Aspects of the Belousov−Zhabotinsky Reaction in Polymer Gels

Fabrication of submillimeter-sized spherical self-oscillating gels and control of their isotropic volumetric oscillatory behaviors

In this study, we established a fabrication method and analyzed the volumetric self-oscillatory behaviors of submillimeter-sized spherical self-oscillating gels. We validated that the manufactured submillimeter-sized spherical self-oscillating gels exhibited isotropic volumetric oscillations during the Belousov-Zhabotinsky (BZ) reaction. In addition, we experimentally elucidated that the volumetric self-oscillatory behaviors (i.e., period and amplitude) and the oscillatory profiles depended on the following parameters: (1) the molar composition of N-(3-aminopropyl)methacrylamide hydrochloride (NAPMAm) in the gels and (2) the concentration of Ru(bpy)₃-NHS solution containing an active ester group on conjugation. These clarified relationships imply that controlling the amount of Ru(bpy)₃ in the gel network could influence the gel volumetric oscillation during the BZ reaction. These results of submillimeter-sized and spherical self-oscillating gels bridge knowledge gaps in the current field because the gels with corresponding sizes and shapes have not been systematically explored yet. Therefore, our study could be a cornerstone for diverse applications of (self-powered) gels in various scales and shapes, including soft actuators exhibiting life-like functions.

Chemically controlled pattern formation in self-oscillating elastic shells

Patterns and morphology develop in living systems such as embryos in response to chemical signals. To understand and exploit the interplay of chemical reactions with mechanical transformations, chemomechanical polymer systems have been synthesized by attaching chemicals into hydrogels. In this work, we design autonomous responsive elastic shells that undergo morphological changes induced by chemical reactions. We couple the local mechanical response of the gel with the chemical processes on the shell. This causes swelling and deswelling of the gel, generating diverse morphological changes, including periodic oscillations. We further introduce a mechanical instability and observe buckling-unbuckling dynamics with a response time delay. Moreover, we investigate the mechanical feedback on the chemical reaction and demonstrate the dynamic patterns triggered by an initial deformation. We show the chemical characteristics that account for the shell morphology and discuss the future designs for autonomous responsive materials.

Efficiency range of the Belousov-Zhabotinsky reaction to induce the self-organization of transient bonds in metallo-supramolecular polymeric systems

The periodic change of the oxidation state of the metal catalyst in the oscillating Belousov-Zhabotinsky (BZ) reaction has been reported to establish a periodic organization of metallo-supramolecular bonds in polymeric systems, which results in autonomous viscosity oscillations. To appraise the possible extent of quantitative control on the viscosity oscillation features, we assess how the kinetics of the BZ reaction affects the periodic self-organization of the metal-ligand coordination, and vice versa. Our model system includes mono-, bis-, and tetra-functional polyethyleneglycol (PEG) precursors end grafted with terpyridine ligands that are complexed with ruthenium ions, which oscillate between Ru2+ and Ru3+ oxidation states in the BZ reaction medium. The control parameters are divided into microscopic factors, which are responsible for the local reaction rate, and mesoscopic factors, which are responsible for the spatial distribution of the concentration patterns. The reactant concentrations are found to nonlinearly control the amplitude and periods of reduction and oxidation phases, independent of the precursor functionalization degree. An increased medium viscosity, and therewith cease of mixing, accelerates the reaction rate by localization of the reaction phases, even though the diffusion of reaction intermediates causes a periodic chemical wave with distinct harmonics. Time-course viscosity measurements of the tetra-arm precursors in the BZ medium demonstrate an initial overshoot followed by minor oscillations around a plateau that is significantly lower than the viscosity of an equivalent fully associated network. Apparently, the slow association kinetics of Ru2+-bis(terpyridine) limits the frequency and the extent of self-organization, and this way, avoids full establishment of the expected viscosity oscillation.

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.

