Belousov-Zhabotinsky Reaction Research Articles

Oscillating Reactions Meet Polymers at Interfaces.

Chemo-mechanical phenomena, including oscillations and peristaltic motions, are widespread in nature—just think of heartbeats—thanks to the ability of living organisms to convert directly chemical energy into mechanical work. Their imitation with artificial systems is still an open challenge. Chemical clocks and oscillators (such as the popular Belousov–Zhabotinsky (BZ) reaction) are reaction networks characterized by the emergence of peculiar spatiotemporal dynamics. Their application to polymers at interfaces (grafted chains, layer-by-layer assemblies, and polymer brushes) offers great opportunities for developing novel smart biomimetic materials. Despite the wide field of potential applications, limited research has been carried out so far. Here, we aim to showcase the state-of-the-art of this fascinating field of investigation, highlighting the potential for future developments and providing a personal outlook.

Spatial and temporal dynamics of Belousov-Zhabotinsky reaction: A STEM approach

An integrative methodology for teaching science is proposed through the STEM methodology (Science-Technology-EngineeringMathematics).The STEM methodology provides students the opportunity to combine knowledge in an interdisciplinary and collaborative manner, allowing the development of creative and systemic thinking. As a model we propose the experimental reproduction of the Belousov-Zhabotinsky reaction (BZ), which is the standard prototype of non-linear chemistry, in addition we used the Python V2.7 programming software and the Jupyter platform for the computational reproduction of the BZ reaction. The STEM methodology could help the development of new competences for students, that is, it will provide them with tools to solve complex current problems that require of the interdisciplinarity

Contraction waves in self-oscillating polymer gels

As one type of active soft matter, polymer gels coupled mechanical and chemical oscillations, such as Belousov–Zhabotinsky (BZ) gels are widely researched and developed into biomimetic actuators. In the previous literature, the self-oscillating BZ cylindrical gels can generate swelling waves along their longitudinal direction when they are operated without external stimuli. Here, we explore the contraction waves of BZ gels by the means of changing the external mechanical boundary. We firstly synthesize the self-oscillating gel, which is composed of N-isopropyl acrylamide (NIPAAm) gel and a covalently bound metal catalyst of the ruthenium complex. Then, the stress-curve of the gels is investigated to evaluate the elastic modulus of each state of the BZ gel and verified our method. Finally, we investigate the effects of several factors including initial diameters of the gel, various strain, and measuring process on the generation of contraction waves in gels undergoing the BZ reaction by experiments.

A fractional analysis of Noyes–Field model for the nonlinear Belousov–Zhabotinsky reaction

Nonlinear phenomena play an essential role in various field of natural sciences and engineering. In particular, the nonlinear chemical reactions are observed in various domains, as, for instance, in biological and chemical physics. For this reason, it is important to investigate the solution to this nonlinear phenomenon. This article investigates numerical solutions to a nonlinear oscillatory system called the Belousov–Zhabotinsky with Caputo fractional-time derivative. The simplified Noyes–Field fractional model reads $$\begin{aligned} {\mathcal {D}}_t^{\mu }p= & {} \xi _1p_{xx}+\beta \delta {w}+p-p^2-\delta {pw},\quad 0<\mu \le 1,\\ {\mathcal {D}}_t^{\mu }w= & {} \xi _2w_{xx}+ \gamma {w}-\lambda {pw}, \end{aligned}$$ where $$\xi _1$$ and $$\xi _2$$ are the diffusing constants for the concentration p and w respectively, $$\gamma $$ and $$\beta $$ are given constants, $$\lambda \ne 1$$ and $$\delta $$ are positive parameters. The two iterative techniques used in this work are the fractional reduced differential transform method and q-homotopy analysis transform method. The outcomes using these two methods reveal an efficient numerical solution with high accuracy and minimal computations. Furthermore, to better understand the effect of the fractional order, we present the solution profiles which demonstrate the behavior of the obtained results.

Chemistry and Mathematics of the Belousov–Zhabotinsky Reaction in a School Laboratory

Chemical reactions far from equilibrium can exhibit oscillatory behavior. Full understanding of this phenomenon is outside of the school curriculum. However, the importance of such processes in lif...

