not described by a first-order kinetic model, as in the case of high concentration of Fe(II), but better by a zero-order kinetic description, Klupinski et al. (2004) suggest that degradation in these systems in fact is a surface-mediated reaction. They note that, in the reaction system, trace amounts of oxidize Fe(II), which form in situ suspended iron oxide... 

Deviations from this simple expression have been attributed to mechanistic complexity For example, detailed kinetic studies have evaluated the relative importance of the Langmuir-Hinshelwood mechanism in which the reaction is proposed to occur entirely on the surface with adsorbed species and the Eley-Rideal route in which the reaction proceeds via collision of a dissolved reactant with surface-bound intermediates 5 . Such kinetic descriptions allow for the delineation of the nature of the adsorption sites. For example, trichloroethylene is thought to adsorb at Ti sites by a pi interaction, whereas dichloroacetaldehyde, an intermediate proposed in the photo-catalyzed decomposition of trichloroethylene, has been suggested to be dissociatively chemisorbed by attachment of the alpha-hydrogen to a surface site... 

The basic premise of the original kinetic description of inhibition was that, for a reaction to proceed on a surface, one or more of the reactants (A) must be adsorbed on that surface in reversible equilibrium with the external solution, having an equilibrium adsorption constant of KA, and the adsorbed species must undergo some transformation involving one or more adsorbed intermediates (n) in the rate-limiting step, which leads to product formation. The product must desorb for the reaction cycle to be complete. If other species in the reaction mixture (I) can compete for the same adsorption site, the concentration of the adsorbed reactant (Aad) on the surface will be lower than when only pure reactant A is present. Thus, the rate of conversion will depend on the fraction of the adsorption sites covered by the reactant (0A) rather than the actual concentration of the reactant in solution, and the observed rate coefficient (fcobs) will be different from the true rate coefficient (ktme). In its simplest form the kinetic expression for this phenomenon in a first-order reaction can be described as follows ... 

The complex nature of heterogeneous catalytic reactions, which consist of a sequence of at least three steps (adsorption, surface reaction and desorption), the possible intervention of transport processes and the uncertainty about the actual state of the surface makes every attempt to obtain a complete formal kinetic description without simplifying assumptions futile. In this situation, some authors prefer fully empirical equations of the type... 

The kinetic equations are useful as a fitting procedure although their basis - the homogeneous system - in general does not exist. Thus they cannot deal with segregation and island formation which is frequently observed [27]. Computer simulations incorporate fluctuation and correlation effects and thus are able to deal with segregation effects but so far the reaction systems under study are oversimplified and contain only few aspects of a real system. The use of computer simulations for the study of surface reactions is also limited because of the large amount of computer time which is needed. Especially MC simulations need so much computer time that complicated aspects (e.g., the dependence of the results on the distribution of surface defects) in practice cannot be studied. For this reason CA models have been developed which run very fast on parallel computers and enable to study more complex aspects of real reaction systems. Some examples of CA models which were studied in the past years are the NH3 formation [4] and the problem of the universality class [18]. However, CA models are limited to systems which are suited for the description by a purely parallel ansatz. 

The source of this discrepancy is unknown to us. Equation (349) is, undoubtedly, adequate for the description of the reaction kinetics on an iron-chromium oxide catalyst. The fact that in one of the works (124) magnetite without the addition of chromium oxide served as a catalyst can hardly be of consequence since a study of adsorption-chemical equilibrium (344) on an iron-chromium oxide catalyst (7% Cr203) (52) led to the value of the average energy of liberation of a surface oxygen atom that practically coincides with that found earlier (50) for an iron oxide catalyst with no chromium oxide. It may be suspected that in the first work (124) the catalyst was poisoned with sulfur of H2S that possibly was contained in unpurified C02... 

The compensation relationships mentioned here for the decomposition of formic acid on metals (Table III, K-R and Figs. 6 and 7) cannot be regarded as established, meaningful kinetic descriptions of the reactions concerned, since the magnitudes of the calculated values of B and e depend on the selection of data to be included in the calculation. While there is evidence of several sympathetic interrelationships between log A and E, the data currently available do not accurately locate a specific line and do not define values of B and e characteristic of each system, or for all such systems taken as a group. The pattern of observations is, however, qualitatively attributable to the existence of a common temperature range within which the adsorbed formate ion becomes unstable. The formation of this active intermediate, metal salt, or surface formate, provides a mechanistic explanation of the observed kinetic behavior, since the temperature dependence of concentration of such a participant may vary with the prevailing reaction conditions. 

Non-uniformity of catalytic sites A characteristic of a catalytic surface is that its sites may differ in their thermodynamic and kinetic properties. In the kinetic description of catalytic reactions on non-uniform surfaces, a parameter a is frequently used to connect changes in the activation energy of activated adsorption with the enthalpy of the adsorption... 

In order to assess the feasibility of any nuclear waste disposal concept, mathematical models of radionuclide sorption processes are required. In a later section kinetic descriptions of the three common sorption isotherms (3) are compared with experimental data from the mixing-cell tests. For a radionuclide of concentration C in the groundwater and concentration S on the surface of the granite, the net rate of sorption, by a first-order reversible reaction, is given by... 

Another important characteristic of the surface processes is a ratio g of the adspecies migration rate constant to those of the surface reaction, adsorption, and desorption rates. At small coverages the parameter g controls the surface process conditions r 1 in the kinetic and g l in the diffusion mode. A fast surface mobility of the adspecies and their equilibrium distribution on the surface are the most frequently adopted assumptions. At r < 1 the macroscopic concentrations of adspecies 6 cannot be used for calculating the process rates, and a more detailed description of their distribution is essential. 

The development of the kinetic theory made it possible to obtain a solution of the problem on the self-consistent description in time and in an equilibrium state of the distributions of interacting species between the sites of homogeneous and inhomogeneous lattices. This enables one to solve a large number of matters in the practical description of processes at a gas-solid interface. The studied examples of simple processes, namely, adsorption, absorption, the diffusion of particles, and surface reactions, point to the fundamental role of the cooperative effects due to the interaction between the components of the reaction system in the kinetics of these processes. 

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