Search

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.

The effects of global coupling through the gas phase in oscillatory surface chemical reactions are investigated using a model which represents the complex Ginzburg–Landau equation with an additional integral term. Depending on the parameters of the model, global coupling is found to have either a synchronizing or desynchronizing effect. Respectively, the breakdown of global coupling requires the presence of strong supercritical inhomogeneities or spontaneously occurs in a uniform system.

General expressions are derived for the critical wave numbers for two‐ and three‐species reaction mechanisms when their homogeneous steady states are destabilized by a relative flow of at least one species. Analysis of a model of the oscillating peroxidase–oxidase reaction indicates that the reaction exhibits this kind of instability. Computer simulations of the reaction‐flow‐diffusion equations generate traveling concentration waves under appropriate conditions.

A model for the reactions of NO+NH3 and NO+H2 has been developed for simulating the reduction of NO on Pt(100) in the 10−6 mbar pressure range for temperatures between 300 and 700 K. The model consists of seven ordinary differential equations for describing the coverage changes of six adsorbed species as well as an equation for describing the 1×1⇄hex phase transformation. Simulations of the N2 and H2O reaction rates for both reaction mixtures reproduced the hysteresis effects and the existence range for kinetic oscillations, which were found in the experiments. In addition, the occurrence of the so‐called ‘‘surface explosion’’ in both reaction systems is well described by the model. In contrast to the NO+CO reaction on Pt(100), where oscillations may also take place on a pure 1×1 substrate, the 1×1⇄hex phase transition occurs during oscillations for the NO+NH3 and NO+H2 reactions. The transitions between different adsorbate/substrate phases during one oscillatory cycle which are predicted by the model are...

When a chemical reaction is carried out on a catalytic ribbon, the spatial average temperature of which is kept constant by electrical heating, spatiotemporal temperature patterns form when the uniform steady state is unstable at the set temperature. Numerical simulations reveal periodic and aperiodic patterns of moving pulses, ‘‘breathing’’ pulses, or stationary and oscillatory fronts. The transitions between some of these patterns are intricate and proceed via global bifurcations. Bifurcation maps of parameter regions leading to specific patterns are used to gain insight into pattern formation and organization of these parameter regions. The relations among the dynamics of the uncontrolled system, the ribbon length, and the selected pattern are discussed. Similar patterns are expected to evolve in other reaction–diffusion systems subject to control of space‐averaged properties.

The dynamical behavior of the chlorine dioxide–iodide reaction has been studied in a system consisting of two continuous flow stirred tank reactors (CSTRs). The reactors are coupled by computer monitoring of the electrochemical potential in each reactor, which is then used to control the input into the other reactor. Two forms of coupling are employed: reciprocally triggered, exponentially decreasing stimulation, and alternating mass exchange. The reaction, which exhibits oscillatory and excitable behavior in a single CSTR, displays neuronlike bursting behavior with both forms of coupling. Reciprocal stimulation yields bursting in both reactors, while with alternating mass exchange, bursting is observed in one reactor and complex oscillation in the other. A simple model of the reaction gives good agreement between the experimental observations and numerical simulations.

We analyze two reaction networks for the Belousov–Zhabotinsky reaction at a Hopf bifurcation by methods developed in a previous paper. One network is equivalent to the oregonator, the other is an extended oregonator with seven species and eleven reactions. For each model the current polytope has a simple geometry and the paper serves to illustrate the analytic methods and explain their relation to the chemistry of the reactions. All possible models based on each network are compared with experimental quenching results and other experimental data at a supercritical Hopf bifurcation. The best possible fit is obtained through a systematic search of the current cone and concentration space. For the oregonator, the optimization is essentially complete and results in a determination from scratch of all six rate constants of the model. The agreement of the optimum with the experiments is very good, and the agreement of the deduced rate constants with the most recent set determined from kinetic measurements on subsystems seems quite remarkable. The larger model is too big for a really complete search, but the best point found shows a significant improvement over our previous results based on continuation methods. Despite the good agreement with the experiments, a graphical eigenvector analysis definitively shows that perfect agreement is impossible for any of the models, no matter how the rate constants are chosen; additional reactions are needed.