Multivariate statistical analysis of chemical and electrochemical oscillators for an accurate frequency selection

The effect of experimental parameters on the frequency of chemical oscillators has been systematically studied since the first observations of clock reactions. The approach is mainly based on univariate changes in one specific parameter while others are kept constant. The frequency is then monitored and the effect of each parameter is discussed separately. This type of analysis, however, does not take into account the multiple interactions among the controllable parameters and the synergic responses on the oscillation frequency. We have carried out a multivariate statistical analysis of chemical (BZ-ferroin catalyzed reaction) and electrochemical (Cu/Cu₂O cathodic deposition) oscillators and identified the contributions of the experimental parameters on frequency variations. The BZ reaction presented a strong dependence on the initial concentration of sodium bromate and temperature, resulting in a frequency increase. The concentration of malonic acid, the organic substrate, affects the system but with lower intensity compared with the combination of sodium bromate and temperature. On the other hand, the Cu/Cu₂O electrochemical oscillator was shown to be less sensitive to changes in the temperature. The applied current density and pH were the two parameters which most perturbed the system. Interestingly, the frequency behaved nonmonotonically with a quadratic dependence. The multivariate analysis of both oscillators exhibited significant differences - while the homogenous oscillator displayed a linear dependence with the factors, the heterogeneous one revealed a more complex dependence with quadratic terms. Our results may contribute, for instance, in the synthesis of self-organized materials in which an accurate frequency selection is required and, depending on its value, different physicochemical properties are obtained.

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.

Designing polymer gels and composites that undergo bio-inspired phototactic reconfiguration and motion

Inspired by the adaptive behavior of photo-responsive biological organisms, we develop analytical and computational models to design polymer gels and composites that can be dynamically reconfigured and driven to move with the application of light. We focus on gels formed from poly(N-isopropylacrylamide) and functionalized with spirobenzopyran (SP) chromophores, which become hydrophobic under blue light in acidic aqueous solution. Using our modeling approaches, we irradiate the gels through photomasks and demonstrate that the shapes of the samples can be reversibly and remotely 'remolded' by varying the apertures in the masks. By simulating the effect of repeatedly moving the light across the sample, we also show that the gel can undergo directed motion. We then examine gels that contain both SP chromophores and the ruthenium catalysts that drive the oscillatory Belousov-Zhabotinsky reaction. These dual-functionalized gels undergo spontaneous, self-sustained motion even when the lights are held stationary. We also simulate the behavior of composites formed from SP-functionalized fibers embedded in the poly(N-isopropylacrylamide) gel. With the SP-functionalization confined to the fibers, light and heat act as orthogonal stimuli and thus the composites display distinctly different modes of movement when the different cues are applied to the samples. Overall, our findings provide guidelines for using light to controllably reconfigure the shape and drive the movement of gel-based materials and thus, tailor the material to display different functionalities.

Nonlinear behavior and fluctuation-induced dynamics in the photosensitive Belousov-Zhabotinsky reaction

The photosensitive Belousov-Zhabotinsky (pBZ) reaction has been used extensively to study the properties of chemical oscillators. In particular, recent experiments revealed the existence of complex spatiotemporal dynamics for systems consisting of coupled micelles (V < 10^-21 L) or droplets (V ≈ [10^-8-10^-11] L) in which the pBZ reaction takes place. These results have been mostly understood in terms of reaction-diffusion models. However, in view of the small size of the droplets and micelles, large fluctuations of concentrations are to be expected. In this work, we investigate the role of fluctuations on the dynamics of a single droplet with stochastic simulations of an extension of the Field-Körös-Noyes (FKN) model taking into account the photosensitivity. The birhythmicity and chaotic behaviors predicted by the FKN model in the absence of fluctuations become transient or intermittent regimes whose lifetime decreases with the size of the droplet. Simple oscillations are more robust and can be observed even in small systems (V > 10^-12 L), which justifies the use of deterministic models in microfluidic systems of coupled oscillators. The simulations also reveal that fluctuations strongly affect the efficiency of inhibition by light, which is often used to control the kinetics of these systems: oscillations are found for parameter values for which they are supposed to be quenched according to deterministic predictions.

