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The oscillatory behavior is not the only interesting nonlinear phenomena that appeared in the Briggs–Rauscher (BR) reaction. The BR reaction containing malonic acid may undergo a sudden transition from low (the state I) to high iodide and iodine (the state II) concentration states. This paper focuses on the mixture with an immutable [CH2(COOH)2]0/[IO3 −]0 = 1.5 value, where state I to state II transition occurs after a time delay and BR reaction ended with a solution abundant of solid iodine. The state I to the state II transition curves obtained at different temperatures were analyzed using the Kolmogorov–Johnson–Mehl–Avrami (KJMA) theory. The KJMA theory was applied for monitoring the crystallization process of isolated solid iodine product at various levels of operating temperatures. At T

The simultaneous influence of temperature and flow rate (k0) in the oscillatory regime of the bromate-oxalic acid-acetone-Ce(III) oscillating reaction was investigated. The influence of temperature was evaluated in terms of the oscillatory activation energy (Eω), which was determined at different flow rates. Increasing k0, the oscillatory activation energy is decreased, tending to a limit value, Eω∞. The sensitivity of Eω with k0 is described by the parameter η = dEω/d(1/k0). Eω∞ and η are global properties of any particular oscillating reaction and describes a correlation between the dynamical behavior and temperature, and should be used when comparing different oscillating reactions.

Belousov-Zhabotinsky chemical reactions and new variants were developed and studied at 277.5 K, 296.15 K, and 341.15 K using potassium bromate, sodium bromide, malonic acid, and ferroin as an indicator for the oscillating reaction. This reaction type is a minimal oscillator, which belongs to the fifth “uncatalyzed” family known as minimal bromate oscillators. A mathematical model is a proposal from the reaction mechanism of Zhabotinsky, the Oregonator model, and the modified Arrhenius equation. The control parameters of the mathematical model are the activation enthalpies of the oscillating reaction. Experimental and numerical results at 341.15 K show an increase in the amplitude and frequency of chemical oscillations and a decrease in the total oscillation time, while at 277.15 K the opposite mechanism happens.

The Briggs-Rauscher reaction containing malonic acid may undergo a sudden transition from low (state I) to high iodide and iodine (state II) concentration states after a well-defined and strongly reproducible oscillatory period. This study clearly shows that even though the time-dependent behavior of the oscillatory state is reproducible, the time lag necessary for the appearance of the state I to state II transition after the system leaves the oscillatory state becomes irreproducible for an individual kinetic run. This crazy clock behavior of the state I to state II transition is identified by repeated experiments in which stirring rate is taken as a control parameter and all other parameters such as initial conditions, temperature, vessel surface, and the age of solution were kept constant. Surprisingly, a better stirring condition does not make the transition reproducible; it simply does not allow the transition to happen at all. The proposed mechanism, additional explanations, and proposals for this irreproducibility of state I to state II transition have been presented. Considering the fact that the number of crazy clock reactions is only a few, this study may contribute to a better understanding of fundaments of this phenomenon.

The interplay of reaction and diffusion processes can trigger localized spatiotemporal patterns when two solutions containing separate reactants A and B of an oscillating reaction are put in contact. Using the Brusselator, a classical model for chemical oscillations, we show numerically that localized waves and Turing patterns as well as reaction-diffusion (RD) patterns due to an interaction between these two kinds of modes can develop in time around the reactive contact zone depending on the initial concentration of reactants and diffusion coefficients of the intermediate species locally produced. We further explore the possible hydrodynamic destabilization of an initially buoyantly stable stratification of such an A + B → oscillator system, when the chemical reaction provides a buoyant periodic forcing via localized density changes. Guided by the properties of the underlying RD dynamics, we predict new chemo-hydrodynamic instabilities on the basis of the dynamic density profiles which are here varying with the concentration of one of the intermediate species of the oscillator. Nonlinear simulations of the related reaction-diffusion-convection equations show how the active coupling between the localized oscillatory kinetics and buoyancy-driven convection can induce pulsatile convective fingering and pulsatile plumes as well as rising or sinking Turing spots, depending on the initial concentration of the reactants and their contribution to the density.

