Surface reaction models, oscillatory

The abstract models can be divided into two categories, each of which can be further subdivided into three classes (Fig. 5). Some of the models consist of coverage equations only, and these models will be called surface reaction models. The remaining models use additional mass and/or heat balance equations that include assumptions about the nature of the reactor in which the catalytic reaction takes place (the reactor could be simply a catalyst pellet). These models will be called reactor-reaction models. Some of the models mentioned under the heading surface reaction models also incorporate balance equations for the reactor. However, these models need only the coverage equations to predict oscillatory behavior reactor heat and mass balances are just added to make the models more realistic [e.g., the extension of the Sales-Turner-Maple model (272) given in Aluko and Chang (273)]. Such models are therefore included under surface reaction models, which will be discussed first. 

Oscillatory surface reaction models were first proposed in the second half of the 1970s and developed in two parallel strains. The buffer-step models originated with the work of Eigenberger (274) and models with coverage-dependent activation energies were first proposed by Belyaev et al. (154). 

There are some oscillatory surface reaction models that contain neither buffer steps nor coverage-dependent activation energies. The first model able to predict oscillatory behavior without these mechanisms was introduced by Takoudis et al. (275,279) and later was analyzed in great detail by McKarnin et al. (286). The model consists of the following three steps, the third of which is strongly autocatalytic ... 

How relevant are these phenomena First, many oscillating reactions exist and play an important role in living matter. Biochemical oscillations and also the inorganic oscillatory Belousov-Zhabotinsky system are very complex reaction networks. Oscillating surface reactions though are much simpler and so offer convenient model systems to investigate the realm of non-equilibrium reactions on a fundamental level. Secondly, as mentioned above, the conditions under which nonlinear effects such as those caused by autocatalytic steps lead to uncontrollable situations, which should be avoided in practice. Hence, some knowledge about the subject is desired. Finally, the application of forced oscillations in some reactions may lead to better performance in favorable situations for example, when a catalytic system alternates between conditions where the catalyst deactivates due to carbon deposition and conditions where this deposit is reacted away. 

NMR properties, 33 213, 274 in nutation-NMR spectroscopy, 33 333 in sheer silicate smdies of, 33 340-341 layer structure, 32 184-186 on metal surfaces, 32 194-197 model, oscillatory reactions, 39 97-98 number... 

Now possibilities of the MC simulation allow to consider complex surface processes that include various stages with adsorption and desorption, surface reaction and diffusion, surface reconstruction, and new phase formation, etc. Such investigations become today as natural analysis of the experimental studying. The following papers [282-285] can be referred to as corresponding examples. Authors consider the application of the lattice models to the analysis of oscillatory and autowave processes in the reaction of carbon monoxide oxidation over platinum and palladium surfaces, the turbulent and stripes wave patterns caused by limited COads diffusion during CO oxidation over Pd(110) surface, catalytic processes over supported nanoparticles as well as crystallization during catalytic processes. 

In a review article on oscillatory reactions (294), Sheintuch discusses the effect of introducing a heat balance for the catalyst rather than a mass balance for the reactor into the differential equation system for a surface reaction with oxidation/reduction cycles. Although the coverage equations alone can yield oscillatory behavior, as was the case for the models discussed in the previous section, Sheintuch s model is discussed in this section because introduction of the heat balance adds qualitatively new features. In this extended system complex, multiple peak behavior and quasiperiodicity was observed as shown in Fig. 8. Sheintuch also investigated the interaction of two oscillators. This work, however, will be treated in detail in Section V, were synchronization and chaos are discussed. 

The observation of oscillations in heterogeneous catalytic reactions is an indication of the complexity of catalyst kinetics and makes considerable demands on the theories of the rates of surface processes. In experimental studies the observed fluctuations may be in catalyst temperature, surface species concentrations, or most commonly because of its accessibility, in the time variation of the concentrations of reactants and products in contact with the catalyst. It is now clear that spontaneous oscillations are primarily due to non-linearities associated with the rates of surface reactions as influenced by adsorbed reactants and products, and the large number of experimental studies of the last decade have stimulated a considerable amount of theoretical kinetic modelling to attempt to account for the wide range of oscillatory behaviour observed. 

Matveev, A.V., Latkin, E.I., Elokhin, V.I., and Gorodetskii, V.V., Manifestation of the adsorbed CO diffusion anisotropy caused by the structure properties of the Pd(l 1 0)-(l x 2) surface on the oscillatory behavior during CO oxidation reaction — Monte-Carlo model, Chem. Sustain. Dev., 11, 173-180,2003. 

