Spatial bistability and waves in a reaction with acid autocatalysis

The phenomenon of spatial bistability has recently been proposed for a comprehensive understanding of a number of chemical patterns observed in open spatial reactors consisting of thin films of gel diffusively fed from one side. We study experimentally and numerically this phenomenon in the tetrathionate-chlorite reaction characterized by an acid superautocatalysis. We focus on the similarities and differences with previous studies on the chlorine dioxide-iodide reaction. In addition, we show that this reaction, which is only bistable in a continuous stirred tank reactor, can exhibit oscillatory and traveling waves when diffusion comes into play. Our computations suggest that the nonstationary behaviour originates from differential diffusive transport.     

Turing patterns, spatial bistability, and front interactions in the [ClO2, I2, I-, CH2(COOH)2] reaction

Recent experiments by Szalai and De Kepper performed in open spatial reactors have shown that the rich variety of dynamic properties of the chlorine dioxide-iodide-chlorite-iodine-malonic acid family of reactions is far from being exhausted: stable inhomogeneous patterns due to front interactions and transient labyrinthine structures are now added to the spatial bistability and Turing patterns as possible spatial behavior. The two latter phenomena, already observed in the chlorine dioxide-iodide (CDI) and the chlorine dioxide-iodide-malonic acid (CDIMA) reactions, respectively, were kept as limiting cases in the new setup. In this paper, we numerically analyze an extension of the most detailed available model of the CDI system (Lengyel et al.) including a reaction between I2 and MA that comes from the presence of the latter into the flow. The resulting nine-variable model is simulated in one and two dimensions, taking into account the proper constraints of the boundary-fed system. The nonequilibrium phase diagram closely follows the results of the experiments of ref 1. In particular, the model reproduces observations on spatial bistability, stationary front interactions, and Turing patterns. In addition, it predicts a new region of spatial bistability.     

Multiple types of spatio-temporal oscillations induced by differential diffusion in the Landolt reaction

The acid autoactivated iodate-sulfite redox reaction (Landolt reaction) exhibits bistability but no oscillatory dynamics when operated in a continuous stirred tank reactor (CSTR). However, it has been previously found experimentally that this reaction can exhibit both spatial bistability and oscillations when carried out in a one side diffusely fed spatial reactor. The precise origin of the oscillatory instability remained mainly elusive. We unambiguously show, in numerical simulations based of a kinetic model recently proposed by Csek?et al., J. Phys. Chem., 2008, 112, 5954), that the observed oscillations are due to the faster diffusion of the proton relative to the other feed species (long range activation instability). Furthermore, our calculations account for the previous experimental observation of two different oscillatory modes. The first one is associated to localized front oscillations, as already reported in another reaction. The other one is a periodic switch between the two states of the spatial bistability and affects the system as a whole. This oscillatory mode was undocumented in the previous studies of long range activation instabilities. More complex dynamical behaviors that mix these two types of oscillations are also reported.     

Complex behavior in the formaldehyde-sulfite reaction

The formaldehyde-sulfite reaction is an example of an "acid-to-alkali" clock. It displays an induction period, during which the pH varies only slowly in time, followed by a reaction event, during which the pH increases rapidly by several units. When the reaction is performed in a closed (batch) reactor, the clock time is found to increase with a decrease in initial concentrations of formaldehyde and sulfite and an increase in the total initial concentration of S(IV). At long times, following the clock event, there is a slow decrease in pH. In an open (flow) reactor, bistability between a low-pH steady state (pH approximately 6-8) and a high-pH steady state (pH approximately 11) is observed. Additionally, we report the existence of sustained, small-amplitude oscillations in pH in this system. An extended kinetic mechanism reproduces the batch behavior but fails to account for the complex behavior observed in the flow reactor. Possible additional reaction steps are discussed.     

pH oscillations and bistability in the methylene glycol-sulfite-gluconolactone reaction

The Methylene Glycol-Sulfite-Gluconolactone (MGSG) reaction is the first example of an organic-based pH oscillator. This reaction is of particular interest as it displays large amplitude oscillations in hydroxide ion accompanied by small amplitude (10(-3) V) oscillations in potential, indicating that it is not driven by redox processes. We investigate the reaction in a batch (closed) and flow (open) reactor and examine the role of the aging of the gluconolactone stock solution. The system is found to display oscillations and bistability for a wide range of flow rates and initial compositions. The experimental results are reproduced in numerical simulations in an extended model of the reaction in which the decay of the stock solution is incorporated. Finally, we analyse the features of the reaction that make it a suitable basis for the development of novel pH oscillators.     

