Oscillatory kinetics

As on previous occasions, the reader is reminded that no very extensive coverage of the literature is possible in a textbook such as this one and that the emphasis is primarily on principles and their illustration. Several monographs are available for more detailed information (see General References). Useful reviews are on future directions and anunonia synthesis [2], surface analysis [3], surface mechanisms [4], dynamics of surface reactions [5], single-crystal versus actual catalysts [6], oscillatory kinetics [7], fractals [8], surface electrochemistry [9], particle size effects [10], and supported metals [11, 12]. 

Imbihl R and ErtI G 1995 Oscillatory kinetics in heterogeneous catalysis Chem. Rev. 95 697-733... 

R. Imbhil, G. Ertl. Oscillatory kinetics in heterogeneous catalysis. Chem Rev 95 697-733, 1995. 

The LC concept has been applied to describe collective chemical and physicochemical reactions with an oscillatory kinetics, circadian and cardiac rhythm, brain function and rhythm etc. Details of this concept may be found in a recent article (8), where... 

If a chemical reaction is operated in a flow reactor under fixed external conditions (temperature, partial pressures, flow rate etc.), usually also a steady-state (i.e., time-independent) rate of reaction will result. Quite frequently, however, a different response may result The rate varies more or less periodically with time. Oscillatory kinetics have been reported for quite different types of reactions, such as with the famous Belousov-Zha-botinsky reaction in homogeneous solutions (/) or with a series of electrochemical reactions (2). In heterogeneous catalysis, phenomena of this type were observed for the first time about 20 years ago by Wicke and coworkers (3, 4) with the oxidation of carbon monoxide at supported platinum catalysts, and have since then been investigated quite extensively with various reactions and catalysts (5-7). Parallel to these experimental studies, a number of mathematical models were also developed these were intended to describe the kinetics of the underlying elementary processes and their solutions revealed indeed quite often oscillatory behavior. In view of the fact that these models usually consist of a set of coupled nonlinear differential equations, this result is, however, by no means surprising, as will become evident later, and in particular it cannot be considered as a proof for the assumed underlying reaction mechanism. 

Oscillatory kinetics in heterogeneous catalysis, first reported about two decades ago, stimulated extensive study of this interesting phenomenon. G. Ertl gives us an indepth review of this subject in the article Oscillatory Catalytic Reactions at Single Crystal Surfaces. ... 

The kinetics of CO oxidation on a pyramidal supported catalyst particle (Fig. 4) was simulated [11,27] by assuming CO adsorption to cause restructuring of the top (100) facet. The restructuring was described on the basis of the lattice-gas model, predicting phase separation in the overlayer. CO diffusion was much faster compared to other steps. Oscillatory and chaotic kinetic regimes were found in the simulations. One of the reasons of irregular oscillatory kinetics was demonstrated to be the interplay of the reactions on the (100) and (111) facets. 

In the simulations [11,27,29] the size of a lattice representing a catalyst particle was relatively large [typically (100 x 100)]. The effect of the lattice size on oscillatory kinetics was demonstrated [28] in simulations of CO oxidation accompanied by oxide formation. To mimic nm catalyst particles, the lattice size was varied from 50 X 50 to 3 X 3. With rapid CO diffusion, more or less regular oscillations were found (Fig. 9) for sizes down to 15 x 15. 

Sheintuch (1981) analyzed an oscillatory kinetic mechanism with surface oxide and gas phase reactant as variables, and showed that depending on operating conditions an asymmetric state of surface oxide is reached. The asymmetric state was found to be stable, except near the bifurcation point where it might be oscillatory. A mathematical model was developed. Sheintuch and Pismen (1981) investigated the existence of inhomogeneous surface states for three oscillatory kinetic models, i.e. autocatalytic gas-phase variable, autocatalytic surface variable and two surface variables. Sheintuch (1982) also analyzed an oscillatory kinetic mechanism by employing two surface concentrations as variables and the mechanism was simulated by the proposed model and discussed. 

The oscillatory kinetics of CO oxidation over Pt single crystals has been studied at atmospheric pressure by Yeates et al. (95). They present a model to explain rate oscillations that relies on the oscillatory formation of surface platinum oxide, which was observed in postreaction analysis and was related to the presence of silicon impurity. 

Olsen, L.F. H. Degn. 1978. Oscillatory kinetics of the peroxidase-oxidase reaction in an open system. Experimental and theoretical studies. Biochim. Biophys. Acta 523 321-34. 

