Oscillations In Chemical Systems Research Articles

Coupled X-ray Absorption/UV-vis Monitoring of a Prototypical Oscillating Reaction.

Oscillating reactions are among the most intriguing phenomena in chemistry, but many questions on their mechanisms still remain unanswered, due to their intrinsic complexity and to the low sensitivity of the most common spectroscopic techniques toward the reaction brominated species. In this work, we investigate the cerium ion-catalyzed Belousov-Zhabotinsky (BZ) oscillating reaction by means of time-resolved X-ray absorption spectroscopy (XAS), in combination with UV-vis spectroscopy and unsupervised machine learning, multivariate curve resolution, and kinetic analyses. Altogether, we provide new insights into the collective oscillatory behavior of the key brominated species involved in the classical BZ reaction and measure previously unreported oscillations in their concentrations through Br K-edge XAS, while simultaneously tracking the oscillatory Ce4+-to-Ce3+ transformation by coupling XAS with UV-vis spectroscopy. Our work evidences the potential of the XAS technique to investigate the mechanisms of oscillatory chemical systems whose species are often not detectable with conventional experimental methods.

Science, serendipity, coincidence, and the Oregonator at the University of Oregon, 1969–1974

This historical review of the development of the Oregonator model of the Belousov–Zhabotinsky reaction is based on a lecture Dick Field presented during IrvFest2015—Celebrating a founding father of chaos!, a meeting in commemoration of Irving R. Epstein’s 70th birthday. For Dick’s 80th birthday festschrift, we focus here on the five papers in the series named “Oscillations in chemical systems,” published in 1972 [Noyes et al., J. Am. Chem. Soc. 94, 1394–1395 (1972); Field et al., J. Am. Chem. Soc. 94, 8649–8664 (1972); Field and Noyes, Nature 237, 390–392 (1972)] and 1974 [Field and Noyes, J. Chem. Phys. 60, 1877–1884 (1974); Field and Noyes, J. Am. Chem. Soc. 96, 2001–2006 (1974)].

Chemical Oscillations With Sodium Perborate as Oxidant.

The peroxo compounds H2O2 and K2S2O8 represent one of the major constituents in many oscillatory chemical systems. In this contribution we demonstrate that beside H2O2 and S2 the sodium perborate (NaBO3·H2O) can act as alternative oxidizing agent in oscillatory reactions. So far the H2O2 has been successfully substituted with NaBO3 in two oscillators: in the BO–S2–Cu(II) flow system potential and pH oscillations, in the strongly alkaline Cu(II)-catalyzed BO–SCN− batch reaction, which are rather different in their chemistry and dynamics, potential oscillations were observed. In spite of the significant differences in the oxidizing nature of H2O2 and NaBO3 we assume that the oscillatory cycle in the BO–substrate and in the H2O2–substrate systems is similar in many aspects, therefore the numbers of this new subgroup of the oscillators may be considered to be borate-mediated H2O2 oscillators. Mechanisms are suggested and simulations are shown to describe the oscillatory behaviors observed in the perborate chemistry based oscillators by using the assumption that the oxidation reactions of the intermediates (HO)3B(OOH)− and (HO)2B(OOH) anions, which are dominant species in alkaline and neutral pH solutions of perborate, are much faster than that of H2O2.

Broadening the scope of Pd-catalyzed oscillatory carbonylation reactions: solvent, substrate, catalyst

On our way to producing all-polymeric self-oscillatory materials, we have expanded the horizons of oscillatory carbonylation reactions by searching for alternative substrates, solvents and even catalysts. In this paper, we demonstrate that pH oscillations in carbonylation reactions have the potential to occur in a broad range of aliphatic alcohol solutions when using either a small molecule substrate (phenylacetylene) or a polymeric substrate (pegylated alkyne) with either a small molecule catalyst (Pd-diacetate) or a non-leaching polymeric catalyst (Pd-polyacrylate). The alcohols studied are methanol, ethanol, 1-propanol, 1-butanol and 1-hexanol. In this carbonylation reaction an alcohol serves as both the solvent and as a reactant. The resulting oscillations suggest that carbonylation reactions have strong potential for the discovery and development of new oscillatory chemical systems. Replacing methanol, commonly used in oscillatory carbonylation processes, with ethanol is an important step in enhancing the biocompatibility of these systems. Furthermore, showing that oscillations in pH are feasible in ethanol solutions when polymeric substrate and polymeric catalyst are used supports the vision of employing oscillatory chemical reactions to build oscillatory materials.

Autonomous Chemical Modulation and Unidirectional Coupling in Two Oscillatory Chemical Systems.

