Chemical Oscillators Research Articles

Thermodynamic Optimality of Glycolytic Oscillations.

Temporal order in living matters reflects the self-organizing nature of dynamical processes driven out of thermodynamic equilibrium. Because of functional reasons, the period of a biochemical oscillation must be tuned to a specific value with precision; however, according to the thermodynamic uncertainty relation (TUR), the precision of the oscillatory period is constrained by the thermodynamic cost of generating it. After reviewing the basics of chemical oscillations using the Brusselator as a model system, we study the glycolytic oscillation generated by octameric phosphofructokinase (PFK), which is known to display a period of several minutes. By exploring the phase space of glycolytic oscillations, we find that the glycolytic oscillation under the cellular condition is realized in a cost-effective manner. Specifically, over the biologically relevant range of parameter values of glycolysis and octameric PFK, the entropy production from the glycolytic oscillation is minimal when the oscillation period is (5-10) min. Furthermore, the glycolytic oscillation is found at work near the phase boundary of limit cycles, suggesting that a moderate increase of glucose injection rate leads to the loss of oscillatory dynamics, which is reminiscent of the loss of pulsatile insulin release resulting from elevated blood glucose level.

Cellular automata implementation of Oregonator simulating light-sensitive Belousov–Zhabotinsky medium

Cellular automata (CA) have been used to simulate a variety of different chemical, biological and physical phenomena. Their ability to emulate complex dynamics, emerging from simple local interactions of their elementary cells, made them a strong candidate for mimicking these phenomena, especially when accelerated computation through parallelization is required. Belousov–Zhabotinsky (BZ) is a class of chemical reactions that due to their potential as nonlinear chemical oscillators, have inspired scientists to use them as chemical computers. The Oregonator equations, which approximate the dynamics of BZ reactions, were implemented here using CA methods. This new modelling approach (CA-based Oregonator) was tested in terms of accuracy and efficiency against previous models and laboratory-based experimental results, while the benefits of this method were outlined. It was observed that the results from the CA-based Oregonator are in good agreement with both modelled and laboratory experiments. The main advantage of this method can be summarized as the acceleration achieved in current implementations (serial computers), but also towards potential future implementations in massively parallel computational systems (like field-programmable gate array hardware and nano-neuromorphic circuits) that have been proved to be good substrates for accelerating the implemented CA models.

Thermal Hysteresis Involving Reversible Self-Catalytic Reactions.

Hysteresis is ubiquitous in nature and biology. It appears in ferromagnetism, ferroelectrism, traffic congestion, river sedimentation, electronics, thermoresponses, cell division, differentiation, and apoptosis. Hysteresis phenomena are beyond equilibrium and involve nonlinear, bistable, time delay, and memory events, which are described in input/output profiles by different outputs during continuous decreases and increases in input intensity. Although hysteresis profiles in these phenomena appear similar, the mechanisms underlying them are complex, and their basic understanding is desired. In this Account, I describe thermal hysteresis caused by molecules dispersed in dilute solutions containing optically active helicene oligomers, which form homo- and heterodouble helices, the cooling and heating processes of which cause different structural changes with regard to their relative concentrations. Reversible self-catalytic reactions are involved in the formation of a double helix, which catalyzes its own formation. The reactions accelerate as they progress, in contrast to ordinary reactions, which exhibit monotonic retardation as they progress. Thermal hysteresis involving reversible self-catalytic reactions exhibits notable phenomena, when various cooling/heating inputs are applied during the reaction; these phenomena are shown herein with profiles of experimental results of Δε outputs obtained by circular dichroism (CD) plotted against temperature inputs. Thermal hysteresis is discussed in terms of (1) two states of the homodouble helix and a random coil involving one reversible self-catalytic reaction and (2) three states of enantiomeric heterodouble helices and a random coil involving two reversible self-catalytic reactions. Repeated cooling and heating processes provide the same stable thermal hysteresis loops, when the initial and final high-temperature states are under equilibrium, and nonloop and unstable thermal hysteresis appears when whole the systems are beyond equilibrium. Diverse thermal hysteresis loops are obtained under different temperature change conditions for different oligomers. The mechanism of thermal hysteresis involves different macroscopic mechanisms at a fixed temperature, when the relative concentrations of substrates/products and the reaction direction differ. Microscopic mechanisms, which are shown by energy diagrams, are fixed at a temperature irrespective of cooling or heating. A comparison of thermal hysteresis loops and equilibrium curves provides distances to the metastable states on the loops from equilibrium, and reactions occur from the metastable states toward equilibrium. Notable phenomena described herein include bistability, high sensitivity to small concentration changes, equilibrium crossing, three-state one-directional structural change caused by a single heating procedure, reaction shortcuts, the memory effect on thermal history, figure-eight thermal hysteresis, chemical oscillation, stable and unstable thermal hysteresis, double-helix formation only under heating, and chiral symmetry breaking.

