Bray Liebhafsky Research Articles

Oscillatory System I−, H2O2, HClO4: The Modified Form of the Bray−Liebhafsky Reaction

The kinetics of iodide ions oxidation with hydrogen peroxide in solutions of perchloric acid at temperature of 60 degrees C has been studied in detail. We have found conditions under which this reaction proceeds oscillatory. The Bray-Liebhafsky (BL) oscillatory reaction started by the oxidation of iodide ions with hydrogen peroxide is described for the first time. The described results support our assumption (Olexová, A.; Mrákavová, M.; Melichercík, M.; Treindl, L. Collect. Czech. Chem. Commun. 2006, 71, 91-106) that singlet oxygen ((1)O(2)) is an important intermediate of the BL oscillatory reaction in the sense of the Noyes-Treindl (N-T) skeleton mechanism (Treindl, L.; Noyes, R.M. J. Phys. Chem. 1993, 97, 11354-11362).

Improvement of the stoichiometric network analysis for determination of instability conditions of complex nonlinear reaction systems

Stoichiometric network analysis (SNA), a known method for analyzing complex reaction systems including biochemical ones, is improved and applied to a nonlinear process studied far from equilibrium in a continuously fed, well stirred tank reactor (CSTR). A particular attention is focused on the determination of the narrow range of the control parameter values where the main steady state is unstable and where different dynamic states can be simulated numerically. The instability region, the most important feature of nonlinear reaction systems, is calculated as a function of the SNA parameters (current rates and reciprocal concentrations of intermediate species in the steady state) and simplified by retaining only the dominant terms. Since the number of the current rates is usually larger than the number of linearly independent equations to be used for their calculation, it is shown here that the current rates can be replaced with a smaller number of reaction rates at the steady state. These rates are related to the experimental data in a simple manner. The instability condition is also written as a function of dimensionless parameters derived from the SNA. This general approach is applied to a model of the Bray–Liebhafsky (BL) reaction having seven reactions without direct autocatalysis or autoinhibition, studied under CSTR conditions. Since the model has six intermediate species, it would be very difficult to analyze its instability condition by the conventional procedure, where a sixth order characteristic equation would have to be solved. On the other hand, the instability condition, obtained easily by the improved SNA, locates correctly the oscillatory region using numerical integration. Other dynamic states found earlier with a larger model of the BL reaction, such as mixed-mode oscillations, period doubling and chaos, are also obtained within the theoretically predicted oscillatory region. Thus, besides the general advantages of the improved stoichiometric network analysis as a method appropriate for the examination of complex nonlinear reactions, we show that the various mentioned dynamic states can be obtained by a very simple variant of the model of the BL reaction realized under CSTR conditions.

Activity of polymer supported cobalt catalyst in the Bray-Liebhafsky oscillator

The infuence of poly-4-vinylpyridine-co-divinylbenzene-Co2+ catalyst on the Bray-Liebhafsky (BL) oscillator used as the matrix for establishing catalyst’s activity was analyzed. The addition of the catalyst do not change the dynamics of the reaction in the BL matrix, but the periods of the oscillatory evolution as well as the preoscillatory period (τ1) and the duration from the beginning of the reaction to the end of the oscillatory state (τend). All experimental results are simulated satisfactory.

The chaotic sequences in the Bray–Liebhafsky reaction in an open reactor

Attractor reconstruction is done from the time series obtained by experimental investigation and by deterministic and stochastic simulation of the Bray-Liebhafsky oscillatory reaction. The appearance of deterministic chaos is confirmed and proven by both simulation and experiment, determining Lyapunov exponents for the sequences of flow rate values, as the control parameter. Moreover, unusual chaotic series were additionally recorded in the experiments, which cannot be found in deterministic numerical simulations. Therefore, an explanation of the difference between the dynamic behavior in the experiment and the deterministic simulation was sought and stochastic simulations based on the same reaction model were particularly useful. The fine structure of the chaotic windows, derived from the analysis of deterministic simulations in the range of flow rate values, made the system highly susceptible to noise induced effects, in general.

