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.     

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.     

Spatial bistability in a pH autocatalytic system: from long to short range activation

The acid-auto-activated chlorite-tetrathionate reaction is studied in a one-side-fed spatial reactor. It was previously shown that in these conditions the unstirred reaction-diffusion system can generate oscillatory and excitable states even though under well-stirred nonequilibrium conditions only steady-state bistability is observed. Numerical simulations suggest that these temporal reaction-diffusion instabilities result from long-range activation by rapidly diffusing protons. We study here experimentally and numerically the effect of introducing into this reaction-diffusion system macromolecular carboxylate species that reduce the effective diffusivity of protons. Consistent with the original assumption, the introduction of such slow mobility proton-binding species quenches both oscillatory and excitability dynamics. Within the bistability domain the direction of the propagation of an interface between the two steady states depends on control parameter value. We elaborate on the fact that beyond a low critical concentration of macromolecular carboxylate species, the stability limit of the "thermodynamic" branch of spatial steady state does not depend on this concentration. Despite the relative simplicity of the kinetic model used in the numerical simulations, the results are in quasi-quantitative agreement with the experimental observations.     

Modeling chlorite-iodide reaction dynamics using a chlorine dioxide-iodide reaction mechanism

The mechanism of Lengyel, Li, Kustin, and Epstein (J. Am. Chem. Soc. 1996, 118, 3708) for the oscillatory chlorine dioxide-iodide reaction accurately models the reaction in closed and open systems. We investigated whether this mechanism minus the single reaction involving chlorine dioxide models the chlorite-iodide reaction equally well. It agrees qualitatively with clock reaction results. As for open system dynamics, the mechanism predicts the existence of two steady states and bistability in very nearly the same regions where these features are found experimentally in the pH range 2-4. A discrepancy in the range of bistability emerges as pH decreases, and it cannot be remedied by taking into account chlorous acid decomposition. That we were unable to locate an oscillatory region is of greater significance. Because the chlorite-iodide reaction is sensitive to mixing effects, we incorporated a two-parameter model of imperfect mixing but still found no oscillations at physically reasonable parameter values. These discrepancies strongly suggest that to obtain predictive utility for the chlorite-iodide reaction, revision of the chlorine dioxide-iodide mechanism is required.     

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.     

Excitability in chemical and biochemical pH-autocatalytic systems

Using two different kinds of pH systems--the papain catalyzed hydrolysis of N-benzoyl-L-arginine ethyl ester in a membrane reactor and the bromate-sulfite-ferrocyanide (BSF) reaction in the CSTR--we study the relation among excitability, oscillations and bistability, and the ability of the system to respond to external periodic perturbations. Excitable properties of dynamical systems are examined in terms of a threshold set which is used to characterise dynamics in the reactor subject to external periodic stimuli. A precise definition and a method of calculating the threshold set are formulated. Two kinds of excitability distinguished by either direct or indirect initiation of the activatory process are found in both pH systems. Periodic pulsed perturbations of the BSF system display a nontrivial dependence of an excitation number on the forcing period. We examined this system also in oscillatory mode by looking at the phase shifts caused by single-pulse perturbations and constructing the phase transition curves (PTCs).     

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.     

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.     

Intermittent Chaos in the Bray–Liebhafsky Oscillator. Dependence of Dynamic States on the Iodate Concentration

Chaotic dynamic states with intermittent oscillations were generated in a Bray–Liebhafsky (BL) oscillatory reaction in an isothermal open reactor i.e., in the continuously-fed well-stirred tank reactor (CSTR) when the inflow concentration of potassium iodate was the control parameter. They are found between periodic oscillations obtained when [KIO₃]₀ < 3.00 × 10^–2 M and stable steady states when [KIO₃]₀ > 4.10 × 10^–2 M. It was shown that the most chaotic states obtained experimentally somewhere in the middle of this region are in high correlation with results obtained by means of largest Lyapunov exponents and phenomenological analysis based on the quantitative characteristics of intermittent oscillations.     

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.     

