Exploring Gas Evolution Oscillators: Mechanisms and Applications

We review an iconic class of chemical oscillators driven by phase transition instabilities, namely Gas Evolution Oscillators (GEOs). These systems show oscillatory dynamics in the delivery of gas sustained simple reactions yielding gaseous products in a liquid mixture, due to nucleation and supersaturation phenomena. After presenting the main features and properties of these systems, we deepen the underlying mechanism through a unified picture of the various models that have been proposed to describe this kind of oscillations. We finally discuss a concrete example of how such instabilities can impact chemical processes with applied relevance.

Transport-driven chemical oscillations: a review

Chemical oscillators attract transversal interest not only as useful models for understanding and controlling (bio)chemical complexity far from the equilibrium, but also as a promising means to design smart materials and power synthetic functional behaviors. We review and classify oscillatory phenomena in systems where a periodic variation in the concentration of the constitutive chemical species is induced by transport instabilities either triggered by simple reactions or without any reactive process at play. These phenomena, where the origin of the dynamical complexity is shifted from chemical to physical nonlinearities, can facilitate a variety of processes commonly encountered in chemistry and chemical engineering. We present an excursus through the main examples, discussing phenomenology, properties and modeling of different mechanisms that can lead to these kinds of oscillations. In particular, we reproduce the relevant results reported in the pertinent literature and, in parallel, propose new kinds of proof-of-concept systems substantiated by preliminary studies which can inspire new research lines. In the landscape of physically driven chemical oscillations, we devote particular attention to transport phenomena, actively or passively combined to (reactive or nonreactive) chemical species, which provide multiple pathways towards spontaneous oscillatory instabilities. Though with different specificities, the great part of these systems can be reduced to a common theoretical description. We finally overview possible perspectives in the study of physically driven oscillatory instabilities, showing how the related control can impact fundamental and applied open problems, ranging from origin of life studies to the optimization of processes with environmental relevance.

Multiscale Approach for Tuning Communication among Chemical Oscillators Confined in Biomimetic Microcompartments

Inspired by the biological world, new cross-border disciplines and technologies have emerged. Relevant examples include systems chemistry, which offers a bottom-up approach toward chemical complexity, and bio/chemical information and communication technology (bio/chemical ICT), which explores the conditions for propagating signals among individual microreactors separated by selectively permeable membranes. To fabricate specific arrays of microreactors, microfluidics has been demonstrated as an excellent method. In particular, droplet-based microfluidics is a powerful tool for encapsulating biological entities and chemical reagents in artificial microenvironments, mostly water-in-oil microdroplets. In these systems, the interfaces are liquid-liquid, and their physicochemical properties are key factors for tuning the coupling between molecular diffusion. Simple and double emulsions, where aqueous domains are in equilibrium with oil domains through boundary layers of amphiphilic molecules, are organized assemblies with high interfacial-area-to-volume ratios. These membranes can be engineered to obtain different surface charges, single- or multilayer stacking, and a variable degree of defects in molecular packing. Emulsions find application in many fields, including the food industry, pharmaceutics, and cosmetics. Furthermore, micro- and nanoemulsions can be used to model the propagation of chemical species through long distances, which is not only vital for cell signaling but also significant in molecular computing. Here we present in-depth research on the faceted world of solutions confined in restricted environments. In particular, we focused on the multiscale aspects of structure and dynamics from molecular to micro and macro levels. The Belousov-Zhabotinsky chemical reaction, known for its robustness and well-documented oscillatory behavior, was selected to represent a generic signal emitter/receiver confined within microenvironments separated by liquid-liquid interfaces. In this pulse generator, the temporal and spatial progressions are governed by periodic fluctuations in the concentration of chemical species, which act as activatory or inhibitory messengers over long distances. When organized into "colonies" or arrays, these micro-oscillators exhibit emergent dynamical behaviors at the population level. These behaviors can be finely tuned by manipulating the geometrical distribution of the oscillators and the properties of the interfaces at the nanoscale. By carefully selecting the membrane composition, it is possible to drive the system toward either in-phase, antiphase, or mixed synchronization regimes among individual oscillators, depending on messenger molecules. This relatively simple lab-scale model replicates some of the communication strategies commonly found in biological systems, particularly those based on the passive diffusion of chemical and electrical signals. It can help shed light on fundamental life processes and inspire new implementations in molecular computing and smart materials.

