Belousov-Zhabotinsky Reaction Research Articles

Intermittent regimes as a synchronization phenomenon in two sets of nonlinear chemical oscillators.

Systems of nonlinear chemical oscillators can exhibit a large diversity of non-trivial states depending on the parameters that characterize them. Among these, a synchronization phenomenon is of special interest due to its direct link with chemical and biological processes in nature. We carry out numerical experiments for two different sets of chemical oscillators with different properties and immersed in a Belousov-Zhabotinsky solution. We document the emergence of different states of synchronization that depend on the parameters characterizing the solution. We also show that, in the interface regions, this system generates a stable dynamics of intermittency between the different synchronization states where interesting phenomena, such as the "devil's staircase," emerge. In general, the added complexity introduced with the additional set of oscillators results in more complex non-trivial synchronization states.

Chaos Synchronization of Two Györgyi–Field Systems for the Belousov–Zhabotinsky Chemical Reaction

Chemical reactions with oscillating behavior can present a chaos state in specific conditions. In this study, we analyzed the dynamic of the chaotic Belousov–Zhabotinsky (BZ) reaction using the Györgyi–Field model in order to identify the conditions of the chaos behavior. We studied the behavior of the reaction under different parameters that included both a low and high flux of chemical species. We performed our analysis of the flow regime in the conditions of an open reaction system, as this provides information about the behavior of the reaction over time. The proposed method for determining the favorable conditions for obtaining the state of chaos is based on the time evolution of the intermediate species and phase portraits. The synchronization of two Györgyi–Field systems based on the adaptive feedback method of control is presented in this work. The transient time until synchronization depends on the initial conditions of the two systems and on the strength of the controllers. Among the areas of interest for possible applications of the control method described in this paper, we can include identification of the reaction parameters and the extension to the other chaotic systems.

Periodical propagation of torsion in polymer gels

Gel actuators have potential in soft robotics. Although gel actuators can realize various motions like contraction, expansion, and bending, most require external inputs such as batteries and circuits. Herein we propose a periodical torsional motion hydrogel driven by chemical energy from the Belousov-Zhabotinsky (BZ) reaction. Our BZ gel system exhibits autonomous motion without a battery. The elastic moduli of the redox states of the BZ gel are investigated using stress–strain analysis. An experimental system, which integrates the BZ gel and two PDMS (dimethylpolysiloxane) rotators, is designed to evaluate torsion angles. The experimental pre-twist angle dependence of the rotary motion is compared with a theoretical rotation model. The results agree qualitatively. This study should contribute to the development of soft actuators without external components.

Origin of the Second-Order Proton Catalysis of Ferriin Reduction in Belousov-Zhabotinsky Reactions: Density Functional Studies of Ferroin and Ferriin Aggregates with Outer Sphere Ligands Sulfate, Bisulfate, and Sulfuric Acid.

The detailed mechanisms of Belousov-Zhabotinsky oscillating reactions continue to present grand challenges, even after half a century of study. The origin of the pH dependence of the oscillation pattern had never been rigorously identified. In our recent kinetic study of one of the key Belousov-Zhabotinsky reactions, the iron-catalyzed bromate oxidation of malonic acid, compelling agreement between experiments and kinetic simulations was achieved only with the inclusion of second-order proton catalysis of the reduction of the [Fe(phen)3]3+ species. After exhausting all other avenues in search of an explanation of this proton catalysis, we considered the possibility that the parent iron-phenanthroline complexes could aggregate with neutral and anionic outer sphere ligands (OSLs) in the highly concentrated sulfuric acid solution, and we hypothesized that OSL protonation would increase the capacity of the aggregated complex to oxidize the organic fuel. We performed potential energy surface analyses at the SMD(APFD/6-311G*) level of complexes of the types [Fe(phen)3(SO42-)m(HSO4-)n(H2SO4)o](c-2m-n)+ for ferriin (c = 3) and ferroin (c = 2) aggregated with m sulfate, n bisulfate, and o sulfuric acid OSLs. We present structures of the OSL aggregates, develop a nomenclature for their description, and characterize their electronic structure. The structural chemistry provides the foundation to discuss the ferroin/ferriin redox couple with emphasis on the relationship between the vertical electron affinities of ferriin aggregates and their OSL protonation states. For proton catalysis to manifest itself, double-protonation paths that are slightly endergonic should be present, and proton affinities of aggregated OSLs allow the identification of such double-protonation chains. As a first test of our mechanistic proposal for the second-order proton catalysis of the Belousov-Zhabotinsky reaction, the results presented here provide compelling evidence in support of the importance of outer sphere ligation of the iron catalyst.

Rotational synchronization of pinned spiral waves.

