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Self-regulation of the dynamic actuation of a chemical oscillating reaction-based gel was realized by altering the network structure of the gradient double network gel. We demonstrated that the propagation mode of the chemical wave was influenced by the network structure, and consequently determined the dynamic feature of the gel actuator.

A self-deformable gel system is constructed by coupling a gradient structured gel with a chemical oscillating reaction. The system exhibits periodic and asymmetric shape change. The asymmetric shape change of the gel is based on the gradient structure.

Most analytical methods are based on "analogue" inputs from sensors of light, electric potentials, or currents. The signals obtained by such sensors are processed using certain calibration functions to determine concentrations of the target analytes. The signal readouts are normally done after an optimised and fixed time period, during which an assay mixture is incubated. This minireview covers another-and somewhat unusual-analytical strategy, which relies on the measurement of time interval between the occurrences of two distinguishable states in the assay reaction. These states manifest themselves via abrupt changes in the properties of the assay mixture (e.g. change of colour, appearance or disappearance of luminescence, change in pH, variations in optical activity or mechanical properties). In some cases, a correlation between the time of appearance/disappearance of a given property and the analyte concentration can be also observed. An example of an assay based on time measurement is an oscillating reaction, in which the period of oscillations is linked to the concentration of the target analyte. A number of chemo-chronometric assays, relying on the existing (bio)transformations or artificially designed reactions, were disclosed in the past few years. They are very attractive from the fundamental point of view but-so far-only few of them have be validated and used to address real-world problems. Then, can chemo-chronometric assays become a practical tool for chemical analysis? Is there a need for further development of such assays? We are aiming to answer these questions.

By utilizing a chemical oscillating reaction as a periodical driving source, the fluorescence in a responsive polymer system is autonomously regulated based on the reversible formation of dynamic covalent bonds.

We consider the case of the Belousov–Zhabotinsky (BZ) oscillating reaction where the metal catalyst is confined in a discrete phase of cation-exchange resin particles. We show that modelling of the sudden transitions from the steady state to fully synchronized oscillations, which were previously described only in terms of quorum sensing, does not necessarily require fine-graining of the models into individual particles. As a minimal representation of the system, we propose a generalized version of the Oregonator with only one additional parameter φ that corresponds to the total volume fraction of the catalytic phase in the system. We show that the kinetic consequences of catalyst confinement can be interpreted through φ acting as the second variable stoichiometric factor in the Oregonator mechanism that decreases the order of autocatalysis and simultaneously weakens the negative feedback. Based on the proposed model, an analysis of the so-called quorum sensing is provided in terms of the standard concepts of Hopf bifurcation. The model reproduces correctly that (1) oscillations are only exhibited above a certain critical threshold of φ; (2) as φ decreases, so do the amplitudes of oscillations; whereas (3) the periods of oscillations are almost independent of φ. The model thus appears to be a reasonable minimal representation of uniform states in the BZ reaction with catalyst confinement, and therefore might be a convenient starting point for further refinements representing more complicated transitions in this system.

Revival waves, which emerge spontaneously long after the oscillatory bromate–1,4-cyclohexanedione–ferroin reactions become quiescent, are found susceptible to the illumination of visible light. Depending on the intensity and the duration of the light perturbation, an illumination can drive the system either to a reduced reaction state with a high concentration of ferroin, or to an oxidized state with a high concentration of ferriin. When hydroquinone, a main product from 1,4-cyclohexanedione oxidation, is used to gradually replace 1,4-cyclohexanedione as the reductants, the induction period of the formation of revival waves is shortened significantly; however, there is no clear difference in their photosensitivity. These new experimental results suggest that the observed photosensitivity is determined by the photochemistry of the products of hydroquinone.