Study of dynamics of glucose-glucose oxidase-ferricyanide reaction

This work is focused on dynamics of the glucose-glucose oxidase-ferricyanide enzymatic reaction with or without sodium hydroxide in a continuous-flow stirred tank reactor (CSTR) and in a batch reactor. This reaction exhibits pH-variations having autocatalytic character and is reported to provide nonlinear dynamic behavior (bistability, excitability). The dynamical behavior of the reaction was examined within a wide range of inlet parameters. The main inlet parameters were the ratio of concentrations of sodium hydroxide and ferricyanide and the flow rate. In a batch reactor we observed an autocatalytic drop of pH from slightly basic to medium acidic values. In a CSTR our aim was to find bistability in the presence of sodium hydroxide. However, only a basic steady state was found. In order to reach an acidic steady state, we investigated the system in the absence of sodium hydroxide. Under these conditions the transition from the basic to the acidic steady state was observed when inlet glucose concentration was increased.     

维生素C氧化反应的研究——用氧气氧化的动力学

维生索C(抗坏血酸, H_2A)的氧化反应是与生理过程密切相关的反应。在Cu~(++)催化下用氧气氧化H_2A的动力学研究已有不少报导。早期的研究所得“反应速率常数”往往与浓度有关, 不是真正的常数。从六十年代末又有一些作者对此反应进行了动力学研究, 得到不同形式的反应速率方程, 这些研究大多是在较低pH值下进行的(一般实验条件pH值低于6,大多数低于4)。Russell虽在pH值为4.2—11.9的范围内研究了这一反应, 但只报导了在pH值为6—8区间内反应速率有极大值, 而没有提供相应的反应速率方程。Young等人提出在pH值为6—8范围内此反应可能出现化学振荡现象, 虽然指出这种振荡现象不容易完全重复, 但提供了比较容易出现振荡的条件。为了进一步探讨在此pH值范围内此反应的动力学行为, 我们对此反应进行了较深入的研究。我们在pH值为6.0—7.5范围内研究了该反应非振荡条件下的动力学行为, 得到相应的反应速率方程r=(K_1[Cu~(++)]~1/2[H_2A])/√——(1+K_2[H_2A]) (1)其中[Cu~(++)]在反应过程中视为不变的常数, K_1、K_2与pH值和温度有关。同时我们也提了相应的反应机理。(1) 式与文献所报导的反应速率方程有很大不同。     

非缓冲介质中硫脲氧化的非线性动力学

研究了在非缓冲介质中高碘酸盐氧化硫脲的复杂反应动力学。实验结果表明：高碘酸盐氧化硫脲的非线性反应不但呈现多种不同的化学计量方程式,而且体系的pH、[I-]、[I2]及Pt电极电位呈现封闭条件下的准振荡和单峰振荡以及开放条件下的双稳态和衰减振荡行为。综合考虑硫价态与碘价态变化的各自非线性过程及相互耦合,提出了包含质子快速预平衡反应、碘化合物自身反应、碘化合物-硫化合物反应以及硫－硫反应的12步反应机理,模拟出了封闭体系中pH、[I-]以及[I2]的准振荡和单峰振荡以及开放体系中的双稳态行为。     

Oscillatory Dynamics of CO Oxidation on Platinum-Group Metal Catalysts

Rate oscillations are theoretically studied for the CO + O₂ reaction proceeding according to a modified Langmuir-Hinshelwood mechanism on a platinum-group metal catalyst. A new hierarchical system of consistent mathematical models is suggested for the identification of oscillatory regimes in the stochastic model. This system includes the stochastic model based on the Monte Carlo method and a point deterministic model in the medium field approximation. Three fundamentally different types of oscillatory behavior of the stochastic model are revealed and studied. These are kinetic oscillations corresponding to autooscillations of the point model, fluctuation-induced oscillations occurring in an excitable medium in the region of the unique stable stationary solution of the point model, and fluctuation-induced random phase transitions between stable stationary solutions of the point model in the bistability region. The effect of internal fluctuations (which are inherent in stochastic models) on the oscillatory dynamics of the reaction is studied.__________Translated from Kinetika i Kataliz, Vol. 46, No. 4, 2005, pp. 485–496.Original Russian Text Copyright © 2005 by Kurkina, Semendyaeva.     

