Energy and power characteristics of nanocatalyzed Belousov-Zhabotinsky reactions via bifurcation analyses.

Active stimuli-responsive materials, intrinsically powered by chemical reactions, have immense capabilities that can be harnessed for designing synthetic systems for a variety of biomimetic applications. It goes without saying that the key aspect involved in the designing of such systems is to accurately estimate the amount of energy and power available for transduction through various mechanisms. Belousov-Zhabotinsky (BZ) reactions are dynamical systems, which exhibit self-sustained nonlinear chemical oscillations, as their catalyst undergoes periodic redox cycles in the presence of reagents. The unique feature of BZ reaction based active systems is that they can continuously perform mechanical work by transducing energy from sustained chemical oscillations. The objective of our work is to use bifurcation analyses to identify oscillatory regimes and quantify energy-power characteristics of the BZ reaction based on nanocatalyst activity and BZ reaction formulations. Our approach involves not only the computation of higher order Lyapunov and frequency coefficients but also Hamiltonian functions, through normal form reduction of the kinetic model of the BZ reaction. Ultimately, using these calculations, we determine amplitude, frequency, and energy-power densities, as a function of the nanocatalysts' activity and BZ formulations. As normal form representations are applicable to any dynamical system, we believe that our framework can be extended to other self-sustained active systems, including systems based on stimuli-responsive materials.

Hydrodynamics of a confined active Belousov-Zhabotinsky droplet.

Self-sustained locomotion of synthetic droplet swimmers has been of great interest due to their ability to mimic the behavior of biological swimmers. Here we harness the Belousov-Zhabotinsky (BZ) reaction to induce Marangoni stresses on the fluid-droplet interface and elucidate the spontaneous locomotion of active BZ droplets in a confined two-dimensional channel. Our approach employs the lattice Boltzmann method to simulate a coupled system of multiphase hydrodynamics and BZ-reaction kinetics. Our investigation reveals the mechanism underlying the propulsion of active BZ droplets, in terms of convective and diffusive fluxes and deformation of the droplets. Furthermore, we demonstrate that by manipulating the degree of confinement, strength, and nature of coupling between surface tension and active species' concentration, the motion of the BZ droplet can be directed. In addition, we are able to capture two different kinds of droplet behaviors, namely, sustained and stationary, and establish conditions for the sustained long-time motion. We envisage that our findings can be used not only to understand the mechanics of biological swimmers but also to design reaction-driven self-propelled systems for a variety of biomimetic applications.

Fast-Moving Self-Propelled Droplets of a Nanocatalyzed Belousov-Zhabotinsky Reaction.

Self-sustained locomotion by virtue of an internalized chemical reaction is a characteristic feature of living systems and has inspired researchers to develop such self-moving biomimetic systems. Here, we harness a self-oscillating Belousov-Zhabotinsky (BZ) reaction, a well-known chemical oscillator, with enhanced kinetics by virtue of our graphene-based catalytic mats, to elucidate the spontaneous locomotion of BZ reaction droplets. Specifically, our nanocatalysts comprise ruthenium nanoparticle decorations on graphene oxide, reduced graphene oxide, and graphene nanosheets, thereby creating 0D-2D heterostructures. We demonstrate that when these nanocatalyzed droplets of the BZ reaction are placed in an oil-surfactant medium, they exhibit a macroscopic translatory motion at the velocities of few millimeters per second. This motion is brought about by the combination of enhanced kinetics of the BZ reaction and the Marangoni effect. Our investigations reveal that the velocity of locomotion increases with the electrical conductivity of our nanocomposites. Moreover, we also show that the positive feedback generated by the reaction-diffusion phenomena results in an asymmetric distribution of surface tension that, in turn, facilitates the self-propelled motion of the BZ droplets. Finally, we explore a system of multiple nanocatalyzed BZ droplets and reveal a variety of motions caused by their mutual interactions. Our findings suggest that through the use of 0D-2D hybrid nanomaterials, it is possible to design fast-moving self-propelled synthetic objects for a variety of biomimetic applications.

