Belousov-Zhabotinsky Reaction Research Articles

Periodic perturbation of chemical oscillators: entrainment and induced synchronization.

It is well known that a large number of catalyst-carrying beads immersed in an oscillatory chemical medium (Belousov-Zhabotinsky reaction) display collective oscillatory behavior. Using a light sensitive version of BZ, we show that this collective behavior can be entrained to an external light source with an oscillatory intensity. Thus, the emerging collective behavior can be controlled by an external perturbation.

Unpinning of scroll waves under the influence of a thermal gradient.

Three-dimensional scroll waves of electrical activity are among the mechanisms believed to be responsible for the rapid, unsynchronized contraction of cardiac ventricles, thereby reducing the heart's ability to pump blood. Scroll waves can attach themselves to unexcitable obstacles, and this sometimes highly elongates their life span. Hence, the unpinning and annihilation of these vortices has attracted much attention in recent decades. In this work, we study the influence of a thermal gradient on scroll waves pinned to inert obstacles, in the Belousov-Zhabotinsky reaction. Under a temperature gradient, scroll rings were seen to unpin from these obstacles, thus strikingly reducing their lifetimes. These results were also reproduced by numerical simulations using the Barkley model.

Pinned chemical waves in the presence of Stokes flow.

Excitable reaction-diffusion systems form a wealth of dissipative concentration patterns that exist not only in chemical systems but also control or disrupt biological functions. An important example are rotating spiral waves in the autocatalytic Belousov-Zhabotinsky reaction. We show that the viscosity of this system can be increased by the addition of the polymer xanthan gum. In the resulting system, we pin spiral waves to a thin glass rod and then reposition the vortex centers by a linear motion of the heterogeneity. The Stokes flow generated by this motion can be a weak perturbation to the wave pattern and follows a simple, analytical expression. Numerical simulations of a corresponding reaction-diffusion-flow model reproduce the experimental observations and show that the spatial extent of the flow field can vary widely around the characteristic wavelength of the spiral. We find that a sharp spatial decay of the flow pattern corresponds to our experimental observations, whereas more expansive flow fields surprisingly allow the repositioning of spiral tips at speeds faster than the wave velocity.

Function and Autonomous Behavior of Self-Oscillating Polymer Systems

A novel gel undergoes the Belousov-Zhabotinsky (BZ) reaction in strong-acid-free conditions. Under such conditions, the gel can switch the BZ reaction on or off in conventional self-oscillating gels that undergo self-oscillation only in aqueous solutions with strong acids, such as HNO3 or H2SO4. The self-oscillation of the polymer chain can be controlled by varying the temperature, owing to its thermoresponsive property. Moreover, the polymer chain undergoes viscosity self-oscillations in strong-acid-free conditions. In this review, the direct observation of self-oscillations in polymer chains attached to glass or gold surfaces, by using scanning probe microscopy and quartz crystal microbalances with dissipation monitoring, is discussed.

Spectral imaging of chemical reactions using a computer display and a digital camera

Various processes in chemistry lead to formation of spatial gradients, and cannot be directly studied using conventional spectroscopic techniques. Here we aimed to develop a simple method for the monitoring of light absorption at three wavelengths in two dimensions. The experimental setup consists of a commercial liquid crystal display (LCD) computer screen with light-emitting diode (LED) back illumination, and a digital camera equipped with a complementary metal oxide semiconductor imager. The computer screen serves as a multi-wavelength light source while the camera records distributions of the light transmitted through a two-dimensional non-homogeneous dynamic sample (reaction mixture). A program in C# language constantly changes the background colour of a console window, so as to alternately relay the light of different wavelength (λmax = 608, 540, and 455 nm, respectively) onto the sample. The light emitted by the screen passes through a Petri dish containing the sample, while the digital camera records images revealing distributions of chemical substances absorbing at different wavelengths. The interval between two successive colour displays is 200–300 milliseconds. In this demonstration of the method, we followed two processes: the Belousov–Zhabotinsky oscillating reaction and the Old Nassau (Halloween) clock reaction. Every experiment produced a series of light absorption images corresponding to the wavelengths of the LCD/LED screen. Chemical front formation could be observed for analytes absorbing light at one of the three wavelength bands. In future, this approach can be extended to imaging at multiple wavelengths (by introducing customized LCD matrices and modified LED back illumination), and used in the monitoring of other non-homogeneous chemical processes.