Based on a ten-step chemical model involving the concentrations of I2(aq), O2(aq), and the intermediates of I- and HIO2, four independent variables and seven irreversible steps, the nonlinear behavior of Bray-Liebhafsky (BL) oscillating reaction was investigated. The results showed that with different values of initial concentrations of reactants in the process of simulation, both periodic oscillation and chaotic behavior could be observed. In addition, at the same initial concentrations and rate constants, the system becomes more and more regular after being chaos. That is to say, the translation from chaos to periodic oscillation at the same initial conditions appeared in the BL system. The nonlinear behavior of system was also investigated briefly

The KSCN-H2O2-NaOH-Cu(II)-catalyzed system is one of the few reactions in which chemical oscillations can be observed in batch conditions. In the present paper, this oscillating reaction was revisited in a wide range of initial concentrations of all components in batch. A mixture with a long lasting oscillation time (1 h 34 min) and a great number of oscillations (24) was found and used to investigate the effect of temperature. An Arrhenius-type temperature dependence was observed from which an apparent “average activation energy” Eav = 76 ± 5 kJ for the overall oscillatory reaction was observed. A mechanistic study based on a modified model analyzed by the stoichiometric network analysis approach gave a satisfactory agreement between calculated and experimental oscillating behaviors and temperature dependence. The addition of the three diphenols (catechol, resorcinol, and hydroquinone) causes perturbations similar to those observed in the Briggs-Rauscher oscillating system, i.e., an inhibition of the oscillatory regime. These inhibitory effects were described in detail, and a reasonable qualitative interpretation is given.

The classical Oregonator model of the Belousov–Zhabotinsky reaction is used to examine the response of an oscillating reaction to a chemical perturbation in a batch calorimeter. To do this, a reaction step for the perturbing chemical substance and the energy balance equation are added to the model. Changes in the frequency and amplitude of the oscillations occur as a function of the concentration of the perturbing substance, and these changes are quantified by applying the thermodynamics of irreversible processes in order to determine the rate of entropy production. Various criteria are proposed to evaluate the time series and measurable quantities with linear correlations between the entropy production due to transfer and the concentration of the chemical perturbation are obtained, showing that it is possible to implement experimental protocols in the proposed methodology.

When performing oscillating reactions, periodical changes in the concentrations of reactants, intermediaries, and products take place. Due to the mentioned periodical changes of the concentrations, the information about the diffusivity of the components included into oscillating reactions is very important for the control of the oscillating reactions. Non-linear dynamics makes oscillating reactions very interesting for analysis in different reactor systems. In this paper, the analysis of diffusivity of the oscillating reaction components was performed in a microreactor, with the aim of identifying the limiting component. The geometry of the microreactor microchannel and a well defined flow profile ensure optimal conditions for the diffusion phenomena analysis, because diffusion profiles in a microreactor depend only on the residence time. In this paper, the analysis of diffusivity of the oscillating reaction components was performed in a microreactor equipped with 2 Y-shape inlets and 2 Y-shape outlets, with active volume of V = 4 μL at different residence times.

In this paper we show that the active interplay of nonlinear kinetics and transport phenomena in a chemical oscillator can be exploited to induce and control chaos. To this aim we use as a model system the ferroin-catalysed Belousov-Zhabotinsky (BZ) oscillating reaction, which is known to evolve to characteristic chaotic transient dynamics when carried out under batch and unstirred conditions. In particular, chemical chaos was found to appear and disappear by following a Ruelle-Takens-Newhouse (RTN) scenario. Here we use medium viscosity as a bifurcation parameter to tune the reaction-diffusion-convection (RDC) interplay and force the reaction in a specific sequence of dynamical regimes: either (i) periodic → quasi-periodic → chaotic or (ii) periodic → quasi-periodic or (iii) only periodic. The medium viscosity can be set by adding different amounts of surfactant (sodium dodecyl sulphate), known to have a little impact on the reaction mechanism, above its critical micelle concentration. Experimental results are supported by means of numerical simulations of a RDC model, which combines self-sustained oscillations to the related chemically-induced buoyancy convection.

Variations of H+, Mn2+, and \({{\rm BrO}_3^-}\) during chemical oscillating reactions involving amino acids were investigated using H2SO4–\({{\rm BrO}_3^{-}}\) –Mn2+–acetone as an oscillator, and the thermodynamic functions (ΔS, ΔH, and ΔG) were calculated. The results indicated that the oscillating reaction is a process from disorder to order. In the oscillating system, the heat provided by the environment is used to increase the internal energy and entropy. When external positive entropy flow could make the system reach negative entropy flow, the system starts to oscillate and to maintain oscillations by a stable entropy.