Coupled rotors can spontaneously synchronize, giving rise to a plethora of intriguing dynamics. We present here a pair of spiral waves as two synchronizing rotors, coupled by diffusion. The spirals are pinned to unexcitable obstacles, which enables us to modify their frequencies and restrain their drift. In experiments with the Belousov-Zhabotinsky reaction, we show that two counterrotating spiral rotors, pinned to circular heterogeneities, can synchronize in frequency and phase. The nature of the phase synchronization varies depending on the difference in their characteristic frequencies. We observe in-phase and out-of-phase synchronization, lag synchronization, and phase resetting across the experiments. The time required for the two spirals to synchronize is found to depend upon the relative size of their pinning obstacles and the distance separating them. This distance can also modify the phase lag of the two rotors upon synchronization. Our experimental observations are reproduced and explained further on the basis of numerical simulations of an excitable reaction-diffusion model.

Synchronization of Belousov-Zhabotinsky oscillators with electrochemical coupling in a spontaneous process.

A passive electrochemical coupling approach is proposed to induce spontaneous synchronization between chemical oscillators. The coupling exploits the potential difference between a catalyst redox couple in the Belousov-Zhabotinsky (BZ) reaction, without external feedback, to induce surface reactions that impact the kinetics of the bulk system. The effect of coupling in BZ oscillators under batch condition is characterized using phase synchronization measures. Although the frequency of the oscillators decreases nonlinearly over time, by a factor of 2 or more within 100 cycles, the coupling is strong enough to maintain synchronization. In such a highly drifting system, the Gibbs-Shannon entropy of the cyclic phase difference distribution can be used to quantify the coupling effect. We extend the Oregonator BZ model to account for the drifting natural frequencies in batch condition and for electrochemical coupling, and numerical simulations of the effect of acid concentration on synchronization patterns are in agreement with the experiments. Because of the passive nature of coupling, the proposed coupling scheme can open avenues for designing pattern recognition and neuromorphic computation systems using chemical reactions in a spontaneous process.

Analysis and new simulations of fractional Noyes-Field model using Mittag-Leffler kernel

In this manuscript, the fractional-in-time NoyesField model for Belousov-Zhabotinsky reaction transport is considered with a novel numerical technique, which was used to approximate the Atangana-Baleanu (ABC) operator which models the subdiffusion partial derivative in time. The effect of the ABC operator is observed and captured more interesting physical behavior of some real-life phenomena. Applicability and suitability of the adopted method were carried out on some cases of nonlinear Belousov-Zhabotinsky sub-reaction-diffusion models, their dynamic behaviors with respect to fractional-order parameters were displayed in figures.

Spiral wave drift under optical feedback in cardiac tissue.

Spiral waves occur in various types of excitable media and their dynamics determine the spatial excitation patterns. An important type of spiral wave dynamics is drift, as it can control the position of a spiral wave or eliminate a spiral wave by forcing it to the boundary. In theoretical and experimental studies of the Belousov-Zhabotinsky reaction, it was shown that the most direct way to induce the controlled drift of spiral waves is by application of an external electric field. Mathematically such drift occurs due to the onset of additional gradient terms in the Laplacian operator describing excitable media. However, this approach does not work for cardiac excitable tissue, where an external electric field does not result in gradient terms. In this paper, we propose a method of how to induce a directed linear drift of spiral waves in cardiac tissue, which can be realized as an optical feedback control in tissue where photosensitive ion channels are expressed. We illustrate our method by using the FitzHugh-Nagumo model for cardiac tissue and the generic model of photosensitive ion channels. We show that our method works for continuous and discrete light sources and can effectively move spiral waves in cardiac tissue, or eliminate them by collisions with the boundary or with another spiral wave. We finally implement our method by using a biophysically motivated photosensitive ion channel model included to the Luo-Rudy model for cardiac cells and show that the proposed feedback control also induces directed linear drift of spiral waves in a wide range of light intensities.

Information Processing Using Networks of Chemical Oscillators.

I believe the computing potential of systems with chemical reactions has not yet been fully explored. The most common approach to chemical computing is based on implementation of logic gates. However, it does not seem practical because the lifetime of such gates is short, and communication between gates requires precise adjustment. The maximum computational efficiency of a chemical medium is achieved if the information is processed in parallel by different parts of it. In this paper, I review the idea of computing with coupled chemical oscillators and give arguments for the efficiency of such an approach. I discuss how to input information and how to read out the result of network computation. I describe the idea of top-down optimization of computing networks. As an example, I consider a small network of three coupled chemical oscillators designed to differentiate the white from the red points of the Japanese flag. My results are based on computer simulations with the standard two-variable Oregonator model of the oscillatory Belousov–Zhabotinsky reaction. An optimized network of three interacting oscillators can recognize the color of a randomly selected point with >98% accuracy. The presented ideas can be helpful for the experimental realization of fully functional chemical computing networks.