Controlling and coupling of out-of-equilibrium reaction networks have great importance in chemistry and biology. We provide an example for the ideal master-slave coupling between two pH oscillators (the sulfite-bromate and the hydrogen peroxide-sulfite pH oscillators operated in continuous-flow stirred tank reactors). The coupling between the reactors was realized by transport of carbon dioxide through a silicon membrane, which is a common chemical species in both systems. We showed that by using this strategy, the master system can generate forced pH oscillations in the slave system. We could control the amplitude and frequency of the oscillations in the slave system and reversibly drive the transition in the oscillations between the regular and chaotic regimes. Using this coupling strategy, we could present an example of amplitude modulation in a coupled chemical system.

Pedagogical Approach to the Modeling and Simulation of Oscillating Chemical Systems with Modern Software: The Brusselator Model

A classical nonlinear system, the “Brusselator”, was used to illustrate the modeling and simulation of oscillating chemical systems using stability analysis techniques with modern software tools such as Comsol Multiphysics, Matlab, and Excel. A systematic approach is proposed in order to establish a regime of parametric conditions that lead to oscillations in chemical systems. A Matlab script that symbolically finds the equilibrium points of the system, and the Jacobian of the assembly matrix at equilibrium was written. The Matlab script also calculates the trace, determinant and discriminant of the Jacobian and finds the critical points for which the trace and determinant are zero. An emphasis on finding the bifurcation points is made in the simulations and on the conditions for the onset of limit cycles, which are of most interest in biological systems.

Dynamics of the stochastic low concentration trimolecular oscillatory chemical system with jumps

This paper is devoted to discern long time dynamics through the stochastic low concentration trimolecular oscillatory chemical system with jumps. By Lyapunov technique, this system is proved to have a unique global positive solution, and the asymptotic stability in mean square of such model is further established. Moreover, the existence of random attractor and Lyapunov exponents are obtained for the stochastic homeomorphism flow generated by the corresponding global positive solution. And some numerical simulations are given to illustrate the presented results.

Optical Communication among Oscillatory Reactions and Photo‐Excitable Systems: UV and Visible Radiation Can Synchronize Artificial Neuron Models

AbstractNeuromorphic engineering promises to have a revolutionary impact in our societies. A strategy to develop artificial neurons (ANs) is to use oscillatory and excitable chemical systems. Herein, we use UV and visible radiation as both excitatory and inhibitory signals for the communication among oscillatory reactions, such as the Belousov–Zhabotinsky and the chemiluminescent Orban transformations, and photo‐excitable photochromic and fluorescent species. We present the experimental results and the simulations regarding pairs of ANs communicating by either one or two optical signals, and triads of ANs arranged in both feed‐forward and recurrent networks. We find that the ANs, powered chemically and/or by the energy of electromagnetic radiation, can give rise to the emergent properties of in‐phase, out‐of‐phase, anti‐phase synchronizations and phase‐locking, dynamically mimicking the communication among real neurons.

Optical Communication among Oscillatory Reactions and Photo-Excitable Systems: UV and Visible Radiation Can Synchronize Artificial Neuron Models.

Neuromorphic engineering promises to have a revolutionary impact in our societies. A strategy to develop artificial neurons (ANs) is to use oscillatory and excitable chemical systems. Herein, we use UV and visible radiation as both excitatory and inhibitory signals for the communication among oscillatory reactions, such as the Belousov-Zhabotinsky and the chemiluminescent Orban transformations, and photo-excitable photochromic and fluorescent species. We present the experimental results and the simulations regarding pairs of ANs communicating by either one or two optical signals, and triads of ANs arranged in both feed-forward and recurrent networks. We find that the ANs, powered chemically and/or by the energy of electromagnetic radiation, can give rise to the emergent properties of in-phase, out-of-phase, anti-phase synchronizations and phase-locking, dynamically mimicking the communication among real neurons.

Oregonator Scaling Motivated by the Showalter-Noyes Limit.

The Belousov-Zhabotinsky (BZ) reaction is the prototype oscillatory chemical system. We investigate here a new scaling of the Oregonator model of BZ chemical kinetics and use this scaling to elucidate fundamental properties of BZ dynamics. In particular, the Showalter-Noyes criterion for oscillation, that the product [BrO3-][H+] exceeds a critical value, arises naturally as a subcritical Hopf bifurcation in this setting, as does the reduction to a two-variable model. We thus provide chemical explanations of the role of time scales in the BZ reaction.

