Quantitative investigation of spatiotemporal chaos in the ferroin-catalyzed Belousov-Zhabotinskii reaction in a batch reactor

We have analyzed experimental data on the time dependence of the potentials of 16 platinum point-contact electrodes for spatiotemporal chaos in the Belousov-Zhabotinskii reaction. We show that the largest Lyapunov exponent is a convenient characteristic for spatiotemporal chaos. We found that in going from temporal to spatiotemporal chaos, the embedding dimension of the system increases by a factor of three. We have observed that as the largest Lyapunov exponent increases, we observe a decrease in the degree of spatial correlation of the process.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 31, No. 1, pp. 34–39, January–February, 1995.We would like to thank the Foundation for Basic Research of the State Science and Technology Committee of Ukraine for financial support of this work (Project 3.3/87).     

Chemical chaos in novel iodate-driven oscillator-thiophenol-iodate-H2SO4 system

Chaotic oscillations in redox potential have been observed in thiophenol-KIO₃-H₂SO₄ system in batch reactors. These occur in a concentration and temperature range. Bifurcation from a stable regime to a chaotic regime occurs in a straight way in the entire concentration and temperature range. Oscillations were also studied in continuously stirred tank reactors. These oscillations are deterministic chaos. It is tentatively suggested that chaos in the system is due to a time delay caused by a large number of intermediates.     

Spatiotemporal chaos arising from standing waves in a reaction-diffusion system with cross-diffusion

We show that quasi-standing wave patterns appear in the two-variable Oregonator model of the Belousov-Zhabotinsky reaction when a cross-diffusion term is added, no wave instability is required in this case. These standing waves have a frequency that is half the frequency of bulk oscillations displayed in the absence of diffusive coupling. The standing wave patterns show a dependence on the systems size. Regular standing waves can be observed for small systems, when the system size is an integer multiple of half the wavelength. For intermediate sizes, irregular patterns are observed. For large sizes, the system shows an irregular state of spatiotemporal chaos, where standing waves drift, merge, and split, and also phase slips may occur.     

Complex and chaotic oscillations in a model for the catalytic hydrogen peroxide decomposition under open reactor conditions

Numerous periodic and aperiodic dynamic states obtained in a model for hydrogen peroxide decomposition in the presence of iodate and hydrogen ions (the Bray-Liebhafsky reaction) realized in an open reactor (CSTR), where the flow rate was the control parameter, have been investigated numerically. Between two Hopf bifurcation points, different simple and complex oscillations and different routes to chaos were observed. In the region of the mixed-mode evolution of the system, the transitions between two successive mixed-mode simple states are realized by period-doubling of the initial state leading to a chaotic window in which the next dynamic state emerges mixed with the initial one. It appears in increasing proportions in concatenated patterns until total domination. Thus, with increasing flow rate the period-doubling route to chaos was obtained, whereas with decreasing flow rate the peak-adding route to chaos was obtained. Moreover, in very narrow regions of flow rates, chaotic mixtures of mixed-mode patterns were observed. This evolution of patterns repeats until the end of the mixed-mode region at high flow rates that corresponds to chaotic mixtures of one large and many small amplitude oscillations. Starting from the reverse Hopf bifurcation point and decreasing the flow rate, simple small amplitude sinusoidal oscillations were encountered and then the period-doubling route to chaos. With a further decreasing flow rate, the mixed-mode oscillations emerge inside the chaotic window.     

Structures of chaos in open reaction systems

By numerically simulating the Bray-Liebhafsky (BL) reaction (the hydrogen peroxide decomposition in the presence of hydrogen and iodate ions) in a continuously fed well stirred tank reactor (CSTR), we find "structured" types of chaos emerging in regular order with respect to flow rate as the control parameter. These chaotic "structures" appear between each two successive periodic states, and have forms and evolution resembling to the neighboring periodic dynamics. More precisely, in the transition from period-doubling route to chaos to the arising periodic mixture of different mixed-mode oscillations, we are able to recognize and qualitatively and quantitatively distinguish the sequence of "period-doubling" chaos and chaos consisted of mixed-mode oscillations (the "mixed-mode structured" chaos), both appearing in regular order between succeeding periodic states. Additionally, between these types of chaos, the chaos without such recognizable "structures" ("unstructured" chaos) is also distinguished. Furthermore, all transitions between two successive periodic states are realized through bifurcation of chaotic states. This scenario is a universal feature throughout the whole mixed-mode region, as well as throughout other mixed-mode regions obtained under different initial conditions.     

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.     

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.     

Analysis of complex oscillatory dynamics of a pH oscillator

Reaction systems that display pronounced periodic and aperiodic variations in the pH value of the reaction medium are known as pH oscillators. A member of this family of reactions studied here, the Cu(II)-catalyzed oxidation of thiosulfate by hydrogen peroxide in acidic solution, is known to display a rich variety of oscillatory dynamics. We focus on experimental time series showing complex aperiodic dynamics that simultaneously possesses the characteristics of period-doubled large-amplitude oscillations and irregular small-amplitude oscillations reminiscent of mixed-mode dynamics. An analysis based on the reconstruction of the attractor from the measured time series by two different methods and subsequent calculation of the maximal Lyapunov exponent reveals that this interesting dynamical regime is a manifestation of deterministic chaos. The text was submitted by the authors in English.     