Marangoni- vs. buoyancy-driven flows: competition for spatio-temporal oscillations in A + B → C systems

The emergence of self-organized behaviors such as spatio-temporal oscillations is well-known for complex reactions involving nonlinear chemical or thermal feedback. Recently, it was shown that local oscillations of the chemical species concentration can be induced under isothermal batch conditions for simple bimolecular A + B → C reactions, provided they are actively coupled with hydrodynamics. When two reactants A and B, initially separated in space, react upon diffusive contact, damped spatio-temporal oscillations could develop when the surface tension increases sufficiently in the reaction zone. Additionally, if the density decreases, the coupling of both surface tension- and buoyancy-driven contributions to the flow can further sustain this oscillatory instability. Here, we investigate the opposite case of a reaction inducing a localized decrease in surface tension and an increase in density in the reacting zones. In this case, the competition arising from the two antagonistic flows is needed to create oscillatory dynamics, i.e., no oscillations are observed for pure chemically driven Marangoni flows. We study numerically these scenarios in a 2-dimensional system and show how they are controlled by the following key parameters: (i) ΔM and ΔR governing the surface tension and density variation during the reaction, respectively, (ii) the layer thickness of the system, and (iii) its lateral length. This work is a further step toward inducing and controlling chemical oscillations in simple reactions.

Buoyancy-Driven Chemohydrodynamic Patterns in A + B → Oscillator Two-Layer Stratifications

Chemohydrodynamic patterns due to the interplay of buoyancy-driven instabilities and reaction-diffusion patterns are studied experimentally in a vertical quasi-two-dimensional reactor in which two solutions A and B containing separate reactants of the oscillating Belousov-Zhabotinsky system are placed in contact along a horizontal contact line where excitable or oscillating dynamics can develop. Different types of buoyancy-driven instabilities are selectively induced in the reactive zone depending on the initial density jump between the two layers, controlled here by the bromate salt concentration. Starting from a less dense solution above a denser one, two possible differential diffusion instabilities are triggered depending on whether the fast diffusing sulfuric acid is in the upper or lower solution. Specifically, when the solution containing malonic acid and sulfuric acid is stratified above the one containing the slow-diffusing bromate salt, a diffusive layer convection (DLC) instability is observed with localized convective rolls around the interface. In that case, the reaction-diffusion wave patterns remain localized above the initial contact line, scarcely affected by the flow. If, on the contrary, sulfuric acid diffuses upward because it is initially dissolved in the lower layer, then a double-diffusion (DD) convective mode develops. This triggers fingers across the interface that mix the reactants such that oscillatory dynamics and rippled waves develop throughout the whole reactor. If the denser solution is put on top of the other one, then a fast developing Rayleigh-Taylor (RT) instability induces fast mixing of all reactants such that classical reaction-diffusion waves develop later on in the convectively mixed solutions.

Periodic Motion in the Chaotic Phase of an Unstirred Ferroin-Catalyzed Belousov Zhabotinsky Reaction

The Belousov Zhabotinsky reaction, a self-organized oscillatory color-changing reaction, can show complex behavior when left unstirred in a cuvette environment. The most intriguing behavior is the transition from periodicity to chaos and back to periodicity as the system evolves in time. It was shown that this happens thanks due to the decoupling of reaction, diffusion and convection. We have recently discovered that, as the so-called chaotic transient takes place, periodic bulk motions in form of convective cells are created in the reaction solution. In this work we investigated this phenomenon experimentally by changing cuvette size and reaction volume, in order to allow different types of convection patterns to appear. So far, we have observed single and double convection cells in the system. There are indications that the convection patterns are connected to the duration of the chaotic phase. A simplified mathematical model confirms the form and dynamics of the observed convection cells and explains the connection between chemical chaos and hydrodynamical order.

Drastic effects of an inert Pt wire on the redox behavior of the Belousov-Zhabotinsky reaction

This research investigated responses of the Belousov-Zhabotinsky (BZ) reaction to the presence of a chemically inert Pt wire in solution. Experiments showed that connecting the Pt wire to a neutral ground caused a spontaneous drastic shift in the redox potential and might even induce complex behavior. Characterizations using an unstirred ferriin solution demonstrated the formation of a red colored propagating front at the grounded Pt wire, suggesting the reduction of ferriin to ferroin. Measurements with different combinations of electrodes in both stirred and reaction-diffusion media further confirmed the reduction of BZ metal catalysts at the Pt wire and the accompanying oxidation reaction at the reference electrode. The observed drastic change in redox potential and oscillation waveform can be understood based on the passive reduction reaction at the indicator electrode that is connected to the reference electrode through a potential meter. The obtained influence can be further manipulated by adding a resistor between the Pt wire and the neutral ground, making this convenient perturbation method attractive for the study of redox chemical reaction dynamics.

