Oscillation, chemical model, catalytic

Although the Lorenz model is not a model of chemical kinetics, there is some similarity in both model types the right-hand side is of the polynomial type with first- and second-order terms. In this chapter, we will present results of the analysis of a nonlinear model—also with three variables— the catalytic oscillator model. 

Now the question is how to construct the simplest model of a chemical oscillator, in particular, a catalytic oscillator. It is quite easy to include an autocatalytic reaction in the adsorption mechanism, for example A+B—> 2 A. The presence of an autocatalytic reaction is a typical feature of the known Bmsselator and Oregonator models that have been studied since the 1970s. Autocatalytic processes can be compared with biological processes, in which species are able to give birth to similar species. Autocatalytic models resemble the famous Lotka-Volterra equations (Berryman, 1992 Valentinuzzi and Kohen, 2013), also known as the predator-prey or parasite-host equations. 

We begin this chapter with a discussion of the automaton and present the details of the model construction in Section 2. A number of different systems has been studied using this method in order to investigate fluctuation effects on chemical wave propagation and domain growth in bistable chemical systems [6], excitable media and Turing pattern formation [3,4,7], surface catalytic oxidation processes [8], as well as oscillations and chaos [9]. Our discussions will be confined to the Willamowski-Rossler [10] reaction which displays chemical oscillations and chaos as well as a variety of spatiotemporal patterns. This reaction scheme is sufficiently rich to illustrate many of the internal noise effects we wish to present the references quoted above can be consulted for additional examples. Section 3 applies the general considerations of Section 2 to the Willamowski-Rossler reaction. Sections 4 and 5 describe a variety of aspects of the effects of fluctuations on pattern formation and reaction processes. Section 6 contains the conclusions of the study. 

Recently there has been an increasing interest in self-oscillatory phenomena and also in formation of spatio-temporal structure, accompanied by the rapid development of theory concerning dynamics of such systems under nonlinear, nonequilibrium conditions. The discovery of model chemical reactions to produce self-oscillations and spatio-temporal structures has accelerated the studies on nonlinear dynamics in chemistry. The Belousov-Zhabotinskii(B-Z) reaction is the most famous among such types of oscillatory chemical reactions, and has been studied most frequently during the past couple of decades [1,2]. The B-Z reaction has attracted much interest from scientists with various discipline, because in this reaction, the rhythmic change between oxidation and reduction states can be easily observed in a test tube. As the reproducibility of the amplitude, period and some other experimental measures is rather high under a found condition, the mechanism of the B-Z reaction has been almost fully understood until now. The most important step in the induction of oscillations is the existence of auto-catalytic process in the reaction network. 

In addition to the catalytic-ignition problem, this approach has been successfully implemented on opposed-flow strained-flame simulations with the inlet flow oscillating at high frequency [193]. It has also been used to model transient chemical-vapor deposition processes where the inlet flow is varies under a real-time control algorithm [324]. Although it is unlikely that a practical process-control system would be designed to induce extremely fast transients, it is important that the simulation remain stable to any potential controller command. 

Self-sustained reaction rate oscillations have been shown to occur in many heterogeneous catalytic systems Cl—8]. By now, several comprehensive review papers have been published which deal with different aspects of the problem [3, 9, 10]. An impressive volume of theoretical work has also been accumulated [3, 9, ll], which tries to discover, understand, and model the underlying principles and causative factors behind the phenomenon of oscillations. Most of the people working in this area seem to believe that intrinsic surface processes and rates rather than the interaction between physical and chemical processes are responsible for this unexpected and interesting behavior. However, the majority of the available experimental literature (with a few exceptions [7, 13]) does not contain any surface data and information which could help us to critically test and further Improve the hypotheses and ideas set forth in the literature to explain this type of behavior. 

Figure 8.27. FEM-images of the oscillating CO-oxidation reaction on Pt ( (1 0 0) (E.T. Latkin, V. I. Elokhin, V. V. Gorodetskii, Spiral concentration waves in the Monte Carlo model of CO oxidation over Pd(l 1 0) caused by synchronisation via COads diffusion between separate parts of catalytic surface. Chemical Engineering Journal, 91 (2003) 123).

Atomic Scale Imaging of Oscillation and Chemical Waves at Catalytic Surface Reactions Experimental and Statistical Lattice Models... 

Nonlinear oscillators (NLOs) have been extensively used as realistic models for chemical bonds (Merzbacher 1970 Morse 1929), especially for describing the bondbreaking process (dissociation), simulating vibrational spectra of molecules (Child and Lawton 1981 Lehmann 1992), and modeling the nonlinear optical responses of several classes of molecules (Kirtman 1992 Takahashi and Mukamel 1994), catalytic bond activation, and dissociation processes (McCoy 1984). The nonlinear (anharmonic) oscillator, defined by the equation... 

Self-sustained oscillations of the reaction rate the dashed line marks the value of the reaction rate at the unstable steady state. Reprinted from Yabhnskii, G.S., Bykov, V.I., Gorhan, A.N., Blokhin, V.I., 1991. Kinetic models of catalytic reactions. In Compton, R. G. (Ed.), Comprehensive Chemical Kinetics, vol. 32. Elsevier, Amsterdam, Copyright (1991), with permission from Elsevier. 

---