Heat and mass transfer in MHD boundary layer flow of a second‐grade fluid past an infinite vertical permeable surface

AbstractHeat and mass transfer of non‐Newtonian fluids is increasingly being studied by researchers due to its applications in many branches of science and engineering, such as metallurgical processes, polymer extrusion, glass blowing, crystal growing, and so forth. The present work is mainly concerned with the unsteady laminar magnetohydrodynamic flow of a heat‐generating or absorbing second‐grade fluid past an infinite vertical porous plate. The nondimensional governing equations are solved for the best analytical solution. Results for various flow characteristics are presented through graphs and tables delineating the effect of various parameters characterizing the flow. For engineering interest, the shear stresses, Nusselt number, and Sherwood number are computed and exchanged of views with reference to the important parameters. Our analysis explored that the influences of a chemical reaction and fluid oscillations reduced the concentration distribution in the entire liquid region. The rotation effect decreases the shear stress, whereas it is augmented through an increase in the permeability of porous medium and second‐grade fluid parameters' impact.

The role of activation enthalpy modeled with a modified Arrhenius equation in a variant of a minimal bromate oscillator for temperatures changes

Abstract Belousov-Zhabotinsky chemical reactions and new variants were developed and studied at 277.5 K, 296.15 K, and 341.15 K using potassium bromate, sodium bromide, malonic acid, and ferroin as an indicator for the oscillating reaction. This reaction type is a minimal oscillator, which belongs to the fifth “uncatalyzed” family known as minimal bromate oscillators. A mathematical model is a proposal from the reaction mechanism of Zhabotinsky, the Oregonator model, and the modified Arrhenius equation. The control parameters of the mathematical model are the activation enthalpies of the oscillating reaction. Experimental and numerical results at 341.15 K show an increase in the amplitude and frequency of chemical oscillations and a decrease in the total oscillation time, while at 277.15 K the opposite mechanism happens.

Chemical oscillators synchronized via an active oscillating medium: Dynamics and phase approximation model

Different types of synchronization states are found when non-linear chemical oscillators are embedded into an active medium that interconnects the oscillators but also contributes to the system dynamics. Using different theoretical tools, we approach this problem in order to describe the transition between two such synchronized states. Bifurcation and continuation analysis provide a full description of the parameter space. Phase approximation modeling allows the calculation of the oscillator periods and the bifurcation point.

Designing self-oscillating matter

Designing self-oscillating matter

A unified and automated approach to attractor reconstruction

We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful reconstruction of systems inheriting different time scales. In contrast to the established methods, the minimization of an appropriate cost function determines the embedding dimension without using a threshold parameter. Moreover, the method is capable of detecting stochastic time series and, thus, can handle noise contaminated input without adjusting parameters. The superiority of the proposed method is shown on some paradigmatic models and experimental data from chaotic chemical oscillators.

