Belousov-Zhabotinsky Chemical Reaction Research Articles

On phase correspondence between chemical oscillations in liquid Belousov-Zhabotinsky mixture filling catalyst-containing matrix and resulted gel's chemomechanical oscillations

We investigated phases and phase differences between coupled mechanical and chemical self-oscillations running in two kinds of newly synthesised chemomechanical gels. Processing of experimental data was model-free and it was based on spectral and wavelet approaches of the theory of dynamical systems. It was applied to samples of different sizes and compositions (Ru- and Fe-based gels). It was revealed that the Ru-based gels demonstrate a faster mechanical response to the redox changes of the Ru-moiety coupled to the Belousov-Zhabotinsky chemical reaction than the Fe-based gels. This demonstrated a significant phase difference between the redox changes of the Fe-moiety and the mechanical oscillations. Special attention was paid to the phase-coupling features for averaged higher harmonics, which are significant due to the high degree of nonlinearity of the chemomechanical oscillatory process.

Empirically developed model of the stirring-controlled Belousov–Zhabotinsky reaction

The Belousov–Zhabotinsky chemical reaction is famous for its oscillatory behavior occurring due to inherent physicochemical processes. Oscillations of the Belousov–Zhabotinsky reaction may be periodic or chaotic, depending on parameters, and these dynamics can be controlled by external impacts such as stirring. The complex behavior, the variability of the oscillatory modes, and controllability make the Belousov–Zhabotinsky reaction an important research subject in many fields of science, including various applications such as chemical computing or smart materials. One of the key limitations for the practical application of this oscillatory reaction is the absence of its exact mathematical model which can reproduce dynamics close to the real chemical process. This work aims to fill this gap by designing a novel model of the Belousov–Zhabotinsky reaction based on experimental data. To solve this task, we designed a complex experimental setup based on a photometric station with controllable stirring mechanisms. We performed two experiments in batch reactors (cuvettes). In the first experiment, we investigated how constant stirring with different rates affects the reaction behavior, and in the second experiment, we periodically stirred the reaction and observed its response. As a result, we found that chemical oscillations in the Belousov–Zhabotinsky reaction are in both cases chaotic, their amplitude depends on stirring more than their period does, and they are highly non-stationary: in the course of the reaction, their sensitivity to stirring decreases, so the oscillations remain controllable only during the first hour. Using a novel two-stage differential equation reconstruction approach, we managed to develop a complex of local dynamical models for the stirring-controlled BZ reaction with good correspondence to the empirical data. The presented models are more consistent with experimentally observed Belousov–Zhabotinsky dynamics than earlier models. The developed model can be used in various applications and extended to a wide class of controlled oscillatory reactions.

Pressure and Light Multi-Physics Fields Comodulate the Multi-Length Scales of Chemical Wave Propagation in Diffusion-Fed Gels

During plant growth, the combined effects of multi-physics fields such as light, temperature, and material concentration create a complex multi-length scales phenomenon. However, the mechanism of multi-physical field interactions on biological multi-length scales has not been thoroughly investigated. In this paper, an open diffusion-fed system is constructed by coupling gels with a Belousov-Zhabotinsky (BZ) chemical reaction system. The multi-length scales propagation of chemical waves in the gel system under the combined effect of multi-physical fields such as light (I) and pressure (ΔP) is investigated. It is found that when 85 Pa ≤ ΔP ≤ 100 Pa or 200 μW·cm-2 ≤ I ≤ 300 μW·cm-2, the complexity of the multi-length scales periodic structure of chemical waves shows a nonlinear change with increasing light intensity or pressure. Beyond this range, the complexity of the chemical wave multi-length scales periodic structure decreases linearly on enhancing the light intensity or increasing the pressure.

Reconstruction of three-dimensional scroll waves in excitable media from two-dimensional observations using deep neural networks.