We analyse the transient spatio-temporal chaos that we observe in the Belousov-Zhabotinsky reaction performed in a closed unstirred batch reactor by recurrence quantification analysis (RQA). We characterize the chaotic transient by measuring the Lyapunov exponent and the Kaplan-Yorke dimension. The latter shows the fractality of the attractor. The importance of the coupling between hydrodynamics and kinetics for the onset of chaos is also 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 effect of spatially localized, time-periodic forcing on the Fe∣1 M H2SO4 system is studied experimentally within the oscillatory and excitable region. The electrode surface is perturbed locally or globally by a laser beam. The resulting response depends strongly on the period and phase of the external forcing. When periodic laser perturbations are applied to the excitable state, the resulting response is large excitations for a large forcing period and pairs of small and large excitations for a small forcing period. During autonomous oscillations the response is entrained either completely or by combinations of autonomous and excitable peaks. A systematic procedure is applied, based on single perturbation experiments, for the construction of one-dimensional maps for the periodically forced oscillator. A mathematical model is proposed for the description of the dynamical phenomena induced by the laser light. The model equations predict most of the experimental findings.

The role of global and non-local coupling involving mass and heat transfer in oscillating heterogeneous catalytic systems under normal pressure conditions is studied for the oxidation of CO on zeolite supported palladium. Two catalysts with sufficiently different dynamic properties, i.e., different amplitudes and frequencies of the oscillations, were used in model experiments of coupled oscillators in a reactor operated as a continuous stirred tank. Global coupling through the gas phase was identified to play the dominant role in synchronizing a catalyst bed consisting of oscillators with different properties. In addition, non-local coupling by diffusion within the porous support has to be considered. Global coupling can also be achieved ia heat transfer in the case of a support with high thermal conductivity.

The role of methylene blue (MB) and its interaction with various enzymic and nonenzymic intermediates in the oscillating peroxidase–oxidase reaction were investigated. Time dependent spectral changes were deconvoluted into time series of the different intermediates. Ferric peroxidase, ferrous peroxidase, and peroxidase compound III account for most of the spectral changes, while the two remaining oxidation states of the enzyme (compound I and II) are only present in very low amounts during any phase of the oscillations. The presence of MB is required for the generation of sustained oscillations and complex dynamics. The amount of ferrous peroxidase formed during an oscillatory cycle decreases with increasing concentrations of MB. At ‘‘high ’’ concentrations of MB only damped oscillations are observed. These findings are interpreted in terms of either a competition between MB and other reactants for NAD• radicals, or of a reaction between MB and ferrous peroxidase. In the absence of MB only damped oscillations can be observed due to slow and irreversible degradation of the enzyme. This suggests that MB also protects the enzyme against degradation.

The initiation of chemical reaction–diffusion waves by visible light of wavelength λ=633 nm from a 20 mW He–Ne laser in the ferroin-catalysed BZ reaction on a polysulfone membrane is repor ted. With low loading of the catalyst on the membrane, oxidation waves can be initiated from the resting steady state and in the recovering tail of a wave. With high loading, waves can only be initiated in the ‘vulnerable’ region behind an existing wavefront. The mechanism of this initiation is discussed in terms of the photoreduction of the metal–ligand catalyst and expressed in terms of a modified Oregonator model. These new observations are in contrast to the inhibitory effect of visible light in the light-sensitive Ru-catalysed BZ system.

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.

We have reinvestigated the kinetics of the Dushman reaction, IO3−+5 I−+6 H+→3 I2+3 H2O, under the conditions of the oscillating Bray–Liebhafsky reaction, perchloric acid solutions and low iodide concentrations, using a CSTR (continuous flow stirred tank reactor) and an iodide ion selective electrode. We show that it is possible to get meaningful results with this electrode at iodide concentrations in the range [I−]=5×10−8 to 5×10−6 M. The experimental rate law is r=[IO3−][H+]2 {k′[I−]+k″[I−]2} with k′=(1200±150) M−3 s−1 and k″=(4.2±0.8)×108 M−4 s−1 at 25°C and 0.2 M ionic strength. It is the first time that the two terms, first and second order in [I−], are observed simultaneously.