The complex mixed‐mode and chaotic oscillations in the reduction of indium(III) at a hanging mercury drop electrode in thiocyanate solution are studied in experimental detail in the parameter plane. With the aid of a simple model developed previously, we critically discuss the relation of the experimentally observed periodic–chaotic sequences with those predicted by the Shil’nikov theory of homoclinic orbits. It appears helpful to distinguish between two fundamentally different types of mixed‐mode behavior: ‘‘type 1’’ related to the incomplete homoclinic scenarios observed in the present system and its model; ‘‘type 2’’ related more directly to the Shil’nikov behavior and the classical Rossler type of reinjection mechanism. The definitions and properties of both types of mixed‐mode oscillation are worked out in some detail.

A prototype model is exploited to reveal the origin of mixed‐mode oscillations. The initial oscillatory solution is born at a supercritical Hopf bifurcation and exhibits subsequent period doubling as some parameter is varied. This period‐2 solution subsequently loses stability, but continues to exist−regaining stability to form the 11 mixed‐mode state (one large plus one small excursion). Other mixed‐mode states lie on isolated branches or ‘‘isolas’’ of limit cycles in the one‐parameter bifurcation diagram and are separated by regions of chaos. As a second parameter is varied, the number of isola solutions increases and the ‘‘gaps’’ between them become narrower, leading to correspondingly more complete Devil’s staircases. An exactly comparable scenario is shown to arise in the three variable model of the Belousov–Zhabotinsky reaction proposed recently by Gyorgyi and Field [Nature 335, 808 (1992)].

A Pt single crystal of cylindrical shape (axis II [001]) whose surface exhibits all orientations of the [001] zone has been used to study coupling effects between orientations which exhibit kinetic oscillations in catalytic CO oxidation. On the clean surface, one can distinguish between an orientational range in between (110) and (320) which exhibits a 1×2 reconstruction, a nonreconstructed surface range around (210) and a hex reconstructed surface range around (100). Structural transitions proceed continuously via atomic steps between (110) and (210), while the orientational range extending from (210) to (100) is faceted. With a rotatable Kelvin probe, the orientational dependence of the work function could be followed. The results revealed that the variation of the oxygen sticking coefficient sO2 displays a mirror‐like behavior with respect to the work function variation of the clean surface such that the orientation with the lowest work function (210) exhibits the highest sO2. Kinetic oscillations were...

A dynamic model designed to describe bistability and kinetic oscillations of the reaction rate during the oxidation of CO on a Pt(110) single crystal surface is extended by incorporating surface diffusion of adsorbed CO in order to analyze the properties of traveling waves propagating on the catalytically active surface. In the range of control parameters (partial pressure of oxygen and carbon monoxide and temperature) which corresponds to excitable dynamics, solitary pulses and periodic wave trains can be triggered. Using both asymptotic and numerical methods, the velocity and shape of the pulses as well as the dispersion relation for periodic wave trains are determined and compared to experimental data where available.

Responses to single and periodic pulse perturbations have been studied experimentally and numerically for the reaction of chlorine dioxide and iodide ion in a stirred tank reactor. Excitability with transient oscillations was obtained for perturbations by chlorine dioxide or chlorite, while stimulation by iodide produced no excitable response. Periodic stimulations of the reaction by chlorite display bursting behavior. The experimental observations are in agreement with numerical simulations.

This paper illustrates an approach that can refine mechanisms and obtain information about rate constants from dynamical phase diagrams which show the regions of oscillation of a mechanism as a function of the experimental parameters. Possible mechanisms for the experimentally oscillating oxalate–persulfate–silver system are examined. Starting with a proposed mechanism by Ouyang and de Kepper, which they could not make oscillate, we show that some variations of the mechanism are stable for all nonnegative values of the rate constants. Other variations are unstable. For these variations, feedback cycles that lead to instability are compared with a conceptual picture of feedback in the experimental system. One unstable mechanism fits the picture well. Its unimportant reactions are omitted and an analytical solution for the unstable region using 13 adjustable parameters is obtained. The rate constants are adjusted to match this solution to the experimentally measured phase diagram. A good fit can only be obt...

Systematic measurements of the stability of chemical waves were carried out over a wide range of reagent concentrations in the cerium‐catalyzed Belousov–Zhabotinsky reaction. The critical radius and the width of the autocatalyst band in the wave fronts were measured in order to verify the computed prediction for the region of parameters where lateral instabilities of the wave ends appear. The data yield an experimental parameter set for the onset of unstable behavior and allow a discussion about different theoretical descriptions of the critical curvature.