Energy Dissipation at Interfaces Drives Multicompartment Remodeling

In this issue of Chem, Cheng and Perez-Mercader use the dissipative assembly of amphiphilic polymers coupled to a Belousov-Zhabotinsky reaction to generate dynamic compartments. The results highlight the importance of active interfacial processes in driving compartment formation and provide a route for controlling the dynamic self-assembly of molecules into life-like assemblies.

Dynamics of the Stochastic Belousov-Zhabotinskii Chemical Reaction Model

In this paper, we discuss the dynamic behavior of the stochastic Belousov-Zhabotinskii chemical reaction model. First, the existence and uniqueness of the stochastic model’s positive solution is proved. Then we show the stochastic Belousov-Zhabotinskii system has ergodicity and a stationary distribution. Finally, we present some simulations to illustrate our theoretical results. We note that the unique equilibrium of the original ordinary differential equation model is globally asymptotically stable under appropriate conditions of the parameter value f, while the stochastic model is ergodic regardless of the value of f.

Interaction of a Weak Acid Cation Exchange Resin (Dowex Mac 3H) with the Belousov‐Zhabotinsky Reaction and Estimation of Metal Ions

AbstractThe work pertains to the study on direct and indirect interaction of a macroporous weak acid cation exchange resin‐Dowex Mac 3H form with Belousov‐Zhabotinsky (BZ) reaction based on malonic acid‐cerium‐bromate‐sulfuric acid system. In the direct mode, the above reaction was perturbed by adding 10% (w/w) of Dowex Mac 3H at three different time intervals, i. e., before the start of induction period, during the induction period and after the commencement of oscillations. This mode of interaction was studied to investigate the effect of heterogeneity on the dynamics of BZ reaction. The indirect interaction of the resin was studied by interacting the resin individually with the optimized metal catalyst for a particular period of time after which the supernatant was used as initial reagent in the otherwise optimized BZ system. The interaction was monitored with respect to the change in oscillatory parameters before and after loading the resin with metal catalyst. The selectivity of the resin towards cerium and iron (ferroin) was studied through the said BZ reaction using potentiometry as the main technique. It was found that resin is more selective towards ferroin. The selectivity of the resin towards the various metal ions was followed by their estimation using UV‐Visible spectrophotometry. The effect of solvents on the ion exchange capacity (IEC) of the resin was also studied through the BZ reaction. Some solvents increased its IEC while others decreased it. The potentiometric results obtained were validated by spectroscopic findings and electrochemical studies.

Capillarity-Induced Propagation Reversal of Chemical Waves in a Self-oscillating Gel.

In a self-oscillating gel, unidirectional chemical waves generated by the Belousov-Zhabotinsky reaction can drive locomotion, which results from the difference between the push and pull forces in the wavefront and waveback, respectively. In a narrow tube, such a gel is subject not only to the asymmetric force engendered by the propagation of the chemical waves but also to additional forces originating from the capillary effect in the polymer skeleton. The ends of a self-oscillating gel in a tube are squeezed unequally during unidirectional motion, causing new waves of higher frequency and ultimately giving rise to reversal of the direction of chemical wave propagation. This peculiar phenomenon of a self-oscillating gel in a narrow glass tube results in a nonmonotonic evolution of the gel locomotion velocity.

The Belousov-Zhabotinsky Reaction in Thermoresponsive Core-Shell Hydrogel Microspheres with a Tris(2,2'-bipyridyl)ruthenium Catalyst in the Core.

The Belousov-Zhabotinsky (BZ) reaction shows temporal or spatiotemporal structures such as redox oscillation of the catalyst, [ruthenium(II)tris(2,2'-bipyridine)][PF6]2 ([Ru(bpy)3][PF6]2). In this study, autonomously oscillating hydrogel microspheres (microgels) were investigated, which show swelling/deswelling oscillation induced by the redox oscillation of the BZ reaction inside the gel. Despite the periodically and autonomously induced oscillation that does not require an external stimulus, it has not been possible to perform any manipulation of the oscillatory behavior over time. The results of the present study show that it is possible to reversibly switch the microgel oscillations from an "on" active state of the BZ reaction to an "off" inactive state by changing the temperature in combination with thermoresponsive microgels. To realize on-demand switching, the construction of double-shell structures is crucial; the thermoresponsive first shell allows the microgels to modulate the diffusion of the substrates or intermediates in the BZ reaction, while the second shell maintains colloidal stability under high temperatures and high ion concentrations. The functionalized double-shell microgels were prepared via multistep seeded precipitation polymerization. The oscillatory switching behavior of the BZ reaction was observed directly and evaluated by ultraviolet-visible (UV-vis) spectroscopy. The central concept of this study, i.e., "on-off switching" can be expected to benefit the development of advanced bioinspired materials.

