An Oregonator-Class Model for Photoinduced Behavior in the Ru(bpy)32+-Catalyzed Belousov−Zhabotinsky Reaction

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.

Synthesis of Non-Uniform Functionalized Amphiphilic Block Copolymers and Giant Vesicles in the Presence of the Belousov-Zhabotinsky Reaction

Giant vesicles with several-micrometer diameters were prepared by the self-assembly of an amphiphilic block copolymer in the presence of the Belousov-Zhabotinsky (BZ) reaction. The vesicle is composed of a non-uniform triblock copolymer synthesized by multi-step reactions in the presence of air at room temperature. The triblock copolymer contains poly(glycerol monomethacrylate) (PGMA) as the hydrophilic block copolymerized with tris(2,2'-bipyridyl)ruthenium(II) (Ru(bpy)3), which catalyzes the BZ reaction, and 2-hydroxypropyl methacrylate (HPMA) as the hydrophobic block. In this new approach, the radicals generated in the BZ reaction can activate a reversible addition-fragmentation chain transfer (RAFT) polymerization to self-assemble the polymer into vesicles with diameters of approximately 3 µm. X-ray photoelectron spectroscopy (XPS) measurements demonstrated that the PGMA-b-Ru(bpy)3-b-PHPMA triblock copolymer is brominated and increases the osmotic pressure inside the vesicle, leading to micrometer-sized features. The effect of solvent on the morphological transitions are also discussed briefly. This BZ strategy, offers a new perspective to prepare giant vesicles as a platform for promising applications in the areas of microencapsulation and catalyst support, due to their significant sizes and large microcavities.

The Tris(2,2'-Bipyridyl)Ruthenium-Catalysed Belousov–Zhabotinsky Reaction

The Belousov – Zhabotinsky (BZ) reaction is the prototypical oscillating chemical reaction. The tris(2,2'-bipyridine)ruthenium-catalysed BZ reaction (often simply referred to as the ruthenium-catalysed BZ reaction) displays photosensitivity and has been widely exploited for examination of the effects of illumination on nonlinear reaction kinetics. In this review, we investigate the behaviour of the ruthenium-catalysed BZ reaction. The mechanism of the reaction is analysed and we examine how light sensitivity is incorporated into kinetic models of the reaction. The temporal dynamics of the photosensitive reaction is presented and, finally, we discuss the extraordinary wealth of behaviour that has been observed in the spatially-distributed system when perturbed by visible light.

Tuning the oscillatory dynamics of the Belousov–Zhabotinsky reaction using ruthenium nanoparticle decorated graphene

Ruthenium nanoparticle decorated graphene nano-mats to enhance chemical oscillations in BZ reactions.

Long-Lasting Complex Reaction Behavior in a Closed Ferroin-Bromate-Hydroxybenzenesulfonate System

The bromate-phenolsulfonate reaction was found to exhibit spontaneous oscillations in a batch reactor, where the addition of small amounts of ferroin would result in nonoscillatory behavior. As the ferroin concentration was increased, the system produced very rich nonlinear behavior, including three isolated oscillatory regimes that were separated by as long as 48 h nonoscillatory period. The long-lasting nonlinear behavior may be attributed to the slow desulfonation of phenolsulfonate in an acidic solution, forming phenol-like intermediates. However, unlike the bromate-phenol oscillator, oxygen was found to greatly influence the reaction, and various complex oscillations could be observed by tuning the oxygen concentration. Mechanistic studies performed through employing ¹H NMR spectroscopy and mass spectrometry to measure intermediate species at different stages of the reaction were able to identify 1,4-benzoquinone, 2-bromo-1,4-benzoquinone, 2,6-dibromo-1,4-benzoquinone, and 2,4,6-tribromophenol as major components during the reaction.