Dynamical attributes of nanocatalyzed self-oscillating reactions via bifurcation analyses.

Self-oscillating chemical reactions that undergo reaction-diffusion (RD) phenomena have shown great potential for designing stimuli-responsive materials. Belousov-Zhabotinsky (BZ) reactions are one such class of reactions that exhibit nonlinear chemical oscillations due to redox cycles of the metal-ion catalyst by virtue of Hopf bifurcation. Using bifurcation analyses, here we investigate the BZ reactions, catalyzed by 0D-2D catalytic nanomats and bare nanosheets, which are known to exhibit enhanced dynamic response due to catalysts' heterogeneity. Specifically, we incorporate the nanocatalysts' activity in the kinetic model of the BZ reactions and, subsequently, use catalysts' activity as the bifurcation parameter for analyses. By computing higher-order Lyapunov and frequency coefficients, we have revealed new oscillatory regimes in the bifurcation diagram, including re-entrant regions where sustained oscillations are unexpectedly suppressed, even with high catalytic activity. In addition, we also calculate the amplitude and frequency of BZ oscillations in each of these regions as a function of nanocatalysts' activity. We believe that our current findings can be used to harness the nonlinearity of RD-based dynamical systems to provide unique functionalities to active stimuli-response systems.

0D-2D heterostructures as nanocatalysts for self-oscillating reactions: an investigation into chemical kinetics.

Self-oscillating chemical reactions are dynamical reaction-diffusion systems that show immense potential in the design of synthetic soft materials with biomimetic functionalities. The Belousov-Zhabotinsky (BZ) reaction is one such reaction, where the periodic change in the redox state of the metal ion catalyst drives the rhythmic chemical oscillations. Inspired by the exceptional properties of graphene, specifically its catalytic activity for redox reactions, we investigate the effect of graphene-based nanocomposites on the dynamics of the BZ reaction. In particular, we synthesized catalytic mats by decorating ceria nanoparticles (CeNPs) on graphene-based nanosheets, thereby creating 0D-2D heterostructures and subsequently, incorporate these catalytic mats into the BZ reaction. Our investigations reveal that CeNP decorated nanocomposites significantly enhance the oscillating frequency of the BZ reaction, not only compared to the traditional solution-based catalysts but also compared to the bare graphene-based nanosheets. From our experiments at various temperatures and concentrations, together with modelling and simulations, we determine the apparent rate constant for different CeNP decorated graphene nanocomposites. Ultimately, we determine the apparent rate and estimate various kinetic parameters, including activation energy and reaction order. In short, we demonstrate that CeNP decorated nanomats are excellent catalysts and elucidate that the kinetics of the BZ reaction can be simulated using the Oregonator model with our kinetic parameters. We envisage that our findings can be utilized to harness multiscale interactions to design a variety of multifunctional stimuli responsive materials.

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

The classic Belousov-Zhabotinsky (BZ) reaction, which involves transition metal catalysed redox reactions, represents a family of nonlinear chemical oscillators. Here, we show that it is possible to tune the oscillatory dynamics of the BZ reaction by using a hybrid 2D material, i.e., graphene-based nanosheets decorated with Ru nanoparticles. Specifically, we demonstrate that the frequency of chemical oscillations in a BZ reaction increases, by up to four-fold, when catalyzed by the Ru-graphene nanocomposite. We show that this observed behaviour is attributed to enhanced access to active catalytic sites on Ru nanoparticles, as well as the rapid shuttling of electrons facilitated by the highly conductive graphene platform. We further demonstrate that this enhancement of oscillations facilitated by the graphene platform can be simulated using the Oregonator model. Our numerical simulations reveal a strong correlation between the rate of charge transfer and the frequency of chemical oscillations. This ability of a 2D material, like graphene, to influence the dynamics of an oscillatory chemical reaction, as showcased in this work, is studied for the first time and opens up new avenues to tune the dynamics of chemical oscillators. We anticipate that these findings would enable us to design a variety of intrinsically powered biomimetic systems with controllable dynamic behavior.