Because there are cyclical phenomenons in lives so that the influence of the medicine on oscillating reaction is becoming a hotspot.The author prepares a pharmaceutical intermediate. It is 2,6-dihydroxy-4-methylpyrimidine.In this paper the influence of the pharmaceutical intermediate on BZ oscillation system have been studied at different temperature and different concentration. For instance, dropping the concentration of 0.01mol/Lpharmaceutical intermediate before and after, apparent activation energy E and E’ of the systems are 68094J/mol and 71786J/mol.Higher temperature and higher concentration,oscillating cycles and amplitude are lower.

With the help of the kinetic parameters (the rate constant (kinkp) and the apparent activation energy (EinEp) of the oscillatory induction period and oscillation period) of the oscillating reaction using thirteen amino acids, leucine (Leu), threonine (Thr), arginine (Arg), lysine (Lys), histidine (His), alanine (Ala), glutamine (Glu), glycine (Gly), methionine (Met), cystine (Cys), tryptophan (Trp), serine (Ser) and tyrosine (Tyr), as organic substrates in amino acid-BrO3−-Mn2+-H2SO4-acetone system, then based on the Oregonator model and the thermodynamics theory on irreversible process, the thermodynamic function (ΔHin, ΔGin, ΔSin and ΔHp, ΔGp, ΔSp) of these oscillating system are studied. The results indicate the entropy ΔS of these oscillating reaction are negative, thereby it is proved that the oscillating reaction is a noequilibrium system with dissipation structure in agreement with the character of the oscillating reaction from disorder to order in irreversible thermodynamics. These are satisfactorily to explain the experimental phenomena.

Novel aspects of influence of gas evolution on oscillating chemical reaction are considered on a model of the modified Briggs-Rauscher reaction with acetone. The mechanism proposed by Noyes with Furrow and De Kepper with Epstein, adapted for acetone and expanded with oxygen evolution and first-order escape of iodine by interphase transport, was subjected to further extension, and calculations assuming direct proportionality of the rate of iodine escape on the surface area of the oxygen gas trapped in the solution as well as calculations considering first-order back-flow of iodine from the gas phase into the solution were performed. Furthermore, the concentrations of iodine vapors were considered to be variable within the bubble population, as all the bubbles are not in contact with the reaction mixture for the same length of time. Distribution functions of the surface size over the range of concentrations of iodine in the contacting gas phase were introduced and derived, and whereas they were proved not to play any role in the total intensity of iodine return when it is first-order, the article also demonstrates their explicit consideration in calculations to be essential if the dependence of the rate of iodine return into the solution on its concentration is not linear, for example, in future extensions of the model with bubble radius also considered variable.

A computational algorithm based on the lattice Boltzmann method (LBM) is proposed to model reaction–diffusion systems. In this paper, we focus on how nonlinear chemical oscillators like Belousov–Zhabotinsky (BZ) and the chlorite–iodide–malonic acid (CIMA) reactions can be modeled by LBM and provide with new insight into the nature and applications of oscillating reactions. We use Gaussian pulse initial concentrations of sulfuric acid in different places of a bidimensional reactor and nondiffusive boundary walls. We clearly show how these systems evolve to a chaotic attractor and produce specific pattern images that are portrayed in the reactions trajectory to the corresponding chaotic attractor and can be used in robotic control.

The temporal dynamics of the Bray–Liebhafsky reaction (iodate-based catalytic decomposition of hydrogen peroxide in an acidic aqueous solution) was experimentally characterized in a continuous stirred tank reactor by independently varying the temperature and the mixed inflow hydrogen peroxide concentration. When the temperature was the bifurcation parameter, the emergence/disappearance of oscillatory behavior via a supercritical Andronov–Hopf bifurcation was observed for different mixed inflow hydrogen peroxide concentrations. An increase in the mixed inflow hydrogen-peroxide concentration resulted in a shift of the bifurcation point towards higher values of temperature, but did not alter the bifurcation type.