Chlorine Dioxide–Iodine–Sodium Thiosulfate Oscillating Reaction Investigated by the UV–Vis Spectrophotometric Method

A new chlorine dioxide–iodine–sodium thiosulfate chemical oscillatory reaction was studied by the UV–Vis spectrophotometric method. The initial concentrations of sodium thiosulfate, chlorine dioxide, iodine, sulfuric acid, and pH have great influences on the oscillations observed at wavelength 238 nm. The oscillations occur as long as the reactants are mixed. The amplitude and the number of oscillations are associated with the initial concentrations of reactants. The equations for the triiodide ion reaction rate changes with reaction time and the initial concentrations in the oscillation stage are an attenuation sine function. Based upon the experimental data in this work and in the literature, a plausible reaction mechanism was proposed for the oscillation reaction.     

The reaction of chlorine water with carbohydrates

Summary On the basis of data from a study of the reaction of chlorine water with carbohydrates and cellulose at various pH values, the conclusion was reached that, in an acid medium, part of the pyrane rings in the cellulose molecule are in the open form.     

Spatiotemporal dynamics of the Landolt reaction in an open spatial reactor with conical geometry

In a previous study, the iodate-sulfite proton autoactivated reaction (Landolt reaction) was shown to exhibit spatial bistability and spatiotemporal oscillations when operated in an open spatial reactor with fixed "thickness", i.e., feed boundary to core distance. Here, we show that the spatial reactors with conical geometry enable one to rapidly probe the sensitivity of the above phenomena over a large range of the "thickness" parameter. This often-neglected parameter in chemical pattern studies plays an important role on the selection and stability of states. We reveal that the quenching capacity of slow diffusing polyacrylate ions on the spatiotemporal oscillations depends on this "thickness". The presented results should be useful for further research on reaction diffusion patterns and chemomechanical structures.     

A novel route to pH oscillators

The formaldehyde–sulfite reaction is an acid to alkali clock reaction in batch, which displays complex behaviour in a flow reactor. Current published mechanisms do not account for the behaviour in an open system. In this Letter, we construct a minimal model based on this system and demonstrate that a base-catalysed rate-determining step coupled with an appropriate OH⁻ consuming reaction can result in bistability and oscillations. The model may provide a method for the design of organic-based pH oscillators.     

Kinetics and mechanism of the chlorine dioxide-trithionate reaction

The trithionate-chlorine dioxide reaction has been studied spectrophotometrically in a slightly acidic medium at 25.0 ± 0.1 °C in acetate/acetic acid buffer monitoring the decay of chlorine dioxide at constant ionic strength (I = 0.5 M) adjusted by sodium perchlorate. We found that under our experimental conditions two limiting stoichiometries exist and the pH, the concentration of the reactants, and even the concentration of chloride ion affects the actual stoichiometry of the reaction that can be augmented by an appropriate linear combination of these limiting processes. It is also shown that although the formal kinetic order of trithionate is strictly one that of chlorine dioxide varies between 1 and 2, depending on the actual chlorine dioxide excess and the pH. Moreover, the otherwise sluggish chloride ion, which is also a product of the reaction, slightly accelerates the initial rate of chlorine dioxide consumption and may therefore act as an autocatalyst. In addition to that, overshoot-undershoot behavior is also observed in the [(·)ClO(2)]-time curves in the presence of chloride ion at chlorine dioxide excess. On the basis of the experiments, a 13-step kinetic model with 6 fitted kinetic parameter is proposed by nonlinear parameter estimation.     

Three autocatalysts and self-inhibition in a single reaction: a detailed mechanism of the chlorite-tetrathionate reaction

The chlorite-tetrathionate reaction has been studied spectrophotometrically in the pH range of 4.65-5.35 at T = 25.0 +/- 0.2 degrees C with an ionic strength of 0.5 M, adjusted with sodium acetate as a buffer component. The reaction is unique in that it demonstrates autocatalysis with respect to the hydrogen and chloride ion products and the key intermediate, HOCl. The thermodynamically most-favorable stoichiometry, 2S(4)O(6)2- + 7ClO2- + 6H2O --> 8SO(4)2- + 7Cl- + 12H+, is not found. Under our experimental conditions, chlorine dioxide, the chlorate ion, or both are detected in appreciable amounts among the products. Initial rate studies reveal that the formation of chlorine dioxide varies in an unusual way, with the chlorite ion acting as a self-inhibitor. The reaction is supercatalytic (i.e., second order with respect to autocatalyst H+). The autocatalytic behavior with respect to Cl- comes from chloride catalysis of the chlorite-hypochlorous acid and hypochlorous acid-tetrathionate subsystems. A detailed kinetic study and a model that explains this unusual kinetic behavior are presented.     