Mathematical model of three-way catalytic converter (TWC) has been developed. It includes mass balances in the bulk gas, mass transfer to the porous catalyst, diffusion in the porous structure and simultaneous reactions described by a complex microkinetic scheme of 31 reaction steps for 8 gas components (CO, O2, C2H4, C2H2, NO, NO2, N2O and CO2) and a number of surface reaction intermediates. Enthalpy balances for the gas and solid phase are also included. The method of lines has been used for the transformation of a set of partial differential equations (PDEs) to a large and stiff system of ordinary differential equations (ODEs . Multiple steady and oscillatory states (simple and doubly-periodic) and complex spatiotemporal patterns have been found for a certain range of operation parameters. The methodology of studies of such systems with complex dynamic patterns is briefly introduced and the undesired behaviour of the used integrator is discussed. 

Recently, Vigil and Willmore [67] have reported mean field and lattice gas studies of the oscillatory dynamics of a variant of the ZGB model. In this example oscillations are also introduced, allowing the reversible adsorption of inert species. Furthermore, Sander and Ghaisas [69] have very recently reported simulations for the oxidation of CO on Pt in the presence of two forms of oxygen, namely chemisorbed atomic O and oxidized metal surface. These species, which are expected to be present for reaction under atmospheric pressure, are relevant for the onset of oscillatory behavior [69]. 

In chapter 12 we discussed a model for a surface-catalysed reaction which displayed multiple stationary states. By adding an extra variable, in the form of a catalyst poison which simply takes place in a reversible but competitive adsorption process, oscillatory behaviour is induced. Hudson and Rossler have used similar principles to suggest a route to designer chaos which might be applicable to families of chemical systems. They took a two-variable scheme which displays a Hopf bifurcation and, thus, a periodic (limit cycle) response. To this is added a third variable whose role is to switch the system between oscillatory and non-oscillatory phases. 

These models consider the mechanisms of formation of oscillations a mechanism involving the phase transition of planes Pt(100) (hex) (lxl) and a mechanism with the formation of surface oxides Pd(l 10). The models demonstrate the oscillations of the rate of C02 formation and the concentrations of adsorbed reactants. These oscillations are accompanied by various wave processes on the lattice that models single crystalline surfaces. The effects of the size of the model lattice and the intensity of COads diffusion on the synchronization and the form of oscillations and surface waves are studied. It was shown that it is possible to obtain a wide spectrum of chemical waves (cellular and turbulent structures and spiral and ellipsoid waves) using the lattice models developed [283], Also, the influence of the internal parameters on the shapes of surface concentration waves obtained in simulations under the limited surface diffusion intensity conditions has been studied [284], The hysteresis in oscillatory behavior has been found under step-by-step variation of oxygen partial pressure. Two different oscillatory regimes could exist at one and the same parameters of the reaction. The parameters of oscillations (amplitude, period, and the... 

Formulating appropriate rate laws for CO adsorption, OH adsorption and the reaction between these two surface species, a set of four coupled ordinary differential equations is obtained, whereby the dependent variables are the average coverages of CO and OH, the concentration of CO in the reaction plane and the electrode potential. In accordance with the experiments, the model describes the S-shaped I/U curve and thus also bistability under potentiostatic control. However, neither oscillatory behavior is found for realistic parameter values (see the discussion above) nor can the nearly current-independent, fluctuating potential be reproduced, which is observed for slow galvanodynamic sweeps (c.f. Fig. 30b). As we shall discuss in Section 4.2.2, this feature might again be the result of a spatial instability. 

The inherently nonisothermal models that require temperature variations for oscillatory behavior fall into two groups. In both cases, the reaction is blocked and reactivated at different temperatures. The blockage is caused either by a surface blocking or by a bulk-phase transition of the catalyst. 

A similar model was analyzed by Pikios and Luss (283). They analyzed the same set of reaction steps with the coverage-dependent activation energy interpreted in terms of surface heterogeneity. They derived criteria for the occurrence of oscillations as did Belyaev et al. (154,162). They also found a singular steady state, which became a limit cycle for values of the surface heterogeneity lying above a certain threshold value, and they performed numerical analyses of these oscillatory states. 

Although this model is able to predict oscillatory behavior, it has one major flaw, because a crucial step in the model is the adsorption of N2 on Pt to yield adsorbed N atoms on the Pt surface. This reaction step is not supported by an existent experimental evidence. This crucial step can also be interpreted as a buffer step as discussed in the general schemes in Section IV,A, and thus omission of this step would probably destroy the oscillatory behavior of the model predictions. 

A third Pt surface on which oscillations of the CO/O2 reaction have been observed is the (210) plane (75,78). In this case, a surface-phase transition was again proposed as an explanation for the oscillations. The (210) surface was observed to facet into (310) and (110) orientations during an induction period, after which oscillations began to occur on the (110) facets (78). An alternative model for the oscillatory behavior has been proposed by Ehsasi et al. (76). 

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