The parameters entering the kinetics for the mechanism of catalytic CO oxidation have been adapted for a Pt(110) surface, giving rise to a two‐variable model correctly predicting bistability. Oscillations are obtained when, in addition, the adsorbate‐driven 1×2–1×1 structural phase transition of Pt(110) is taken into account. Mixed‐mode oscillations can be qualitatively explained by including the faceting of the surface as a fourth variable. The limitations of the model essentially stem from the fact that only ordinary differential equations have been analyzed so far neglecting spatial pattern formation. It is discussed which dynamic phenomena observed experimentally in the CO oxidation on Pt(110) will probably not be adequately describable without taking spatial effects into account.

We develop a simple but general three‐variable model skeleton to describe complex nonlinear behaviors in electrochemical processes taking place at either a hanging mercury drop electrode (HMDE) or a rotating‐disk electrode (RDE). We apply our formalism to the reduction of indium(III) at a HMDE in the presence of thiocyanate, a reaction known to exhibit complex mixed‐mode and chaotic oscillations. Besides the role of the negative Faradaic impedance in destabilizing the electrochemical system, mass transport appears to be crucial as the model explicitly takes into account, in a truncated fashion, the time‐dependent relaxation of the concentration profile. We study in detail the nonlinear dynamic behavior of our model of the indium/thiocyanate system and a RDE model. The models support mixed‐mode sequences that appear either as incomplete Farey sequences or as periodic‐chaotic sequences, which we discuss in terms of an incomplete homoclinic scenario whose definition and properties are worked out here. Our results compare very well to the experimental observations in the indium/thiocyanate system and the electrodissolution of a rotating copper disk in phosphoric acid. This satisfactory agreement strongly suggests that diffusion relaxation is an important phenomenon in electrochemical oscillations and could be the essential third variable in many dynamical electrochemical processes.

Spatial pattern formation in the NO+CO reaction on a cylindrical Pt single crystal surface (axis parallel [001] direction) has been investigated using photoemission electron microscopy (PEEM) as an in‐situ method to image the lateral adsorbate distribution during the reaction with a resolution of ≊1 μm. The experiments were conducted in the 10−6 Torr range, between 380 and 430 K, under conditions where the (100) orientation exhibits oscillatory behavior. Of the different orientations of the [001] zone which are present on the surface only the orientational range between (100) and (310) was found to be very active in NO dissociation and hence in the surface reaction. A sharp phase boundary meandering between (210) and (410) parallel to the [001] direction separates the active from the inactive zone on the cylinder surface. In the active zone between (100) and (310) one finds propagating reaction fronts and complex spatiotemporal patterns. The velocity of the reaction fronts is strongly anisotropic with the...

Under isothermal conditions at low pressure (10−6 mbar range), the NO+CO reaction exhibits oscillatory behavior on a Pt(100) surface. Based on the results of in situ low‐energy electron diffraction (LEED) measurements which showed that the 1×1⇄hex phase transition is not essential for producing oscillations, a three‐variable model of coupled differential equations was developed which instead relies solely on the autocatalysis provided by the stoichiometry of the individual reaction steps. This model has been analyzed with the help of bifurcation theory using realistic values for the constants in the equations. The results demonstrate that the model reproduces, quite well, the existence range for oscillations on Pt(100). Two oscillatory regions exist with a large one located above the stoichiometry ratio pNO: pCO=1 and a very small one which is found just below pNO: pCO=1. Only the former one has a counterpart in the experiment. At low temperature two isolated branches of the reaction exist which merge at ...

A multispecies reactive lattice‐gas automaton model is constructed and used to study chemical oscillations and pattern formation processes in a spatially distributed two‐dimensional medium. Both steady state and oscillatory dynamics are explored. Nonequilibrium spatial structures are also investigated. The automaton simulations show the formation of rings of chemical excitation, spiral waves, and Turing patterns. Since the automaton model treats the dynamics at a mesoscopic level, fluctuations are included and nonequilibrium spatial structures can be investigated at a deeper level than reaction–diffusion equation descriptions.