This paper introduces the use of the analyte pulse perturbation technique to the Belousov–Zhabotinskii reaction, developed in a continuous-flow stirred-tank reactor, in quantitative oscillating reaction-based determinations. This straightforward, expeditious approach was tested on the kinetic determination of various polyphenols (hydroquinone, catechol, resorcinol, pyrogallol and gallic acid) by their perturbation on the oscillating reaction. The proposed method relies on the relationship between changes in the oscillation amplitude of the chemical system and the analyte concentration, which is revealed for the first time in this work. The dynamic range is between 0.3–6.0 μmol and the method features good precision (RSD ca. 2%) and excellent throughput (60 samples h−1); the latter is a result of the expeditiousness with which regular oscillations are regained after each perturbation. The potential mechanism of action of polyphenols on the oscillating system is discussed.

A new method applying a non-linear chemical system under conditions far from thermodynamic equilibrium in microvolume/microconcentration quantitative analysis is described. The chemical system used as a matrix is the Bray–Liebhafsky reaction in a non-equilibrium stationary state close to a bifurcation point. The method is based on monitoring the response of this system to perturbations by Cl–, Br–, I–, Mn2+, malonic acid and quercetin analyte solutions, which are followed potentiometrically either by an Ag+/S2– ion-sensitive or by a Pt electrode. A linear response of the potential shift versus the logarithm of the analyte concentrations is found in the following ranges: 1.3 × 10–6 mol dm–3 ≤ [Cl–] ≤ 1.6 × 10–4 mol dm–3, 1.0 × 10–6 mol dm–3 ≤ [Br–] ≤ 8.3 × 10–5 mol dm–3, 2.0 × 10–6 mol dm–3 ≤ [I–] ≤ 1.0 × 10–4 mol dm–3, 8.4 × 10–7 mol dm–3 ≤ [Mn2+] ≤ 8.3 × 10–5 mol dm–3, 3.8 × 10–7 mol dm–3 ≤ [malonic acid] ≤ 2.1 × 10–5 mol dm–3 and 1.5 × 10–8 mol dm–3 ≤ [quercetin] ≤ 3.7 × 10–5 mol dm–3. Under the investigated conditions an improved detection limit for all halides tested is obtained. Unknown concentrations of the analytes can be determined from a standard series of calibration curves to an accuracy within ±5%. In addition, the application of potentiometric measurements in microvolume/microconcentration quantitative analysis is diversified.

Discrete and continuous control strategies are applied to regulate the Belousov–Zhabotinsky–continuous stirred tank reactor (BZ–CSTR) chaotic chemical reaction onto the stabilized states. The orderly intrinsic states of the chaotic system, such as unstable periodic-1 orbit (UPO-1), unstable periodic-2 orbit (UPO-2) and unstable periodic-4 orbit (UPO-4) are obtained by the discrete nonlinear perturbation feedback method from within the whole chaotic region (NPF-WCR). The non-intrinsic orderly states, such as period-4, period-2, period-1 and steady state can be maintained by the continuous linear and nonlinear self-interacting feedback control strategy. The differences between the two methods are also discussed. An '‘extremum space control’' method is suggested.

An existing scaling model of a reaction–diffusion system is extended to a circular trajectory. The equations describe the evolution of a slow (X) and a fast (Y) concentration variable. The fast variable jumps between extreme values across a reaction interface as the rate parameter becomes very large. The model is reduced to one equation for the dynamics of the smooth (slow) variable while the Y-jumps occur at two interfaces spatially located on a ring. The equation is solved subject to 2π-periodicity conditions on the ring and continuity conditions at the interfaces. Both static (with zero velocity) and moving (with velocity v) wave solutions are found. An analogy is then drawn between our reaction–diffusion system and oscillating chemical reactions such as the Belousov–Zhabotinskii (BZ) reagent, confined to a torus-shaped container. A toroidal thin tube with a very small diameter could simulate the ring geometry. The conjectured waves capture the oscillations of the catalyst (ferroin), with the maxima and minima corresponding to the ferroin and ferriin, spatial domains in the doughnut, respectively. The non-stationary wave solutions predict a migration of those domains yielding swinging (back and forth) patterns along the ring. The azimuthal position of the interfaces exhibits temporal oscillations. Thus these simulations suggest interesting experiments on spatio–temporal patterns in excitable chemical media in annular reactors.

