Oscillating reactions, kinetics

We demonstrate the use of Matlab s numerical integration routines (ODE-solvers) and apply them to a representative collection of interesting mechanisms of increasing complexity, such as an autocatalytic reaction, predator-prey kinetics, oscillating reactions and chaotic systems. This section demonstrates the educational usefulness of data modelling. 

Exotic Kinetics Oscillating Reactions in the Troposphere (J. Phys. Chem. A 2001, 105, 11212-11219. "Steady State Instability and Oscillation in Simplified Models of Tropospheric Chemistry")... 

This chapter focuses on analytical CL methodologies, with emphasis on the kinetic connotations of typical approaches such as the stopped-flow, the continuous-addition-of-reagent (a new kinetic methodology) and the pulse perturbation technique developed for oscillating reactions, among others. Recent contributions to kinetic simultaneous determinations of organic substances using CL detection (kinetometric approaches included) are also preferentially considered here. 

The other technique which has poved valuable in this area is computer simulation. When the kinetic data become very complicated, as with oscillating reactions involving two elementary steps, it is still possible to obtain rate constants from the data by doing computer simulation. That is actually not as outlandish as it might appear. It is really in the same category as the Fourier transform approach. I think this is an area that will make a considerable impact upon inorganic kinetic studies in the future. 

Ortho-para deuterium, 27 25, 50 Ortho-para hydrogen conversion, 27 23 Oscillatory catalytic reactions, 37 213-215, 271-272 see also Platinum catalytic CO oxidation on Pt(l 11) and Pt(llO) surfaces COj formation, 37 216-217 kinetic oscillation mechanism, 37 220-228... 

PbOj anode, 40 155-156 oxygen evolution, 40 109-110 PCE, catalytic synthesis of, l,l,l-trifluoro-2,2-dischloroethane, 39 341-343 7t complex multicenter processes of norboma-diene, 18 373-395 PdfllO), CO oxidation, 37 262-266 CO titration curves, 37 264—266 kinetic model, 37 266 kinetic oscillations, 37 262-263 subsurface oxygen phase, 37 264—265 work function and reaction rate, 37 263-264 Pd (CO) formation, 39 155 PdjCrjCp fCOljPMe, 38 350-351 (J-PdH phase, Pd transformation, 37 79-80 P-dimensional subspace, 32 280-281 Pdf 111) mica film, epitaxially oriented, 37 55-56... 

Hj Dj exchange on, 26 39-43 heteropolyanion-supported, 41 230-231 high MiUer index, 26 12-15,35,36 -H-USY zeoUte, 39 186-187 hydrocarbons adsorption, 38 229-230 reactions of cyclopropane, cyclohexane, and n-heptane, 26 51-53 structural effects, 30 25-26 hydrogen adsorption on, 23 15 hydrogenation, 30 281-282 olefins, in ethanol, 30 352-353 in hydrogenation reaction, 33 101 -iron alloys, 26 75 isomerization, 30 2-3 isotope, NMR properties, 33 213,274 kinetic oscillations, 37 220-228 ball models of densely packed surfaces, 37 221-222... 

Scanning LEED, oscillatory reactions, 39 69 Scanning photoemission microscopy, kinetic oscillations, Pt(lOO), 37 250-253 Scanning photoemission spectroscopy oscillatory reactions, 39 69... 

The kinetics experiments are subdivided into classical kinetics experiments, Table XX photochemistry, Table XXI catalysis, oscillating reactions and miscellaneous topics in kinetics, Table XXII. 

Table XXII. Experiments on Catalysis, Oscillating Reactions and Miscellaneous Topics in Kinetics...

L. Beavers, and J. A. Draeger, The Kinetics of Oscillating Reactions, J. Chem. Ed 1992,69, 596 J. M. Merino, A Simple, Continuous-Flow Stirred-Tank... 

Lastly, non-elementary several-stage reactions are considered in Chapters 8 and 9. We start with the Lotka and Lotka-Volterra reactions as simple model systems. An existence of the undamped density oscillations is established here. The complementary reactions treated in Chapter 9 are catalytic surface oxidation of CO and NH3 formation. These reactions also reveal undamped concentration oscillations and kinetic phase transitions. Their adequate treatment need a generalization of the fluctuation-controlled theory for the discrete (lattice) systems in order to take correctly into account the geometry of both lattice and absorbed molecules. As another illustration of the formalism developed by the authors, the kinetics of reactions upon disorded surfaces is considered. 

Kinetic study of the self-oscillating reaction observed in a potassium iodate-hydrogen peroxide-cysteine-sulfuric acid (acid medium) system was carried out [57], It is found that according to an adequate model the feedback mechanism is associated with autocatalytic reaction... 

Mechanistic studies with real catalysts near atmospheric pressure conditions are complicated by several factors the surface structure and composition will be inhomogeneous and hence also the reactivity may be spatially different. In addition, the heat released by the reaction may change the (local) temperature, and as a consequence, kinetic oscillations are frequently associated with strong nonisothermal effects. These prob-... 