On logical universality of Belousov-Zhabotinsky vesicles

Belousov-Zhabotinsky (BZ) excitable chemical medium exhibits a rich variety of spatial patterns of excitation. In a sub-excitable light-sensitive chemical medium, an asymmetric disturbing or excitation, causes formation of localized travelling excitation wave-fragments. When two or more wave-fragments collide, they annihilate or merge into new wave-fragment. The wave-fragments can be thought as elementary units of information and their interaction sites as a logical gates. Size and life span of a wave-fragment depends on a level of medium’s illumination. By encapsulating BZ reaction into a lipid vesicle, we can manipulate the BZ-derived logical gates. By interpreting wave-fragments as values of Boolean variables, we design a collision-based polymorphic logical gate in BZ vesicles. The gate implements operation xnor for low illumination, and it acts as nor gate for high illumination.

Quasi-elastic laser scattering for measuring inhomogeneous interfacial tension in non-equilibrium phenomena with convective flows.

An inhomogeneous distribution of interfacial tension can induce different types of non-equilibrium spontaneous motion at the interface by convective flow, or by the solutal Marangoni effect. Several applications of the quasi-elastic laser scattering (QELS) method used to study these effects are presented here. The relationship between the interfacial tension and the non-equilibrium phenomena has been verified experimentally for each application. In a water/nitrobenzene oscillatory system with continuous surfactant addition to the interface, the local adsorption of surfactants at the interface has been demonstrated and shown to be strongly related to the presence of electrolytes. In a donor/membrane/acceptor system, the dual-beam QELS method shows that surfactant adsorption at the membrane/acceptor interface is responsible for oscillations in the electric potential. The differences in the adsorption/desorption behavior of metal complex catalysts between air/liquid and liquid/liquid interfaces were considered in the propagating chemical waves of the Belousov-Zhabotinsky reaction. We successfully measured the distribution of interfacial tension around a self-propelled camphor boat and an alcohol droplet floating on an aqueous phase, and compared the mechanisms of their motion.

Using light to control the interactions between self-rotating assemblies of active gels

Polymer gels undergoing the oscillating Belousov-Zhabotinsky (BZ) reaction exhibit an autonomous, periodic swelling and deswelling, where the mechanical oscillations are driven by the chemical reaction within the polymer network. Using computer simulations, we show that these BZ gels can undergo a form of auto-chemotaxis, enabling the gels to spontaneously move in response to self-generated chemical gradients. Focusing on four millimeter-sized pieces of these BZ gels, we show that the pieces can organize into self-rotating clusters that resemble a moving pinwheel or gear. By analyzing the factors that promote the formation of a single self-rotating cluster, we attempt to design systems of multiple, interacting gears. We show that light, which suppresses the oscillations of the gels, can be harnessed to promote the formation of two self-rotating clusters. These studies point to a novel form of photo-chemo-mechanical transduction, where light is utilized to control the conversion of chemical and mechanical energy in the system. Moreover, the interaction between the BZ gel gears reveals a new form of entrainment between these moving units. Namely, their coordinated motion is achieved through chemical coupling or communication, rather than a mechanical coupling. These findings can lead to the formation of chemically “communicating” devices that can be programmed to perform autonomous work through the use of light.

Influence of Belousov-Zhabotinsky substrate concentrations on autonomous oscillation of polymer chains with Fe(bpy)3 catalyst.

We studied the effect of initial substrate concentrations in the Belousov-Zhabotinsky (BZ) reaction on the optical transmittance self-oscillation behavior of a polymer chain consisting of N-isopropylacrylamide (NIPAAm) and a Fe catalyst ([Fe(bpy)3]). The driving force of this transmittance self-oscillation was the solubility difference between the reduced and oxidized states of the [Fe(bpy)3] moiety in the polymer chain. The amplitude of the soluble-insoluble self-oscillation of poly(NIPAAm-co-[Fe(bpy)3]) was significantly smaller than that of poly(NIPAAm-co-[Ru(bpy)3]). Theoretical simulation results attributed this behavior to the small difference in the solvent qualities, C*, of the reduced and oxidized states. Furthermore, we clarified that poly(NIPAAm-co-[Fe(bpy)3]) required a narrower concentration range of HNO3 to exhibit self-oscillation than poly(NIPAAm-co-[Ru(bpy)3]), since transmittance self-oscillation occurred only for [HNO3] = 0.3 M. The period of self-oscillation of poly(NIPAAm-co-[Fe(bpy)3]) in solution was controlled mainly by NaBrO3 concentration and was hardly influenced by the initial concentration of malonic acid.

Activation Energy of Autonomous Polymer Chains with High LCST

A self-oscillating polymer chain consisting ofN-ethylacrylamide (NEAAm) and a Ru catalyst of the BelousovZhabotinsky (BZ) reaction was prepared. The polymer chain underwent soluble-insoluble self-oscillation induced by the BZ reaction, originating from the differing solubility of the Ru moiety in the reduced and oxidized states. The amplitude of self-oscillation was small compared to that for the polymer chains prepared fromN-Isopropylacrylamide (NIPAAm). The activation energy observed with the novel, NEAAm-based polymer chain was 68 kJ/mol, similar to that found with the NIPAAm-based polymer chain and normal (no Ru catalyst incorporated in the polymer) BZ reaction.