Determination of ascorbic acid in pharmaceutical dosage forms and urine by means of an oscillatory reaction system using the pulse perturbation technique

A simple and reliable method for the determination of ascorbic acid (AA) is proposed and validated. It is based on potentiometric monitoring of the concentration perturbations of an oscillatory reaction system in a stable nonequilibrium stationary state close to the bifurcation point. The response of the Bray-Liebhafsky (BL) oscillatory reaction as a matrix, to the perturbation by different concentrations of AA, is followed by a Pt electrode. The linear relationship between maximal potential shift and the logarithm of the amount of AA is obtained between 0.01 and 1.0 micromol. The sensitivity of the proposed method (as the limit of detection) is 0.009 micromol and the method has excellent sample throughput (30 samples per hour). The procedure was used for AA determination in pharmaceutical formulations and urine. The results are in agreement with those obtained using the official method. Some aspects of the possible mechanism of AA action on the BL oscillating chemical system are discussed.

Analyte Pulse Perturbation Technique for the Determination of 6-O-Acetylmorphine in Seized Street Drug Samples

Abstract A pulse perturbation technique was applied to the Bray–Liebhafsky (BL) oscillatory reaction system in a stable nonequilibrium stationary state close to the bifurcation point, to determine micro-quantitatively 6-O-acetylmorphine (6-O-AM). The proposed method, in optimized reaction conditions ([KIO3]0 = 5.9×10−2 M, [H2SO4]0 = 5.5×10−2 M, and [H2O2]0 = 2.0×10−1 M, jo=2.95×10−2 min−1, and T=42.9 °C), relied on the linear relationship between maximal potential shift, ΔEm, caused by perturbation, and the logarithm of the amount of 6-O-acetylmorphine. The method had a rather good sample throughput of 40 samples h−1 with the sensitivity determined to be 0.9 μg mL−1 and the precision RSD = 1.8%. The proposed method was successfully applied to the quantitative determination of 6-O-AM in a real seized street drug sample. The obtained result agrees with those obtained by HPLC. There was no interference from structurally related and associated compounds, such as papaverin, noscapin, and heroin.

Experimentally observable transitions between dynamical states in complex reaction systems

Identification of trends and their correspondence with dynamical state transitions are briefly discussed on several reaction network models. The influence of different threshold values on the trend analysis and dynamical state analysis results is examined. Both methods are applied here to the results of the numerical simulation. For this purpose the models of three reaction systems are used: simple model of consecutive, first order, equilibrium reactions, partial oxidation of cyclohexane, and model of the oscillatory reaction Bray Liebhafsky. Detailed kinetic analysis confirmed that transient dynamical states may be identified through the symbolic representation of the sequence of trend episodes in experimentally obtainable time series. Stoichiometric Network Analysis of possible dynamical states was used to identify reaction pathways responsible for the sequences of trend episodes. Some technical problems were also addressed, connected with selection of the threshold value and dynamical state notion.

Computational Simulation of Bray-Liebhafsky (BL) Oscillating Chemical Reaction

The computational simulation of the Bray-Liebhafsky (BL) oscillating chemical reaction by differential kinetic methodology is carried out in this work. According to the mechanism of Treindl and Noyes involving 10 reaction steps, the changes of the concentrations of I 2 and O 2 in solution are simulated. When the control parameters are α = 0.55, β = 0.2882 and δ ＜ 0.6, the differential equations present periodic solution, and the oscillations can be observed in 150 min. If α , β and δ are taken as the control parameters, respectively, the bifurcation points would be observed in the processes of control parameters, changing successively with the critical values of α = 0.55 ，β = 0.2882 ， and δ = 0.6. The acidity of solution on the nonlinear phenomena is also investigated in detail.

Kinetic determination of morphine by means of Bray–Liebhafsky oscillatory reaction system using analyte pulse perturbation technique

A novel kinetic method for micro-quantitative determinations of morphine (MH) is proposed and validated. The method is based on the potentiometric monitoring of the concentration perturbations of the oscillatory reaction system being in a stable non-equilibrium stationary state close to the bifurcation point between stable and oscillatory state. The response of the Bray–Liebhafsky (BL) oscillatory reaction as a matrix system, to the perturbations by different concentrations of morphine, is followed by a Pt-electrode. The proposed method relies on the linear relationship between maximal potential shift, Δ E m, and the logarithm of the added morphine amounts in the range of 0.004–0.18 μmol. Under optimum conditions, the sensitivity of the proposed method (as the limit of detection) is 0.001 μmol and the method is featured by good precision (R.S.D. = 1.6%) as well as the excellent sample throughput (45 samples h −1). In addition to standard solution analysis, this approach was successfully applied for quantitative determination of morphine in a typical pharmaceutical dosage form. Some aspects of the possible mechanism of morphine action on the BL oscillating chemical system are discussed in detail.