Novel phase-fitted symmetric splitting methods for chemical oscillators

Splitting strategy is considered for the numerical solution of oscillatory chemical reaction systems. When applied to the harmonic oscillator, traditional splitting methods with constant coefficients are shown to be have some order of phase lag though they are zero-dissipative. Phase-fitted symmetric splitting methods of order two and order four are constructed. The result of the numerical experiment on the Lotka–Volterra system shows that the new phase-fitted symmetric splitting methods are more effective than their prototype splitting methods and can preserve the invariant of the system in long-term compared with the classical Runge–Kutta method.

Validity conditions for moment closure approximations in stochastic chemical kinetics.

Approximations based on moment-closure (MA) are commonly used to obtain estimates of the mean molecule numbers and of the variance of fluctuations in the number of molecules of chemical systems. The advantage of this approach is that it can be far less computationally expensive than exact stochastic simulations of the chemical master equation. Here, we numerically study the conditions under which the MA equations yield results reflecting the true stochastic dynamics of the system. We show that for bistable and oscillatory chemical systems with deterministic initial conditions, the solution of the MA equations can be interpreted as a valid approximation to the true moments of the chemical master equation, only when the steady-state mean molecule numbers obtained from the chemical master equation fall within a certain finite range. The same validity criterion for monostable systems implies that the steady-state mean molecule numbers obtained from the chemical master equation must be above a certain threshold. For mean molecule numbers outside of this range of validity, the MA equations lead to either qualitatively wrong oscillatory dynamics or to unphysical predictions such as negative variances in the molecule numbers or multiple steady-state moments of the stationary distribution as the initial conditions are varied. Our results clarify the range of validity of the MA approach and show that pitfalls in the interpretation of the results can only be overcome through the systematic comparison of the solutions of the MA equations of a certain order with those of higher orders.

Peter Gray. 25 August 1926 — 7 June 2012

Peter Gray was an internationally recognized research leader in the areas of combustion chemistry and chemical instabilities. His undergraduate education and early research career were in Cambridge. He moved to the University of Leeds in 1955, becoming Head of Physical Chemistry there in 1965. In 1988 he returned to Cambridge as Master of Gonville and Caius College. Peter’s scientific contributions covered experimental and theoretical studies of chemical and thermal instabilities in combustion systems and in isothermal systems exhibiting autocatalysis, and of flames and chemical waves. His work provided the framework for understanding the thermokinetic origin of cool flames and multiple-stage ignitions and for the onset of ignition and oscillations in chemical systems more generally. He served on a series of important government committees and held major office for the Faraday Society and the Combustion Institute. He published more than 300 research articles and one monograph and was awarded a series of major prizes, including the Marlow Medal, the Bernard Lewis Gold Medal and the Italgas Prize.

Molecular noise induces concentration oscillations in chemical systems with stable node steady states

It is well known that internal or molecular noise induces concentration oscillations in chemical systems whose deterministic models exhibit damped oscillations. In this article we show, using the linear-noise approximation of the chemical master equation, that noise can also induce oscillations in systems whose deterministic descriptions admit no damped oscillations, i.e., systems with a stable node. This non-intuitive phenomenon is remarkable since, unlike noise-induced oscillations in systems with damped deterministic oscillations, it cannot be explained by noise excitation of the deterministic resonant frequency of the system. We here prove the following general properties of stable-node noise-induced oscillations for systems with two species: (i) the upper bound of their frequency is given by the geometric mean of the real eigenvalues of the Jacobian of the system, (ii) the upper bound of the Q-factor of the oscillations is inversely proportional to the distance between the real eigenvalues of the Jacobian, and (iii) these oscillations are not necessarily exhibited by all interacting chemical species in the system. The existence and properties of stable-node oscillations are verified by stochastic simulations of the Brusselator, a cascade Brusselator reaction system, and two other simple chemical systems involving auto-catalysis and trimerization. It is also shown how external noise induces stable node oscillations with different properties than those stimulated by internal noise.

Temperature Control of Continuous Chemical Reactors Under Noisy Measurements and Model Uncertainties

The aim of this paper is to present the synthesis of a robust control law for the control of a class of nonlinear systems named Liouvillian. The control design is based on a sliding-mode uncertainty estimator developed under the framework of algebraic-differential concepts. The estimation convergence is done by the Lyapunov-type analysis and the closed-loop system stability is shown by means of the regulation error dynamics. Robustness of the proposed control scheme is tested in the face of noise output measurements and model uncertainties. The performance of the proposed control law is illustrated with numerical simulations in which a class of oscillatory chemical system is used as application example.