Oscillatory kinetics with a surface reaction had been observed as early as in 1828 by Fechner [4] with an electrochemical system. As an example for these t) es of reactions. Fig. 7.1 shows the variation of the potential at a Pt electrode with time for the electrochemical oxidation of H2 in the presence of copper ions [5]. While the potential at low-current density j is constant (a), at higher j kinetic oscillations occur because of periodic poisoning and activation transitions of the electrode by underpotential deposition and dissolution of a passivating Cu overlayer. With further increase of , at first period doubling and then transition to an irregular situation (chaos) take place. 

The rich variety of this type of temporal self-organization was mainly explored in detail with the famous Belousov-Zhabotinsky reaction [6,7], but with heterogeneously catalyzed reactions the oscillatory kinetics were first reported only aroimd 1970 for the oxidation of CO on Pt catalysts [8,9]. Since then oscillatory kinetics have been found with more than a dozen catalytic reactions, and this field has also been extensively reviewed [10,17]. 

A consideration of the oscillatory kinetic curve suggests that in the course of the experiment the activity of the membranes is switched over from the ATP synthesis (during odd half-periods) to hydrolysis of the accumulated product (during even half-periods) ... 

The oscillatory kinetics reflects the nonequilibrium nature of the single-enzyme kinetics. The chemical energy in the transformation of S —> P becomes the heat dissipated into the aqueous solution in the heat bath. The steady-state probabilities of the three states are... 

Tian M, Conway BE (2008) Electrocatalysis in oscillatory kinetics of anodic oxidation of formic acid At Pt nanogravimetry and voltammetry studies on the role of reactive surface oxide. J Electroanal Chem 616 45-56... 

Instationary catalytic methods were reviewed previously by some authors [26-43]. We will confine the considerations to catalytic gas/solid reactions, where the instationary conditions are generated by forced perturbations. Oscillatory kinetics and spatio-temporal selforganization in reactions at solid surfaces are not reviewed here (see e.g. [44-46]). 

Heyden et al. suggested that hydrated and dehydrated monomolecular iron sites in Fe-ZSM-5 are responsible for N2O decomposition. They proposed that Z [FeO]+ is a key intermediate. Furthermore, water strongly adsorbs to give Z Fe(OH)2 "h This deactivates the Z [FeO]+ site. The activation energy for N2O decomposition in the presence of water increases steeply compared with the anhydrous situation, because water has to desorb from Z Fe(OH)2 in order for N2O reduction to occur. Hydration and subsequent dehydration of the oxy-iron complex may provide an alternative explanation for the oscillatory reaction found by El-Malki et al. shown in Fig. 4.28. If the reaction is not isothermal, the temperature fluctuations arising from the exothermic N2O decomposition reaction may lead to fluctuation in the water adsorption. This may provide an alternative explanation of the oscillatory kinetic behavior in the Fe +-ZSM-5 system. 

In the previous chapters we predominantly considered catalysis as a molecular event, in which substrate molecules are activated by the catalyst. In this chapter and the next we will emphasize catalytic features of dimensions in space much larger than that of single catalytic centers and times much longer than those associated with the individual molecular catalytic cycles. Often mass and heat transport cause reaction cycles, which occur at different sites, to interact. Under particular conditions this gives rise to cooperative phenomena with oscillatory kinetics and temporal spatial organization. As such, interesting surface patterns such as spirals or pulsars may form. Such complex cooperative phenomena are known in physics as appearances of excitable systems. Their characteristic features are easily influenced by small variations in external conditions. Hence these systems have also features that are called adaptive. 

First elementary reaction steps at an isolated reaction center have been considered and then the increasing complexity of the catalytic stem when several reaction centers operate in parallel and communicate. This situation is common in heterogeneous catalysis. On the isolated reaction center, the key step is the self repair of the weakened or disrupted bonds of the catalyst once the catalytic cycle has been concluded. Catalytic systems which are comprised of autocatalytic elementary reaction steps and communication paths between different reaction centers, mediated through either mass or heat transfer, may show self-organizing features that result in oscillatory kinetics and spatial organization. Theory as well as experiment show that such self-organizing phenomena depend sensitively on the size of the catalytic system. When the system is too small, collective behavior is shut down. 

K. R. Sharma, Analysis of Damped Oscillatory Kinetics in Simple Reactions in Circle, 35th Great Lakes Regional Meeting of the ACS, GLRM 03, Chicago, IL, June, 2003. 

Nonlinear Dynamics Oscillatory Kinetics and Spatio-Temporal Pattern Formation... 

---