Microwaves and coherence in the Bray–Liebhafsky oscillatory reaction

Simultaneous application of microwave (MW) heating and mechanical stirring to the Bray–Liebhafsky reaction supports the ‘nucleation’ theory of nonequilibrium transitions. The opposite effects of microwaves and stirring on the oscillatory reaction dynamics stress the predominant effect of microwaves on the coherence mechanism, preventing in-phase macroscopic oscillations. The obtained results can contribute to the understanding of the mechanism of nonequilibrium transitions on a more general level.

Determination of paracetamol in pure and pharmaceutical dosage forms by pulse perturbation technique

A new procedure for kinetic determination of paracetamol in pharmaceuticals is proposed. The method is based on potentiometric monitoring of the concentration perturbations of the matrix reaction system being in a stable non-equilibrium stationary state close to the bifurcation point. In the case considered as the matrix system, the Bray–Liebhafsky oscillatory reaction is used. The response of the matrix system to the perturbations by different concentrations of paracetamol is followed by a Pt-electrode. Proposed method relies on the linear relationship between maximal potential shift, Δ E m, and the logarithm of added paracetamol amounts. It is obtained in optimized experimental conditions for variable amounts of paracetamol in the range 0.0085 and 1.5 μmol. The sensitivity and precision of proposed method were quite good (0.0027 μmol as the limit of detection and 2.4% as R.S.D.). Some aspects of possible chemical interactions between paracetamol and matrix are discussed. Applicability of the proposed method to the direct determination of paracetamol in pharmaceutical formulations was demonstrated.

Investigation of microwave effects on the oscillatory Bray–Liebhafsky reaction

A specific control of the Bray–Liebhafsky oscillatory reaction is achieved by changing the microwave (MW) participation in heating the reaction mixture. Experiments are performed at temperatures T rm = 62, 65, 68 °C. Before the bifurcation point, increased MW participation has no effect on the reaction mechanism. In the sensitive state close to the bifurcation point, increased MW participation stops the oscillatory evolution. To explain the reaction dynamics in the MW field, we consider classical causes (overheating and convection effects) in contrast to some specific effects of the MW heating.

Microwave driven Bray-Liebhafsky oscillatory reaction.

Oscillatory reactions are important in controlling processes in living organisms, in the same way that a clock controls processes in modern computers. Investigations of the microwave heating of the Bray–Liebhafsky oscillatory reaction revealed nonthermal effects by the favoring of monotonic dynamics (see graphic). The important role of bulk water is discussed.

Kinetic Determination of Microquantities of Rutin by Perturbation of the Bray-Liebhafsky Oscillatory Reaction in an Open System

A kinetic method is described for the microquantitative (microconcentration/microvolume) determination of rutin based on potentiometric monitoring of the concentration perturbations of the Bray-Liebhafsky (BL) oscillatory reaction being in a non-equilibrium stationary state close to a bifurcation point. The experiments are carried out in an open reactor. The response of the matrix system to perturbations by different concentrations of rutin ethanolic solutions is followed by a Pt-electrode. In the concentration range between 7.8×10−8 mol dm−3 and 9.1×10−6 mol dm−3, we found a linear dependence of the maximal potential shift, ΔEm, on the logarithm of the rutin concentrations. The unknown concentrations can be determined from the calibration curve up to an accuracy of ±5%. The detection limit is 3.6×10−8 mol dm−3. The amount of required sample can be as small as 10 µL.

Investigation of the Influence of Heavy Water on Kinetic Pathways in the Bray−Liebhafsky Reaction

A more detailed investigation of the influence of heavy water on the two main kinetic pathways underlying the mechanism of the Bray−Liebhafsky (BL) reaction is performed. The course of the BL reaction at four temperatures was monitored with an improved experimental setup, enabling simultaneous recordings of the potential of the platinum electrode, the concentration of I2, and the oxygen production rate. It is confirmed that by replacing ordinary water with heavy water, the oxidation pathway is more effectively accelerated than the reduction pathway. Influence of the isotopic substitution on the acidity of the BL system, VIS spectra of iodine in D2O, and the reaction between iodine and deuterated peroxide are investigated in separate experiments. It is concluded that the observed enhancement of the oxidation pathway cannot be simply explained by the isotopic effect. Hence, the possible role of bulk water in the process of shifting the whole reaction mechanism toward the oxidation pathway is discussed.