Intrinsic noise alters the frequency spectrum of mesoscopic oscillatory chemical reaction systems

Mesoscopic oscillatory reaction systems, for example in cell biology, can exhibit stochastic oscillations in the form of cyclic random walks even if the corresponding macroscopic system does not oscillate. We study how the intrinsic noise from molecular discreteness influences the frequency spectrum of mesoscopic oscillators using as a model system a cascade of coupled Brusselators away from the Hopf bifurcation. The results show that the spectrum of an oscillator depends on the level of noise. In particular, the peak frequency of the oscillator is reduced by increasing noise, and the bandwidth increased. Along a cascade of coupled oscillators, the peak frequency is further reduced with every stage and also the bandwidth is reduced. These effects can help understand the role of noise in chemical oscillators and provide fingerprints for more reliable parameter identification and volume measurement from experimental spectra.

Quantitative determination of some water-soluble B vitamins by kinetic analytical method based on the perturbation of an oscillatory reaction

A novel procedure for kinetic determination of some water-soluble vitamins of the B-group (thiamine (B1), riboflavin (B2), niacin (B3) and pyridoxine (B6)) by the concentration perturbations of the Bray-Liebhafsky (BL) oscillatory chemical system involving the catalytic decomposition of hydrogen peroxide in the presence of both hydrogen and iodate ions is proposed and validated. The method uses a Pt electrode for potentiometric monitoring of the concentration perturbations of the BL matrix in a stable non-equilibrium stationary state close to the bifurcation point. The proposed method relies on the linear relationship between maximal potential displacements, ΔEm, caused by the additional known quantities of a B species. Under the optimal established analytical conditions, linear calibration curves were obtained over the range of 0.01-1.0, 0.016-0.128, 5.0-50.0 and 0.05-2.5 μmol with the limits of detection of 0.01, 0.018, 2.6 and 0.03 μmol, as well as analytical throughput of 30, 5, 12 and 20 determinations per hour, for B1, B2, B3 and B6, respectively. The used technical approach also provides simple, effective and convenient method to assay the pharmaceutical formulations containing B1 together with other active principles such as nicotinamide and vitamin B12 as well as B3.

On the Poincaré–Hill cycle map of rotational random walk: locating the stochastic limit cycle in a reversible Schnakenberg model

Recent studies on stochastic oscillations mostly focus on the power spectral analysis. However, the power spectrum yields information only on the frequency of oscillation and cannot differentiate between a stable limit cycle and a stable focus. The cycle flux, introduced by Hill (Hill 1989 Free energy transduction and biochemical cycle kinetics ), is a quantitative measure of the net movement over a closed path, but it is impractical to compute for all possible cycles in systems with a large state space. Through simple examples, we introduce concepts used to quantify stochastic oscillation, such as the cycle flux, the Hill–Qian stochastic circulation and rotation number. We introduce a novel device, the Poincaré–Hill cycle map (PHCM), which combines the concept of Hill’s cycle flux with the Poincaré map from nonlinear dynamics. Applying the PHCM to a reversible extension of an oscillatory chemical system, the Schnakenberg model, reveals stable oscillations outside the Hopf bifurcation region in which the deterministic system contains a limit cycle. Bistable behaviour is found on the small volume scale with high probabilities around both the fixed point and the limit cycle. Convergence to the deterministic system is found in the thermodynamic limit.

Bromide Control, Bifurcation and Activation in the Belousov−Zhabotinsky Reaction

The unstirred, ferroin (Fe(phen)3(2+)) catalyzed Belousov-Zhabotinsky (BZ) reaction is the prototype oscillatory chemical system. Reaction media with added Br(-) appear red (reduced, low [Fe(phen)3(3+)]) during an induction period of several minutes, followed by the "spontaneous" formation of "pacemaker" sites, which oscillate between a blue, oxidized state (high [Fe(phen)3(3+)]) and the red, reduced state and generate target patterns of concentric, outwardly moving waves of oxidation (blue). Auto-oscillatory behavior is also seen in the Oregonator model of Field, Koros and Noyes (FKN), a robust, reduced model that captures qualitative BZ kinetics in the auto-oscillatory regime. However, the Oregonator model predicts a blue (oxidized) induction phase. Here we develop a generalized Oregonator-like model with no explicit bifurcation parameter that yields the observed transition from a red initial state to oscillatory dynamics, and displays a new bifurcation mechanism not seen in the original Oregonator.

Resonant pattern formation in active media driven by time-dependent flows

The effect of a time-dependent flow in an oscillatory chemical system supporting front propagation is studied. Resonant target patterns depend on the strength and frequency of the time-dependent flow. The flow time scale needed to entrain the system to the resonant target period of oscillation depends on the closeness to the natural oscillation frequency of the medium. The flow strength needed to obtain these patterns is interpreted in terms of mixing optimization, and we give conditions for the flow that guarantee the best mixing with the Bernoulli property.