Belousov-Zhabotinsky type reactions: the non-linear behavior of chemical systems

Chemical oscillators are open systems characterized by periodic variations of some reaction species concentration due to complex physico-chemical phenomena that may cause bistability, rise of limit cycle attractors, birth of spiral waves and Turing patterns and finally deterministic chaos. Specifically, the Belousov-Zhabotinsky reaction is a noteworthy example of non-linear behavior of chemical systems occurring in homogenous media. This reaction can take place in several variants and may offer an overview on chemical oscillators, owing to its simplicity of mathematical handling and several more complex deriving phenomena. This work provides an overview of Belousov-Zhabotinsky-type reactions, focusing on modeling under different operating conditions, from the most simple to the most widely applicable models presented during the years. In particular, the stability of simplified models as a function of bifurcation parameters is studied as causes of several complex behaviors. Rise of waves and fronts is mathematically explained as well as birth and evolution issues of the chaotic ODEs system describing the Györgyi-Field model of the Belousov-Zhabotinsky reaction. This review provides not only the general information about oscillatory reactions, but also provides the mathematical solutions in order to be used in future biochemical reactions and reactor designs.

NLO evaluation on opto-electronic application and chemical potential oscillation analysis of 2-Chloro-4-nitro-N-methylaniline crystal using crystallographic, spectroscopic and theoretical tools

The new organic composite crystal was grown from 2-Chloro-4-nitro-N-methylaniline compound using Bridgman method and the grown crystal was characterized morphologically, optically, opto-electronically using suitable analytical tools. All the theoretical data were obtained for interpreting physical, chemical and optical characteristics of chemical species- crystal by performing different types of calculations. The crystal dimensions were measured as 0.19 × 0.68 × 0.38 mm3 and the Birefringence (Δn) Kλ/t was calculated to be 1.02. The nonlinear coefficient and nonlinear optical (NLO) efficiency were calculated as 0.8381 at 6.81pm/V. The FT-Raman and FT-IR vibrational data were evaluated to find the scattering bond lengths and bond angles and the homogeneity and heterogeneity of the bond profile was checked for estimating dielectric susceptibility. The chemical shift results for core as well as allied carbons are assessed and the delocalization of chemical potential on different atomic nodal regions was keenly studied. The dielectric property inducement over the molecule and crystal structure was monitored and the direct band gap for amplifying the optical energy was noted and the band gap tuning was discussed. The physico-chemical parameters were evaluated and the support of such parameters was tested. The geometrical parameters were evaluated and the optimized bond lengths and bond angles were checked for customizing trans free structure for constructing prearranged crystal. The UV-Visible absorption and transmission spectral data was evaluated to find the CT complex of the compound. The vibrational circular dichroism (VCD) spectral sequence was thoroughly checked for identifying the important dipole and polarized bonds for fixing enantiomer characteristics.

Concurrent self-regulated autonomous synthesis and functionalization of pH-responsive giant vesicles by a chemical pH oscillator.

The semibatch BrO3--SO32- pH oscillator serves as the radical source for the in situ polymerization of the pH-responsive 2-(diisopropylamino)-ethyl methacrylate monomer on poly(ethylene-glycol)-macroCTA chain and generates an amphiphilic block copolymer. These building blocks concurrently self-assemble to micelles and then transforms to vesicles as the chain length of the hydrophobic block growths. Large amplitude oscillations in the concentration of H+ by the semibatch BrO3--SO32- are provoked when the conditions in the system are favorable. The oscillations control the protonation state of the tertiary amine group in the core segment of the block copolymer. Rhythmic assembly-disassembly of the polymer structures is observed. All processes, from the time- regulated autonomous formation of the building blocks, their self-assembly and the rhythmic disassembly-reassembly are governed by the same simple chemical system, in the same reaction vessel, without complicated multi step procedures and are fueled and kept out of equilibrium by the uniform inflow of SO32-.

Synchronization scenarios induced by delayed communication in arrays of diffusively coupled autonomous chemical oscillators.

We study the impact of delayed feedbacks in the collective synchronization of ensembles of identical and autonomous micro-oscillators. To this aim, we consider linear arrays of Belousov-Zhabotinsky (BZ) oscillators confined in micro-compartmentalised systems, where the delayed feedback mimics natural lags that can arise due to the confinement properties and mechanisms driving the inter-oscillator communication. The micro-oscillator array is modeled as a set of Oregonator-like kinetics coupled via mass exchange of the chemical messengers. Changes in the synchronization patterns are explored by varying the delayed feedback introduced in the messenger species Br2. A direct transition from anti-phase to in-phase synchronization and back to the initial anti-phase scheme is observed by progressively increasing the time delay from zero to the value T0, which is the oscillation period characterising the system without any delayed coupling. The route from anti- to in-phase oscillations (and back) consists of regimes where windows of in-phase oscillations are periodically broken by anti-phase beats. Similarities between these phase transition dynamics and synchronization scenarios characterising the coordination of oscillatory limb movements are finally discussed.