The reactions of oxygen are not a necessary part of the explanation of the oscillations in the Bray–Liebhafsky reaction. However, oxygen can modify the shape of the oscillations and the range of concentrations where they are observed. We discuss the mechanism previously proposed and suggest that the chemical effects of oxygen result mainly from the oxidation of iodide by radical processes. The escape of oxygen has also a physical effect, the loss of iodine in the gas phase. The effects of light and stirring rate are related to the effects of oxygen.

The application of oscillating reactions to the analysis of real samples by the analyte pulse perturbation technique is reported. The oscillating reaction involving the H 2 O 2 –NaSCN–CuSO 4 system in an alkaline medium was used for the expeditious, convenient, automatic determination of vanillin, paracetamol and ascorbic acid in food and pharmaceutical samples. Six methods (two per analyte) were developed that allow the determination of 1.5–40 µmol of vanillin, 0.5–6 µmol of paracetamol and 0.5–5 µmol of ascorbic acid in real samples. The proposed methods are precise (RSD < 5%) and have a reasonable sample throughput (6–10 h - 1 ) for this type of reaction, which can be implemented with modular equipment available at any laboratory. The effect of influential variables and the selectivity of the determinations was studied in relation to the types of sample used. Determinations are virtually direct and require no removal of interfering species. The results were validated by comparison with standard methods.

An analytical method for the determination of trace amounts of reduced glutathione (GSH) by its perturbation on the copper(II)-catalysed oscillating reaction between hydrogen peroxide and sodium thiocyanate is proposed. The reaction is implemented in a continuous-flow stirred-tank reactor, and changes in the oscillating period on each perturbation are proportional to the GSH concentration. The use of the analyte pulse perturbation technique permits sequential determinations on the same oscillating system owing to the expeditiousness with which the starting conditions are restored after each perturbation. Two different methodologies were used to address the determination. The dynamic range lies between 0.1 an 0.7 µmol of GSH and the precision is excellent (less than 0.7% as relative standard deviation). Some aspects of the potential mechanism of action of GSH on the oscillating system are discussed.

A microscopic lattice gas model for the catalytic CO + O2 reaction on Pt(110) subject to external periodic forcing is studied by means of cellular automaton simulations. Harmonic resonance, subharmonic and superharmonic entrainment, quasiperiodic as well as chaotic behavior are among the observed phenomena in this model when the gas phase concentration of CO as an external control parameter is periodically varied and interacts with the self-oscillating reaction system.

The Brusselator is a classical model predicting kinetic oscillations in chemical reactions. Using a lattice version of this model, we show by employing Monte Carlo simulations how due to fluctuations the periodic oscillations may first become aperiodic and then disappear with decreasing system size.

The behaviour of the uncatalysed Belousov–Zhabotinskii reaction with pyrogallol in a flow reactor has been determined experimentally. The introduction of ferroin as catalyst provides an ‘internally’ coupled system. The evolution of the oscillatory waveform with various experimental constraints (mean residence time, inflow concentrations of the different reactants and the temperature) is reported. These phenomena are successfully reproduced by a 12-step model based on bromide-ion control and this allows additional features of the bifurcation sequences through complex oscillations and chaos to be determined.

The dicarboxymethyl radicals (derived from malonic acid) and their peroxyl radicals play an important role in the Belousov–Zhabotinsky reaction, and detailed knowledge of the rate constants are required for modelling this oscillating reaction. Dicarboxymethyl radicals were produced pulse radiolytically in aqueous solutions. They are characterized by absorption maxima at 310 nm at pH 0 (fully protonated, e = 1210 dm3 mol−1 cm−1) and at 340 nm at pH 8 (dianion, e = 1070 dm3 mol−1 cm−1). The radicals decay bimolecularly with rate constants of 4 × 108 dm3 mol−1 s−1 at pH 0 and 1.4 × 107 dm3 mol−1 s−1 at pH 8. In the presence of O2, the dicarboxymethyl radicals add O2, and their absorption decays with rate constants of 1.6 × 109 dm3 mol−1 s−1 at pH 0 and 1.3 × 109 dm3 mol−1 s−1 at pH 8. Whereas the second pKa value of the radical is identical to that of the parent compound (5.7), the value of the corresponding peroxyl radical is as low as 3.

