Numerical evidence of complex nonlinear phenomena of the Belousov-Zhabotinsky oscillatory reaction under batch conditions

By numerical calculations based on our previously proposed model with Br₂O intermediate species we were able to simulate complex evolution of the Belousov-Zhabotinsky (BZ) reaction under batch conditions. In the defined region of initial malonic acid concentration [MA]₀ (1.00 × 10^?3 mol dm³ ≤ [MA]₀ ≤ 1.50 mol dm^?3) different sequences of regular and complex periodic and aperiodic oscillations were obtained. It is noticed that the bromine evaporation significantly affects the dynamics of the reaction.     

Sensitivity analysis of the two kinetic states of the Belousov-Zhabotinsky reaction

A recently published kinetic model of the Belousov-Zhabotinsky reaction was studied by the feature sensitivity analysis of the slow bromide consumption and slow bromide production periods of the relaxing-type oscillatory system. The computed sensitivities allowed us to reveal the kinetic importance of the 17 individual reactions during the two, “kinetically homogeneous” states of the oscillation. Similarities and differences in the relative kinetic importances of the reaction steps were carefully studied when changing the magnitude of the rate constants (high set and low set). Of the 17 reactions examined, the attack of Ce⁴⁺ on malonic acid proved to be an essential step of the mechanism. Using the low set, there emerge more reactions which significantly affect the length of the two kinetic states.     

An elegant method to study an isolated spiral wave in a thin layer of a batch Belousov-Zhabotinsky reaction under oxygen-free conditions

A method to prepare a uniform thin layer of a batch Belousov-Zhabotinsky (BZ) reaction under oxygen-free conditions for the study of an isolated spiral wave is presented. After a first layer of gel soaked with the BZ solution has been delivered into the reactor, a single spiral wave was initiated, and finally the remaining reactor volume was filled with gel and BZ medium. The completely filled reactor is sealed gas-tightly, yielding oxygen-free, and thus more controlled, reaction conditions. A systematic study of the behaviour of an isolated spiral wave in a ferroin-catalyzed BZ reaction under batch conditions has been performed. Recipes for BZ media that support a slowly rotating meandering spiral were developed. In cases of extremely low excitability (i.e., relative large stimuli are required to induce a propagating wave), the number of petals in the trajectory of a spiral tip decreased due to aging of the reaction system. Since oxygen-free conditions are necessary for the study of the dynamics in three-dimensional excitable media, and the wave velocities of a spiral are sufficiently low, the developed chemical recipes are suitable for studies of the behaviour of scroll waves in three-dimensional systems by optical tomography.     

Self-oscillation of polymer chains induced by the Belousov-Zhabotinsky reaction under acid-free conditions

A novel self-oscillating polymer was prepared by utilizing the Belousov-Zhabotinsky (BZ) reaction. In this study, a sulfonic acid group was newly introduced as a pH-control site into the copolymer of N-isopropylacrylamide, and the ruthenium complex was introduced as a catalyst site. By introducing the pH-control site, we succeed in causing the soluble-insoluble self-oscillation of the polymer solution under acid-free conditions in which only two BZ substrates, malonic acid and sodium bromate, were present as added agents. The self-oscillating behavior was remarkably influenced by the temperature and polymer concentration, which reflects the intermolecular aggregative capacity of the polymer chains in the reduced state to change the lower critical solution temperature. This achievement of self-oscillation of polymer chains under acid-free conditions may lead to their practical use as novel biomimetic materials under biological conditions.     

Bromide control, bifurcation and activation in the Belousov-Zhabotinsky reaction

The unstirred, ferroin (Fe(phen)3(2+)) catalyzed Belousov-Zhabotinsky (BZ) reaction is the prototype oscillatory chemical system. Reaction media with added Br(-) appear red (reduced, low [Fe(phen)3(3+)]) during an induction period of several minutes, followed by the "spontaneous" formation of "pacemaker" sites, which oscillate between a blue, oxidized state (high [Fe(phen)3(3+)]) and the red, reduced state and generate target patterns of concentric, outwardly moving waves of oxidation (blue). Auto-oscillatory behavior is also seen in the Oregonator model of Field, Koros and Noyes (FKN), a robust, reduced model that captures qualitative BZ kinetics in the auto-oscillatory regime. However, the Oregonator model predicts a blue (oxidized) induction phase. Here we develop a generalized Oregonator-like model with no explicit bifurcation parameter that yields the observed transition from a red initial state to oscillatory dynamics, and displays a new bifurcation mechanism not seen in the original Oregonator.     