Comparison of Complexity and Predictability of a Cellular Automaton Model in Excitable Media Cardiac Wave Propagation Compared with a FitzHugh-Nagumo Model

Background: Excitable media are spatially distributed systems that propagate signals without damping. Examples include fire propagating through a forest, the Belousov-Zhabotinsky reaction, and cardiac tissue. (1) Excitable media generate waves which synchronize cardiac muscle contraction with each heartbeat. Spatiotemporal patterns formed by excitation waves distinguish healthy heart tissues from diseased ones. (3) Discrete Greenberg-Hastings Cellular- Automaton (CA) (1) and the continuous FitzHugh- Nagumo (FHN) model (7) are two methods used to simulate cardiac wave propagation. However, previous observations have shown that these models are not accurately predictive of experimental results as a function of time. We hypothesize that cardiac simulations deviate from the experimental data at a rate that depends on the complexity of the experimental data’s initial conditions (I.C.).Methods: To test this hypothesis, we investigated two types of propagating waves with different complexities: a planar (i.e. simple) and a spiral wave (i.e. complex). With the same I.C., we first compared simulation results of a Greenberg-Hastings Cellular Automaton (GH-CA) model to that a FitzHugh-Nagumo (FHN) continuous model which we used as a surrogate for experimental data. We then used median-filtered real-time cardiac tissue experimental data to initialize the GH-CA model and observe the divergence of wave propagation in the simulation and the experiment.Results: The alignment between the CA model of a planar wave and the FHN model remains constant, while the degree of overlap between the CA and FHN models decreases for a spiral wave as a function of time. CA simulation initialized by a planar wave real-time cardiac tissue data propagates like the experimental data, however, this is not the case for the spiral wave experimental data.Conclusion: We were able to confirm our hypothesis that the divergence between the two models is due to initial condition (I.C.) complexity.Discussion: We discuss a promising strategy to represent a GH-CA model as a Convolutional Neural Network (CNN) to enhance predictability of the model when an initial condition is given by the experimental data with a higher level of complexity.

Chemically oscillating reactions in the formation of botryoidal malachite

Abstract The origin of banding patterns in malachite [Cu2CO3(OH)2] is an enduring problem in geology. While the bright green, vivid colors of this mineral have been attributed to the presence of Cu, no specific process has been proposed that can explain the perfect circularly concentric banding and geometrical shapes in botryoidal malachite. These patterns of concentric equidistant laminations are comparable to those arising from chemically oscillating experiments using the classical reactants of the Belousov-Zhabotinsky (B-Z) reaction. Through optical microscopy and micro-Raman imaging, this contribution documents that the geometric centers of the self-similar geometric patterns are often composed of organic matter. Carbon isotopes and trace elements further suggest that non-biological decarboxylation reactions of biological organic matter took place during diagenesis. Hence, the morphological and chemical characteristics of chemically oscillating reactions offer a plausible explanation for the formation of botryoidal malachite and abiotic environmental decarboxylation reactions.

Study on the Formation of Complex Chemical Waveforms by Different Computational Methods

Chemical wave is a special phenomenon that presents periodic patterns in space-time domain, and the Belousov–Zhabotinsky (B-Z) reaction is the first well-known reaction-diffusion system that exhibits organized patterns out of a homogeneous environment. In this paper, the B-Z reaction kinetics is described by the Oregonator model, and formation and evolution of chemical waves are simulated based on this model. Two different simulation methods, partial differential equations (PDEs) and cellular automata (CA) are implemented to simulate the formation of chemical waveform patterns, i.e., target wave and spiral wave on a two-dimensional plane. For the PDEs method, reaction caused changes of molecules at different location are considered, as well as diffusion driven by local concentration difference. Specifically, a PDE model of the B-Z reaction is first established based on the B-Z reaction kinetics and mass transfer theory, and it is solved by a nine-point finite difference (FD) method to simulate the formation of chemical waves. The CA method is based on system theory, and interaction relations with the cells nearest neighbors are mainly concerned. By comparing these two different simulation strategies, mechanisms that cause the formation of complex chemical waves are explored, which provides a reference for the subsequent research on complex systems.

