Belousov-Zhabotinsky Reaction Research Articles

Autonomous Motion of Hydrogels Driven by Semi-Interpenetrating Chemical Processing Systems.

Developing artificial autonomous materials is crucial for a deeper understanding of the emergence of life-like behavior. In nature, cells achieve autonomy through chemical processing systems incorporated into soft material-based frameworks. Inspired by natural cells, we herein describe a straightforward methodology for constructing artificial autonomous materials consisting of a polymer-based chemical processing system and a hydrogel-based soft framework. Using a material comprising a hydrogel framework devoid of active components in combination with semi-interpenetrating self-oscillating linear polymers, we discovered that semi-interpenetrating polymer-based chemical processing systems drive the autonomous motion of the hydrogel framework. The material exhibited autonomous volumetric oscillation powered by the Belousov-Zhabotinsky reaction. Furthermore, the autonomous behavior is controllable by changing the content of the chemical processing system incorporated into the hydrogel framework. Our findings shed light on a class of autonomous materials based on polymer-based chemical processing systems with soft frameworks.

Analytical solutions for the Noyes Field model of the time fractional Belousov Zhabotinsky reaction using a hybrid integral transform technique

In this work, we employed an attractive hybrid integral transform technique known as the natural transform decomposition method (NTDM) to investigate analytical solutions for the Noyes-Field (NF) model of the time-fractional Belousov–Zhabotinsky (TF-BZ) reaction system. The aforementioned time-fractional model is considered within the framework of the Caputo, Caputo–Fabrizio, and Atangana–Baleanu fractional derivatives. The NTDM couples the Adomian decomposition method and the natural transform method to generate rapidly convergent series-type solutions via an elegant iterative approach. The existence and uniqueness of solutions for the considered time-fractional model are first investigated via a fixed-point approach. The reliability and efficiency of the considered solution method is then demonstrated for two test cases of the TF-BZ reaction system. To demonstrate the validity and accuracy of the considered technique, numerical results with respect to each of the mentioned fractional derivatives are presented and compared with the exact solutions as well as with those from existing related literature. Graphical representations depicting the dynamic behaviors of the chemical wave profiles of the concentrations of the intermediates are presented with respect to varying fractional parameter values as well as temporal and spatial variables. The obtained results indicate that the execution of the method is straightforward and can be employed to explore nonlinear time-fractional systems modeling complex chemical reactions.

Discovering dynamics and parameters of nonlinear oscillatory and chaotic systems from partial observations

Despite rapid progress in data acquisition techniques, many complex physical, chemical, and biological systems remain only partially observable, thus posing the challenge to identify valid theoretical models and estimate their parameters from an incomplete set of experimentally accessible time series. Here, we combine sensitivity methods and ranked-choice model selection to construct an automated hidden dynamics inference framework that can discover predictive nonlinear dynamical models for both observable and latent variables from noise-corrupted incomplete data in oscillatory and chaotic systems. After validating the framework for prototypical FitzHugh-Nagumo oscillations, we demonstrate its applicability to experimental data from squid neuron activity measurements and Belousov-Zhabotinsky reactions, as well as to the Lorenz system in the chaotic regime. Published by the American Physical Society 2024

Pullback and uniform exponential attractors for non-autonomous Oregonator systems

Abstract We consider the long-time global dynamics of non-autonomous Oregonator systems. This system is a coupled system of three reaction-diffusion equations, that arises from the Belousov-Zhabotinskii reaction. We first present some sufficient conditions for the existence of pullback and uniform exponential attractors for non-autonomous dynamical system. Then, we apply abstract results to prove the existence of a pullback exponential attractor for Oregonator systems affected by time-dependent forces and a uniform exponential attractor for Oregonator systems driven by quasi-periodic external forces.