The effect of putrescine (PUT) on KSCN-H2O2-CuSO4-NaOH oscillating system was investigated by calorimetric method. The oscillating reaction was monitored in a closed reactor with stirring, and the result showed that the oscillating period was linearly related with putrescine concentration and the numbers of oscillation decreased with increase in putrescine concentration. When [PUT]=2.83·10−4 M, no oscillation was observed. A possible mechanism is proposed that putrescine is a scavenger of the active-oxygen species. The result of numerical simulation by a simplified mechanism consisting of 18 kinetic steps and 16 variables is consistent with the experimental findings.

A hierarchy of models of chemically reactive low-pressure plasma was considered. On the basis of the Field–Noyes model as a formal set of homogeneous reactions initiated by plasma-generated reactive particles, the possibility of complex dynamic oscillating reaction modes was demonstrated. The form of the solution of the set of equations was analyzed for the process in the afterglow zone at excess concentration of the plasma-generated reactant and with allowance made for the reactant consumption in chemical reactions, and also for the process in the plasma zone with due regard to chemical feedback. It was shown that the form of the solution is determined by the character of chemical feedback.

The stoichiometric relations of complex reaction networks were discussed with the general theory of stoichiometric number introduced and developed by Horiuti et al. Horiuti introduced the concept of reaction route in the theory, in which the reaction route was expressed by a set of stoichiometric numbers. The theory was applied to analyses of the stoichiometries in the reaction network of the 11 pseudo-elementary reactions (steps) of the Belousov–Zhabotinski (BZ) reaction and its reduced mechanism called the amplified Oregonator. Both of the mechanisms were developed by Noyes et al. for analysis of the oscillatory phenomena of the BZ reaction. The amplified Oregonator was concluded sufficiently to describe the stoichiometries of the original network of 11 steps by using the general theory of stoichometric number. In comparison of these analyses of the stoichiometries in the above two mechanisms, a criterion for preserving overall stoichiometry in reduced mechanisms was introduced.

The volume of gaseous oxygen produced during the Briggs−Rauscher (BR) oscillating reaction with acetone was measured. The rates of oscillatory oxygen evolution were calculated and the effects of stirring rate and addition of acrylamide on the oscillations were studied. The dynamic behavior of the modified BR reaction was modeled by mechanisms suggested by Noyes and Furrow (J. Am Chem. Soc. 1982, 104, 45) and De Kepper and Epstein (J. Am. Chem. Soc. 1982, 104, 49), supplemented by the physical processes of the iodine and oxygen interphase transport. The calculated oscillatory parameters are in satisfactory agreement with experiment.

The complexity of oscillating chemical reactions makes difficult a direct calorimetric study of them. It is more advantageous to carry out studies of the component steps and then try to put the parts together. Here, a mass-flow heat conduction calorimeter was used to study component reactions of two of the principal chemical oscillators. The studied reactions were: the net reaction of the inorganic set of the Belousov-Zhabotinsky reaction BrO3 -+4Ce3++5H+D4≤;8805;Ce4++HOBr+2H2O), and the Dushman reaction IO3 -+5I-+6H+≤;8805;3I2+3H2O), which is a component of the Bray-Liebhafsky oscillator. The experimental values of the enthalpies of these two reactions are reported in this work.

Thermokinetic oscillations obtained during the heterogeneous catalytic oxidation of methanol on Pd/LiAl5O8 in a dynamic calorimeter were characterized by an overall activation energy. This parameter was determined using the minimum and maximum values of the temperature oscillations. Using bifurcation diagrams with oxygen or methanol as bifurcation parameters. E values for all heating loss laws were calculated which are within the range for heterogeneous catalytic oxidation reactions. The obtained results have been discussed.

A model for the Briggs–Rauscher reaction mechanism with four intermediates and seven steps is proposed by simplifying the model of De Kepper and Epstein [J. Am. Chem. Soc. 104, 49 (1982)]. Assigning suitable rate constants for the steps of the simplified model, we obtain numerical results for the nonlinear dynamic behaviors such as oscillations, limit cycle, multistability, and inverse regulation of the iodine concentration. The results are compared with experiments and other previous models. The comparison shows that the present simplified model expresses the nonlinear dynamic behaviors better than the previous models.

Complex periodic and aperiodic behaviours are reported in an unstirred Belousov-Zhabotinsky oscillatory reaction performed at temperatures varying between 0°C and 8°C. A route to chaos following a Ruelle-Takens-Newhouse (RTN) scenario is identified. Thus, temperature effects on the coupling between chemical kinetics, diffusion and convection, seem to be responsible for the observed RTN scenario. In this Letter we demonstrate that the temperature is a bifurcation parameter for the sequence period-1 -> quasiperiodicity -> chaos.