Amoeba-like self-oscillating polymeric fluids with autonomous sol-gel transition

In the field of polymer science, many kinds of polymeric material systems that show a sol-gel transition have been created. However, most systems are unidirectional stimuli-responsive systems that require physical signals such as a change in temperature. Here, we report on the design of a block copolymer solution that undergoes autonomous and periodic sol-gel transition under constant conditions without any on–off switching through external stimuli. The amplitude of this self-oscillation of the viscosity is about 2,000 mPa s. We also demonstrate an intermittent forward motion of a droplet of the polymer solution synchronized with the autonomous sol-gel transition. This polymer solution bears the potential to become the base for a type of slime-like soft robot that can transform its shape kaleidoscopically and move autonomously, which is associated with the living amoeba that moves forward by a repeated sol-gel transition.

Most polymeric materials that show sol-gel transitions are unidirectional and stimuli-responsive systems. Here the authors show a block copolymer solution that undergoes autonomous and periodic sol-gel transitions under constant conditions.

Designing self-powered materials systems that perform pattern recognition

Inspired by the advances in both materials and computer science, we describe efforts to design “materials that compute” where the material and the computer are the same entity.

Multiblock copolymers exhibiting spatio-temporal structure with autonomous viscosity oscillation

Here we report an ABA triblock copolymer that can express microscopic autonomous formation and break-up of aggregates under constant condition to generate macroscopic viscoelastic self-oscillation of the solution. The ABA triblock copolymer is designed to have hydrophilic B segment and self-oscillating A segment at the both sides by RAFT copolymerization. In the A segment, a metal catalyst of chemical oscillatory reaction, i.e., the Belousov-Zhabotinsky (BZ) reaction, is introduced as a chemomechanical transducer to change the aggregation state of the polymer depending on the redox states. Time-resolved DLS measurements of the ABA triblock copolymer confirm the presence of a transitional network structure of micelle aggregations in the reduced state and a unimer structure in the oxidized state. This autonomous oscillation of a well-designed triblock copolymer enables dynamic biomimetic softmaterials with spatio-temporal structure.

Autonomous droplet architectures

The quintessential living element of all organisms is the cell-a fluid-filled compartment enclosed, but not isolated, by a layer of amphiphilic molecules that self-assemble at its boundary. Cells of different composition can aggregate and communicate through the exchange of molecules across their boundaries. The astounding success of this architecture is readily apparent throughout the biological world. Inspired by the versatility of nature's architecture, we investigate aggregates of membrane-enclosed droplets as a design concept for robotics. This will require droplets capable of sensing, information processing, and actuation. It will also require the integration of functionally specialized droplets into an interconnected functional unit. Based on results from the literature and from our own laboratory, we argue the viability of this approach. Sensing and information processing in droplets have been the subject of several recent studies, on which we draw. Integrating droplets into coherently acting units and the aspect of controlled actuation for locomotion have received less attention. This article describes experiments that address both of these challenges. Using lipid-coated droplets of Belousov-Zhabotinsky reaction medium in oil, we show here that such droplets can be integrated and that chemically driven mechanical motion can be achieved.

Modeling Chemoresponsive Polymer Gels

Stimuli-responsive gels are vital components in the next generation of smart devices, which can sense and dynamically respond to changes in the local environment and thereby exhibit more autonomous functionality. We describe recently developed computational methods for simulating the properties of such stimuli-responsive gels in the presence of optical, chemical, and thermal gradients. Using these models, we determine how to harness light to drive shape changes and directed motion in spirobenzopyran-containing gels. Focusing on oscillating gels undergoing the Belousov-Zhabotinksy reaction, we demonstrate that these materials can spontaneously form self-rotating assemblies, or pinwheels. Finally, we model temperature-sensitive gels that encompass chemically reactive filaments to optimize the performance of this system as a homeostatic device for regulating temperature. These studies could facilitate the development of soft robots that autonomously interconvert chemical and mechanical energy and thus perform vital functions without the continuous need of external power sources.

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.