The Belousov–Zhabotinskii reaction with oxalic acid in a closed, stirred batch reactor has been investigated in H2SO4–NaHSO4, H2SO4–SO2–4(cations Na+ or Mg2+) and H2SO4–MClO4(M+= Na+ or Li+) mixtures. While the addition of sulphate ions has little effect on the oscillating reaction, perchlorate ions can inhibit it or increase the number of oscillations.

The experimental behaviour of the Belousov–Zhabotinskii reaction in a continuously stirred tank reactor is examined. We present a complete, systematic listing of results gained for residence times in between two values of a stable stationary state, and discover an absence of symmetry about period-one oscillations. Particular attention is paid to chaotic behaviour at long residence times and its analysis. Two new mixed-mode oscillatory states are described phenomenologically by the use of slow manifolds.

Contrary to what has been thought, systems classified as bromine-hydrolysis-controlled (BHC) show an induction period. In studies on the effect of a family of ketones upon this type of oscillators, it was found that an induction period appears in an interval of concentrations of the ketone, or in an interval of the value of the enolization constant. Simulations of the processes involved and a corresponding explanation are shown in this paper.

A new method for the determination of hexacyanoferrates in an oscillating chemical system involving the Mn(II)-catalysed reaction between diacetone and potassium bromate in an acidic medium is proposed. The best reaction conditions and reactant concentrations are reported. The method relies on the linear relationship between the changes in the oscillation period of the chemical system and the concentration of hexacyanoferrates in the range 1.0 × 10–7–3.3 × 10–5 mol dm–3. The relative standard deviation for 4 × 10–6 mol dm–3 Fe(CN)63– is 2.0% (n = 6). The possible mechanism of this reaction is discussed.

It is shown that the Belousov–Zhabotinskii oscillating reaction can be produced and sustained over long periods in a flow system with high precision and without the usual disturbing features of spatial inhomogeneity and gas evolution. However, the reaction can be perturbed, as measured by the induction time, by the addition of species which react with bromide, a critical intermediate in the reaction. The analytical possibilities for the determination of metals at ppb concentrations are demonstrated.

Various processes in chemistry lead to formation of spatial gradients, and cannot be directly studied using conventional spectroscopic techniques. Here we aimed to develop a simple method for the monitoring of light absorption at three wavelengths in two dimensions. The experimental setup consists of a commercial liquid crystal display (LCD) computer screen with light-emitting diode (LED) back illumination, and a digital camera equipped with a complementary metal oxide semiconductor imager. The computer screen serves as a multi-wavelength light source while the camera records distributions of the light transmitted through a two-dimensional non-homogeneous dynamic sample (reaction mixture). A program in C# language constantly changes the background colour of a console window, so as to alternately relay the light of different wavelength (λmax = 608, 540, and 455 nm, respectively) onto the sample. The light emitted by the screen passes through a Petri dish containing the sample, while the digital camera records images revealing distributions of chemical substances absorbing at different wavelengths. The interval between two successive colour displays is 200–300 milliseconds. In this demonstration of the method, we followed two processes: the Belousov–Zhabotinsky oscillating reaction and the Old Nassau (Halloween) clock reaction. Every experiment produced a series of light absorption images corresponding to the wavelengths of the LCD/LED screen. Chemical front formation could be observed for analytes absorbing light at one of the three wavelength bands. In future, this approach can be extended to imaging at multiple wavelengths (by introducing customized LCD matrices and modified LED back illumination), and used in the monitoring of other non-homogeneous chemical processes.