Numerical simulations of the oxygen production in the batch Bray–Liebhafsky (BL) oscillating reaction were performed. The dynamic behaviour of the BL reaction was modelled by a scheme suggested by Schmitz and Kolar-Anic, complemented by the physical processes of iodine and oxygen interphase transport. The calculated number and periods of oscillations of the rate of the gaseous oxygen production are in satisfactory agreement with experiment. Oscillations in iodate concentration have been found if some escape of iodine from the batch reactor was allowed.

The statistical lattice model has been constructed for the oscillatory (CO+O2)/Pt(1 0 0) reaction. The model takes into account the change of surface properties due to the adsorbate-induced reversible surface transformation hex↔1×1. The Monte Carlo simulations reproduce the hysteresis and the synchronous oscillations of reaction rate, Oads and COads coverages and hex and 1×1 surface phases under the conditions close to the experimental ones. Self-oscillations of the reaction rate are accompanied by autowave processes on the model platinum surface. The existence of the reaction zone between the moving adsorbate islands has been shown.

The development of propagating patterns arising from the differential flow of reactants through a tubular reactor is investigated. The results from a series of experimental runs, using the BZ reaction, are presented to show how the wavelength and propagation speed of the patterns depend on the imposed flow velocity and the concentration of BrO3− in the inflow. A model for this system, based on a two-variable Oregonator model for the BZ reaction, is considered. A stability analysis of the model indicates that the mechanism for pattern formation is through a convective instability. Numerical simulations confirm the existence of propagating patterns and are in reasonable agreement with the experimental observations.

The chemical oscillating reaction of the MnSO4-KBrO3-diacetoneH2SO4 system has been studied in a continuous-flow stirred-tank reactor (CSTR), and the new characteristics of nonlinear kinetics of this oscillating system are reported. The effects of the temperature, flow rate, concentration of reactants and acidity were investigated. Two different oscillating states (bistability) were observed in this system; the transient color, waveform, potential, oscillating amplitude and period of the two states were different. A change in the solution acidity or flow rate can translate one state to the other, and the two states can exist under the same experimental conditions. Potential and spectrophotometric methods were used to track the change in the reaction intermediates, and possible mechanism of this oscillating system is proposed.

The oscillatory behavior during CO oxidn. over Pd supported on glass fibers was studied in a recycle reactor. The properties of oscillations as a function of temp. and inlet CO concn. were investigated in detail. The peculiarity of the obsd. oscillations is their long period up to 6 h. Math. model considering oxidn.-redn. processes of the Pd was developed to describe the exptl. results. The model accounts for the obsd. reaction rate dependence on the CO inlet concn., the region of oscillations and the dependence of the oscillatory behavior upon temp. and CO inlet concn. [on SciFinder (R)]

A mechanistic model for the galvanostatic potential oscillation in the electrochemical oxidation of formic acid on Pt (H. Okamoto, N. Tanaka and M. Naito, Chem. Phys. Lett., 1996, 248, 289) is analyzed here from the viewpoints of nonlinear dynamics and bifurcation. The model assumes the potential-dependent adsorption, desorption, and reaction of water and carbon monoxide. It is shown that the adiabatic elimination of the potential is warranted in the dynamics and so the essential variables for the dynamics are only chemical ones. The potential oscillation occurs in a certain range of the applied current due to a Hopf instability. The potential dependence of the adsorption and desorption of water to and from the electrode plays an essential role in the Hopf bifurcation. The current dependence of the stability of the system is also a result of the potential dependence of the amount of adsorbed water.

Chemical reactivity is generally taught by considering the chemical properties of the reacting entities (acid-base, oxidation-reduction, complexation, and precipitation) and the values of the corresponding equilibrium thermodynamic constants (Ka, E0 Kd, Ks). This approach, however, is not well-suited to the dynamic chemical systems that are often encountered in industrial and environmental chemistry where nonequilibrium conditions prevail. In this respect, oscillating reactions are a good illustration of the limits of equilibrium thermodynamics and show the need for a complementary dynamic nonequilibrium study. We describe here an oscillating reaction that is easy to carry out in an inorganic chemistry practical class as it uses common reactants (H2O2, KSCN, CuSO4, NaOH). This example should enable students to obtain a more realistic grasp of chemical reactivity based on a comprehension of coupled reaction processes, similar to those encountered in population dynamics or in enzymatic regulation.