Travelling wavefronts for the Belousov–Zhabotinsky system with non-local delayed interaction

Travelling wavefronts for the Belousov–Zhabotinsky system with non-local delayed interaction

Dynamics of a Two-Dimensional Slow–Fast Belousov–Zhabotinsky Model

Dynamics of a Two-Dimensional Slow–Fast Belousov–Zhabotinsky Model

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.

Investigating the nonlinear dynamics of photosensitive Belousov-Zhabotinsky gels via bifurcation analyses.

Controlling the dynamics of active stimuli-responsive smart materials is essential to replicate the biomimetic functionalities at different length scales for a variety of biological systems-based applications. Photosensitive Belousov-Zhabotinsky (BZ) gels, powered by a nonlinear chemical oscillator, called a BZ reaction are one of the stimuli-responsive smart materials in demand due to their ability to continuously transduce chemical oscillations into mechanical deformations. The chemical oscillations in a BZ reaction and subsequent mechanical oscillations in photosensitive BZ gels occur due to the redox cycle of photosensitive ruthenium complex-based catalysts. In this work, our objective is to identify how the behavior of photosensitive BZ gels can be tuned and used for biomimetic applications by investigating its dynamical characteristics using bifurcation analyses. Specifically, we use the normal form approach and perform linear and nonlinear stability analyses to identify high-order bifurcations by computing higher-order Lyapunov and frequency coefficients. We revealed the existence of domains that encompass coexisting stable and unstable limit cycles (LCs), which merge to form a semi-stable LC at the limit point of cycle (LPC). Their existence shows how a slight variation in the BZ gel recipe can significantly alter its dynamics. Subsequently, we quantify the amplitude and frequency of oscillations in different domains under the effect of variation of BZ reaction formulations. We believe that the outcomes of our work serve as an efficient template for the design and control of BZ gel-based applications. The usage of a normal form and a systematic representation of nonlinear dynamics allow our framework to be extended for other nonlinear dynamical systems.

Experimental studies of spiral wave teleportation in a light sensitive Belousov-Zhabotinsky system.

Cardiac arrythmias are a form of heart disease that contributes toward making heart disease a significant cause of death globally. Irregular rhythms associated with cardiac arrythmias are thought to arise due to singularities in the heart tissue that generate reentrant waves in the underlying excitable medium. A normal approach to removing such singularities is to apply a high voltage electric shock, which effectively resets the phase of the cardiac cells. A concern with the use of this defibrillation technique is that the high-energy shock can cause lasting damage to the heart tissue. Various theoretical works have investigated lower-energy alternatives to defibrillation. In this work, we demonstrate the effectiveness of a low-energy defibrillation method in an experimental 2D Belousov-Zhabotinsky (BZ) system. When implemented as a 2D spatial reaction, the BZ reaction serves as an effective analog of general excitable media and supports regular and reentrant wave activity. The defibrillation technique employed involves targeted low-energy perturbations that can be used to "teleport" and/or annihilate singularities present in the excitable BZ medium.

Complete synchronization of two spirals by a messenger wave in a reaction diffusion system

Synchronization phenomena are ubiquitous in nature. They can be observed in physical, chemical, and biological systems. In the present study, we examine synchronization phenomena in chemical reaction–diffusion systems in the experimental Belousov–Zhabotinsky reaction. We study how two counter-rotating spirals pinned to unexcitable heterogeneities separated by a wall interact with a third free spiral of higher frequency. We found that the latter, which we call the messenger wave, synchronizes the two non-interacting pinned spirals. We also carried out numerical simulations of a model system with Barkley’s reaction–diffusion equations and found corroborating results.

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.

Semi-wavefront for a Belousov–Zhabotinskii reaction–diffusion system with spatio-temporal delay

This paper considers a Belousov–Zhabotinskii reaction–diffusion system with spatio-temporal delay. The spatio-temporal delay is modeled as the convolution of u(t,x) with a kernel function g(t,x)≥0, where ∫R∫0+∞g(s,y)dsdy=1. By constructing an auxiliary system, applying Schauder’s fixed point theorem, and using a limiting argument, we demonstrate that the model admits non-negative traveling wave solutions connecting the equilibrium (0,0) to some unknown positive steady states (also referred to as a semi-wavefront) when the wave speed satisfies c≥c∗=21−r. Moreover, no such semi-wavefront exists if c<c∗. It is noteworthy that the kernel function is not required to have compact support in this analysis.