A Self-Oscillating Polymer Chain with High LCST

A novel self-oscillating polymer displaying a high lower critical solution temperature (LCST) was developed. The novel polymer chain underwent soluble-insoluble self-oscillation induced by a Belousov–Zhabotinsky reaction. The driving force of the self-oscillation was the differing solubility of the polymer chain in the reduced and oxidized states. The amplitude of self-oscillation was hardly affected by the concentration of the oxidant, sodium bromate. In addition, the period of the polymer solution could be controlled by careful selection of the concentration of the sodium bromate.

Evolution of self-oscillating polymer gels as autonomous polymer systems

We have developed ‘self-oscillating’ gels that undergo spontaneous cyclic swelling–deswelling changes without any on–off switching of external stimuli, as with heart muscle. The self-oscillating gels were designed by utilizing the Belousov–Zhabotinsky (BZ) reaction, an oscillating reaction, as a chemical model of the tricarboxylic acid cycle. We have systematically studied these polymer gels since they were first reported in 1996. Our studies represent innovative research, creating new concepts of functional gels and expanding their potential, and they have attracted attention in many research fields and have inspired related studies. Here, our recent progress on self-oscillating polymer gels is summarized. We developed ‘self-oscillating’ polymer gels that undergo spontaneous cyclic swelling–deswelling changes without any on–off switching of external stimuli like a heart muscle. Here, our recent progress on the self-oscillating polymer gels was summarized. Muscles and other soft tissues in the body experience spontaneous rhythmic changes, such as a heartbeat, hormonal secretion and the cell cycle, without requiring external stimulation. Ryo Yoshida and Takeshi Ueki from the University of Tokyo, Japan, review their team's progress to develop polymer gels that freely undergo cyclic swelling and shrinking. Although tremendous efforts to mimic biological systems have generated numerous synthetic responsive materials for smart tissue engineering and therapeutic applications, these existing systems lack autonomy and depend on induced pH, temperature and other environmental fluctuations to operate. In contrast, the team's gels rely on the oscillating Belousov–Zhabotinsky reaction — a metal-catalyzed oxidation reaction that exhibits spontaneous periodic temporal and spatial patterns. The self-oscillating gels have applications that include biomimetic actuators and tubular intestine-like mass transport systems, providing new perspectives for materials science, robotics and biophysics.

Painlevé analysis and exact solutions for the Belousov–Zhabotinskii reaction–diffusion system

A system of equations for description of the Belousov–Zhabotinskii chemical reaction is considered. The Painlevé analysis of this reaction–diffusion system is studied. Exact traveling wave solutions of the system for the Belousov–Zhabotinskii reaction are found. Periodic solutions expressed in terms of the Weierstrass elliptic function are also given.

Chiral selection and frequency response of spiral waves in reaction-diffusion systems under a chiral electric field

Chirality is one of the most fundamental properties of many physical, chemical, and biological systems. However, the mechanisms underlying the onset and control of chiral symmetry are largely understudied. We investigate possibility of chirality control in a chemical excitable system (the Belousov-Zhabotinsky reaction) by application of a chiral (rotating) electric field using the Oregonator model. We find that unlike previous findings, we can achieve the chirality control not only in the field rotation direction, but also opposite to it, depending on the field rotation frequency. To unravel the mechanism, we further develop a comprehensive theory of frequency synchronization based on the response function approach. We find that this problem can be described by the Adler equation and show phase-locking phenomena, known as the Arnold tongue. Our theoretical predictions are in good quantitative agreement with the numerical simulations and provide a solid basis for chirality control in excitable media.

SELF-OSCILLATIONS OF HYDROGELS DRIVEN BY CHEMICAL REACTIONS

A model is developed for the mechanical response of hydrogels whose deformation is accompanied by swelling–shrinkage driven by the Belousov–Zhabotinsky reaction. A hydrogel is treated as a compressible network of flexible chains with a time-dependent reference (stress-free) state whose evolution is driven by oxidation of a catalyst pendent to chains. The model involves three components: stress–strain relations for deformation of a polymer network coupled with swelling, kinetic equations for chemical reactions with diffusing species, and relations connecting changes in the reference configuration with concentration of oxidized catalyst. Results of simulation confirm the ability of the model to describe autonomous oscillations of a hydrogel layer under constrained swelling. The effect of material parameters on amplitude and frequency of oscillations is studied numerically. In agreement with the available experimental data, it is shown that amplitude of oscillations decreases and their period increases when (i) elastic modulus of the polymer network grows, (ii) a good solvent is replaced with a poor one, (iii) concentration of a catalyst is reduced, (iv) size of a sample decreases, and (v) diffusivities of solvent and activator grow.