In this work we present theoretical and experimental studies of a laboratory scale continuous flow stirred tank reactor (CSTR) in which the iron-(III)-nitrate catalyzed oxidation of ethanol with hydrogen peroxide to ethanal and acetic acid takes place. This reaction displays temperature and concentration oscillations when it is performed in a CSTR. A liquid-phase model is known in the literature derived from a more detailed mechanism. This model predicts the location of stationary solutions and bifurcations well, but the calculated reactor temperatures are high above the boiling point of the reaction mixture under certain conditions. Therefore, two different gas/liquid models were developed and compared with the experimental results.

This work qualitatively and quantitatively compares spatiotemporal patterns in homogeneous and heterogeneous models of a fixed catalytic bed for reactions with oscillatory kinetics. Pattern selection is based on the oscillatory or bistable nature of the kinetics and on the nature of fronts. The heterogenous model can exhibit local bistability while the homogeneous model does not admit this property: when flow terms are accounted for both models can be approximated by a cell-model suggesting a simple conversion between the parameters of both models. The parameter-conversion approximation (1/Pe,eff=1/Pe+1/β, where β is the external transport parameter) can predict quite well the dynamics of the heterogenous model with a pseudohomogeneous one when β≫Pe, but it fails when both parameters are comparable. The dynamic behavior is sensitive to the boundary conditions applied. Several qualitative differences between the two models are pointed out.

To investigate how an oscillating reaction rate might influence the hydration of cementitious solids, a simple iterative mathematical model that includes recurrent passivation of the surface has been constructed. The algorithm generates a wide variety of hydration curves with a limited number of input parameters: i.e.. V0 (volume of unreacted solid after initial reaction), a, (degree of reaction upon initial wetting), x0 (fraction of particle surface passivated after initial wetting); running index: n (cycle number, with an arbitrary unit of time per cycle); constants: m (number of cycles with constant x, the relative rate of the hydration and passivation reactions), k (maximum linear rate of reaction front), and lambda (range 0-1, determines the general passivation behaviour, modelled by the algorithm x(new) = 4 lambda xold[1 - xold]). The hydration process is described by the sequence: (1) Delta V = k(1 - x)V^2/3, (2) Vnew = Vold - Delta V, (3) alpha = 1 - (V/V0) + alpha0.

In this paper studies on the oscillation regularity of the classical B–Z reaction system, and the calorimetric curves of the reaction system measured at three temperatures, 25, 27 and 29°C are described. A new way is presented for studying the regularity properties of chemical oscillation phenomena from the viewpoint of reaction heat effects.

Our recently developed mathematical model for the description of the NO+H 2 /Pt(100)-(1×1) reaction [J. Chem. Phys. 108 (1998) 3740] is extended to include the adsorbate-induced (1×1)⇔hex phase transition of a Pt(100) surface. Under certain pressure and temperature conditions, the phase transition is of critical importance for the kinetics of the reaction, since the two phases exhibit strongly different catalytic activity. The model successfully reproduces the experimentally observed non-linear phenomena: rate hysteresis during a heat–cool cycle and oscillatory behaviour, including periodic and chaotic oscillations. In agreement with experiment, rate oscillations occur in the vicinity of the hex⇒(1×1) phase transition as the hex-reconstructed surface is cooled down in a NO+H 2 atmosphere. At relatively high temperatures, oscillations take place on a largely hex-reconstructed surface. Decreasing the temperature causes an increase in the adsorbate coverage and, as a result, an increase in the fraction of the (1×1) phase. At relatively low temperatures, oscillations take place on a surface that is completely in the (1×1) structure. Thus, the simulation results show that the (1×1)⇔hex surface phase transition of Pt(100) is not essential for producing oscillatory behaviour, even if oscillations may proceed on a largely hex-reconstructed surface. The requirement of vacant sites for NO dissociation on Pt(100)-(1×1) is the most important step in the oscillation mechanism for the NO+H 2 /Pt(100) system.