Weakly and strongly coupled Belousov-Zhabotinsky patterns

We investigate experimentally and numerically the synchronization of two-dimensional spiral wave patterns in the Belousov-Zhabotinsky reaction due to point-to-point coupling of two separate domains. Different synchronization modalities appear depending on the coupling strength and the initial patterns in each domain. The behavior as a function of the coupling strength falls into two qualitatively different regimes. The weakly coupled regime is characterized by inter-domain interactions that distorted but do not break wave fronts. Under weak coupling, spiral cores are pushed around by wave fronts in the other domain, resulting in an effective interaction between cores in opposite domains. In the case where each domain initially contains a single spiral, the cores form a bound pair and orbit each other at quantized distances. When the starting patterns consist of multiple randomly positioned spiral cores, the number of cores decreases with time until all that remains are a few cores that are synchronized with a partner in the other domain. The strongly coupled regime is characterized by interdomain interactions that break wave fronts. As a result, the wave patterns in both domains become identical.

Dynamical regimes of four almost identical chemical oscillators coupled via pulse inhibitory coupling with time delay

The dynamics of four almost identical pulse coupled chemical oscillators with time delay are systematically studied.

Experimental, numerical, and mechanistic analysis of the nonmonotonic relationship between oscillatory frequency and photointensity for the photosensitive Belousov-Zhabotinsky oscillator

The oscillation frequency of a nonlinear reaction system acts as a key factor for interaction and superposition of spatiotemporal patterns. To control and design spatiotemporal patterns in oscillatory media, it is important to establish the dominant frequency-related mechanism and the effects of external forces and species concentrations on oscillatory frequency. In the Ru(bipy)3(2+)-catalyzed Belousov-Zhabotinsky oscillator, a nonmonotonic relationship exists between light intensity and oscillatory frequency (I-F relationship), which is composed of fast photopromotion and slow photoinhibition regions in the oscillation frequency curve. In this work, we identify the essential mechanistic step of the I-F relationship: the previously proposed photoreaction Ru(II)* + Ru(II) + BrO3(-) + 3H(+) → HBrO2 + 2Ru(III) + H2O, which has both effects of frequency-shortening and frequency-lengthening. The concentrations of species can shift the light intensity that produces the maximum frequency, which we simulate and explain with a mechanistic model. This result will benefit studies of pattern formation and biomimetic movement of oscillating polymer gels.

New type of excitatory pulse coupling of chemical oscillators via inhibitor

A new type of excitatory pulse coupling of two chemical oscillators via a short interruption of inhibitor inflow is introduced.

Insights into collective cell behaviour from populations of coupled chemical oscillators

Biological systems such as yeast show coordinated activity driven by chemical communication between cells. Experiments with coupled chemical oscillators can provide insights into the collective behaviour.

Mechano-chemical coupling in Belousov-Zhabotinskii reactions

Mechano-chemical coupling has been recently recognised as an important effect in various systems as chemical reactivity can be controlled through an applied mechanical loading. Namely, Belousov-Zhabotinskii reactions in polymer gels exhibit self-sustained oscillations and have been identified to be reasonably controllable and definable to the extent that they can be harnessed to perform mechanical work at specific locations. In this paper, we use our theoretical work of nonlinear mechano-chemical coupling and investigate the possibility of providing an explanation of phenomena found in experimental research by means of this theory. We show that mechanotransduction occurs as a response to both static and dynamic mechanical stimulation, e.g., volume change and its rate, as observed experimentally and discuss the difference of their effects on oscillations. Plausible values of the quasi-stoichiometric parameter f of Oregonator model are estimated together with its dependence on mechanical stimulation. An increase in static loading, e.g., pressure, is predicted to have stimulatory effect whereas dynamic loading, e.g., rate of volume change, is predicted to be stimulatory only up to a certain threshold. Further, we offer a physically consistent explanation of the observed phenomena why some Belousov-Zhabotinskii gels require an additional mechanical stimulation to show emergence of oscillation or why "revival" of oscillations in Belousov-Zhabotinskii reactions is possible together with indications for further experimental setups.