Multiscale Approach for Tuning Communication among Chemical Oscillators Confined in Biomimetic Microcompartments.

ConspectusInspired by the biological world, new cross-border disciplines and technologies have emerged. Relevant examples include systems chemistry, which offers a bottom-up approach toward chemical complexity, and bio/chemical information and communication technology (bio/chemical ICT), which explores the conditions for propagating signals among individual microreactors separated by selectively permeable membranes. To fabricate specific arrays of microreactors, microfluidics has been demonstrated as an excellent method. In particular, droplet-based microfluidics is a powerful tool for encapsulating biological entities and chemical reagents in artificial microenvironments, mostly water-in-oil microdroplets. In these systems, the interfaces are liquid-liquid, and their physicochemical properties are key factors for tuning the coupling between molecular diffusion. Simple and double emulsions, where aqueous domains are in equilibrium with oil domains through boundary layers of amphiphilic molecules, are organized assemblies with high interfacial-area-to-volume ratios. These membranes can be engineered to obtain different surface charges, single- or multilayer stacking, and a variable degree of defects in molecular packing. Emulsions find application in many fields, including the food industry, pharmaceutics, and cosmetics. Furthermore, micro- and nanoemulsions can be used to model the propagation of chemical species through long distances, which is not only vital for cell signaling but also significant in molecular computing. Here we present in-depth research on the faceted world of solutions confined in restricted environments. In particular, we focused on the multiscale aspects of structure and dynamics from molecular to micro and macro levels. The Belousov-Zhabotinsky chemical reaction, known for its robustness and well-documented oscillatory behavior, was selected to represent a generic signal emitter/receiver confined within microenvironments separated by liquid-liquid interfaces. In this pulse generator, the temporal and spatial progressions are governed by periodic fluctuations in the concentration of chemical species, which act as activatory or inhibitory messengers over long distances. When organized into "colonies" or arrays, these micro-oscillators exhibit emergent dynamical behaviors at the population level. These behaviors can be finely tuned by manipulating the geometrical distribution of the oscillators and the properties of the interfaces at the nanoscale. By carefully selecting the membrane composition, it is possible to drive the system toward either in-phase, antiphase, or mixed synchronization regimes among individual oscillators, depending on messenger molecules. This relatively simple lab-scale model replicates some of the communication strategies commonly found in biological systems, particularly those based on the passive diffusion of chemical and electrical signals. It can help shed light on fundamental life processes and inspire new implementations in molecular computing and smart materials.

Coupled X-ray Absorption/UV-vis Monitoring of a Prototypical Oscillating Reaction.

Oscillating reactions are among the most intriguing phenomena in chemistry, but many questions on their mechanisms still remain unanswered, due to their intrinsic complexity and to the low sensitivity of the most common spectroscopic techniques toward the reaction brominated species. In this work, we investigate the cerium ion-catalyzed Belousov-Zhabotinsky (BZ) oscillating reaction by means of time-resolved X-ray absorption spectroscopy (XAS), in combination with UV-vis spectroscopy and unsupervised machine learning, multivariate curve resolution, and kinetic analyses. Altogether, we provide new insights into the collective oscillatory behavior of the key brominated species involved in the classical BZ reaction and measure previously unreported oscillations in their concentrations through Br K-edge XAS, while simultaneously tracking the oscillatory Ce4+-to-Ce3+ transformation by coupling XAS with UV-vis spectroscopy. Our work evidences the potential of the XAS technique to investigate the mechanisms of oscillatory chemical systems whose species are often not detectable with conventional experimental methods.