The NO+CO reaction, which has been shown to exhibit damped kinetic oscillations on a Pt(100) surface after initial excitation, has been subjected to periodic and random forcing of the temperature and of the CO partial pressure. The experiments were conducted in the 10−7 mbar range and measurements of the CO2 production rate and of the work function were used to follow the response of the system. The response behavior is characterized by strong resonance effects and by the absence of quasiperiodic oscillations. The system is highly sensitive to temperature modulation, but rather insensitive to modulation of pCO with the latter requiring an amplitude of more than 5% of pCO for producing sustained oscillations. Random forcing experiments demonstrate that the response of the system can be described as a bandpass filter since only frequencies close to the natural frequency of the system are amplified. The results of the experiments led to the conclusion that the damping effect is due to the absence of an effic...

Oscillations in light emission and species concentrations, are measured as periodic perturbations are simultaneously applied to the input rates of acetaldehyde and oxygen in the gas‐phase combustion of acetaldehyde in a continuous‐flow stirred tank reactor for conditions where the autonomous reaction itself is oscillatory. The experimental results are compared with the predictions of a five‐variable thermokinetic model. We measure periodic responses in the fundamental entrainment band (ratio of frequency of perturbation to frequency of response equal to unity) for four different values of phase shift between the acetaldehyde and oxygen perturbation wave forms as we vary the frequency and amplitude of the external periodic perturbations. Outside of the entrainment bands we find quasiperiodic response. We determine the phases of the light emission and six species concentrations, as measured with a mass spectrometer, with respect to the periodic perturbation, the variation of these phases across the fundamental entrainment band for different values of reactant phase shift and for different amplitudes of perturbation, and the effects of the phase shift between the two input perturbations on the light emission response of the system for different frequencies of perturbation. Both the experiments and calculations predict a widening of the entrainment band with an increase in perturbation amplitude, and the same variation in bandwidths for the four values of reactant phase shift studied. The experiments and calculations also predict the same general trends in light phase and species phases (difference between the light emission and species concentrations with respect to the perturbing wave form) as the band is traversed for different amplitudes of perturbation and for different values of reactant phase shift. Some discrepancies in the species phases exist; however, the similarities which exist between the experiments and the calculations provide further substantiation for the model. We find that changing the phase shift between reactant inflows from 0° to 360° produces a sharp change in light phase near 180°, in both the experiments and calculations. In general, we also find that the light emission remains entrained near the total flux minimum of the perturbing wave form, and we attribute this correlation to the net heat loss which arises from the reactant flux through the reactor.

We have used the oxide model proposed by Sales, Turner, and Maple to calculate spatial patterns in the oscillatory oxidation of CO over polycrystalline Pt, Pd, and Ir catalysts. Specifically, by introducing CO diffusion, we have studied the dispersion of one‐dimensional traveling waves and their linear stability. These results could be tested by experiments which resolve the spatial structure of the catalytic oscillations.

The frequency dependence of the average rates of reactions catalyzed by one or more catalysts in a weak oscillating field is derived. The average rates are sums of Lorentzian curves whose characteristic frequencies are the inverse relaxation times of the normal modes of the kinetic system and whose amplitudes are quadratic in the field. The signs of the Lorentz amplitudes can be either positive or negative, so the rates versus frequency can have a variety of shapes, including frequency windows. One can get relaxation times and amplitudes by measuring steady‐state rates as a function of the frequency of the field. The theory is applied to determine the Lorentz amplitudes and characteristic frequencies of ion transport rates catalyzed by Na+–K+–ATPase in erythrocytes.

Models of excitability fall into two broad categories: one with a sharp threshold, the other with a narrow but finite threshold region. In an attempt to clarify the notion, we have studied the application of two models of excitability to experiments on a variant of the Belousov–Zhabotinskii reaction in a well‐stirred reactor. An interrupted separatrix model, which has a sharp threshold, is found to describe our experimental results better than a simple nullcline model, which has a finite threshold region.

We have investigated in detail the transition from stable steady state to chaos in the DOP model of the peroxidase–oxidase reaction. Two consecutive Hopf bifurcations give rise to toroidal oscillations. Chaotic oscillations occur after the circle map associated with the torus becomes noninvertible. The supercritical region of parameter space is characterized by a periodic‐chaotic sequence in which the periodic states form severely, but systematically, pruned Farey trees. In terms of both the transition to chaos and the periodic‐chaotic sequence, the DOP model appears to share important qualitative characteristics with a variety of oscillating chemical reaction systems and their models.