The onset of dissipative chaos driven by nonequilibrium conditions

Dissipative chaos appears widely in various nonequilibrium systems; however, it is not clear how dissipative chaos originates from nonequilibrium. We discuss a framework based on the potential-flux approach to study chaos from the perspective of nonequilibrium dynamics. In this framework, chaotic systems possess a wide basin on the potential landscape, in which the rotational flux dominates the system dynamics, and chaos occurs with the appearance of this basin. In contrast, the probability flux is particularly associated with the detailed balance-breaking in nonequilibrium systems. This implies that the appearance of dissipative chaos is driven by nonequilibrium conditions.

Origins of oscillatory dynamics in the model of reactive oxygen species in the rhizosphere

Oscillatory processes are essential for normal functioning and survival of biological systems, and reactive oxygen species have a prominent role in many of them. A mechanism representing the dynamics of these species in the rhizosphere is analyzed using stoichiometric network analysis with the aim to determine its capabilities to simulate various dynamical states, including oscillations. A detailed analysis has shown that unstable steady states result from four destabilizing feedback cycles, among which the cycle involving hydroquinone, an electron acceptor, and its semi-reduced form is the dominant one responsible for the existence of saddle-node and Andronov-Hopf bifurcations. This requires a higher steady-state concentration for the reduced electron acceptor compared to that of the remaining species, where the level of oxygen steady-state concentration determines whether the Andronov-Hopf or saddle-node bifurcation will occur.

Detection of embedded dynamics in the Györgyi-Field model

The main aim of this paper is to detect embedded dynamics of the Györgyi-Field model of the Belousov-Zhabotinsky chemical reaction. The corresponding three-variable model given as a set of nonlinear ordinary differential equations depends on one parameter, the flow rate. As certain values of this parameter can give rise to chaos, an analysis was performed in order to identify different dynamics regimes. Dynamical properties were qualified and quantified using classical and also new techniques; namely, phase portraits, bifurcation diagrams, the Fourier spectra analysis, the 0-1 test for chaos, approximate entropy, and the maximal Lyapunov exponent. The correlation between approximate entropy and the 0-1 test for chaos was observed and described in detail. The main discovery was that the three-stage system of nested sub-intervals of flow rates showed the same pattern in the 0-1 test for chaos and approximate entropy at every level. The investigation leads to the open problem of whether the set of flow rate parameters has Cantor-like structure.

Hofmeister Effect in Self-Organized Chemical Systems

We studied the effect of spectator ions in the prototype of far-from-equilibrium self-organized chemical systems, the Belousov-Zhabotinsky (BZ) reaction. In particular, we investigated the specific ion effect of alkali metal cations, connoted for their kosmotropic and chaotropic properties. By means of combined experimental and numerical approaches, we could show a neat and robust evidence for the Hofmeister effect in this system. Spectator cations induce a marked increment of the induction period that preludes regular oscillations and decrease the oscillation amplitude following the sequence Li⁺ < Na⁺ ≪ K⁺ ∼ Cs⁺. These ions affect the system kinetics by interfering in the interaction between the oxidized form of the catalyst and the organic substrate, responsible for resetting the BZ system to pre-autocatalytic (reduced) conditions. The specific ion effect on these key reactive steps is systematically characterized and correlated with different parameters which describe the interaction of the cations with the solvent.

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.

A New Image Encryption Algorithm Based on Composite Chaos and Hyperchaos Combined with DNA Coding

In order to obtain chaos with a wider chaotic scope and better chaotic behavior, this paper combines the several existing one-dimensional chaos and forms a new one-dimensional chaotic map by using a modular operation which is named by LLS system and abbreviated as LLSS. To get a better encryption effect, a new image encryption method based on double chaos and DNA coding technology is proposed in this paper. A new one-dimensional chaotic map is combined with a hyperchaotic Qi system to encrypt by using DNA coding. The first stage involves three rounds of scrambling; a diffusion algorithm is applied to the plaintext image, and then the intermediate ciphertext image is partitioned. The final encrypted image is formed by using DNA operation. Experimental simulation and security analysis show that this algorithm increases the key space, has high sensitivity, and can resist several common attacks. At the same time, the algorithm in this paper can reduce the correlation between adjacent pixels, making it close to 0, and increase the information entropy, making it close to the ideal value and achieving a good encryption effect.

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.