Oscillatory Belousov-Zhabotinsky Research Articles

Nonconcentration phenomenon for one‐dimensional reaction–diffusion systems with mass dissipation

AbstractReaction–diffusion systems with mass dissipation are known to possess blow‐up solutions in high dimensions when the nonlinearities have super quadratic growth rates. In dimension 1, it has been shown recently that one can have global existence of bounded solutions if nonlinearities are at most cubic. For the cubic intermediate sum condition, that is, nonlinearities might have arbitrarily high growth rates, an additional entropy inequality had to be imposed. In this paper, we remove this extra entropy assumption completely and obtain global boundedness for reaction–diffusion systems with cubic intermediate sum condition. The novel idea is to show a nonconcentration phenomenon for mass dissipating systems, that is the mass dissipation implies a dissipation in a Morrey space for some . As far as we are concerned, it is the first time such a bound is derived for mass dissipating reaction–diffusion systems. The results are then applied to obtain global existence and boundedness of solutions to an oscillatory Belousov–Zhabotinsky system, which satisfies cubic intermediate sum condition but does not fulfill the entropy assumption. Extensions include global existence mass controlled systems with slightly super cubic intermediate sum condition.

Co-Complexes-Based Self-Oscillating Gels Driven by the Belousov-Zhabotinsky Reaction.

We report the synthesis of novel cobalt complexes-based catalysts designed for the oscillatory Belousov-Zhabotinsky (BZ) reaction. For the first time, we introduce cobalt complex-based self-oscillating gels that demonstrate autonomous color oscillations within a BZ reagent solution, functioning without the need for any external stimuli. We created acrylamide-based self-oscillating gels containing immobilized tris(2,2'-bipyridine)cobalt(II) or tris(1,10-phenanthroline)cobalt(II) complexes and gels containing covalently bound (5-acrylamido-1,10-phenanthroline)bis(2,2'-bipyridine)cobalt(II), (5-acrylamido-1,10-phenanthroline)bis(1,10-phenanthroline) cobalt(II), or tris(5-acrylamido-1,10-phenanthroline)cobalt(II) complexes. When the BZ reaction takes place within the gels, it results in the observation of moving chemical waves and reversible color changes. We believe that Co-complexes-based self-oscillating gels have potential applications in the design of soft actuators and chemical devices for signal processing.

Emergent Synchronous Volumetric Oscillation in Hierarchically Structured Self-Oscillating Gel Clusters.

Emergent properties accompanying synchronization among oscillators are vital characteristics in biological systems. Belousov-Zhabotinsky (BZ) oscillators are an artificial model to study the emergence and synchronization in life. This research represents a self-oscillating gel system with clusterable properties to experimentally examine synchronous and emergent properties at a fundamental hierarchical level. Incorporating acrylic acid (AAc) moieties within the gel network facilitates cluster formation through hydrogen bonding in an acidic BZ substrate solution. Upon clustering, both homogeneous and heterogeneous gel assemblies─ranging from double to quadruple clusters─exhibit increased and synchronized periods and amplitudes during the BZ reaction. Notably, in heterogeneous clusters, gel units with initially short periods and small volumetric amplitudes display a significant increase, aligning with the lonfger periods and larger amplitudes of other elements within the cluster, an emergent property. This research can pave the way for a better understanding of synchronous and emergent properties in biological oscillators such as cardiomyocytes.

Photosensitive Control and Network Synchronization of Chemical Oscillators.

The Belousov-Zhabotinsky (BZ) reaction has long been a paradigmatic system for studying chemical oscillations. Here, we experimentally studied the synchronization control within photochemically coupled star networks of BZ oscillators. Experiments were carried out in wells performed in soda-lime glass constructed using novel laser technologies. Utilizing the inherent oscillatory nature of the BZ reaction, we engineered a star network of oscillators interconnected through photochemical inhibitory coupling. Furthermore, the experimental setup presented here could be extrapolated to more complex network architectures with both excitatory and inhibitory couplings, contributing to the fundamental understanding of synchronization in complex systems.