Reconfigurable assemblies of active, autochemotactic gels

Using computational modeling, we show that self-oscillating Belousov-Zhabotinsky (BZ) gels can both emit and sense a chemical signal and thus drive neighboring gel pieces to spontaneously self-aggregate, so that the system exhibits autochemotaxis. To the best of our knowledge, this is the closest system to the ultimate self-recombining material, which can be divided into separated parts and the parts move autonomously to assemble into a structure resembling the original, uncut sample. We also show that the gels' coordinated motion can be controlled by light, allowing us to achieve selective self-aggregation and control over the shape of the gel aggregates. By exposing the BZ gels to specific patterns of light and dark, we design a BZ gel "train" that leads the movement of its "cargo." Our findings pave the way for creating reconfigurable materials from self-propelled elements, which autonomously communicate with neighboring units and thereby actively participate in constructing the final structure.

Self-oscillating gels beating like a heart muscle

So far stimuli-responsive polymer gels and their application to smart materials have been widely studied. On the other hand, as a novel biomimetic gel, we developed gels with an autonomous self-oscillating function like a heart muscle, which was firstly reported in 1996. We designed the self-oscillating polymers and gels by utilizing the oscillating reaction, called the Belousov-Zhabotinsky (BZ) reaction. The self-oscillating polymer is composed of a poly(N-isopropylacrylamide) network in which the catalyst for the BZ reaction is covalently immobilized. In the presence of the reactants, the polymer gel undergoes spontaneous cyclic swelling-deswelling changes without any on-off switching of external stimuli. Potential applications of the self-oscillating polymers and gels include several kinds of functional material systems, such as bio-mimetic actuators and mass transport surface. In this review, recent progress on the polymer gels is introduced.

Activation energy of aggregation-disaggregation self-oscillation of polymer chain

In this paper, we investigated the activation energies of the aggregation–disaggregation self-oscillation induced by the Belousov-Zhabotinsky (BZ) reaction by utilizing the nonthermoresponsive polymer chain in a wide temperature range. This is because the conventional type self-oscillating polymer chain, with thermoresponsive poly(Nisopropylacrylamide) (poly(NIPAAm) main-chain covalently bonded to the ruthenium catalyst (Ru(bpy)₃) of the BZ reaction, cannot evaluate the activation energy over the lower critical solution temperature (LCST). The nonthermoresponsive self-oscillating polymer chain is composed of a poly-vinylpyrrolidone (PVP) main-chain with the ruthenium catalyst (Ru(bpy)₃). As a result, we clarified that the activation energy of the aggregation–disaggregation self-oscillation of the polymer chain is hardly affected by the concentrations of the BZ substrates. In addition, the activation energy of the nonthermoresponsive self-oscillating polymer chain was found to be almost the same value as normal BZ reaction, i.e., not including the self-oscillating polymer system with Ru moiety.

Mechano-chemical oscillations and waves in reactive gels

We review advances in a new area of interdisciplinary research that concerns phenomena arising from inherent coupling between non-linear chemical dynamics and mechanics. This coupling provides a route for chemical-to-mechanical energy transduction, which enables materials to exhibit self-sustained oscillations and/or waves in both concentration and deformation fields. We focus on synthetic polymer gels, where the chemo-mechanical behavior can be engineered into the material. We provide a brief review of experimental observations on several types of chemo-mechanical oscillations in gels. Then, we discuss methods used to theoretically and computationally model self-oscillating polymer gels. The rest of the paper is devoted to describing results of theoretical and computational modeling of gels that undergo the oscillatory Belousov-Zhabotinsky (BZ) reaction. We discuss a remarkable form of mechano-chemical transduction in these materials, where the application of an applied force or mechanical contact can drive the system to switch between different dynamical behavior, or alter the mechanical properties of the material. Finally, we discuss ways in which photosensitive BZ gels could be used to fabricate biomimetic self-propelled objects. In particular, we describe how non-uniform illumination can be used to direct the movement of BZ gel 'worms' along complex paths, guiding them to bend, reorient and turn.

