Oscillatory reactions patterns

Until the 1950s, the rare periodic phenomena known in chemistry, such as the reaction of Bray [1], represented laboratory curiosities. Some oscillatory reactions were also known in electrochemistry. The link was made between the cardiac rhythm and electrical oscillators [2]. New examples of oscillatory chemical reactions were later discovered [3, 4]. From a theoretical point of view, the first kinetic model for oscillatory reactions was analyzed by Lotka [5], while similar equations were proposed soon after by Volterra [6] to account for oscillations in predator-prey systems in ecology. The next important advance on biological oscillations came from the experimental and theoretical studies of Hodgkin and Huxley [7], which clarified the physicochemical bases of the action potential in electrically excitable cells. The theory that they developed was later applied [8] to account for sustained oscillations of the membrane potential in these cells. Remarkably, the classic study by Hodgkin and Huxley appeared in the same year as Turing s pioneering analysis of spatial patterns in chemical systems [9]. 

Obviously, to find a specific set of conditions for the onset of a concentration jump between stable states, or for the occurrence of oscillations, for that matter, would require the testing of a huge number of reaction mixtures under conditions maintained far from equilibrium. Since such an experiment is not easily accomplished in ordinary glassware, we conducted our studies of oscillatory reactions in continuous flow reactors patterned after those used at the Paul Pascal Research Center in Bordeaux, France35). 

The vast body of literature on electrochemical oscillations has revealed a quite surprising fact dynamic instabilities, manifesting themselves, for example, in bistable or oscillatory reaction rates, occur in nearly every electrochemical reaction under appropriate conditions. An impressive compilation of all the relevant papers up to 1993 can be found in a review article by Hudson and Tsotsis. This finding naturally raises the question of whether there are common principles governing pattern formation in electrochemical systems. In other words, are there universal mechanisms leading to self-organization phenomena in systems with completely different chemical compositions, and thus also distinct rate laws ... 

Oscillatory reactions provide one of the most active areas of research in contemporary chemical kinetics and two published studies on the photochemistry of Belousov-Zhabotinsky reaction are very significant in this respect. One deals with Ru(bpy)3 photocatalysed formation of spatial patterns and the other is an analysis of a modified complete Oregonator (model scheme) system which accounts for the O2 sensitivity and photosensitivity. ... 

Figure 8.2 Patterns generated in numerical simulations of an oscillatory reaction-advection-diffusion system (from Perez-Munuzuri (2006)). The flow is composed of two point vortices that are switched-on alternatingly. The figures are snapshots of the concentration field for different values of the distance between the two vortex centers (decreasing from left to right).

In contrast to standard two-species reaction-diffusion systems, the uniform steady state of the hyperbolic reaction-diffusion system can undergo a spatial Hopf bifurcation to oscillatory spatial pattern, if A3 = 0 can be fulfilled for some % 0-This condition gives rise to a second-order polynomial in k ... 

Oscillatory Cluster Patterns in the BZ Reaction with Global... 

The occurrence of kinetic instabilities as well as oscillatory and even chaotic temporal behavior of a catalytic reaction under steady-state flow conditions can be traced back to the nonlinear character of the differential equations describing the kinetics coupled to transport processes (diffusion and heat conductance). Studies with single crystal surfaces revealed the formation of a large wealth of concentration patterns of the adsorbates on mesoscopic (say pm) length scales which can be studied experimentally by suitable tools and theoretically within the framework of nonlinear dynamics. [31]... 

One particular pattern of behaviour which can be shown by systems far from equilibrium and with which we will be much concerned is that of oscillations. Some preliminary comments about the thermodynamics of oscillatory processes can be made and are particularly important. In closed systems, the only concentrations which vary in an oscillatory way are those of the intermediates there is generally a monotonic decrease in reactant concentrations and a monotonic, but not necessarily smooth, increase in those of the products. The free energy even of oscillatory systems decreases continuously during the course of the reaction AG does not oscillate. Nor are there specific individual reactions which proceed forwards at some stages and backwards at others in fact our simplest models will comprise reactions in which the reverse reactions are neglected completely. 

Oscillatory behaviour and exotic stationary-state patterns of extent of reaction versus flow rate in the simplest of open systems survive. 

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. 

Just as there are numerous systems that display oscillations, so too are there numerous ways in which the oscillatory behavior manifests. The observed oscillation patterns include approximately sinusoidal time series, relaxation-type oscillations (the reaction remains in one state for most of the... 

A phase change scheme similar to those described above was proposed by Schwartz and Schmidt 141,142) on the basis of LEED experiments, and by Schiith and Wicke (91,101) on the basis of IR measurements for the oscillatory CO/NO reaction on Pt(lOO). The experiments of Schwartz and Schmidt demonstrated that the transition from the high- to the low-reaction-rate state was accompanied by a change from the 1 x 1 to the hex phase in LEED patterns. The position of the L-CO band in the IR spectra recorded during oscillations varied between the high- and low-reaction-rate states with a relatively high absorption band below 2050 cm present in the low-reaction-rate state, which is characteristic of CO on the Pt(lOO) hex surface. Further proof was provided by Clausius-Clapeyron plot of the conditions for the occurrence of oscillations, which yielded points near the isostere associated with the hex 1 x 1 phase transition (Fig. 14). 

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