We designed and synthesised two new polymerizable ruthenium complexes that catalyse the Belousov–Zhabotinsky (BZ) oscillating reaction and incorporated them into a copolymer to form hydrogels. The periodic oxidation and reduction of the attached ruthenium complex in the BZ reaction induces hydrating and dehydrating effects, respectively, that result in self-oscillatory volume changes of the hydrogel. We evaluated the correlation between the chemomechanical oscillation properties of the hydrogel and the proximity of the catalyst to the polymer backbone. Our results indicate that, like the change of such macroscopic parameters as temperature, reactant concentrations and pH, varying the microscopic distance between the catalyst and the polymeric chain provides a new way to tailor the chemomechanical behaviour, e.g., the initiation time, the frequency of oscillation, and the volume change of BZ hydrogels. Moreover, variation of the catalysts offers a new means to control the microstructure of the copolymer by expanding the range of monomer ratios. Modulation of molecular structure appears to be an effective way to alter the reaction–diffusion profile of species within heterogeneous chemoresponsive gels, thus contributing to the development of multifunctional, active soft materials capable of converting chemical energy into controllable mechanical forces.

The catalytic reduction of nitric oxide by carbon monoxide on the Pt(100) surface is studied by a simulation method in which experimentally accessible parameters, such as temperature, partial pressures, adsorption/desorption energies, are explicitly introduced. The algorithm is able to exhibit the existence of a narrow upper temperature window, where substrate-induced sustained temporal oscillations in the rate formation of CO2 are found, in qualitative agreement with experiments. The formation of restructured islands is also observed in the oscillatory region, both for the substrate and the species lattices. As the temperature is increased, a single period doubling in the rate oscillations is found at the upper boundary of the oscillatory window, before chaotic oscillations settle in, while experiments show a cascade of period doubling toward chaos. The analysis of the calculated adsorbate coverage oscillatory timesequences indicate rather that the period doubling observed here may not belong to a Feigenbaum-scenario route toward chaos.

Regular pH oscillations with small amplitude are observed during the decomposition of hydrogen peroxide in the presence of ferrocyanide ions in an unbuffered mixture of water–acetonitrile under closed conditions in the dark.

The catalyst precursor and calcination conditions used in the preparation of La2O3 have been found to have a marked influence on the surface properties, basicity and base strength distribution, and catalytic activity and selectivity in the oxidative coupling of methane (OCM) under different reaction conditions. Among the La2O3 catalysts, only that prepared from lanthanum acetate by decomposition in N2(but not in O2) showed symmetric temperature and concentration oscillations in OCM at or below 933 K over a narrow temperature range. The unsteady reaction behaviour is found to be very complex and strongly dependent upon the OCM process parameters and the catalyst parameters. Furthermore, the results on the La2O3 obtained from the acetate indicated a strong possibility of the formation of new catalytic sites active at lower temperatures (below 873 K) during the OCM reaction at higher temperatures.

Periodical self-oscillating behaviour in the reaction rate was observed in the selective catalytic reduction of NO by propene on alumina in a tubular fixed-bed reactor.

In the oxidation of thiourea by iodate in weakly acidic solution the concentration of iodide may exhibit several extrema. The number of extrema mainly depends on the initial ratio of the concentrations of thiourea and iodate, and is at most four. The first step of the reaction results in the formation of iodide which then reacts with iodate to give iodine. The latter oxidizes thiourea in several steps, the end products being sulphate ions, ammonium ions, and carbon dioxide. Taking into account the independently determined rate constants for the sub-systems, the change in the concentrations of iodide and iodine with time can be calculated. There is good agreement between the experimental and theoretical curves.

The heat output and the accumulation of monobromomalonic acid during chemical oscillation in the bromate, malonic acid, sulphuric acid and catalyst [Ce(III), Mn(II), Fe(phen)2+3, Ru(dipy)2+3] systems were measured and the results interpreted. The behaviour of the reacting oscillating systems depends to a certain extent on the catalyst applied. Both the rate of heat evolution and the rate of accumulation of monobromomalonic acid are periodic. The heat of the cerium-catalysed Belousov oscillating reaction is 130 ± 5 kJ mol–1 bromate.