Temperature influence on the malonic acid decomposition in the Belousov-Zhabotinsky reaction

The kinetic investigations of the malonic acid decomposition (8.00 × 10⁻³ mol dm⁻³ ≤ [CH₂(COOH)₂]₀ ≤ 4.30 × 10⁻² mol dm⁻³) in the Belousov-Zhabotinsky (BZ) system in the presence of bromate, bromide, sulfuric acid and cerium sulfate, were performed in the isothermal closed well stirred reactor at different temperatures (25.0°C ≤ T ≤ 45.0°C). The formal kinetics of the overall BZ reaction, and particularly kinetics in characteristic periods of BZ reaction, based on the analyses of the bromide oscillograms, was accomplished. The evolution as well as the rate constants and the apparent activation energies of the reactions, which exist in the preoscillatory and oscillatory periods, are also successfully calculated by numerical simulations. Simulations are based on the model including the Br₂O species. The article is published in the original.     

Carbon dioxide evolution in a Belousov-Zhabotinsky type oscillating reaction with acetonedicarboxylic acid

Oscillations in the platinum redox potential during the reaction of bromate ions with acetonedicarboxylic acid catalyzed by Mn(II) ions were observed. The volume of gaseous carbon dioxide produced was measured. A nonoscillatory course was found both at the slow and rapid stirring rates for carbon dioxide evolution. The perturbation experiments suggest supersaturation during the Belousov-Zhabotinsky reaction with acetonedicarboxylic acid. Possible reasons for such observations are discussed.     

Effects of delayed linear electrical perturbation of the Belousov-Zhabotinsky reaction: a case of complex mixed mode oscillations in a batch reactor

Delayed feedbacks are quite common in many physical and biological systems and in particular many physiological systems. Delay can cause a stable system to become unstable and vice versa. One of the well-studied non-biological chemical oscillators is the Belousov-Zhabotinskii (BZ) reaction. This gives relaxation oscillations for a considerable period of time under batch conditions. This paper deals with the effect of perturbing the limit cycle oscillation of BZ reaction by employing a delayed electrical feedback to the system under batch conditions. The parameters chosen to study are external resistance and delay. For various resistances and delays the system was electrically perturbed and found to exhibit various complex mixed mode oscillations. The dynamic features are accounted for by the Oregonator model, with time delay incorporated in one of the variables. This revised version was published online in June 2006 with corrections to the Cover Date.     

Spatio-temporal perturbation of the dynamics of the ferroin catalyzed Belousov-Zhabotinsky reaction in a batch reactor caused by sodium dodecyl sulfate micelles

The effects of the anionic surfactant sodium dodecyl sulfate (SDS) on the spatio-temporal and temporal dynamics of the ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction have been studied over a wide surfactant concentration range. For the first time, investigations were performed also for unstirred systems. The presence of SDS in the reaction mixture influences the oscillatory parameters to an extent that significantly depends on the surfactant concentration. The trend of the wave speed v upon the increasing amount of SDS was found to have a maximum at [SDS] = 0.075 mol dm (-3) ( v = 0.071 mm s (-1)), after which the speed decreased to 0.043 mm s (-1) at [SDS] = 0.5 mol dm (-3), which is below the value found in the absence of the surfactant ( v = 0.055 mm s (-1)). The response of the oscillatory BZ system to the addition of SDS has been ascribed to two different causes: (a) the peculiar capability of the organized surfactant assemblies to affect the reactivity by selectively sequestering some key reacting species and (b) the modifications induced by SDS on the physical properties of the medium. These hypotheses have been corroborated by performing spectrophotometric investigations on the stirred BZ system. Complementary viscosity measurements gave useful hints for the clarification of the surfactant role.     