We study Hopf bifurcations in chemical reaction systems for their potential use in quantitative experimental analysis of the kinetics of oscillatory reactions. Three models of the Belousov–Zhabotinsky reaction are investigated as examples. For these we have determined and characterized the sub‐ and supercritical Hopf bifurcations in their dependence on parameters of the models. For supercritical bifurcations we calculate a number of parameters that can be used for quantitative comparison of models and experiment. In particular, we calculate expansion coefficients of the flow rate, the frequency of oscillation, and a Floquet exponent; the small parameter of the expansions is the square of the amplitude of the fundamental Fourier component of the oscillations. We also calculate quenching amplitudes from an adjoint eigenvector of the Jacobi matrix of the kinetics. They determine the conditions under which the small amplitude oscillations can be quenched by addition of the species participating in the reaction. The model properties are compared with experiment. They show qualitative, but not quantitative agreement.

Complex oscillations and even aperiodicity can exist as transient phenomena in closed chemical systems. These effects are illustrated through the analysis of a simple, isothermal chemical model based on mass action kinetics for autocatalytic feedback, involving the conversion of a reactant to a final product via three intermediate species. The use of the so‐called pool chemical approximation and of pseudo‐steady‐state analyses for such systems is indicated and discussed, particularly with relevance to ‘‘real’’ chemical situations where small perturbations due to extraneous noise are inevitably present.

Complex behavior of an oscillating reaction on an array of catalytic regions was modeled using a distributed model consisting of a 10×10 matrix with ten randomly placed oscillators coupled via heat transfer. Each single oscillator was described by a very simple system of two differential equations chosen to model the CO/NO reaction on supported Pd. However, the coupled system exhibited very complex behavior with periodic oscillations, period multiplications, beat structures and chaos. All of these complex features predicted by the model have also been found in experiments. In addition, the model was able to predict the experimentally observed tendencies in the development of complex behavior with changing reaction conditions. Changing distributions of the cells or introducing small differences in the description of the single oscillators did not change the principal features of the system. However, the transition to chaos could be changed in that for one distribution of active cells a Feigenbaum sequence to chaos was found but not in another. With one oscillator twice as active as the rest of the cells, the high activity cell was dominant and entrained the whole system, leading to completely synchronized behavior. Also in this situation, however, chaotic responses were found, when the high activity oscillator was in a stable ignited state. Possible generalizations of this treatment to other oscillating systems are discussed.

The bifurcation behavior of the minimal bromate system (BrO3−/Br−/Ce3+/H2SO4) in a flow reactor shows a wider oscillatory region if the symmetric stirrer rotates in one direction than if the stirring direction is reversed. Thus, at appropriate flow rates, a reversal in the direction of stirring causes a transition between an oscillatory and a steady state. This phenomenon can be explained by a change in the mixing order of the feedstreams.

Various features of NO+CO reaction kinetics on Pt(100) surfaces, including temporal oscillations, are well described by a three‐variable model incorporating only the CO, NO, and O coverages. Here we analyze the corresponding reaction–diffusion equations demonstrating the existence of chemical waves where an ‘‘oscillating phase’’ displaces an unreactive NO/CO phase leaving a spatially periodic structure in its wake; pulses excited via inhomogeneities from an unreactive NO/CO background; and Turing structures for sufficiently unequal NO and CO diffusion rates.

The field of self-organization in nonequilibrium chemical systems comprises the study of dynamical phenomena in chemically reacting systems far from equilibrium. Systematic exploration of this area began with investigations of the temporal behavior of the Belousov-Zhabotinsky oscillating reaction, discovered accidentally in the former Soviet Union in the 1950s. The field soon advanced into chemical waves in excitable media and propagating fronts. With the systematic design of oscillating reactions in the 1980s and the discovery of Turing patterns in the 1990s, the scope of these studies expanded dramatically. The articles in this Focus Issue provide an overview of the development and current state of the field.

Complex oscillations in a simple model of the Briggs-Rauscher reaction mechanism in a continuously stirred tank reactor proposed by Kim et al. [J. Chem. Phys. 117, 2710 (2002)] are investigated numerically. The k(0)-[CH(2)(COOH)(2)](0) phase diagram is constructed first where k(0) is the flow rate and [...](0) is the input concentration. Within the region surrounded by the Hopf bifurcation curve, we find complex oscillation regions which are again separated from the regular oscillation region by the secondary Hopf bifurcation curves. Mixed mode oscillations with an incomplete Farey sequence, periodic-chaotic (or nonperiodic) sequence, and various types of burst oscillations are observed in complex oscillation regions. Also, chaotic burst oscillations, which are due to the transition from one kind of burst to another kind, are reported.