History, versatility and future prospects of oscillatory carbonylation reactions of alkynes.

The paper looks back at three decades of oscillatory carbonylation reactions, summarises core findings and shares perspectives, with particular emphasis on applications. Oscillatory carbonylation reactions of alkynes display remarkable versatility in terms of substrates, catalysts and solvents. Furthermore, in addition to oscillations in pH and redox potential, these organic chemical oscillators can yield oscillations in turbidity and release heat from the reaction in a pulsatile manner. Recent research developments shift attention from small molecule substrates (e.g. phenylacetylene) and small molecule catalysts (e.g. palladium(ii) iodide), to oscillatory carbonylation reactions using polymeric substrates (e.g. PEGylated alkynes) and polymeric catalysts (e.g. imine-functionalized chitosan-palladium) and use of these polymeric building blocks to develop oscillatory (pulsatile) materials fit for pulsatile drug release and other applications.

Oscillations of EPR Signals Accompanying Belousov–Zhabotinsky Reaction

Periodical transformation of ferroin to ferriin is accompanied by changes in magnetic properties of liquids during Belousov–Zhabotinsky (BZ) reaction malonic acid, sodium bromide, sodium bromate, ferroin, and sulfuric acid. Instead of the earlier studied oscillation of microwave conductivity accompanying an oscillating reaction, we propose a flash technique to interrupt the BZ reaction by rapid freezing. Rapid cooling of a solution during chemical oscillations results in a frozen system with a fixed concentration of paramagnetic centers Fe3+. EPR spectrum recorded at different stages of the interrupted reaction corresponds to the exact concentration of the ferroin and ferriin components. Following unfreezing unblocks the BZ reaction, and oscillations are still observed. A simulated spectrum allows one to distinguish two groups of Fe3+ ions of different symmetries. The obtained results are important to explain the earlier observed effect of inhomogeneous magnetic field on BZ reaction front velocity.

Impact of PDMS-Based Microfluidics on Belousov-Zhabotinsky Chemical Oscillators.

Sub-nanoliter volumes of the Belousov-Zhabotinsky (BZ) reaction are sealed in microfluidic devices made from polydimethylsiloxane (PDMS). Bromine, which is a BZ reaction intermediate that participates in the inhibitory pathway of the reaction, is known to permeate into PDMS, and it has been suggested that PDMS and bromine can react ( J. Phys. Chem. A. 108, 2004, 1325-1332). We characterize the extent to which PDMS affects BZ oscillations by varying the volume of the PDMS surrounding the BZ reactors. We measure how the oscillation period varies with PDMS volume and compare with a theoretical reaction-diffusion model, concluding that bromine reacts with PDMS. We demonstrate that minimizing the amount of PDMS by making the samples as thin as possible maximizes the number of oscillations before the BZ reaction reaches equilibrium and ceases to oscillate. We also demonstrate that the deleterious effects of the PDMS-BZ interactions are somewhat mitigated by imposing constant chemical boundary conditions through using a light-sensitive catalyst, ruthenium, in combination with patterned illumination. Furthermore, we show that light can modulate the frequency and phase of the BZ oscillators contained in a PDMS matrix by 20-30%.