Quantum effects in energy and charge transfer in an artificial photosynthetic complex

We investigate the quantum dynamics of energy and charge transfer in a wheel-shaped artificial photosynthetic antenna-reaction center complex. This complex consists of six light-harvesting chromophores and an electron-acceptor fullerene. To describe quantum effects on a femtosecond time scale, we derive the set of exact non-Markovian equations for the Heisenberg operators of this photosynthetic complex in contact with a Gaussian heat bath. With these equations we can analyze the regime of strong system-bath interactions, where reorganization energies are of the order of the intersite exciton couplings. We show that the energy of the initially excited antenna chromophores is efficiently funneled to the porphyrin-fullerene reaction center, where a charge-separated state is set up in a few picoseconds, with a quantum yield of the order of 95%. In the single-exciton regime, with one antenna chromophore being initially excited, we observe quantum beatings of energy between two resonant antenna chromophores with a decoherence time of ～100 fs. We also analyze the double-exciton regime, when two porphyrin molecules involved in the reaction center are initially excited. In this regime we obtain pronounced quantum oscillations of the charge on the fullerene molecule with a decoherence time of about 20 fs (at liquid nitrogen temperatures). These results show a way to directly detect quantum effects in artificial photosynthetic systems.     

硫脲氧化反应动力学研究进展

本文综述了硫脲氧化反应动力学的研究进展,根据氧化剂和氧化方式不同,将硫脲氧化体系分成含卤氧化体系和非卤氧化体系两大类,其中含卤氧化体系包括亚氯酸、碘酸、溴酸、卤素单质氧化硫脲的反应体系;非卤氧化体系包括双氧水、自由基、电化学和金属酸盐氧化硫脲的反应体系。总结了不同反应体系的动力学现象和反应机理研究状况,文中还介绍了在硫脲氧化反应动力学研究中光电磁及色谱方法的发展状况,提出硫脲氧化反应动力学机理研究突破可能途径。     

Spatially Distributed Current Oscillations with Electrochemical Reactions in Microfluidic Flow Cells

The formation of spatiotemporal patterns is investigated by using a chemical reaction on the surface of a high‐aspect‐ratio metal electrode positioned in a flow channel. A partial differential equation model is formulated for nickel dissolution in sulfuric acid in a microfluidic flow channel. The model simulations predict oscillatory patterns that are spatially distributed on the electrode surface; the downstream portion of the metal surface exhibits large‐amplitude, nonlinear oscillations of dissolution rates, whereas the upstream portion displays small‐amplitude, harmonic oscillations with a phase delay. The features of the dynamical response can be interpreted by the dependence of local dynamics on the widely varying surface conditions and the presence of strong coupling. The patterns can be observed for both contiguous and segmented metal surfaces. The existence of spatially distributed current oscillations is confirmed in experiments with Ni electrodissolution in a microfluidic device. The results show the impact of a widely heterogeneous environment on the types of patterns of chemical reaction rates.     

Experimental study of the molecular reorientation induced by the ordinary wave in a nematic liquid crystal film

When an s-polarized laser beam impinges on a homeotropically aligned film of nematic liquid crystal at small incident angle, undamped oscillations of the molecular director may be produced. At high beam intensities the oscillations break up into deterministic chaos. Although this effect has been known for a long time and the route to chaos has been qualitatively analysed, no detailed study of the actual molecular director motion has been carried out. We have designed an experimental apparatus to monitor the dynamics of the molecular director, as described by its two polar angles. We observed different dynamical regimes, depending on the laser intensity: steady states, ocillations, rotation and, at the highest laser intensities, deterministic chaos. Moreover, the transitions between the oscillation and rotation regimes are characterized by intermittency.     

Period Doubling and Chaos of Spontaneous Oscillatory Phenomena on Iron

 A new self-oscillating system introducing spontaneous oscillatory phenomena on iron in a sulfuric acid solution of hydrogen peroxide is discussed. This phenomenon can be explained by a continuous oscillation between the active and passive state of iron. Unlike other published systems that only show one-peak oscillations, the potential of iron shows highly complex dynamics: depending on the concentration of hydrogen peroxide and sulfuric acid, a period doubling and non-periodic oscillations in a self-oscillating system were observed for the first time. The reactions were analyzed by methods based on chaos theory and could finally be identified as an example of deterministic chaos.     

The Gray-Scott model under the influence of noise: reentrant spatiotemporal intermittency in a reaction-diffusion system

We investigate the influence of noise on the spatiotemporal behavior of the Gray-Scott model, a prototype for a simple reaction-diffusion system. In the parameter regime studied it is characterized deterministically by a stable fixed point. As the noise increases a regular periodic pattern is replaced first by an irregularly oscillating periodic pattern and then by spatiotemporal intermittency. With further increasing noise strength the spatiotemporal intermittency is first replaced by a low amplitude noisy regime followed by spatiotemporal intermittency (STI) embedded into a noisy background. At sufficiently high noise intensity high amplitude noise prevails. We point out that the transition from spatiotemporal intermittency to low amplitude noise can be traced back to the fact that the spatially homogeneous state is a global attractor. As the noise strength grows further the "noisy" fixed point starts to communicate with STI leading to noise-induced spatiotemporal intermittency as an excitable state. At high enough noise strength high amplitude noise is left over wiping out all details of the underlying deterministic dynamical system.     