Effect of initial substrate concentration of the Belousov-Zhabotinsky reaction on self-oscillation for microgel system

Self-oscillation for the microgel particles ( approximately 200 nm in diameter) was studied by changing initial substrate concentrations (i.e., malonic acid, sodium bromate, and nitric acid) of the Belousov-Zhabotinsky (BZ) reaction that is used for chemical energy for the self-oscillation. The cross-linked microgels are composed of N-isopropylacrylamide and ruthenium tris(2,2'-bipyridine), Ru(bpy) 3, which is a catalyst for the BZ reaction. Comparing with the homogeneous, stirred solution of the bulk solution for the BZ reaction, swelling/deswelling oscillation of the microgels showed longer induction period, different dependence of initial substrate concentrations on oscillation period, and different oscillation rhythm. The change in oscillation for the microgels can be understood by considering the microgel network effect.     

The role of radicals in the Belousov-Zhabotinsky reaction

A new theory of the Belousov-Zhabotinsky (BZ) reaction, the Radicalator model, is presented. This model is based on a negative feedback loop involving a fast reaction between malonyl and bromine dioxide radicals. Experimental evidence for the validity of the model is given for BZ systems in 3 M and 1 M sulfuric acid solution.     

Modulation of volume fraction results in different kinetic effects in Belousov-Zhabotinsky reaction confined in AOT-reverse microemulsion

The effects of volume fraction modulations on a Belousov-Zhabotinsky reaction catalyzed by the photosensitive Ru(bpy)(3)(+2) confined in an AOT microemulsion system are analyzed. Kinetic observables such as the induction time or the initial oscillation period demonstrate two different types of correlation with the volume fraction depending on whether the system is below or above the microemulsion percolation threshold. Temporal evolution also demonstrates an exponential growth of the period with the number of oscillations independent of the volume fraction of the system.     

Dynamic states of the Bray-Liebhafsky reaction when sulfuric acid is the control parameter

Dynamic behavior of hydrogen peroxide decomposition catalyzed by iodate and hydrogen ions (the Bray-Liebhafsky reaction), in a continuous stirred tank reactor is investigated. The experimental results are obtained at one operational point in concentration phase space by varying mixed inflow concentrations of the sulfuric acid. The experimental evidences for the onset and termination of oscillatory behavior via the saddle node infinite period bifurcation as well as some kind of the Andronov-Hopf bifurcation are presented. In addition, the possibility of excitability of a stable steady state by thiamine was observed. The article is published in the original.     

Influence of most important radicals on the numerically simulated belousov-zhabotinsky oscillatory reaction under batch conditions

In the already proposed model of the Belousov-Zhabotinsky reaction with the Br₂O species as intermediate one, the reactions with malonyl (MA^·), bromomalonyl (BrMA^·) and tartronyl (TA^·) radicals were introduced with aim to explore their role in overall dynamics. The related numerical simulations of the experimentally obtained dynamic states under batch conditions were successfully performed.     

Noise-induced order in the chaos of the Belousov-Zhabotinsky reaction

Noise can stabilize a metastable state in such a way that the system remains in this state for a longer time than in the absence of noise. When this phenomenon is observed in chaos, it is called "noise-induced order." We have experimentally detected noise-induced order in the Belousov-Zhabotinsky reaction. That is, when noise is added to the chaos with the flow rate near the period-three oscillation, a decrease of the maximum Lyapunov exponent and a convergence of the Fourier spectrum are observed. Moreover, the analysis on the one-dimensional return map reveals that noise-induced order is caused by the convergence of the chaotic trajectory into the laminar region.     

Period-doubling and chaotic oscillations the ferroin-catalyzed Belousov-Zhabotinsky reaction in a CSTR

The ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction, the oxidation of malonic acid by acidic bromate, is the most commonly investigated chemical system for understanding spatial pattern formation. Various oscillatory behaviors were found from such as mixed-mode and simple period-doubling oscillations and chaos on both Pt electrode and Br-ISE at high flow rates to mixed-mode oscillations on Br-ISE only at Iow flow rates. The complex dynamic behaviors were qualitatively reproduced with a two-cycle coupling model proposed initially by Gy(o)rgyi and Field. This investigation offered a proper medium for studying pattern formation under complex temporal dynamics. In addition, it also shows that complex oscillations and chaos in the BZ reaction can be extended to other bromate-driven nonlinear reaction systems with different metal catalysts.     