Kinetics, Mechanism, and Reactivity of the Cerium(IV)-Oxalatereaction in a Sulphate Medium

This work presents an approach for studying the kinetics, mechanism, and reactivity of intermediates in a wide class of the redox reactions for which the rate-limiting step is the redox-decomposition of an intermediate complex. This approach is applied to investigate the oxalic acid (H2Ox) oxidation by cerium(IV) in sulfuric acid medium, which is an integral part of the cerium-catalyzed oscillatory Belousov–Zhabotinsky (BZ) reaction. Using experimental, mathematical and computational techniques commonly used to study metal complexes in a stable oxidation state (OS), kinetically generalized by the authors for studying variable-valence metal complexes, the characteristics of intermediate complexes of the cerium(IV)-oxalate reaction were studied, the general rate law was derived on the basis of a set of equations describing the rapid establishment of preequilibria in the system and the subsequent nonequilibrium process. A quantitative reaction model is proposed that includes two parallel reaction pathways, for which two different intermediate cerium(IV)-oxalate complexes with close reactivity have been identified and characterized that may be due to the similarity in the structure of their inner coordination spheres and an inner sphere mechanism of electron transfer in the complexes. Based on the developed model, the distribution diagram was also constructed for the computed fractions of all the detectable cerium(IV) species under conditions of the BZ reaction, which testify to the necessity to take into account under these conditions the formation of intermediate complexes CeOHOx (n = 1, 2) during oxidation of oxalic acid. The main difference of the proposed model of the cerium(IV)-oxalate reaction as part of the BZ-reaction from the previous models is the explicit accounting of the formation of intermediate cerium(IV) complexes with anions of oxalic acid and sulfate background.

Buoyancy-Driven Chemohydrodynamic Patterns in A + B → Oscillator Two-Layer Stratifications

Chemohydrodynamic patterns due to the interplay of buoyancy-driven instabilities and reaction-diffusion patterns are studied experimentally in a vertical quasi-two-dimensional reactor in which two solutions A and B containing separate reactants of the oscillating Belousov-Zhabotinsky system are placed in contact along a horizontal contact line where excitable or oscillating dynamics can develop. Different types of buoyancy-driven instabilities are selectively induced in the reactive zone depending on the initial density jump between the two layers, controlled here by the bromate salt concentration. Starting from a less dense solution above a denser one, two possible differential diffusion instabilities are triggered depending on whether the fast diffusing sulfuric acid is in the upper or lower solution. Specifically, when the solution containing malonic acid and sulfuric acid is stratified above the one containing the slow-diffusing bromate salt, a diffusive layer convection (DLC) instability is observed with localized convective rolls around the interface. In that case, the reaction-diffusion wave patterns remain localized above the initial contact line, scarcely affected by the flow. If, on the contrary, sulfuric acid diffuses upward because it is initially dissolved in the lower layer, then a double-diffusion (DD) convective mode develops. This triggers fingers across the interface that mix the reactants such that oscillatory dynamics and rippled waves develop throughout the whole reactor. If the denser solution is put on top of the other one, then a fast developing Rayleigh-Taylor (RT) instability induces fast mixing of all reactants such that classical reaction-diffusion waves develop later on in the convectively mixed solutions.

Lie point symmetry infinitesimals, optimal system, power series solution, and modulational gain spectrum to the mathematical Noyes–Field model of nonlinear homogeneous oscillatory Belousov–Zhabotinsky reaction

Introduction:The chemical oscillators are identified as open system that demonstrate periodic changes in the concentration of some reaction species as a result of intricate physico-chemical mechanisms which can lead to bi-stability, the occurrence of limit cycle attractors, the emergence of spiral waves and turing patterns, and finally, deterministic chaos. Objectives:The main objective of this paper is to analyze the simple Noyes–Field governing system of differential equations for the nonlinear Belousov–Zhabotinsky reaction which delineates the non-linear oscillatory behavior of chemical systems that occurs in the homogeneous media. Methodology:The Lie symmetry invariance analysis performed to extract the symmetries infinitesimal generators and the adjoint representation carried out to develop optimal system for the obtained Lie vectors. The significant power series approach applied to obtain the analytical solution. The modulation instability criteria ensured the stability of nonlinear oscillatory Belousov–Zhabotinsky reaction process. Results:The one-dimensional Lie symmetry generators algebra of the mathematical Noyes–Field governing system for oscillatory reaction is established. Furthermore, similarity reductions are carried out as well as the development of an optimal system of the sub-algebras. The similarity transformation technique converted the controlling system to ordinary differential equations and generates the large quantity of analytical traveling wave solutions. Moreover, the closed-form analytical solution for the proposed homogeneous nonlinear oscillatory chemical process is secured. The (MI) gain spectrum graphically visualized with the suitable choice of arbitrary parameters. Conclusion:The graphical performance of the Noyes–Field model solution at various settings reveals new perspectives and fascinating model phenomena. The attained outcomes have significant applications and have opened up innovative development areas for research across numerous scientific fields.

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.

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.

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

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.

Pattern formation in a four-ring reaction-diffusion network with heterogeneity.