A programmable chemical computer with memory and pattern recognition

Current computers are limited by the von Neumann bottleneck, which constrains the throughput between the processing unit and the memory. Chemical processes have the potential to scale beyond current computing architectures as the processing unit and memory reside in the same space, performing computations through chemical reactions, yet their lack of programmability limits them. Herein, we present a programmable chemical processor comprising of a 5 by 5 array of cells filled with a switchable oscillating chemical (Belousov–Zhabotinsky) reaction. Each cell can be individually addressed in the ‘on’ or ‘off’ state, yielding more than 2.9 × 1017 chemical states which arise from the ability to detect distinct amplitudes of oscillations via image processing. By programming the array of interconnected BZ reactions we demonstrate chemically encoded and addressable memory, and we create a chemical Autoencoder for pattern recognition able to perform the equivalent of one million operations per second.

Dissipative Self-Assembly of Dynamic Multicompartmentalized Microsystems with Light-Responsive Behaviors

Summary Living cells are compartmentalized systems operating far from thermodynamic equilibrium and consume energy from the environment to carry out their functions. The construction of biomimetic synthetic compartments has both scientific and technological value. Despite many advances, the assembly of synthetic compartments that present nonequilibrium behaviors based on dissipative (or transient) self-assembly remains a grand challenge. Here, we describe the design and synthesis of multicompartmental systems with an active microstructure and complex behaviors. By including an artificial pathway for energy dissipation, we demonstrate the autonomous generation of active polymeric systems using a strategy based on polymerization-induced self-assembly (PISA), driven by chemical fuel. Remarkably, these self-organized synthetic systems exhibit a dynamic change in their multicompartmental structures when exposed to light. This work introduces a strategy toward the design and construction of synthetic compartments with a dynamic structure and also presents pathways to engineer materials with spatially controllable structures and functionalities.

Resonant drift of synchronized spiral waves in excitable media.

Many methods have been employed to investigate the drift behavior of spiral waves in an effort to understand and control their dynamics. Here, we propose a joint method to control the dynamics of spiral waves by applying both a rotating external field and periodic forcing. First, spirals in different regimes (including rigidly rotating, meandering, and drifting spirals) are synchronized by suitable rotating external fields. Then, under weak periodic forcing at frequencies equal to those of the external fields, the synchronized spirals undergo a directional and simple drift. Dependence of the drift velocity of the synchronized spiral on the initial rotational phase of the rotating external field and on the initial phase of the periodic forcing is studied in detail. We hope that our theoretical results can be observed in experiments, such as in the Belousov-Zhabotinsky reaction.

Non-linear Chemical Reactions

In this article, we discuss the Belousov–Zhabotinsky (BZ) reaction and its relation with the Oregonator model of chemical reactions. The Oregonator model has a limit cycle, and the BZ reaction shows chemical oscillations. We compare the time series obtained from the Oregonator model, with the time series obtained froman experimental study of the BZ reaction and show that the qualitative behaviour is similar. We also construct the limit cycle from the experimental data using the Takens’ embedding theorem and compare it with the limit cycle from the Oregonator model. We conclude with a demonstration of the spatio-temporal patterns which can be seen in the two-dimensional version of this system.

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.

The Behavior of BZ Reaction in Small Space with Liquid Marble

The Behavior of BZ Reaction in Small Space with Liquid Marble

Fabrication of Self-Oscillating Micelles with a Built-In Oxidizing Agent.

Various biological behaviors are fueled by "respiration", which is an example of catabolism. So far, we have reported various self-oscillating soft materials exhibiting bioinspired dynamic movements. These autonomous polymer systems are driven by the Belousov-Zhabotinsky (BZ) reaction, which is analogous to the tricarboxylic acid (TCA) cycle that is an integral part of respiration. However, in the BZ reaction, the external addition of an oxidizing agent is necessary to initiate the oxidation process, which is realized by intracellular moieties such as ubiquinone in living systems. Herein, we realized self-oscillating micelles that are driven without the external addition of an oxidizing agent. This was achieved by embedding the oxidizing source into the structure of the self-oscillating AB diblock copolymers. This strategy introduces a new function equivalent to intracellular oxidizing moieties, and is useful for the design of completely autonomous bioinspired materials.