It is shown that the Onsager reciprocal relations are satisfied in systems with multiple stationary states at equilibrium and the occurrence of complex dynamical phenomena such as chemical oscillation in nonideal systems close to equilibrium is not contradictory to linear irreversible thermodynamics.

The iodate oxidation of arsenous acid exhibits single‐hysteresis bistability in a continuous flow stirred tank reactor. Other patterns of multiple stationary states including mushrooms and isolas are exhibited by this system when a constant flow of solvent is introduced to the CSTR in addition to the usual flow of reactants. A simple empirical rate law model provides a near quantitative description of the behavior. This model is analyzed and compared to other model systems.

The Oregonator, a simple but surprisingly successful model of the complex chemistry of the oscillating Belousov–Zhabotinskii reaction, has for years been criticized for the manner in which it accounts for the regeneration of bromide ions. In response to recent objections raised by Noszticzius, Farkas, and Schelly, Noyes has revised the Oregonator model so that the regeneration of Br− is now attributed to the oxidation of organic compounds by HOBr. In this paper the kinetic equations of the revised Oregonator are presented in dimensionless form, and it is shown that the equations admit limit cycle solutions of relaxation type as long as a certain dimensionless ratio of rate constants lies within a relatively narrow interval.

The original Oregonator model to the Belousov–Zhabotinsky oscillating reaction used three composition variables, five rate constants, and one stoichiometric factor involving five irreversible reaction steps. As a result of objections to the stoichiometric factor by Noszticzius, Farkas, and Schelly, we have developed an alternative model of the same complexity based on six irreversible steps. The revised model eliminates some stoichiometric difficulties, and by minor modification of one of the six steps it handles situations in which the final oxidation state of the reduced bromine is +1, 0, or −1. An alternative skeleton model called the Explodator and proposed by Noszticzius, Farkas, and Schelly should not be considered a viable alternative to the Oregonator unless a computational prerequisite and an experimental kinetic prerequisite can both be satisfied.

The original Oregonator model of five irreversible steps and one stoichiometric parameter has been amplified to seven irreversible steps. The amplified model simulates excitability of a reduced steady state induced by silver ions and of an oxidized steady state induced by bromide ions. It also simulates how oscillations during a single run might change from reduction pulses to oxidation pulses. Finally, it simulates a temporary bistability persisting for over two hours in a closed system. If independent measurements determine the rate of enolization of the organic substrate and the rate of reaction of that substrate with the oxidized form of the catalyst, this model may be able to simulate semiquantitatively a large fraction of reported behaviors of catalyzed homogeneous Belousov–Zhabotinsky systems. It will not model systems in which Br2 accumulates or in which there are high‐frequency small‐amplitude oscillations around an oxidized steady state. Procedures are suggested for simulating such behaviors.

The collinear I+HI reaction is studied using an approach based on the concepts of nonlinear dynamics. Three closed regions in phase space are constructed by connecting the dynamical manifolds emanating from physically important periodic orbits. It is shown that many features of the reaction dynamics can be understood with reference to these regions. The oscillating reaction probability in this system is shown to stem from the geometrical pattern of overlap of heteroclinic oscillations of an interaction region. The process of complex formation is quantitatively described in terms of passage into a well defined complex region of phase space. The phase space representation predicts that the complex formation probability oscillates with energy and suggests that the complex lifetime might oscillate as well. We have carried out simulations which confirm both of these effects. The vibrational adiabatic approximation for the reaction is assessed relative to the exact classical dynamics.

A model based on five independent composition variables has been tested by simulating the complex bursting patterns observed experimentally for a Belousov–Zhabotinsky system in a flow reactor. If the system is in a region of constraint space where all stationary states are locally unstable, and if malonic acid concentration in the feed is decreased at constant flow of bromide ion, simple limit‐cycle oscillations persist until the system reaches the Hopf bifurcation which generates a stable stationary state with low concentration of bromide ion. If bromide ion concentration in the feed is increased at constant flow of malonic acid, more and more small‐amplitude oscillations are interspersed between trains of fewer and fewer large‐amplitude excursions until a Hopf bifurcation leads to a stable stationary state with a high concentration of bromide ion. Patterns may be quite complex but usually repeat regularly. If a firing number is defined as ΣS/(ΣS+ΣL), where the summations represent the numbers of small‐ ...