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.

Chemo-responsive, self-oscillating gels that undergo biomimetic communication.

Species ranging from single-cell organisms to social insects can undergo auto-chemotaxis, where the entities move towards a chemo-attractant that they themselves emit. Polymer gels undergoing the self-oscillating Belousov-Zhabotinsky (BZ) reaction exhibit autonomous, periodic pulsations, which produce chemical species collectively referred to as the activator. The diffusion of this activator into the surrounding solution affects the dynamic behavior of neighboring BZ gels and hence, the BZ gels not only emit, but also respond to self-generated chemical gradients. This review describes recent experimental and computational studies that reveal how this biomimetic behavior effectively allows neighboring BZ gels to undergo cooperative, self-propelled motion. These distinctive properties of the BZ gels provide a route for creating reconfigurable materials that autonomously communicate with neighboring units and thereby actively participate in constructing the desired structures.

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.

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.

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.

Using light to guide the self-sustained motion of active gels.

We undertake the first computational study to determine the effect of light on polymer gels undergoing the Belousov-Zhabotinsky (BZ) reaction. The BZ gels are unique materials because they can undergo rhythmic mechanical oscillations in the absence of external stimuli. The BZ reaction, however, is photosensitive. Via simulations, we demonstrate that the interplay between the chemoresponsive gels and the photosensitive reaction can cause millimeter sized BZ gels to exhibit autonomous, directed motion or reorientation away from 4 the light. In effect, we show that these synthetic BZ "worms" display a fundamental biomimetic behavior: movement away from an adverse environmental condition, which in the context of the BZ reaction is the presence of light.

Crystalline-amorphous interaction in relation to the phase diagrams of binary polymer blends containing a crystalline constituent.

The present article describes an equilibrium theory for determining binary phase diagrams of various crystalline-amorphous polymer blends by taking into account the contributions from both liquid-liquid phase separation between the constituents and solid-liquid phase transition of the crystalline component. An analytical expression for determining a crystal-amorphous interaction parameter is deduced based on the solid-liquid transition, involving the solidus and liquidus lines in conjunction with the coexistence curve of an upper critical solution temperature type. Of particular importance is that the crystalline-amorphous interaction parameter can be determined directly from the melting point depression data. The present analysis is therefore different from the conventional Flory-Huggins interaction parameter, which is associated with the liquid-liquid phase separation. The validity of the present theory is tested with the experimental phase diagrams of blends of poly(ethylene oxide)/diacrylate and poly(vinyl alcohol)/cellulose.

Using a single mask to create multiple patterns in three-component, photoreactive blends.

Via simulations, we demonstrate a simple route for forming defect-free patterns in a photosensitive, immiscible ABC blend. The first pattern is established by irradiating the sample through a mask, which serves to pin the C regions and thereby promotes the self-assembly of A and B into ordered domains. When the mask is removed, the photoactivity of the AB blend leads to different periodic patterns. Thus, the use of one mask permits the creation of multiple ordered morphologies, which can be locked into the film by quenching the system at the appropriate time.

Crystal-liquid crystal binary phase diagrams.

We propose a new theoretical scheme for the binary phase diagrams of crystal-liquid crystal mixtures by a combination of a phase field model of solidification, the Flory-Huggins theory for liquid-liquid mixing and Maier-Saupe-McMillan (FH-MSM) model for nematic and smectic liquid crystal orderings. The phase field theory describes the crystal phase transition of anisotropic organic crystal and/or side chain liquid crystalline polymer crystals while the FH-MSM model explains isotropic, nematic and smectic-A phase transitions. Self-consistent calculations reveal several possible phase diagram topologies of the binary crystal-liquid crystal mixtures. The calculated phase diagrams were found to accord well to the reported experimental results.