In networks of nonlinear oscillators, symmetries place hard constraints on the system that can be exploited to predict universal dynamical features and steady states, providing a rare generic organizing principle for far-from-equilibrium systems. However, the robustness of this class of theories to symmetry-disrupting imperfections is untested in free-running (i.e., non-computer-controlled) systems. Here, we develop a model experimental reaction-diffusion network of chemical oscillators to test applications of the theory of dynamical systems with symmeries in the context of self-organizing systems relevant to biology and soft robotics. The network is a ring of four microreactors containing the oscillatory Belousov-Zhabotinsky reaction coupled to nearest neighbors via diffusion. Assuming homogeneity across the oscillators, theory predicts four categories of stable spatiotemporal phase-locked periodic states and four categories of invariant manifolds that guide and structure transitions between phase-locked states. In our experiments, we observed that three of the four phase-locked states were displaced from their idealized positions and, in the ensemble of measurements, appeared as clusters of different shapes and sizes, and that one of the predicted states was absent. We also observed the predicted symmetry-derived synchronous clustered transients that occur when the dynamical trajectories coincide with invariant manifolds. Quantitative agreement between experiment and numerical simulations is found by accounting for the small amount of experimentally determined heterogeneity in intrinsic frequency. We further elucidate how different patterns of heterogeneity impact each attractor differently through a bifurcation analysis. We show that examining bifurcations along invariant manifolds provides a general framework for developing intuition about how chemical-specific dynamics interact with topology in the presence of heterogeneity that can be applied to other oscillators in other topologies.

Dynamical attributes of nanocatalyzed self-oscillating reactions via bifurcation analyses.

Self-oscillating chemical reactions that undergo reaction-diffusion (RD) phenomena have shown great potential for designing stimuli-responsive materials. Belousov-Zhabotinsky (BZ) reactions are one such class of reactions that exhibit nonlinear chemical oscillations due to redox cycles of the metal-ion catalyst by virtue of Hopf bifurcation. Using bifurcation analyses, here we investigate the BZ reactions, catalyzed by 0D-2D catalytic nanomats and bare nanosheets, which are known to exhibit enhanced dynamic response due to catalysts' heterogeneity. Specifically, we incorporate the nanocatalysts' activity in the kinetic model of the BZ reactions and, subsequently, use catalysts' activity as the bifurcation parameter for analyses. By computing higher-order Lyapunov and frequency coefficients, we have revealed new oscillatory regimes in the bifurcation diagram, including re-entrant regions where sustained oscillations are unexpectedly suppressed, even with high catalytic activity. In addition, we also calculate the amplitude and frequency of BZ oscillations in each of these regions as a function of nanocatalysts' activity. We believe that our current findings can be used to harness the nonlinearity of RD-based dynamical systems to provide unique functionalities to active stimuli-response systems.

Oscillatory microcells connected on a ring by chemical waves.

The dynamics of four coupled microcells with the oscillatory Belousov-Zhabotinsky (BZ) reaction in them is analyzed with the aid of partial differential equations. Identical BZ microcells are coupled in a circle via identical narrow channels containing all the components of the BZ reaction, which is in the stationary excitable state in the channels. Spikes in the BZ microcells generate unidirectional chemical waves in the channels. A thin filter is put in between the end of the channel and the cell. To make coupling between neighboring cells of the inhibitory type, hydrophobic filters are used, which let only Br2 molecules, the inhibitor of the BZ reaction, go through the filter. To simulate excitatory coupling, we use a hypothetical filter that let only HBrO2 molecules, the activator of the BZ reaction, go through it. New dynamic modes found in the described system are compared with the "old" dynamic modes found earlier in the analogous system of the "single point" BZ oscillators coupled in a circle by pulses with time delay. The "new" and "old" dynamic modes found for inhibitory coupling match well, the only difference being much broader regions of multi-rhythmicity in the "new" dynamic modes. For the excitatory type of coupling, in addition to four symmetrical modes of the "old" type, many new asymmetrical modes coexisting with the symmetrical ones have been found. Asymmetrical modes are characterized by the spikes occurring any time within some finite time intervals.

A chemical micropump actuated by self-oscillating polymer gel

Abstract We demonstrated a self-driven chemical micropump powered by self-oscillating motions of synthetic polymer gel converting chemical energy into displacements of a thin polydimethylsiloxane (PDMS) sheet to produce a directional flow via micro check valves. The gel oscillations induced by the oscillatory Belousov-Zhabotinsky (BZ) reaction generate large volume change. To effectively exploit this volume change, gel bars were used as drivers. They were sandwiched by a fixed cover glass and a push-bar to communicate the expanding (pushing) force of the gel bars to the pumping chamber. At 25 °C, this gel micropump generated a 0.07 mN stroke force and a 0.28 μL/min positive net flow in the microchannel. Additionally, the flow rate of this gel micropump was increased as the temperature was raised from 20 to 30 °C. Compared to existing chemical micropumps, this gel-based micropump provides advantages of self-oscillating property, easy refueling and thermal controllability. This gel-based soft micropump would be used as wearable or medical devices exploiting the flexibility and quietness.