Scroll wave dynamics are thought to underlie life-threatening ventricular fibrillation. However, direct observations of three-dimensional electrical scroll waves remain elusive, as there is no direct way to measure action potential wave patterns transmurally throughout the thick ventricular heart muscle. Here we study whether it is possible to reconstruct simulated scroll waves and scroll wave chaos using deep learning. We trained encoding-decoding convolutional neural networks to predict three-dimensional scroll wave dynamics inside bulk-shaped excitable media from two-dimensional observations of the wave dynamics on the bulk's surface. We tested whether observations from one or two opposing surfaces would be sufficient and whether transparency or measurements of surface deformations enhances the reconstruction. Further, we evaluated the approach's robustness against noise and tested the feasibility of predicting the bulk's thickness. We distinguished isotropic and anisotropic, as well as opaque and transparent, excitable media as models for cardiac tissue and the Belousov-Zhabotinsky chemical reaction, respectively. While we demonstrate that it is possible to reconstruct three-dimensional scroll wave dynamics, we also show that it is challenging to reconstruct complicated scroll wave chaos and that prediction outcomes depend on various factors such as transparency, anisotropy, and ultimately the thickness of the medium compared to the size of the scroll waves. In particular, we found that anisotropy provides crucial information for neural networks to decode depth, which facilitates the reconstructions. In the future, deep neural networks could be used to visualize intramural action potential wave patterns from epi- or endocardial measurements.

Temperature and Light Multiphysical Fields Modulate the Propagation of Chemical Waves on Multiple Length Scales in a System

Abstract The phenomenon of multiple length scales exists in plants during growth, which is influenced not only by light but also by other physical fields such as substance concentration and temperature, and the combined effects of various physical fields form a complex multi-scale phenomenon. However, the mechanism of the multi-physical interaction of temperature and light on the formation of multiple length scales in plants has not been investigated. In this paper, we coupled a gel with a Belousov-Zhabotinsky (BZ) chemical reaction system, constructed a one-dimensional open reaction diffusion system, and investigated the changes in the multiple length scale periodic structure of chemical waves in the one-dimensional gel system under the combined effect of multiple physical fields of light and temperature. It was found that when increasing the light intensity at T = 26 °C or decreasing the temperature at the light intensity I ≤ 50 µW·cm−2, the chemical wave multiple length scale period structure of the system changed as follows: P8 → P16 → P8 → P4 → P2 → P1, and the chemical wave period structure complexity showed a non-linear change of first increasing and then decreasing. When increasing the light intensity at T ≤ 24 °C or decreasing the temperature at the light intensity I > 50 µW·cm−2, the chemical wave period structure complexity of the system shows a linear decrease.

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

IMPACT OF THE SAME DEGENERATE ADDITIVE NOISE ON A COUPLED SYSTEM OF FRACTIONAL SPACE DIFFUSION EQUATIONS

In this paper, we present a class of stochastic system of fractional space diffusion equations forced by additive noise. Our goal here is to approximate the solutions of this system via a system of ordinary differential equations. Moreover, we study the influence of the same degenerate additive noise on the stability of the solutions of the stochastic system of fractional diffusion equations. We are interested in the systems that have nonlinear polynomial and give applications as Lotka–Volterra system from biology and the Brusselator model for the Belousov–Zhabotinsky chemical reaction from chemistry to illustrate our results.

How Chemistry Computes: Language Recognition by Non-Biochemical Chemical Automata. From Finite Automata to Turing Machines.

SummaryEvery problem in computing can be cast as decision problems of whether strings are in a language or not. Computations and language recognition are carried out by three classes of automata, the most complex of which is the Turing machine. Living systems compute using biochemistry; in the artificial, computation today is mostly electronic. Thinking of chemical reactions as molecular recognition machines, and without using biochemistry, we realize one automaton in each class by means of one-pot, table top chemical reactors: from the simplest, Finite automata, to the most complex, Turing machines. Language acceptance/rejection criteria by automata can be formulated using energy considerations. Our Turing machine uses the Belousov-Zhabotinsky chemical reaction and checks the same symbol in an Avogadro′s number of processors. Our findings have implications for chemical and general computing, artificial intelligence, bioengineering, the study of the origin and presence of life on other planets, and for artificial biology.