Oscillatory dynamics protect enzymes and possibly cells against toxic substances

We have used the oscillating peroxidase-oxidase (PO) reaction as a model system to study how oscillatory dynamics may affect the influence of toxic reaction intermediates on enzyme stability. In the peroxidase-oxidase reaction reactive intermediates, such as hydrogen peroxide, superoxide, and hydroxyl radical are formed. Such intermediates inactivate many cellular macromolecules such as proteins and nucleic acids. These reaction intermediates also react with peroxidase itself to form an inactive enzyme. The fact that the PO reaction shows bistability between an oscillatory and a steady state gives us a unique possibility to compare such inactivation when the system is in one of these two states. We show that inactivation of peroxidase is slower when the system is in an oscillatory state, and using numerical simulations we provide evidence that oscillatory dynamics lower the average concentration of the reactive intermediates.     

Chlorine Dioxide–Iodide–Methyl Acetoacetate Oscillation Reaction Investigated by UV–Vis and an Online FTIR Spectrophotometric Method

In order to study the chemical oscillatory behavior and mechanism of a new chlorine dioxide–iodide ion–methyl acetoacetate reaction system, a series of experiments were done by using UV–vis and an online FTIR spectrophotometric method. The initial concentrations of methyl acetoacetate, chlorine dioxide, potassium iodide, sulfuric acid, and the pH have great influences on the oscillations observed at the wavelength 350 nm. There is a pre-oscillatory or induction period, and the amplitude and number of oscillations are dependent on the initial concentration of the reactants. Equations were obtained for the variation of the triiodide ion reaction rate with the reaction time and the initial concentrations in the oscillation stage. The oscillation reaction was accelerated by increasing the temperature. The apparent activation energies for the induction period and the oscillation period are 55.65 and 33.00 kJ·mol^?1, respectively. The intermediates were detected by the online FTIR analysis. Based upon the experimental data in this work and in the literature, a plausible reaction mechanism is proposed for the oscillation reaction.     

Designing an enzymatic oscillator: bistability and feedback controlled oscillations with glucose oxidase in a continuous flow stirred tank reactor

The reaction of glucose with ferricyanide catalyzed by glucose oxidase from Aspergillus niger gives rise to a wide range of bistability as the flow rate is varied in a continuous flow stirred tank reactor. Oscillations in pH can be obtained by introducing a negative feedback on the autocatalytic production of H+ that drives the bistability. In our experiments, this feedback consists of an inflow of hydroxide ion at a rate that depends on [H+] in the reactor as k0[OH-]0[H+]/(K+[H+]). pH oscillations are found over a broad range of enzyme and ferricyanide concentrations, residence times (k0 (-1)), and feedback parameters. A simple mathematical model quantitatively accounts for the experimentally found oscillations.     

Chlorine Dioxide–Iodine–Ethyl 2-Chloroacetoacetate Oscillation Reaction Investigated by UV–Vis and Online FTIR Spectrophotometric Methods

In order to study the chemical oscillatory behavior and mechanism of a new chlorine dioxide–iodine–ethyl 2-chloroacetoacetate reaction system, a series of experiments were carried out by using UV–Vis and online FTIR spectrophotometric methods. The initial concentrations of ethyl 2-chloroacetoacetate, chlorine dioxide, iodine, sulfuric acid, and the pH value have great influence on the oscillations observed at wavelength of 585 nm for the starch–triiodide complex ( \( \text{QI}_{3}^{ - } \) ). There is a pre-oscillatory or induction stage, the amplitude and the number of oscillations are associated with the initial concentration of reactants. Equations were obtained for the starch–triiodide complex reaction rate change with reaction time and the initial concentrations in the oscillation stage. The intermediates were detected by the online FTIR analysis. Based upon the experimental data in this work and in the literature, a plausible reaction mechanism was proposed for the oscillation reaction.     

Stirring-controlled bifurcations in the 1,4-cyclohexanedione-bromate reaction

We report the experimental observation that stirring in a closed 1,4-cyclohexanedione-bromate reaction can induce transitions not only between oscillatory and nonoscillatory states but also between simple and period-doubled oscillations. Notably, the transition from simple to complex oscillations occurs as a result of increasing stirring rate. When illumination was employed to characterize the importance of microfluctuations of concentrations, the threshold stirring rate for inducing a bifurcation was found to increase proportionally to the intensity of the applied light. Numerical simulations with an existing model illustrate that the experimental phenomena could be qualitatively reproduced by considering effects of mixing on diffusion-limited radical reactions, namely, the disproportion reaction of hydroquinone radicals.