Self-oscillating gels driven by the Belousov-Zhabotinsky reaction as novel smart materials

So far stimuli-responsive polymer gels and their application to smart materials have been widely studied; this research has contributed to progress in gel science and engineering. For their development as a novel biomimetic polymer, studies of polymers with an autonomous self-oscillating function have been carried out since the first reports in 1996. The development of novel self-oscillating polymers and gels have been successful utilizing the oscillating reaction, called the Belousov-Zhabotinsky (BZ) reaction, which is recognized as a chemical model for understanding several autonomous phenomena in biological systems. The self-oscillating polymer is composed of a poly(N-isopropylacrylamide) network in which the catalyst for the BZ reaction is covalently immobilized. In the presence of the reactants, the polymer undergoes spontaneous cyclic soluble-insoluble changes or swelling-deswelling changes (in the case of gel) without any on-off switching of external stimuli. Potential applications of the self-socillating polymers and gels include several kinds of functional material systems, such as biomimetic actuators and mass transport surface.

Design of self-oscillating gels and application to biomimetic actuators

As a novel biomimetic polymer, we have developed polymer gels with an autonomous self-oscillating function. This was achieved by utilizing oscillating chemical reactions, called the Belousov-Zhabotinsky (BZ) reaction, which is recognized as a chemical model for understanding several autonomous phenomena in biological systems. Under the coexistence of the reactants, the polymer gel undergoes spontaneous swelling-deswelling changes without any on-off switching by external stimuli. In this review, our recent studies on the self-oscillating polymer gels and application to biomimetic actuators are summarized.

Three-dimensional model for chemoresponsive polymer gels undergoing the Belousov-Zhabotinsky reaction

We develop a computational model to capture the complex, three-dimensional behavior of chemoresponsive polymer gels undergoing the Belousov-Zhabotinsky reaction. The model combines components of the finite difference and finite element techniques and is an extension of the two-dimensional gel lattice spring model recently developed by two of us [V. V. Yashin and A. C. Balazs, J. Chem. Phys. 126, 124707 (2007)]. Using this model, we undertake the first three-dimensional (3D) computational studies of the dynamical behavior of chemoresponsive BZ gels. For sufficiently large sample sizes and a finite range of reaction parameters, we observe regular and nonregular oscillations in both the size and shape of the sample that are coupled to the chemical oscillations. Additionally, we determine the critical values of these reaction parameters at the transition points between the different types of observed behavior. We also show that the dynamics of the chemoresponsive gels drastically depends on the boundary conditions at the surface of the sample. This 3D computational model could provide an effective tool for designing gel-based, responsive systems.

Theoretical and computational modeling of self-oscillating polymer gels

The authors model wave propagation in swollen, chemoresponsive polymer gels that are undergoing the oscillatory Belousov-Zhabotinsky (BZ) reaction. To carry out this study, they first modify the Oregonator model for BZ reactions in simple solutions to include the effect of the polymer on the reaction kinetics. They then describe the gel dynamics through the framework of the two-fluid model. The polymer-solvent interactions that are introduced through the BZ reaction are captured through a coupling term, which is added to the Flory-Huggins model for polymer-solvent mixtures. The resulting theoretical model is then used to develop the gel lattice spring model (gLSM), which is a computationally efficient approach for simulating large-scale, two-dimensional (2D) deformations and chemical reactions within a swollen polymer network. The 2D calculations allow the authors to probe not only volume changes but also changes in the sample's shape. Using the gLSM, they determine the pattern formation and shape changes in 2D rectangular BZ gels that are anchored to a solid wall. They demonstrate that the dynamic patterns depend on whether the gel is expanded or contracted near the wall, and on the sample's dimensions. Finally, they isolate a scenario where the detachment of the gel from the wall leads to macroscopic motion of the entire sample.

Pattern Formation and Shape Changes in Self-Oscillating Polymer Gels

We developed an efficient model for responsive gels that captures large-scale, two-dimensional (2D) deformations and chemical reactions within a swollen polymer network. The 2D calculations allowed us to probe not only volume changes but also changes in sample shape. By focusing on gels undergoing the oscillatory Belousov-Zhabotinsky reaction, we observed traveling waves of local swelling that form a rich variety of dynamic patterns and give rise to distinctive oscillations in the gel's shape. The observed patterns depend critically on the gel's dimensions. The approach provides a useful computational tool for probing the dynamics of chemomechanical processes and uncovering morphological transformations in responsive gels.