Periodic Motion in the Chaotic Phase of an Unstirred Ferroin-Catalyzed Belousov Zhabotinsky Reaction

The Belousov Zhabotinsky reaction, a self-organized oscillatory color-changing reaction, can show complex behavior when left unstirred in a cuvette environment. The most intriguing behavior is the transition from periodicity to chaos and back to periodicity as the system evolves in time. It was shown that this happens thanks due to the decoupling of reaction, diffusion and convection. We have recently discovered that, as the so-called chaotic transient takes place, periodic bulk motions in form of convective cells are created in the reaction solution. In this work we investigated this phenomenon experimentally by changing cuvette size and reaction volume, in order to allow different types of convection patterns to appear. So far, we have observed single and double convection cells in the system. There are indications that the convection patterns are connected to the duration of the chaotic phase. A simplified mathematical model confirms the form and dynamics of the observed convection cells and explains the connection between chemical chaos and hydrodynamical order.

Self-oscillating gels based on novel catalyst for the Belousov–Zhabotinsky reaction

We report on the synthesis of new Ru(bpy)2(phen) catalyst for the oscillatory Belousov–Zhabotinsky chemical reaction and on the preparation of novel Ru(bpy)2(phen)-based self-oscillating gels. The synthesized gels exhibit high-amplitude autonomous mechanical oscillations when the Belousov–Zhabotinsky reaction proceeds inside these gels

Coexistence of oscillatory and reduced states on a spherical field controlled by electrical potential.

The Belousov-Zhabotinsky (BZ) reaction was investigated to elucidate features of oscillations depending on the applied electrical potential, E. A cation-exchange resin bead loaded with the catalyst of the BZ reaction was placed on a platinum plate as a working electrode and then E was applied. We found that global oscillations (GO) and a reduced state coexisted on the bead at a negative value of E and that the source point of GO changed depending on E. The thickness of the reduced state was determined by a yellow colored region which corresponded to the distribution of Br2. The present studies suggest that the distribution of the inhibitor, Br-, which is produced from Br2, plays an important role in the existence of the reduced state and GO, and the source point of GO.

Drastic effects of an inert Pt wire on the redox behavior of the Belousov-Zhabotinsky reaction.

This research investigated responses of the Belousov-Zhabotinsky (BZ) reaction to the presence of a chemically inert Pt wire in solution. Experiments showed that connecting the Pt wire to a neutral ground caused a spontaneous drastic shift in the redox potential and might even induce complex behavior. Characterizations using an unstirred ferriin solution demonstrated the formation of a red colored propagating front at the grounded Pt wire, suggesting the reduction of ferriin to ferroin. Measurements with different combinations of electrodes in both stirred and reaction-diffusion media further confirmed the reduction of BZ metal catalysts at the Pt wire and the accompanying oxidation reaction at the reference electrode. The observed drastic change in redox potential and oscillation waveform can be understood based on the passive reduction reaction at the indicator electrode that is connected to the reference electrode through a potential meter. The obtained influence can be further manipulated by adding a resistor between the Pt wire and the neutral ground, making this convenient perturbation method attractive for the study of redox chemical reaction dynamics.

Electrochemical Preparation of Copper Nanoparticles in an Oscillatory Belousov–Zhabotinsky Medium

Electrochemical Preparation of Copper Nanoparticles in an Oscillatory Belousov–Zhabotinsky Medium

Belousov–Zhabotinsky reaction: an open-source approach

The time-dependent change in concentration of reactants in the oscillatory Belousov–Zhabotinsky reaction defined by non-linear ordinary coupled differential equations has been derived by applying normalized non-dimensional computational methods and presented graphically. The accurate normalisation procedure eschews complex mathematical steps; however, choosing the appropriate references to define the dimensionless variables necessitates a deep physical understanding of the problem. The dimensionless groups are then derived to provide the functional dependences of the unknowns of interest. Finally, to cross-check all the mentioned dependences, a computational simulation has been carried out using domain-specific to general-purpose programming languages. Although there are countless programming languages present to carry out computer simulations, a flexible, portable, and open-source language like python proves fruitful.

Interaction of multiple spiral rotors in a reaction-diffusion system.