Investigation of dynamic behavior of the Bray–Liebhafsky reaction in the CSTR. Properties of the system examined by pulsed perturbations with I–

In order to investigate the properties of the dynamic states in the Bray–Liebhafsky (BL) reaction, pulsed perturbations with iodide are applied. In particular, the excitability thresholds of several stable stationary states corresponding to the same non-equilibrium stationary state branch, as well as the excitability thresholds and phase response behavior of one oscillatory state, are investigated and characterized quantitatively. In the oscillatory state, the phase response behavior corresponding to perturbations of different strengths is determined, and characterized by phase response curves (PRC and PTC). Finally, all values obtained experimentally are also calculated, using one variant of a model of the Bray–Liebhafsky reaction.

The oxidation of iodine to iodate by hydrogen peroxide

The kinetics of the oxidation of iodine by hydrogen peroxide, a part of the Bray–Liebhafsky reaction, has been studied between 298 and 323 K using a spectrophotometric method. The rate of reaction passes through a maximum when the concentration of hydrogen peroxide increases. At low hydrogen peroxide concentration, the order of reaction with respect to [I2] is roughly one, whereas at high hydrogen peroxide concentration the apparent order is higher and there is no simple kinetic law. This reaction can be observed only with sufficient acid and iodate concentrations. However, its rate does not change much with perchloric acid concentration in the range 0.04 to 0.2 mol dm−3 and iodate concentration in the range 0.005 to 0.05 mol dm−3. The maximum first order rate constant is 8 × 10−3 s−1 at 298 K with an activation energy of 80 kJ mol−1. The results are discussed considering a model proposed previously for the Bray–Liebhafsky reaction.

Numerical simulations of the oxygen production in the oscillating Bray–Liebhafsky reaction

Numerical simulations of the oxygen production in the batch Bray–Liebhafsky (BL) oscillating reaction were performed. The dynamic behaviour of the BL reaction was modelled by a scheme suggested by Schmitz and Kolar-Anič, complemented by the physical processes of iodine and oxygen interphase transport. The calculated number and periods of oscillations of the rate of the gaseous oxygen production are in satisfactory agreement with experiment. Oscillations in iodate concentration have been found if some escape of iodine from the batch reactor was allowed.

Investigation of Dynamic Behavior of the Bray−Liebhafsky Reaction in the CSTR. Determination of Bifurcation Points

Experimental results obtained by operating the Bray−Liebhafsky (BL) reaction in the CSTR are presented. The dynamic behavior of the BL reaction is examined at several operation points in the concentration phase space, by varying different parameters, the specific flow rate, temperature, and mixed inflow concentrations of the feed species, one at a time. Different types of bifurcation leading to simple periodic orbits, supercritical and subcritical Hopf bifurcations, saddle node infinite period bifurcation (SNIPER), saddle loop infinite period bifurcation, and jug handle bifurcation, are observed. Moreover, complex dynamic behavior, including transition from simple periodic oscillations to complex mixed-mode oscillations and chaos, and bistability are also discovered.

Oxygen Production in the Oscillatory Bray−Liebhafsky Reaction

The volume of gaseous oxygen produced during the Bray−Liebhafsky (BL) oscillating reaction was measured. The rates of oscillatory O2 evolution were calculated and the geometrical effects of the Pt electrode surface, stirring rate, and addition of the surfactant on the oscillatory behavior were studied. A significant stirring rate and detergent effect is observed. The oxygen evolution results obtained are in satisfactory agreement with oscillatory behavior of the BL reaction monitored by potentiometric measurements. The idea that physical and chemical processes might couple in the gas evolving oscillators and similar systems was first suggested over fifteen years ago by Bowers and Noyes. The possibility that chemical processes may couple with both oxygen and iodine nucleation and evolution in order to cause, enhance, or suppress oscillations in the BL system is indicated.