Impact of PDMS-Based Microfluidics on Belousov-Zhabotinsky Chemical Oscillators.

Sub-nanoliter volumes of the Belousov-Zhabotinsky (BZ) reaction are sealed in microfluidic devices made from polydimethylsiloxane (PDMS). Bromine, which is a BZ reaction intermediate that participates in the inhibitory pathway of the reaction, is known to permeate into PDMS, and it has been suggested that PDMS and bromine can react ( J. Phys. Chem. A. 108, 2004, 1325-1332). We characterize the extent to which PDMS affects BZ oscillations by varying the volume of the PDMS surrounding the BZ reactors. We measure how the oscillation period varies with PDMS volume and compare with a theoretical reaction-diffusion model, concluding that bromine reacts with PDMS. We demonstrate that minimizing the amount of PDMS by making the samples as thin as possible maximizes the number of oscillations before the BZ reaction reaches equilibrium and ceases to oscillate. We also demonstrate that the deleterious effects of the PDMS-BZ interactions are somewhat mitigated by imposing constant chemical boundary conditions through using a light-sensitive catalyst, ruthenium, in combination with patterned illumination. Furthermore, we show that light can modulate the frequency and phase of the BZ oscillators contained in a PDMS matrix by 20-30%.

Design of bio-inspired muscle sarcomere structure using a hybrid hydrogel-IPMC actuator

Biological muscle is considered a powerful actuator due to its flexibility, lightweight, and efficiency. The building unit of a muscle, sarcomere, and the study of its energy balance cycle is considered in researches due to its importance to mimic the micro-level muscle structure to improve the artificial muscle performance. In this work, a new design of a linear actuator based on the sarcomere behavior is developed. The design is inspired by studying the four steps adenosine triphosphate (ATP) hydrolysis cycle, which is the main source of the required energy for sarcomere contraction. A new developed hybrid hydrogel-polymeric material actuator is designed in this paper using a combination between Ionic Polymeric Metallic Composites (IPMC) and hydrogel to behave like the sarcomere. This new actuator proposes an autonomous cycle using the effect oscillatory Belousov–Zhabotinsky (BZ) reaction. The physical model is proposed, and the mathematical model of the actuator is derived and formulated and identified using MATLAB/Simulink.

Membrane Structure Drives Synchronization Patterns in Arrays of Diffusively Coupled Self-Oscillating Droplets.

Networks of diffusively coupled inorganic oscillators, confined in nano- and microcompartments, are effective for predicting and understanding the global dynamics of those systems where the diffusion of activatory or inhibitory signals regulates the communication among different individuals. By taking advantage of a microfluidic device, we study the dynamics of arrays of diffusively coupled Belousov-Zhabotinsky (BZ) oscillators encapsulated in water-in-oil single emulsions. New synchronization patterns are induced and controlled by modulating the structural and chemical properties of the phospholipid-based biomimetic membranes via the introduction of specific dopants. Doping molecules do not alter the membrane basic backbone, but modify the lamellarity (and, in turn, the permeability) or interact chemically with the reaction intermediates. A transition from two-period clusters showing 1:2 period-locking to one-period antiphase synchronization is observed by decreasing the membrane lamellarity. An unsynchronized scenario is found when the dopant is able to interfere with chemical communication by reacting with the chemical messengers.

Fabrication of New Belousov-Zhabotinsky Micro-Oscillators on the Basis of Silica Gel Beads.

We have fabricated and examined silica gel beads loaded with a catalyst of the Belousov-Zhabotinsky (BZ) reaction, tris(2,2'-bipyridyl)ruthenium(II) chloride, Ru(bpy)3Cl2, the BZ beads. The abilities of silica gel and the widely used ion-exchange resin (Dowex 50WX2) BZ beads to oscillate in a catalyst-free BZ solution are compared. The period of the BZ oscillations increases with an increase in the diameter (40-250 μm) of both types of the BZ beads. The ability of the ion-exchange resin beads to hold catalyst molecules significantly decreases with a decrease in pH, while this value is less dependent on pH for the silica gel BZ beads. The diffusive coupling of two BZ beads separated by either aqueous or oil gaps is studied as well. For the aqueous gap less than 100 μm, the BZ beads of both types demonstrate in-phase synchronization. For the oil phase, the Dowex BZ beads are unable to oscillate for a long enough time and therefore cannot be synchronized, while the silica gel BZ beads are able to oscillate for several hours and demonstrate anti-phase synchronization for gaps less than 40 μm.