Rotors of reaction and diffusion are phase singularities that give rise to spiral waves of chemical activity, which are very similar to spatiotemporal patterns observed across several excitable media. Here we carry out experiments with the Belousov-Zhabotinsky reaction system and numerical simulations based on a reaction-diffusion model to show the possible interactions of multiple spiral rotors. When the cores of two spirals come very close to each other, they could either repel, attract, or remain stationary, depending on their relative chirality, phase, and distance separating them. Multiple pairs of spiral waves, in proximity to each other, could alter the paths of the individual rotors. A spiral core will be influenced most by the rotor that is closest to it, depending on the nature of the corresponding spiral wave arm. We observed rotors lying within a limiting distance of each other attract and annihilate. Otherwise, they push each other away until they reach a critical distance, beyond which all interactions seem to cease. We have established a relationship of this critical distance to the properties of the spiral wave. We also observed spontaneous symmetry-breaking instability for a system of up to eight rotors. Our experiments with the Belousov-Zhabotinsky reaction have successfully demonstrated the validity of the numerical results. A thorough understanding of the dynamics of several spiral rotors within a small area could help us perceive the nature of such excitation waves in cardiac tissue and cell membranes.

Chemical Wave Computing from Labware to Electrical Systems

Unconventional and, specifically, wave computing has been repeatedly studied in laboratory based experiments by utilizing chemical systems like a thin film of Belousov–Zhabotinsky (BZ) reactions. Nonetheless, the principles demonstrated by this chemical computer were mimicked by mathematical models to enhance the understanding of these systems and enable a more detailed investigation of their capacity. As expected, the computerized counterparts of the laboratory based experiments are faster and less expensive. A further step of acceleration in wave-based computing is the development of electrical circuits that imitate the dynamics of chemical computers. A key component of the electrical circuits is the memristor which facilitates the non-linear behavior of the chemical systems. As part of this concept, the road-map of the inspiration from wave-based computing on chemical media towards the implementation of equivalent systems on oscillating memristive circuits was studied here. For illustration reasons, the most straightforward example was demonstrated, namely the approximation of Boolean gates.

Collaborative evolution of regional green innovation system under the influence of high-speed rail based on Belousov-Zhabotinsky reaction.

As a green transportation mode and carrying factors with high knowledge-intensive characteristics, high-speed rail (HSR) has contributed to the improvement of regional green innovation. However, the relationship between HSR and regional green innovation is still limited. Based on the Belousov-Zhabotinsky (B-Z) reaction model, this study establishes a three-dimensional logistic dynamic evolution model for factor flow, knowledge spillover and green innovation performance. Through linear stability analysis, the threshold conditions for the evolution of the regional green innovation system under the influence of HSR are explored, and the impact of HSR policy on the regional green innovation system under four different initial states is examined. The results reveal four major points: (1) Factor flow is the order parameter and shows a significant collaborative relationship with green innovation performance. (2) The opening of HSR can effectively promote the evolution of the regional green innovation system, and the powerful stimulus of HSR contributes to shortening its evolutionary cycle. (3) The initial state of the regional green innovation system plays a crucial role in the green innovation performance. (4) In the process of collaborative evolution of regional green innovation system, factor flow and knowledge spillover serve as the premise and foundation, respectively, to jointly promote green innovation performance enhancement. Findings not only provide references for decision-makers to implement green innovation strategy and boost the green innovation performance, but also extend the theoretical system of HSR effect and collaborative evolution.

Detection of Inhomogeneity After Mixing Solutions by Analyzing the Chemical Wave Pattern in the Belousov-Zhabotinsky Reaction

The correlation between BZ reaction and mixing state has been studied for decades, and the researchers are trying to apply it to chemical engineering. We observed a chemical wave pattern in the Belouzov-Zhabotinsky (BZ) reaction based on the inhomogeneity after mixing BZ and ferroin solutions with a mixing method named the rotation-and-stop method. A one-dimensional chemical wave appeared for large inhomogeneity in mixing. The frequency and wavenumber decreased with decreasing degree of inhomogeneity. In an almost perfectly mixed state, the wavenumber significantly reduced and approached the global oscillation. The degree of mixing could be efficiently determined by this reported method. Perfect mixing has never been realized in natural and biological systems. The results of this study can be applied to estimate the degree of mixing in a solution that is not being stirred after the mixing process.

Science, serendipity, coincidence, and the Oregonator at the University of Oregon, 1969–1974

This historical review of the development of the Oregonator model of the Belousov–Zhabotinsky reaction is based on a lecture Dick Field presented during IrvFest2015—Celebrating a founding father of chaos!, a meeting in commemoration of Irving R. Epstein’s 70th birthday. For Dick’s 80th birthday festschrift, we focus here on the five papers in the series named “Oscillations in chemical systems,” published in 1972 [Noyes et al., J. Am. Chem. Soc. 94, 1394–1395 (1972); Field et al., J. Am. Chem. Soc. 94, 8649–8664 (1972); Field and Noyes, Nature 237, 390–392 (1972)] and 1974 [Field and Noyes, J. Chem. Phys. 60, 1877–1884 (1974); Field and Noyes, J. Am. Chem. Soc. 96, 2001–2006 (1974)].