Giant volume change of active gels under continuous flow.

While living systems have developed highly efficient ways to convert chemical energy (e.g., ATP hydrolysis) to mechanical motion (e.g., movement of muscle), it remains a challenge to build muscle-like biomimetic systems to generate mechanical force directly from chemical reactions. Here we show that a continuous flow of reactant solution leads to by far the largest volume change to date in autonomous active gels driven by the Belousov-Zhabotinsky reaction. These results demonstrate that microfluidics offers a useful and facile experimental approach to optimize the conditions (e.g., fabrication methods, counterions, flow rates, concentrations of reagents) for chemomechanical transduction in active materials. This work thus provides much needed insights and methods for the development of chemomechanically active systems based on combining soft materials and microfluidic systems.

Information coding with frequency of oscillations in Belousov-Zhabotinsky encapsulated disks.

Information processing with an excitable chemical medium, like the Belousov-Zhabotinsky (BZ) reaction, is typically based on information coding in the presence or absence of excitation pulses. Here we present a new concept of Boolean coding that can be applied to an oscillatory medium. A medium represents the logical TRUE state if a selected region oscillates with a high frequency. If the frequency fails below a specified value, it represents the logical FALSE state. We consider a medium composed of disks encapsulating an oscillatory mixture of reagents, as related to our recent experiments with lipid-coated BZ droplets. We demonstrate that by using specific geometrical arrangements of disks containing the oscillatory medium one can perform logical operations on variables coded in oscillation frequency. Realizations of a chemical signal diode and of a single-bit memory with oscillatory disks are also discussed.

Directing the Behavior of Active, Self-Oscillating Gels with Light

In the biological realm, light can act as a powerful stimulus, promoting both positive and negative phototaxis. Using computational modeling, we attempt to design systems that display analogous biomimetic behavior by exhibiting directed, autonomous motion in response to light. We specifically focus on polymer gels that undergo the oscillating Belousov–Zhabotinsky (BZ) reaction and thus manifest periodic chemomechanical pulsations, which can be modulated with light. Reviewing our recent computational studies, we describe how long, rectangular samples of BZ gels, or “worms”, can perform self-sustained movement and via a distinct form of negative phototaxis migrate along complex paths under nonuniform illumination. When the ends of multiple rectangular BZ gels are anchored to a surface, the dynamic behavior of the cilia-like layer can be tuned by light to resemble the motion of a keyboard. With BZ gel pieces that move freely on a surface, we show that these gels exhibit autochemotaxis and, thereby, can self-organize in response to self-generated chemical signals. These examples illustrate that BZ gels constitute optimal materials for creating millimeter-sized soft robots whose self-sustained movement can be regulated through the use of light.

Butterfly effect in a chemical oscillator

The strong sensitivity of aperiodic dynamics to initial conditions is one of the fingerprinting features of chaotic systems. While this dependence can be directly verified by means of numerical approaches, it is quite elusive and difficult to be isolated in real experimental systems. In this paper, we discuss a didactic and self-consistent method to show the divergent behaviour between two infinitesimally different solutions of the famous Belousov–Zhabotinsky oscillator simultaneously undergoing a transition to a chaotic regime. Experimental data are also used to give an intuitive visualization of the essential meaning of a Lyapunov exponent, which allows for a more quantitative characterization of the chaotic transient.

Influence of Micellar Propinquity on Dynamics of Ce(IV)‐Catalyzed BZ Oscillatory Reaction under Stirred Conditions

ABSTRACTOscillating reactions often employed to mimic and understand complex dynamics in biological systems are known to be affected in aggregated host environments. The dynamic evolution of the oscillatory Belousov–Zhabotinsky (BZ) reaction upon addition of increasing amounts of anionic (sodium dodecylbenzenesulfonate; SDBS), cationic (hexadecyltrimethylammonium bromide; CTAB), nonionic (polyoxyethylene(20) cetyl ether; Brij58), and binary mixtures (CTAB + Brij58 and SDBS + Brij58) of surfactants was monitored using potentiometry at 25 and 35°C under stirred batch conditions. The experimental results reveal that the oscillatory parameters of the Ce(IV)‐catalyzed BZ reaction are significantly altered depending on the concentration and nature of restricted micellar host environments. In the presence of ionic surfactants, it is proposed that the evolution of the oscillatory BZ system may be due to atypical proficiency (related to hydrophobic and electrostatic interactions) of such organized self‐assemblies to affect the reactivity by selectively confiscating some key reacting species. However, the response of the BZ system to nonionic Brij58 was attributed to the reaction among the alcoholic functional groups of the surfactant with some vital species of the BZ reaction. Moreover, the nonionic + ionic binary surfactant systems exhibited behaviors representative of both the constitutive single surfactant systems.