The behaviour of Sal'nikov's reaction, P --> A --> B, in a spherical batch reactor with the diffusion of heat and matter

The behaviour of a simple chemical reaction, occurring with the release of heat in a closed batch reactor, is considered for the situation when matter and heat are transported only by diffusive processes; thus, the reacting fluid has negligible velocity, so that heat transfer is by thermal conduction. The reaction is Sal'nikov's, which consists of two, consecutive first-order steps, producing a product B, from a precursor P, via an active intermediate A, in P --> A --> B. The first of these steps is assumed to be thermoneutral, with zero activation energy, whilst the second is exothermic, with an appreciable activation energy. These features make Sal'nikov's reaction the simplest to display thermokinetic oscillations that characterise many, more complex schemes, e.g. cool flames in hydrocarbon combustion. This study involves identifying the regions of parameter space, in which these oscillations in the temperature and the concentration of the intermediate A occur, by means of numerical simulation. These regions are compared with previous analytical stability analyses in one-dimensional systems. It was found that oscillations occur over a much larger range of conditions in the case considered here, i.e. a reactor with spherical symmetry, than in the simple 1-D case, previously studied by Gray and Scott (P. Gray and S. K. Scott, Chemical Oscillations and Instabilities, Clarendon Press, Oxford, 1990, pp. 264-291). In addition, approximate analytical solutions for the temperature and concentration of A are presented for two limiting cases of non-oscillatory behaviour. These analytical solutions have been verified by comparison with full numerical solutions of the governing equations.     

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.     

A numerical study of spatial structure during oscillatory combustion in closed vessels in microgravity

The existence and spatial development of gas-phase, thermokinetic oscillations under the influence of mass and thermal diffusion have been investigated by numerical methods in a 1-dimensional system. The conditions correspond to those that would be experienced under microgravity. The interest arises because there have been recent experimental investigations of oscillatory reactions, involving cool flames during butane oxidation, as part of the NASA, KC135 microgravity flight programme. The Sal'nikov, thermokinetic scheme, which is a two-variable model representing an intermediate chemical species and reactant temperature (taking the form P-->A-->B), forms the basis of the present work. In this model, thermal feedback occurs through the exothermicity of the second step and the non-linearity is derived from its temperature dependence. There are no known chemical examples that satisfy Sal'nikov's formal structure but Griffiths and co-workers conceived an experimental analogue under terrestrial conditions whereby a gaseous reactant was allowed to flow from an external reservoir into a closed, heated reactor at a controlled rate via a capillary tube which fed the reactant to the centre of the vessel. The exothermic reaction that occurred in the vessel satisfied the necessary conditions for the second step and the inflow, with no temperature dependence, represented a physical analogue to the first step of the Sal'nikov scheme. Thermokinetic oscillations were observed and the range of conditions for their existences was investigated. One of the experimental systems was the exothermic reaction between hydrogen and chlorine. To represent the Sal'nikov conditions hydrogen was fed slowly into the reactor, which already contained chlorine. We have exploited this chemical system and its experimental implementation in the present paper to investigate the behaviour when no convection or bulk gas motion occurs and when heat and mass transport is driven solely by diffusion. We study the response of alternative numerical approaches to the way in which the first step of the scheme is simulated. In the first, the precursor (P) is supplied at the same rate simultaneously throughout the cells representing the reactor. This is close to the concept of the Sal'nikov model. In the second method, a fixed rate of supply is applied at the inner boundary of the axisymmetric, 1-dimensional system. This is analogous to the experimental procedure. The numerical results show how oscillatory states can be sustained as a result of heat and mass transport by diffusion. The temporal and spatial evolution of reaction in a range of circumstances is discussed.     

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.     

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。     

Oscillations in the concentration of fluoride ions induced by a pH oscillator

Sustained oscillations in the concentration of free fluoride ions can be generated when the BrO3--SO32--Mn(II) oscillator is coupled either to Al3+-F- complex formation or to the Ca2+-F- precipitation process in a flow reactor. By careful analysis of the relevant equilibria and optimization of the reactant concentrations, one can obtain [F-] oscillations of several orders of magnitude as measured with an ion-selective electrode. The BrO3--SO32--Mn(II)-Al(NO3)3-NaF system also exhibits bistability, that is, simultaneously stable steady states of high and low [F-].     

New Experimental and Mechanistic Investigation on the KSCN‐H2O2‐NaOH‐Cu(II)‐Catalyzed Oscillating System (Orbàn–Epstein Reaction): Inhibitory Effects by Diphenols

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

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.     

Overlapping resonances and Regge oscillations in the state-to-state integral cross sections of the F+H2 reaction

A Regge pole analysis is employed to explain the oscillatory patterns observed in numerical simulations of integral cross section for the F+H(2)(v=0,j=0)-->HF(v(')=2,j(')=0)+H reaction in the translational collision energy range 25-50 meV. In this range the integral cross section for the transition, affected by two overlapping resonances, shows nearly sinusoidal oscillations below 38 meV and a more structured oscillatory pattern at larger energies. The two types of oscillations are related to the two Regge trajectories which (pseudo) cross near the energy where the resonances are aligned. Simple estimates are given for the periods of the oscillations.