Relaxation half‐times have been measured in the bistable iodate‐arsenous acid reaction near a hysteresis limit and the critical point. A one‐variable empirical rate law model is used to examine the apparent divergence in the relaxation times at these points. Relaxation behavior very close to, and exactly at the critical point and hysteresis limits is considered.

In the first part of this work, some shortcomings in the present theories of the Belousov–Zhabotinskii oscillating reaction are discussed. In the second part, a new oscillatory scheme, the limited Explodator, is proposed as an alternative skeleton mechanism. This model contains an always unstable three‐variable Lotka–Volterra core (the ‘‘Explodator’’) and a stabilizing limiting reaction. The new scheme exhibits Hopf bifurcation and limit cycle oscillations. Finally, some possibilities and problems of a generalization are mentioned.

The rate of catalytic carbon monoxide oxidation on a Pt(100) single crystal surface under isothermal, low‐pressure conditions exhibits for certain ranges of parameters (O2 and CO partial pressures, temperature) sustained temporal oscillations whose mechanism had been explored in previous work. Coupling between reaction and diffusion leads to spatial pattern formation as manifested by patches with different work function on the intrinsically homogeneous surface. Imaging is performed by means of the novel technique of scanning photoemission microscopy. Typically, nuclei with dimensions of a few microns, as determined by the instrumental resolution, are formed spontaneously and expand with sharp fronts and velocities of about 0.5 mm/min (at 480 K) up to sizes ≥1 mm. Waves with even more extended fronts propagating with somewhat higher velocities across the sample surface are responsible for the occurrence of large amplitude temporal oscillations of the integral reaction rate.

Near equilibrium thermodynamic analysis of the reversible ‘‘Oregonator kinetic model’’ has been done using the entropy production technique of Prigogine in the range of the validity of the Onsager relations. Expressions for the excess entropy production (δmP) and the corresponding antisymmetric function (δmΠ) have been derived in terms of the rate constants of the steps, the concentrations of the reactants and products, steady state concentrations of the intermediates, and the coefficients of the real and imaginary parts of the complex differentials δX, δY, and δZ, which represent, respectively, the fluctuations from the steady state concentrations of the intermediates X, Y, and Z. Factors destabilizing the steady states have been determined and steps other than autocatalytic and cross catalytic are also found to be involved.

Oscillations with large amplitudes (>500 K), high frequencies (>8 Hz), and good reproducibility are observed in methylamine decomposition on electrically heated Pt, Rh, and Ir wires at pressures of 0.25–8.0 Torr and temperatures between 900 and 1500 K. The major reaction involves formation of HCN which is endothermic by 37 kcal/mol, so that the reaction strongly cools the wire, which counteracts resistive heating. A photodiode array was used to monitor spatial and temporal oscillations with resolutions of 1 mm and 30 Hz, respectively. On Pt, the frequency increased with increasing pressure and with decreasing wire diameter, while amplitude was a weak function of these parameters. On Ir, oscillations were more complex with regions of the wire often oscillating independently and more variability between experiments. However, the overall behavior resembles that on Pt. On Rh, frequencies were much lower (

FT‐ICR techniques were used to probe the surface chemistry of isolated silicon cluster ions in the 7–65 atom size range. Dissociative chemisorption reactions with NH3 were observed to proceed with rates which varied widely with cluster size. One particular cluster, Si+39, was found to be remarkably inert. Clusters with 20, 25, 33, and 45 atoms were found to be unreactive as well, while those with 18, 23, 30, 36, 43, or 46 atoms were quite reactive. Similarly oscillating reaction patterns were observed with CH3OH, whereas highly reactive free radical scavengers such as O2 and NO showed little selectivity. These results suggest the silicon clusters in this size range have well‐defined structures which vary in ability to catalyze dissociative chemisorption at the surface.

A transition that breaks the m‐fold rotational symmetry of a chemical pattern of traveling waves is reported. The chemical waves travel around a thin annular gel, the inner and outer edges of which are in contact with continuous flow chemical reservoirs. Observations of the dependence of the rotating wave pattern as a function of temperature reveal several distinct states, including a wavelength‐doubled state in which successive waves alternate in shape.