The qualitative features of the r( pco) curve of Fig. 1 are the same for all types of platinum metal surfaces and will serve as a guide for exploring the mechanisms of kinetic oscillations occurring with this reaction. The shape of this curve can be modeled quite easily on the basis of the underlying reaction mechanism (8, 25). These equations are nonlinear in nature and can, for example, describe hysteresis effects observed in the transition region between high and low reactivity, but they will not produce sustained temporal oscillations. The latter require additional processes for which numerous suggestions and speculations can be found in the literature (S). 

Figure 4 shows a typical example of sustained kinetic oscillations occurring for particular conditions (pc0, p0r and T) during the catalytic CO oxidation on a Pt(llO) surface (40). The measurements were performed with an UHV system acting as flow reactor, where the C02 partial pressure is directly proportional to the rate. The simultaneously recorded CO pressure oscillates with the same period and with amplitudes of about 1%, whereby pco shows a minimum whenever the reaction rate is maximum. The work function A varies parallel to the rate R. This quantity is essentially determined by the oxygen coverage. Because under oscillatory conditions the rate is determined by oxygen adsorption (see above), it becomes plausible why A and R vary in phase. 

Once the external parameters (pco, p0,- and T) have been established to initiate autonomous kinetic oscillations, these can usually be sustained for periods of time as long as desired, provided that the surfaces are prevented from becoming contaminated (in particular by carbon, originating from spurious traces of hydrocarbons in the feed gas mixture) and that the partial pressures are not drifting off (31). With Pt(l 10) a complication may arise insofar that during the course of the reaction the surface struc-... 

Fig. 13. Kinetic oscillations during the CO/O reaction on Pt(110) at I = 540 K, />0, = 7.5 x 10-5 torr, and for varying pm. (From Ref. 71.) (a) pco = 3.90 x 10 lorr constant behavior (fixed point), (b) pt0 = 3.K4 x I0"5 torr onset of harmonic oscillations with small amplitudes (Hopf bifurcation), (c)pco = 3.66 x 10 5 torr harmonic oscillation with increased amplitude, (d) pc0 = 3.61 x I0-5 torr first period doubling, (e) pc0 = 3.52 x 10 torr second period doubling, (f) pco = 3.42 x 10 5 torr aperiodic (chaotic) behavior.

The mechanism of the kinetic oscillations occurring with the CO + 07 reaction on clean Pt( 100) and Pt( 110) surfaces was based on the reversible transformation of the surface structure by the presence of adsorbed CO and by an associated variation of the oxygen sticking coefficient that increased upon CO-induced lifting of the reconstruction of the clean surface. The most densely packed Pt(lll) surface is not reconstructed and its structure is also not affected by CO adsorption. Accordingly, kinetic oscillations with a clean Pt(lll) surface (i.e., for partial pressure <10 3 torr) could never be observed (13, 26, 27, 38). Again no reconstruction... 

Fig. 34. Development of kinetic oscillations with the CO/O, reaction on Pt(2IO). After establishing the indicated conditions at point C, the system slowly evolved oscillations with continuously changing periods and amplitude. (From Ref.. . )...

The steady state reaction of NO with H2 and NH3 on Pt(l 0 0) has been studied using REMPI detection of the N2 product state distributions [134]. These reactions show very complex kinetics, with strongly coverage dependent reaction rates which lead to kinetic oscillations [135] and explosive desorption [136]. This surface also shows a phase transition between the clean surface hex reconstructed phase and... 

A lattice-gas model of the NO + CO/Pt(l 00) reaction was found by Makeev and Kevrekidis (2004) to exhibit bistability and kinetic oscillations. In this simulation, the catalyst surface was represented by a square lattice with periodic boundary conditions. The model includes both chemical reactions and transitions of adsorbed reactants from the nearest-neighbor sites, which are in the... 

Kuzovkov, V.N., O. Kortiuke, and W. von Niessen. Comment on Surface Restmcturing, Kinetic Oscillations, and Chaos in Heterogeneous Catalytic Reactions. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics (Febmary 2001.)... 

It appears that the incorporation of metal adatoms into adsorbate structures stabilizes the reaction intermediates, and therefore, can be expected to be a general phenomenon on catalytic metal surfaces, at least for metal particles large enough to be considered as metallic. The dynamic processes of incorporation, release, and mass transport of metal adatoms may occur on the time scale of surface reactions and affect the reactive behavior of the intermediates, that is to say, the reaction kinetics. Indeed, STM studies have shown that the kinetic oscillation in some surface reactions can be partially attributed to the spatial organization of reactive species on the surfaces and the structural change in such complex surfaces on the time scale of reaction [69]. The structural complexity of the active surfaces and the origin of unusual surface reaction kinetics are of interest, and may be connected. Recently, such a relationship was established in the autocatalytic decomposition of formate and acetate on the Ni(llO) surface [21]. 

Figure 9 CO (A), O (B), and oxide (Q coverages and reaction rate (CO2 molec. per site per MCS) as a function of time for L = 50 (a), 30 (b), 20 (c), 10 (d), 5 (e), and 3 (f). With decreasing lattice size, kinetic oscillations become more irregular. For the smallest size (L = 3), oscillations rapidly disappear due to complete poisoning of the lattice by oxygen (this is possible because O2 adsorption is considered to occur on nn vacant sites). (Redrawn from Ref. [28].)...

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