Effect of electric field chirality on the unpinning of chemical waves in the Belousov–Zhabotinsky reaction

We investigate the unpinning of chemical spiral waves attached to obstacles in the Belousov–Zhabotinsky (BZ) reaction using a Circularly Polarized Electric Field (CPEF). The unpinning is quantified by measuring the angle at which the spiral leaves the obstacle. Previously, we had found that the wave can unpin when the electric field along the direction of the spiral is above a threshold value. When we apply a DC field, this condition can be satisfied for a range of spiral phases, which we call the unpinning window (UW). With a CPEF, this UW moves either along the direction of the spiral (co-rotating) or against the spiral (counter-rotating). We find that when the field is co-rotating, it can take several rotations of the spiral to get unpinned. With a counter-rotating field, the spiral always unpins during the first rotation. We analyze how unpinning with CPEF depends on the electric field’s relative speed, chirality, and strength using experiments and the Oregonator model. Our work helps to understand and control chemical waves.

Hopf bifurcation and limit cycle of the two‐variable Oregonator model for Belousov–Zhabotinsky reaction

This paper is concerned with a two‐variable Oregonator model for Belousov–Zhabotinsky Reaction. Llibre and Oliveira (2022) proved that Oregonator model with an unstable node or focus has at least one limit cycle in the positive quadrant, and the system has a unique stable limit cycle for some values of the parameters. It is shown in the present paper that the positive equilibrium is not a center, and that if the system has a positive equilibrium which is a weak focus, then its order is at most 2. There exist some parameter values such that system has small limit cycle around the positive equilibrium.

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.

The Formalism of Chemical Thermodynamics Applied to an Oscillatory Multistep Chemical System

The thermodynamic optimization of a process focuses on consumption, production, and efficient use of energy. The unsteady-state nature of batch reactor processing requires describing the set of processes’ dynamic behavior for energy optimization. This work aims to apply the formalism of chemical thermodynamics to a multistep chemical system in a batch reactor, aiming for a dynamic description of its evolution to the equilibrium state. As the system of study, we selected a mathematical model called the Oregonator, derived from the mechanism of the oscillating Belousov-Zhabotinsky reaction. In the methodology, we used the reaction quotient to evaluate the Gibbs function, the thermodynamic affinity, and the entropy generation as a function of the reaction extent. The results show that the overall reaction fulfills the thermodynamic fundamentals of chemical equilibrium, despite having a non-stoichiometric coefficient. However, the multistep coupled reaction system does not allow verifying compliance with the thermodynamic foundations of chemical equilibrium. We conclude that it is necessary to improve thermodynamic formalism to describe multistep chemical processes as a function of a global reaction extent variable. In this scenario, the entropy production rate emerges as a promising quantity.

Periodical alternation between precipitation and dissolution of camphor solid film on an ethanol solution.

Rhythmic behaviors are generally observed in nonlinear chemical reactions such as the Belousov-Zhabotinsky reaction and enzymatic reactions. Similarly, a simple phase change can also lead to rhythmic behavior. It has been reported previously that camphor solid films alternate between generation and disappearance on ethanol (EtOH) solution, and a phenomenological mechanism has been suggested for this. The evaporation of EtOH decreases the temperature on the surface of the solution via vaporization heat and induces precipitation in the camphor solid film. At this time, the film prevents evaporation, and thus, the surface temperature increases due to thermal diffusion from the atmosphere, resulting in dissolution of the solid film. To verify the previously suggested phenomenological mechanism, we controlled the evaporation rate of EtOH using a porous plastic cover. As a result, the period of oscillation increased with decreasing pore diameter, and finally, the oscillation did not occur without pore in the cover, where the camphor solid film was not observed. Additionally, a new mathematical model was proposed, and the numerical calculations agreed well with experimental observations. Linear stability and bifurcation analyses revealed the detailed mechanism of this phenomenon, which agreed well with the phenomenological explanation mentioned above.