A new Monte Carlo simulation of CO oxidation over a non-isothermal supported catalyst is presented. It uses the Monte Carlo method applied to multiple 2D crystallites distributed on a flat support in combination with the partial differential energy balance to simulate the non-isothermal reaction on supported catalysts. The simulation predicts ignition and extinction transitions similar to those observed during a temperature programmed reaction experiment. However, no auto-oscillatory behavior is predicted when the surface is assumed to have constant activity. Stochastic fluctuations at each crystallite cannot be synchronized through the thermal coupling to form global oscillations. The model was extended to include a surface with variable activity. In this case an oxidation/reduction mechanism altering the oxygen sticking coefficient provides a bistable mechanism for auto-oscillations. This variable activity model predicts auto-oscillations and changes in oscillatory behavior with temperature and O 2 /CO ratio similar to those experimentally observed. Simulation results also show that thermal communications among crystallites affect the shape of global oscillations. Irregular and chaotic oscillations are predicted when there are differences in the crystallite size, activity, and distribution of the crystallites on the support.

New reaction schemes showing photochemical instabilities in closed isothermal conditions are proposed. Bistability and oscillations are predicted for a system in which one reactant is in rapid dimer-monomer equilibrium. The necessary feedback originates from the light absorption law at high total absorption of a stirred solution. For the experimental observation of instabilities, the rates of thermal and photochemical reactions must be comparable. The necessary relations of the parameters are obtained from the presented equations.

We describe a model of the Briggs−Rauscher reaction closely related to those due to Furrow and Noyes and to DeKepper and Epstein. The model has been fitted to 16 experimental basic quenching parameters at a Hopf bifurcation point. The fit is quite good. Predictions of the model are compared with experiments close to the Hopf bifurcation as well as at several operating points away from it and with experiments under batch conditions. The angular frequency of the finite limit cycle oscillations near the Hopf bifurcation is half the value observed in the experiments. The relative phases of the concentration oscillations of O2 and I- agree reasonably well with the experiments, but the average values are 1 or 2 orders of magnitude smaller in the simulations. The model demonstrates that it is possible to account for a paradoxical behavior of perturbation by OH- as compared to that of H+ and that quenching from a finite limit cycle may be impossible to realize. It qualitatively explains four distinct quenching ex...

The NO-H2 reaction over Rh(533) shows oscillatory behaviour at H2-rich mixtures in the 10−6 mbar pressure regime around 470 K. The selectivity changes periodically in time: the rate of N2 formation is out of phase with the NH3 and H2O formation rates. Accumulation of atomic N plays a central role in the oscillating behaviour. A comparison will be made with the NO-H2 reaction over Pt(100).

A novel unsteady reactor concept called a circulation loop reactor is presented. It is based on the principle of travelling reaction zones. Thus the reactor, consisting of a co-current heat exchanger and a fixed-bed loop (both filled with catalyst), is well suited for weakly exothermic and equilibrium limited reactions. Experimental studies on ethene oxidation are discussed regarding wave phenomena and nonlinear behaviour as a function of inlet concentration and flow rate. Simple as well as complex periodic and chaotic attractors have been observed. A subcritical Hopf-bifurcation marks the transition between stable ignited steady states and an unstable limit cycle which turns by cyclic fold bifurcation into a complex stable periodic attractor.

Macromixing effects on the oscillating Belousov—Zhabotinsky reaction based on the global fluid field have been investigated. The three-variable irreversible Oregonator and the networks-of-zones model with 2 × N × N zones were chosen for describing the chemical kinetics and the flow field, respectively. With high stirring rate, all zones in the tank will oscillate synchronously and the tank can be taken as an ideally well-mixing continuous-flow stirred-tank reactor. When stirring rate is decreased, locally simple oscillation patterns were found to be sustained, and the oscillation period was decreased accordingly. It is proposed that the output zone acts as an excitable nucleus which determines the overall oscillations. When stirring rate is reduced further, many local zones can be excited as nuclei, and apparent complex oscillations can result.