Autonomic composite hydrogels by reactive printing: materials and oscillatory response

Autonomic materials are those that automatically respond to a change in environmental conditions, such as temperature or chemical composition. While such materials hold incredible potential for a wide range of uses, their implementation is limited by the small number of fully-developed material systems. To broaden the number of available systems, we have developed a post-functionalization technique where a reactive Ru catalyst ink is printed onto a non-responsive polymer substrate. Using a succinimide-amine coupling reaction, patterns are printed onto co-polymer or biomacromolecular films containing primary amine functionality, such as polyacrylamide (PAAm) or poly-N-isopropyl acrylamide (PNIPAAm) copolymerized with poly-N-(3-Aminopropyl)methacrylamide (PAPMAAm). When the films are placed in the Belousov-Zhabotinsky (BZ) solution medium, the reaction takes place only inside the printed nodes. In comparison to alternative BZ systems, where Ru-containing monomers are copolymerized with base monomers, reactive printing provides facile tuning of a range of hydrogel compositions, as well as enabling the formation of mechanically robust composite monoliths. The autonomic response of the printed nodes is similar for all matrices in the BZ solution concentrations examined, where the period of oscillation decreases in response to increasing sodium bromate or nitric acid concentration. A temperature increase reduces the period of oscillations and temperature gradients are shown to function as pace-makers, dictating the direction of the autonomic response (chemical waves).

A self-oscillating gel actuator driven by ferroin

In the wake of the Belousov–Zhabotinsky reaction catalyzed by ferroin, the swelling–deswelling oscillating soft actuator exhibits 7 min period of self-oscillation for the first time.

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.

Chemical oscillators in structured media

Evolution is a characteristic feature of living systems, and many fundamental processes in life, including the cell cycle, take place in a periodic fashion. From a chemistry perspective, these repeating phenomena suggest the question of whether reactions in which concentrations oscillate could provide a basis and/or useful models for the behavior of organisms, and perhaps even their ability to evolve. In this Account, we examine several aspects of the behavior of the prototype oscillating chemical reaction, the Belousov-Zhabotinsky (BZ) system, carried out in microemulsions, arrays of micrometer-sized aqueous droplets suspended in oil, or hydrogels. Each of these environments contains elements of the compartmentalization that likely played a role in the development of the first living cells, and within them we observe behaviors not found in the BZ reaction in simple aqueous solution. Several of these phenomena resemble traits displayed by living organisms. For example, the nanodroplets in a BZ microemulsion "communicate" with each other through a phenomenon analogous to quorum sensing in bacteria to produce a remarkable variety of patterns and waves on length scales 10(5) times the size of a single droplet. A photosensitive version can "remember" an imposed image. Larger, micrometer-sized droplets exhibit similarly rich behavior and allow for the observation and control of individual droplets. These droplets offer promise for building arrays capable of computation by varying the strength and sign of the coupling between drops. Gels that incorporate a BZ catalyst and are immersed in a solution containing the BZ reactants change their shape and volume in oscillations that follow the variation in the redox state of the catalyst. Using this phenomenon, we can construct phototactic gel "worms" or segments of gel that attract one another. Whether such systems will provide more realistic caricatures of life, and whether they can serve as useful materials will largely depend on the successful integration of various properties, including communication, motion, and memory, which we observed in separate experiments. Theoretical approaches that couple reaction and diffusion processes to mechanical and other material properties are likely to play a key role in this integration, and we describe one such approach. The evolution of systems of coupled chemical oscillators presents another challenge to the development of these systems, but one that we expect to be solved.

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.

Spatial confinement controls self-oscillations in polymer gels undergoing the Belousov-Zhabotinsky reaction

Chemoresponsive gels undergoing the Belousov-Zhabotinsky (BZ) reaction exhibit self-sustained pulsations, which can be harnessed to perform mechanical work. In technological applications, the gels would typically be confined between hard surfaces and thus, it is essential to establish how confinement affects these distinctive oscillations. Using theory and simulation, we pinpoint regions in phase space where the dynamic behavior of BZ gels critically depends on the presence of confining walls. We then illustrate how the wave propagation within thin samples can be tailored by selectively introducing "cut outs" in the bounding surfaces. The oscillations in the latter films are localized in specified areas, so the system contains well-defined oscillatory and nonoscillatory regions. The cut outs provide an effective means of tuning the mechanical action within the film and provide a route for tailoring the functionality of the material.

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.