Self-Oscillating Membranes with Polymer Interface Synchronized with Chemical Oscillator to Reproduce Lifelike Pulsatile Flow

Self-oscillating filtration membranes having a lifelike pulsatile flow are prepared thanks to a synchronized coupling between a chemical oscillator and a responsive membrane. Commercial alumina membranes are superficially functionalized with pH-responsive poly(methacrylic acid) (PMAA) chains synthesized by reversible addition–fragmentation chain transfer (RAFT) polymerization of MAA in the presence of a catechol-based RAFT agent. The grafting of PMAA onto alumina, mediated through catechol chemisorption, is analyzed by X-ray photoelectron spectroscopy, scanning electron microscopy combined with energy-dispersive X-ray spectroscopy, and static water contact angle. Bromate–sulfite–ferrocyanide (BSF) is used as a chemical oscillator, enabling autonomous cyclic pH modulation between 3.5 and 6.5. The pH oscillations are setup in the conditions of membrane filtration inside a filtration cell thanks to a careful study of the bifurcation diagram showing the required conditions to reach the oscillation domain. Since PMAA has a pKa around 5.8, a periodic extension–contraction of the polymer chains is obtained during membrane filtration, which leads to a synchronized change in the membrane pore size. Chemically powered autonomous pulsatile flow with an impressive permeability cycles is observed with an effective chemomechanical feedback action of the membrane pore size change on the chemical oscillator mechanism.

Spiral wave chimera states in regular and fractal neuronal networks

Chimera states are spatial patterns in which coherent and incoherent patterns coexist. It was reported that small populations of coupled oscillators can exhibit chimera with transient nature. This spatial coexistence has been observed in various network topologies of coupled systems, such as coupled pendula, coupled chemical oscillators, and neuronal networks. In this work, we build two-dimensional neuronal networks with regular and fractal topologies to study chimera states. In the regular network, we consider a coupling between the nearest neighbours neurons, while the fractal network is constructed according to the square Cantor set. Our networks are composed of coupled adaptive exponential integrate-and-fire neurons, that can exhibit spike or burst activities. Depending on the parameters, we find spiral wave chimeras in both regular and fractal networks. The spiral wave chimeras arise for different values of the intensity of the excitatory synaptic conductance. In our simulations, we verify the existence of multicore chimera states. The cores are made up of neurons with desynchronous behaviour and the spiral waves rotates around them. The cores can be related to bumps or spatially localised pulses of neuronal activities. We also show that the initial value of the adaptation current plays an important role in the existence of spiral wave chimera states.

The Briggs–Rauscher Reaction: A Demonstration of Sequential Spatiotemporal Patterns

The Briggs–Rauscher reaction is a popular demonstration to illustrate chemical oscillations in laboratories, classrooms, and public seminars because of its simplicity and visual appeal. Here, we adapt the Briggs–Rauscher reaction to present reaction–diffusion–convection patterns in the undergraduate general or physical chemistry laboratory. By maintaining the ratio between malonic acid and potassium iodate concentrations as 0.2 in an uncovered Petri dish, sequential patterns (transient dendritic patterns and rotating dendritic patterns) can be observed, which are induced by the interaction of reaction, diffusion, and convection. This beautiful demonstration captures students’ attention and inspires reflection and discussion about similar phenomena in nature as well as the wealth of behaviors in systems far from equilibrium.

Quantitative Determination of Kaempferol by using a novel B-Z Chemical Oscillating system Catalyzed by a Cu (II)-tetraazamacrocyclic Complex

Quantitative Determination of Kaempferol by using a novel B-Z Chemical Oscillating system Catalyzed by a Cu (II)-tetraazamacrocyclic Complex

Parametric instability-induced synchronization in chemical oscillations and spatiotemporal patterns.

We consider a model reaction-diffusion system with two coupled layers in which one of the components in a layer is parametrically driven by a periodic force. On perturbation of a homogeneous stable steady state, the system exhibits parametric instability inducing synchronization in temporal oscillation at half the forcing frequency in absence of diffusion and spatiotemporal patterns in presence of diffusion, when strength of parametric forcing and the strength of coupling are kept above their critical thresholds. We have formulated a general scheme to derive analytically the critical thresholds and dispersion relation to locate the unstable spatial modes lying between the tilted Arnold tongue in the amplitude-frequency plot. Full numerical simulations on Gierer-Meinhardt activator-inhibitor model corroborate our theoretical analysis on parametric instability-induced antiphase synchronization in chemical oscillation and spatiotemporal pattern formation, between the two layers.