How Chemistry Computes: Language Recognition by Non-Biochemical Chemical Automata

Every problem in computing can be cast as decision problems of whether strings are or are not in a language. This makes language recognition fundamental for natural and artificial computation. Computer science teaches that computations and language recognition are carried out by three classes of automata, the most complex of which is the Turing machine. Living systems on Earth compute using the complex machinery of biochemistry; in the artificial, computation today is mostly electronic. Thinking of chemical reactions as molecular recognition machines, and without using biochemistry, we formulate the design, realization, construction and operation of one automaton in each class by means of 1-pot, table top chemical reactors: from the simplest, Finite automata, to the most complex, Turing machines. We test them experimentally by transcribing strings of symbols chemically, sequentially feeding them to the reactor and monitoring the physico/chemical output of the reaction. The strings we use for recognition belong to standard computer science languages specific for each class of automata. We find that language acceptance/rejection criteria by an automaton can be formulated in terms of energy considerations. The free energy spent for every word accepted by our chemical Turing machine can be tuned to a constant value associated with the pair machine-language, where for words in the language the entropy rate offsets the energy dissipation. Our Turing machine uses the Belousov-Zhabotinsky chemical reaction and checks the same symbol in an unprecedented Avogadro’s number of processors. Our findings have implications for chemical and general computing, bio-engineering and technology, for the study of the origin and presence of life in other planetary bodies and for artificial biology.

Calcium ion cyclotron resonance in dissipative water structures

ABSTRACTWeak magnetic and electromagnetic fields affect physiological processes in animals, plants, and microorganisms. Ion cyclotron resonance (ICR) is discussed as one of the sensitive mechanisms, which enable perception of the geomagnetic field and its orientation. Numerous biological effects are observed involving several small ions, showing windows of predicted frequencies and intensities. The pioneering work of Guiliano Preparata and Emilio Del Giudice using quantum electrodynamics showed that spontaneously originating coherent regions in water facilitate ICR effects at incoherent water phase boundaries. Here we examine the ICR response of the calcium ion (Ca2+), crucial for many life processes. We use an aqueous solution containing the biologically ubiquitous membrane lipid L-α-phosphatidylcholine that serves as a biomimetic proxy for dynamic light scattering (DLS) and nonlinear dielectric spectroscopy (NLDS) measurements. One notable result is that this system approaches a new equilibrium upon addition of calcium by means of the oscillatory Belousov–Zhabotinsky chemical reaction, oscillations are significantly reduced under Ca2+ ICR application. Secondly an “oscillator” of calcium ions appears to be able to itself couple coherently and predictably to large-scale coherent regions in water. This system appears able to regulate ion fluxes in response to very weak environmental electromagnetic fields.

Identification of cow milk in goat milk by nonlinear chemical fingerprint technique

The objective of this paper was to develop a nonlinear chemical fingerprint technique for identifying and detecting adulteration of goat milk with cow milk. In this study, by taking the Belousov-Zhabotinsky oscillatory chemical reaction using acetone and substrates in goat milk or cow milk as main dissipative substances, when the same dosage of goat milk and cow milk was introduced to the “H+ + Mn2+ + BrO3− + acetone” oscillating system respectively, nonlinear chemical fingerprints were obtained for goat milk and cow milk from the same origin. The results showed that inductive time value and the content of cow milk in goat milk had a linear relationship in the range of 0–100% and the corresponding regression coefficient was 0.9991. A detection limit of 0.0107 g/g was obtained, and the content of cow milk in mixed milk was calculated. The proposed method in this study was simple, economical and effective. In addition, the method did not need the pretreatment and separation of samples for identifying and evaluating cow milk adulteration in goat milk.

Kinetic Determination of Urea in Milk Powder by Nonlinear Chemical Fingerprint Technique

To detect urea content in milk powder, a nonlinear chemical fingerprint technique was developed. In our study, Belousov-Zhabotinsky oscillatory chemical reaction (B-Z) was performed using milk powder and malonic acid as main dissipative substances. The same dosage of milk powder with or without artificially added urea was introduced to “H+ + Ce4+ + + malonic acid” oscillating system, respectively, and nonlinear chemical fingerprints of different milk powder were thus obtained. The proposed method was based on a linear relationship between inductive time of non-linear chemical fingerprints and urea content in milk powder, which held when urea content in milk powder was in the range of 0 - 40 mg/g. A detection limit of 7.8 × 10-3mg/g was also obtained. Our results showed that the method could be used to certify urea content in milk powder without pretreatment of samples, which was more simple and economical compared with traditional methods.