Period-doubling and chaotic oscillations in the ferroin-catalyzed Belousov-Zhabotinsky reaction in a CSTR

The ferroin-catalyzed Belousov-Zhabotinsky(BZ) reaction,the oxidation of malonic acid by acidic bromate,is the most commonly investigated chemical system for understanding spatial pattern forma-tion. Various oscillatory behaviors were found from such as mixed-mode and simple period-doubling oscillations and chaos on both Pt electrode and Br-ISE at high flow rates to mixed-mode oscillations on Br-ISE only at low flow rates. The complex dynamic behaviors were qualitatively reproduced with a two-cycle coupling model proposed initially by Gy?rgyi and Field. This investigation offered a proper medium for studying pattern formation under complex temporal dynamics. In addition,it also shows that complex oscillations and chaos in the BZ reaction can be extended to other bromate-driven nonlinear reaction systems with different metal catalysts.     

Discontinuously propagating waves in the bathoferroin-catalyzed Belousov-Zhabotinsky reaction incorporated into a microemulsion

Three new types of discontinuously propagating waves are reported in the bathoferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction dispersed in water-in-oil Aerosol OT microemulsion. Jumping waves (JWs) are typically observed at or above room temperature and develop from the familiar trigger waves. Bubble waves (BWs) typically emerge from trigger or JWs at similar temperatures, while rotating waves (RWs) evolve from JW at higher temperatures (>40 degrees C). All these waves propagate discontinuously in a saltatory fashion. Other characteristic features include a discontinuous front for BW consisting of small concentric waves (bubbles) and lateral rotation of annular RWs. All three types of waves, as well as segmented but continuously propagating waves, can coexist. A simple model that is able to describe both jumping and segmented waves is described.     

A viscosity self-oscillation of polymer solution induced by the Belousov-Zhabotinsky reaction under acid-free condition

We succeeded in measuring a viscosity self-oscillation induced by the Belousov-Zhabotinsky (BZ) reaction for a polymer solution on the constant temperature condition under acid-free condition. The polymer chain is consisted of N-isopropylacrylamide, ruthenium complex as a catalyst of the BZ reaction, and an acrylamide-2-methylpropanesulfonic acid (AMPS) as a pH and the solubility control site. The viscosity self-oscillation for the AMPS-containing polymer solution was attributed to the difference between viscosities for the polymer solution in the reduced and oxidized states. The effects of the polymer concentration and the temperature of the polymer solution on the viscosity self-oscillation were investigated. As a result, the viscosity self-oscillating behavior significantly depended on the polymer concentration and the temperature of the polymer solution. The period of the viscosity self-oscillation decreased with increasing temperature in accordance with the Arrenius equation.     

Contribution to the chemistry of the Belousov-Zhabotinsky reaction. Products of the Ferriin-Bromomalonic acid and the Ferriin-Malonic acid reactions

In the present mechanistic schemes of the ferroin-catalyzed oscillatory Belousov-Zhabotinsky (BZ) reaction the oxidation of the organic substrates (bromomalonic or malonic acid) by ferriin (the oxidized form of the catalyst) plays an important role. As the organic products of these reactions were not yet identified experimentally, they were studied here by an HPLC technique. It was found that the main organic oxidation product of bromomalonic acid is bromo-ethene-tricarboxylic acid (BrEETRA), the same compound that is formed when bromomalonic acid is oxidized by Ce4+ (another catalyst of the BZ reaction). Formation of BrEETRA is explained here by a new mechanism that is more realistic than the one suggested earlier. To find any oxidation product of malonic acid in the ferriin-malonic acid reaction was not successful, however. Neither ethane-tetracarboxylic acid (ETA) nor malonyl malonate (MAMA), the usual products of the Ce4+- malonic acid reaction, nor any other organic acid, not even CO2, was found as a product of the reaction. We propose that malonic acid is not oxidized in the ferriin-malonic acid reaction, and it plays only the role of a complex forming catalyst in a process where Fe3+ oxidizes mostly its phenantroline ligand.