Oxidation of organic compounds in the presence of iodate ion is significant to the behaviour of the Briggs–Rauscher oscillating system; a new induced reaction in which iodine is liberated from iodate during the oxidadion of oxalic acid by a one electron oxidant is described.

Periodic fluctuations in reaction temperature indicating nearly symmetrical oscillations in the partial oxidation of methane by oxygen to ethane and ethylene in high yields over an La2O3–BaO–MgO (La/Mg = 0.1; Ba/Mg = 0.05) catalyst at reactor temperatures above 550°C but below 700°C have been observed.

Temporal oscillations in BrO–3–H2SO4–Ce4+–ascorbic acid–acetone/cyclohexanone have been studied in detail. It is observed that two types of oscillatory regimes separated by a time pause occur. Synchronous oscillations in colour and redox potentials are also observed, as are oscillations in [Br–] of very low amplitude (ca. 15 mV). The lower and upper limits of reactant concentrations and the temperature between which oscillations occur have been determined. Addition of a sufficient amount of Ag+, Hg2+, liquid Br2 and CCl4 stops the oscillations which can be revived by the addition of potassium bromate solution in all cases except CCl4. Oscillations in a CSTR (continuously stirred tank reactor) have also been observed. It is suggested that sequential oscillations occur on account of decomposition of ascorbic acid into oxalic acid. The first type of oscillation occurs on account of ascorbic acid–acetone acting as a mixed substrate while type II oscillations occur after a pause due to decomposition of ascorbic acid into oxalic acid so that oxalic acid with acetone or cyclohexanone acts as the second mixed substrate.

The kinetics behaviour of a wide range of autocatalytic systems can be well approximated by the prototype step A + B → 2B, rate =k1ab.A similar rate law is also used extensively when dealing with the important class of branched-chain reactions. The above step is considered in the present paper for a system in which the catalyst B is not infinitely stable but undergoes a removal or decay whose rate increases less than linearly with the catalyst concentration: B → C, rate =k2b/(1 +rb). Such an expression may reflect deactivation of B at a surface where the number of free sites available for adsorption may become significantly reduced.There exists a unique, physically acceptable stationary state at all residence times: multiplicity is not a feature of this system. However, the local stability of the stationary state changes as the residence time varies. At shortest residence times the solution is a stable node and small perturbations decay monotonically. At longer residence times, damped oscillatory responses are found characteristic of a stable focus. For surfaces such that r > k1/k2, the stable focus becomes unstable at some residence time t*res. At this point of Hopf bifurcation the system begins to display sustained oscillations in the concentrations of A and B. The amplitude of the oscillations increases from zero as tres is increased beyond t*res, growing as the square root of this difference.The conditions for Hopf bifurcation and hence for oscillatory reaction are evaluated numerically in terms of the parameters k1, k2, r and a0(the concentration of reactant A in the inflow to the reactor). Finally, some qualitative connections are drawn between the above model scheme and the varied patterns of behaviour observed during the oxidation of carbon monoxide.

Stationary and oscillatory ignition states have been studied in mixtures of hydrogen and oxygen under flowing conditions in a non-adiabatic, well stirred vessel. The conditions bridge the region between ‘slow reactions’ and ignition at the second (p–Ta) limit. An oscillatory mode of ignition is observed at the boundary; it gives way to a stable state corresponding to complete reactant consumption at higher temperatures within the ignition peninsula. The period of oscillations is governed by the composition of the reaction mixture. The effects on the period of addition of diluents (He, Ar, N2, CO, CO2 and C3F8) and changes in the H2/O2 ratio have been studied by monitoring changes in temperature and light output from the system. The global behaviour of these systems can be modelled successfully using the accepted H2/O2 reaction scheme. Comparison of model predictions and experimental findings leads to values of the third-body efficiencies of He, Ar, N2, CO, CO2 and C3F8 relative to H2 of 0.35, 0.35, 0.45, 0.40, 0.90 and 2.90, respectively, in the reaction H + O2+ M → HO2+ M. With some mixtures hysteresis and birhythmicity are observed in their oscillatory behaviour; these effects too can be modelled successfully.