Experimental studies of coherent structures in an advection-reaction-diffusion system.

We present experimental studies of reaction front propagation in a single vortex flow with an imposed external wind. The fronts are produced by the excitable, ferroin-catalyzed Belousov-Zhabotinsky chemical reaction. The flow is generated using an electromagnetic forcing technique: an almost-radial electrical current interacts with a magnetic field from a magnet below the fluid layer to produce the vortex. The magnet is mounted on crossed translation stages allowing for movement of the vortex through the flow. Reaction fronts triggered in or in front of the moving vortex form persistent structures that are seen experimentally for time-independent (constant motion), time-periodic, and time-aperiodic flows. These results are examined with the use of burning invariant manifolds that act as one-way barriers to front motion in the flows. We also explore the usefulness of finite-time Lyapunov exponent fields as an instrument for analyzing front propagation behavior in a fluid flow.

Feedback control strategies for a cerium‐catalyzed Belousov–Zhabotinsky chemical reaction system

A number of control schemes including nonlinear feedback, dislocated feedback, and speed feedback have been proposed and assessed for a bromate‐malonic acid‐cerium Belousov–Zhabotinsky batch reaction process. The tuning parameters of the Oregonator model were firstly adjusted based on a UV‐vis spectrophotometric analysis in the experimental part of the research. The adjusted Oregonator model successfully reproduced the innate induction time and periodicity of the BZ‐batch system. Subsequently, the controllers were implemented and numerical simulations were carried out by employing the multi‐stage Adomian decomposition method. The nominal analysis method was used to study the linear stability of each design. All the controlled systems were found to be linearly stable for certain continuous regions of controller gain. The performance of the proposed control laws was assessed and the dislocated feedback control strategy was shown to be able to drive the system states toward desired setpoints quickly. Furthermore, the validity of the dislocated feedback control design was doubly ensured by the sliding mode control theory. It was found that those feedback schemes which manipulate cerium ion concentration can be practically realized by means of electrochemical oxidation or oxygen aeration. Our results were confirmed by the Simulink software package and the block diagram representations are included in the paper.

Pinning of reaction fronts by burning invariant manifolds in extended flows

We present experiments on the behavior of reaction fronts in extended, vortex-dominated flows in the presence of an imposed wind. We use the ferroin-catalyzed, excitable Belousov-Zhabotinsky chemical reaction, which produces pulse-like reaction fronts. Two time-independent flows are studied: an ordered (square) array of vortices and a spatially disordered flow. The flows are generated with a magnetohydrodynamic forcing technique, with a pattern of magnets underneath the fluid cell. The magnets are mounted on a translation stage which moves with a constant speed Vd under the fluid, resulting in motion of the vortices within the flow. In a reference frame moving with magnets, the flow is equivalent to one with stationary vortices and a uniform wind with speed W = Vd. For a wide range of wind speeds, reaction fronts pin to the vortices (in a co-moving reference frame), propagating neither forward against the wind nor being blown backward. We analyze this pinning phenomenon and the resulting front shapes using a burning invariant manifold (BIM) formalism. The BIMs are one-way barriers to reaction fronts in the advection-reaction-diffusion process. Pinning occurs when several BIMs overlap to form a complete barrier that spans the width of the system. In that case, the shape of the front is determined by the shape of the BIMs. For the ordered array flow, we predict the locations of the BIMs numerically using a simplified model of the velocity field for the ordered vortex array and compare the BIM shapes to the pinned reaction fronts. We also explore transient behavior of the fronts (before reaching their steady state) to highlight the one-way nature of the BIMs.

On the minimal speed of front propagation in a model of the Belousov-Zhabotinsky reaction

In this paper, we answer the question about the existence of the minimal speed of front propagation in a delayed version of the Murray model of the Belousov-Zhabotinsky (BZ) chemical reaction. It is assumed that the key parameter $r$ of this model satisfies $0< r \leq 1$ that makes it formally monostable. By proving that the set of all admissible speeds of propagation has the form $[c_*,+\infty)$, we show here that the BZ system with $r \in (0,1]$ is actually of the monostable type (in general, $c_*$ is not linearly determined). We also establish the monotonicity of wavefronts and present the principal terms of their asymptotic expansions at infinity (in the critical case $r=1$ inclusive).