A feedback method is used to stabilize unstable stationary states in experiments with the chlorite-iodide reaction. The unstable stationary states occur in oscillatory and excitable regions of constraint space. Stabilization of unstable steady states provides information about these states and may be of practical importance. An analytical study of a model mechanism of this reaction is consistent with the experiments. This feedback method does not create new stationary states but stabilizes unstable stationary states present in the autonomous system. Unlike «thermostat» type methods, knowledge of the exact location of the unstable stationary states of the autonomous system is not required to implement this feedback method

The oscillations of the Belousov—Zhabotinskii reaction in a batch reactor vanish due to the consumption of the main reactants, i.e. bromate and malonic acid. This behavior has been analyzed first using the classical Oregonator model, where reactant concentrations are kept constant, and then introducing a modified model, in which the reactant concentration is allowed to vary according to the stoichiometry of the considered set of chemical reactions. Two different routes to the extinction of oscillations have been found, depending on whether the Oregonator exhibits a subcritical or a supercritical Hopf bifurcation. These theoretical findings are consistent with the experimental observations, that indicate that the disappearance of the oscillations takes place in two rather different ways: either suddenly after a series of practically undamped oscillations or through very slowly damped oscillations.

This work presents a new experimental kinetic study at 39° and 50° of the iodine oxidation by hydrogen peroxide. The results allow us to obtain the temperature effect on the rate constants previously proposed at 25° for our model of the Bray-Liebhafsky oscillating reaction (G. Schmitz, Phys. Chem. Chem. Phys. 2010, 12, 6605.). The values calculated with the model are in good agreement with many experimental results obtained under very different experimental conditions. Numerical simulations of the oscillations observed formerly by different authors are presented, including the evolutions of the iodine, hydrogen peroxide, iodide ions and oxygen concentrations. Special attention is paid to the perturbing effects of oxygen and of the iodine loss to the gas phase.

Within the framework of a two species reaction—diffusion model coupled to the hydrodynamic equations we discuss how a chemical reaction drives convective motion in a fluid layer. The model has an oscillatory instability with vanishing wavenumber at onset. We derive from the model equations an envelope equation of Ginzburg—Landau type with complex coefficients. To cubic order in the envelope the generated convective velocity is slaved to the concentration variables and has no independent dynamics. Feedback from the flow in the chemical reaction arises at higher orders in the amplitude. We compare our results with existing experimental data.

Continuous time delayed feedback, based on a method by Pyragas, is applied to the Belousov-Zhabotinsky (BZ) reaction to stabilize unstable periodic orbits embedded in the chaotic attractor. Our experimental results are compared with numerical calculations of the four-variable model (Montanator) for the BZ reaction. The Pyragas method is also applied to calculations of a mechanism (Aguda-Larter model) for the peroxidase-oxidase reaction. In addition to the stabilized orbits in the strange attractor, new periodic, chaotic, and steady states are produced for large values of the feedback function in both models. The possible role of chaos and feedback in nature is discussed

The effect of stirring and temperature on the BZ reaction is reported by using malonic and gallic acid as organic substrates in experiments carried out in a continuously fed stirred tank reactor. Complex oscillations of varying frequencies and amplitudes are reported for the gallic acid system at low flow and stirring rate. High temperature decreases the oscillation amplitude in both systems. The oscillation amplitude increases with increase of stirring rate in the gallic acid system, but no significant stirring effect is observed in the malonic acid system for the concentration of the chemicals used. A bistability between an oscillatory branch and a flow branch is reported for the first time for the GA system by using the stirring rate as the control parameter

DIMOTAKIS and his group have published some papers in which they report for a number of target substances (e.g. [Co(en)3](NO3)3) oscillatory annealing instead of smooth annealing as usually assumed. They discuss their results following the predator-prey model of LOTKA-VOLTERRA. These experiments were repeated. No indication for oscillatory annealing was observed. As expected, a fitted non-oscillatory curve runs-considering the standard deviations of ±0.5%-through “only” approximately 68% of the experimental points as predicted by the statistical nature of radioactivity measurements.

The occurrence of kinetic oscillations in the catalytic oxidation of CO on Pd(110) has been attributed to the periodic formation and depletion of subsurface oxygen. Using a Langmuir–Hinshelwood mechanism and the individual reaction steps, Bassett and Imbihl proposed a simple reaction model for the oscillations. In this article, we apply their model to the results of CO titration of a preadsorbed oxygen adlayer on this surface. This shows that the CO–O reaction rate constant used by Bassett and Imbihl is too large by a factor of ≊100. Using corrected values of the reaction constants, however, we can accurately model the results of the titration experiments, both with and without subsurface oxygen. Further, with these changes the model no longer reproduces the oscillatory behavior. These findings imply that the correct mechanism for oscillations on Pd(110) has yet to be identified. Our results also suggest that the reaction of CO with a preadsorbed oxygen overlayer may proceed isotropically rather than one ...