The decomposition of ca. 3 × 10–5 mol dm–3 aqueous solutions of the cobalt(I)(B12s) to the cobalt(II)(B12r) cobalamin under nitrogen has been studied at 36 °C by u.v.–visible spectrophotometry. The reaction shows marked oscillations in the relative concentrations of the cobalt(I) and cobalt(II) complexes with good isosbestic points and no evidence for the occurrence of any spectroscopically distinct intermediate. The oscillations appear to consist of a basic train with a period of 4–5 min and one or more superimposed trains. The oscillations are destroyed by light and the period decreases with increasing temperature, but the reaction is relatively unaffected by other variables such as pH (2–12).

We examine the influence of mixed cerium(IV) sulphate and ferroin catalysts in the oscillating reduction of bromate by malonic acid. The tests were made by potentiometric and spectrophotometric methods. Results are shown as number of cycles and both maximum and minimum of potential vs. time. The mixed cerium(IV)–ferroin catalysts have almost the same effect as pure ferroin at the beginning and as pure cerium(IV) at the end. The number of cycles is quite steady, but the frequency of oscillations of the cerium(IV) catalyst is very low and very different from that of the mixed catalysts and of pure ferroin.

The model proposed by D'Alba and Di Lorenzo, which explains oscillations by supersaturation and phase exchange, has been applied to the Bray–Liebhafsky system (hydrogen peroxide, potassium iodate and sulphuric acid), the Briggs–Rauscher system (hydrogen peroxide, potassium iodate, sulphuric acid, manganous sulphate and malonic acid) and the arsenite–iodate–chlorite system.The mechanisms of these reactions and the roles of the phase exchanges have been elucidated. The role of the catalyst and of some of the organic substrates is discussed, along with an interpretation of some of the experimental results.

The temperature dependence of the dynamics of the heterogeneous oxidation of CO on palladium supported by an amorphous Al2O3 carrier has been studied. The complex structure of the observed time series has been investigated by fast-Fourier-transform analysis. The resulting spectra are characterized by at most three frequencies, the ratio of which is nearly an integer, and by frequency locking. For lower temperatures sub-harmonics of these frequencies become important. The fractal character of the time series could be explained qualitatively by a one-dimensional automaton representing a concentration wave travelling on a fractal network of Pd particles in the catalyst bed.

Both one-dimensional and two-dimensional trigger-wave propagation in the systems (A) IO–3+ Ce4+/Mn2++ mandelic acid + acetone + H2SO4+ ferroin/starch, (B) IO–3+ Ce4+/Mn2++ acetylacetone + H2SO4+ ferroin/starch and (C) IO–3+ Ce4+/Mn2++ mandelic acid + arsenite + H2SO4+ ferroin/starch has been investigated. Single red bands (with ferroin) and blue bands (with starch) propagate with velocity v given by the relation v=A exp (–Ea/RT)[H+.]–10[IO–3]1/20 where A and Ea are constants. A is different for each of the three systems but Ea has the same value, 12.2+0.2 cal mol–1, for both one-dimensional and two-dimensional waves.

When the Belousov–Zhabotinskii oscillating reaction is perturbed by rapid addition of bromide ions, the oscillations disappear but then recover. The time taken for this recovery depends on the extent of concentration perturbation, but the new frequency and amplitude of oscillation closely resemble the frequency and amplitude before perturbation. These observations show that this oscillating chemical reaction follows a limit cycle type of behaviour. A similar pattern is observed when solutions containing cerium(IV) ions are rapidly added to the oscillating reaction, although there is a more marked change in frequency and amplitude. The experimental results are compared with the results obtained from a numerical analysis of the effects of similar perturbations on the oscillations for two model schemes of oscillating reactions.