Catalytic spatiotemporal thermal patterns during CO oxidation on cylindrical surfaces: experiments and simulations

Dynamics of spatiotemporal thermal patterns during the catalytic CO oxidation over Pd supported on a glass-fiber catalytic cloth rolled into a tube of 20 mm diameter and 80 mm length has been studied in a continuous flow reactor by IR thermography. A specially designed aluminum mirror built in the reactor provided image of the entire surface of the horizontally held catalytic tube. With flow in the main axial direction and through the tube surface, we observed periodic motions of a pulse, which was born downstream and propagated upstream. The temperature pulse motion was accompanied by conversion oscillations of CO2. With flow in the main axial direction, parallel to the surface, we observed a stationary hot zone after an oscillatory transient. These patterns can be simulated with a plug-flow-reactor-like heterogeneous reactor model that incorporates previously determined kinetic and transport parameters.     

Period Doubling and Chaos of Spontaneous Oscillatory Phenomena on Iron

Summary.  A new self-oscillating system introducing spontaneous oscillatory phenomena on iron in a sulfuric acid solution of hydrogen peroxide is discussed. This phenomenon can be explained by a continuous oscillation between the active and passive state of iron. Unlike other published systems that only show one-peak oscillations, the potential of iron shows highly complex dynamics: depending on the concentration of hydrogen peroxide and sulfuric acid, a period doubling and non-periodic oscillations in a self-oscillating system were observed for the first time. The reactions were analyzed by methods based on chaos theory and could finally be identified as an example of deterministic chaos. Received April 24, 2001. Accepted May 7, 2001     

亚氯酸盐-硫代硫酸盐非缓冲体系的动力学

研究了亚氯酸盐-硫代硫酸盐反应体系在非缓冲条件下的复杂动力学行为.结果发现,在开放体系中反应的pH值和Pt电位存在准周期振荡分叉和混合模式振荡分叉通向混沌的过程，且pH峰与Pt电位峰反相位.当与起始浓度比相对较小时，随着流速的逐渐升高，体系的pH值和Pt电位从简单的小振幅振荡(S)经过准周期振荡分叉到混沌，最后回到简单大振幅振荡(L)；而当与起始浓度比相对较高时，随着流速的降低，体系的pH值和Pt电位出现LS1、LS2、LS3…LSn的混合模式振荡,并在每对(LSn、LSn＋1)振荡区间发现了LSn、LSn＋1随机出现的非周期振荡行为.运用硫价态变化的一般动力学模型，模拟出了反应体系的混合模式振荡及非周期振荡.     

Nonlinear viscoelasticity and shear localization at complex fluid interfaces

Foams and emulsions are often exposed to strong external fields, resulting in large interface deformations far beyond the linear viscoelastic regime. Here, we investigate the nonlinear and transient interfacial rheology of adsorption layers in large-amplitude oscillatory shear flow. As a prototypical material forming soft-solid-type interfacial adsorption layers, we use Acacia gum (i.e., gum arabic), a protein/polysaccharide hybrid. We quantify its nonlinear flow properties at the oil/water interface using a biconical disk interfacial rheometer and analyze the nonlinear stress response under forced strain oscillations. From the resulting Lissajous curves, we access quantitative measures recently introduced for nonlinear viscoelasticity, including the intracycle moduli for both the maximum and zero strains and the degree of plastic energy dissipation upon interfacial yielding. We demonstrate using in situ flow visualization that the onset of nonlinear viscoelasticity coincides with shear localization at the interface. Finally, we address the nonperiodic character of this flow transition using an experimental procedure based on opposing stress pulses, allowing us to extract additional interfacial properties such as the critical interfacial stress upon yielding and the permanent deformation.     

Temperature-induced route to chaos in the H2O2-HSO3(-)-S2O3(2-) flow reaction system

Low-frequency, high-amplitude pH-oscillations observed experimentally in the H2O2-HSO3(-)-S2O3(-) flow reaction system at 21.0 degrees C undergo period-doubling cascades to chemical chaos upon decreasing the temperature to 19.0 degrees C in small steps. Period-4 oscillations are observed at 20.0 degrees C and can be calculated on the basis of a simple model. A reverse transition from chaos to high-frequency limit cycle oscillations is also observable in the reaction system upon decreasing further the temperature step by step to 15.0 degrees C. Period-2 oscillations are measured at 18.0 degrees C. Such a temperature-change-induced transition between periodic and chaotic oscillatory states can be understood by taking into account the different effects of temperature on the rates of composite reactions in the oscillatory system. Small differences in the activation energies of the composite reactions are responsible for the observed transitions. Temperature-change-induced period doubling is suggested as a simple tool for determining whether an experimentally observed random behavior in chemical systems is of deterministic origin or due to experimental noise.