Kinetic modelling and bifurcation analysis of chemomechanically miniaturized gels under mechanical load

Chemomechanically responsive gels, with great potential applications in the fields of smart structures and biomedicines, present autonomously oscillatory deformation driven by the Belousov-Zhabotinsky chemical reaction. The dynamic behavior of the responsive gels is obviously affected by the external mechanical load. This approach proposed a kinetic model with an ordinary differential equation to describe the oscillatory deformation of the gels under the mechanical load. Then the periodic solutions and phase diagrams of the oscillation are obtained using the improved Runge-Kutta and shooting methods. The results demonstrated that bifurcations are typically existent in the system and the characters of the oscillatory deformation regularly depend on the mechanical load as well as the concentration of reactants and the stoichiometric coefficient of chemical reaction. This development is supposed to promote the practical applications of the chemomechanically responsive gels.

Barriers to front propagation in ordered and disordered vortex flows

We present experiments on reactive front propagation in a two-dimensional (2D) vortex chain flow (both time-independent and time-periodic) and a 2D spatially disordered (time-independent) vortex-dominated flow. The flows are generated using magnetohydrodynamic forcing techniques, and the fronts are produced using the excitable, ferroin-catalyzed Belousov-Zhabotinsky chemical reaction. In both of these flows, front propagation is dominated by the presence of burning invariant manifolds (BIMs) that act as barriers, similar to invariant manifolds that dominate the transport of passive impurities. Convergence of the fronts onto these BIMs is shown experimentally for all of the flows studied. The BIMs are also shown to collapse onto the invariant manifolds for passive transport in the limit of large flow velocities. For the disordered flow, the measured BIMs are compared to those predicted using a measured velocity field and a three-dimensional set of ordinary differential equations that describe the dynamics of front propagation in advection-reaction-diffusion systems.

Pinning and mode-locking of reaction fronts by vortices

We present results of experiments on the behavior of reaction fronts in the presence of vortex-dominated flows. The flow is either a single vortex or a chain of vortices in an annular configuration, and the reaction is the excitable Belousov–Zhabotinsky chemical reaction. If the vortex chain oscillates periodically in the lateral direction, the reaction front often mode-locks to the oscillations, propagating an integer number of wavelengths of the flow (two vortices) in an integer number of drive periods. In the presence of a uniform “wind”, the front often freezes, remaining pinned to the leading vortex and neither propagating forward against the wind nor being blown backward by it. Studies with an individual vortex verify the ability of a moving vortex to pin and drag a reaction front. We use this pinning behavior to explain the mode-locking for the oscillating case.

Nonlinear dynamics of self-oscillating polymer gels

Self-oscillating polymer gels driven by Belousov-Zhabotinsky (BZ) chemical reaction are a new class of functional gels that have a wide range of potential applications (e.g., autonomously functioning membranes, actuate artificial muscles). However, the precise control of these gels has been an issue due to limited investigations of the influences of key system parameters on the characteristics of BZ gels. To address this deficiency, we studied the self-oscillating behavior of BZ gels using the nonlinear dynamics theory and an Oregonator-like model, with focus placed upon the influences of various system parameters. The analysis of the oscillation phase indicated that the dynamic response of BZ gels represents the classical limit cycle oscillation. We then investigated the characteristics of the limit cycle oscillation and quantified the influences of key parameters (i.e., initial reactant concentration, oxidation and reduction rate of catalyst, and response coefficient) on the self-oscillating behavior of BZ gels. The results demonstrated that sustained limit cycle oscillation of BZ gels can be achieved only when these key parameters meet certain requirements, and that the pattern, period and amplitude of the oscillation are significantly influenced by these parameters. The results obtained in this study could enable the controlled self-oscillation of BZ gels system. This has several potential applications such as controlled drug delivery, miniature peristaltic pumps and microactuators.