Chemical oscillations in the classic Belousov-Zhabotinsky (BZ) system typically have a period of a few minutes, which can be increased significantly by changing the organic substrate. Here we show that by changing the temperature and concentrations, an increase of 3-4 orders of magnitude in the frequency of BZ oscillations can be obtained. At elevated temperatures, in high concentration mixtures, the cerium-catalyzed reaction exhibits sinusoidal oscillations with frequencies of 10 Hz or greater. We report the effect of temperature on the frequency and shape of oscillations in experiments under batch conditions and in a four-variable model. We show that our simple model accurately captures the complex temporal behavior of the system and suggests paths toward even higher frequencies.

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High-Frequency Oscillations in the Belousov−Zhabotinsky Reaction

The uncatalyzed system BrO3−–phenol–H2SO4 exhibits an astonishing variety of dynamic behavior including three stationary
 and two oscillatory states, dual-frequency and dual-amplitude oscillations and aperiodic oscillations in a closed, stirred
 batch reactor. For an explanation of the sequential oscillations we assume that we have subsystems
 (A + B) and (C + B) coupled through the common reactant B (bromate). A is phenol and C is the oxidation/bromination
 product of the A + B reaction. A significant stirring rate and viscosity effect is observed. Stationary complex
 patterns may spontaneously develop
 when
 a solution containing phenol, BrO3− and H2SO4 is poured into an open Petri dish.

Dynamic behavior during the oxidation of phenol with bromate in a closed reactor

We hope that this Review has made readers more aware of solvation of inorganic complexes, and of the importance of such knowledge in understanding their chemistryperhaps particularly their reactivity. The approach just set out for inorganic complexes should be of considerable value in the field or organometallic chemistry. In particular, informed use of solvation characteristics should help in optimising conditions for organometallic reactions and in homogeneous catalysis. Unfortunately, solvation data on reactants are too sparse (the subject index ofComprehensive Organometallic Chemistry contains justthree entries under “solubility”!) for serious examination of reactivity trends in terms of initial state and transition state contributions to be possible in almost all areas. Moreover, there are some fundamental problems over transfer parameters. Thus, a favourite electrochemical assumption is that the ferrocene/ferrocinium redox potential is independent of solvent. Yet, the dependence of rate constants on medium for outer-sphere electron transfer in the ferrocene/ferrocinium system can only be understood(66) in terms of specific solvation effects which are incompatible with the parallel solvation changes of these two substrates implicit in the redox potential assumption. The solvation of organometallic species should prove a most rewarding area for continued study, but it will be some time before the overall picture becomes as clear as in the more limited area of classical transition metal complexes considered in the present Review.

Solvation of transition metal complexes: thermochemical approaches

It is well known that temperature plays an important role in the chemical dynamics of Belousov-Zhabotinsky (BZ) reactions. The five-step Oregonator model of the BZ reaction has been elaborated here to investigate the temperature effect. The bifurcation dynamics has been calculated in the phase space spanned by initial reagents concentration ratio, stoichiometric factor and temperature. The combination of activation energies of the individual reaction steps governs the dependence of oscillation period and amplitude with temperature. The analysis reveals the existence of temperature limits beyond which no oscillations occur.

Temperature dependence of the Oregonator model for the Belousov-Zhabotinsky reaction

Temperature independent period length (temperature-compensation) in pH-oscillators has been simulated with a simple general model. Opposing effects of the composite reactions on the period length with changing temperature have been shown to be responsible for this peculiar phenomenon. Experiments have shown that temperature-compensation exists in the oscillatory hydrogen peroxide–sulfite ion–thiosulfate ion flow system in a narrow range of conditions. A simple mechanism with estimated activation energies of the steps was used successfully to simulate the phenomenon.

Temperature-compensation in pH-oscillators

The frequency of oscillation of the Belousov–Zhabotinskii reaction (oxidation of malonic acid by bromate ions in acidified solution containing cerium ions) depends on the initial concentration of reactants, but in each case, a plot of log (frequency) against reciprocal temperature is linear. The calculated activation energies for eight solutions cover a relatively small range. These findings are examined in the light of proposed reaction schemes. Calculations indicate that the frequency is controlled to a significant extent by the rate of reaction between bromide and bromate ions to form HOBr and HBrO2.

Analysis of the dependence on temperature of the frequency of oscillation of the Belousov–Zhabotinskii reaction

Rate laws and rate constants are reported for reactions of several low-spin iron(II) complexes with hydroxide ion in methanol-water solutions. The dependence of the form of the rate law and of reactivity on ligand type and on substituent nature is discussed. The pattern of reactivity for a range of compounds with hydroxide ion in methanol-water mixtures is compared with the reactivity pattern for analogous reactions in dimethyl sulphoxide-water mixtures.

Reactions of low-spin iron(II) complexes with hydroxide ion in aqueous methanol: the effect of ligand on rates of reaction

Rate constants at 298 K are reported for the reaction of [Fe(phen)3]2+(phen = 1,10-phenanthroline) with hydroxide ion in methanol–water and acetone–water mixtures. From known solubilities of naphthalene in these mixtures, and using the method of Van Meter and Neumann, the effect of added solvent on the solvation of this iron complex has been calculated. Thence, the kinetic results have been split into the effects of solvent on the initial and transition states. The treatment of Van Meter and Neumann has been extended to an analysis of the effect of solvent on the transition state, using solubility data obtained from 2-naphthol in methanol–water mixtures. The results support a mechanism in which hydroxide attacks initially at the 2(9) position of the co-ordinated phen; considerable interaction between this carbon-bonded hydroxyl group and the central iron atom is indicated.

Analysis of the effects of solvent on the initial and transition states in the kinetics of reaction between tris(1,10-phenanthroline)iron(II) cation and hydroxide ions in methanol– and acetone–water mixtures

When the Belousov–Zhabotinskii oscillating reaction is perturbed by rapid addition of bromide ions, the oscillations disappear but then recover. The time taken for this recovery depends on the extent of concentration perturbation, but the new frequency and amplitude of oscillation closely resemble the frequency and amplitude before perturbation. These observations show that this oscillating chemical reaction follows a limit cycle type of behaviour. A similar pattern is observed when solutions containing cerium(IV) ions are rapidly added to the oscillating reaction, although there is a more marked change in frequency and amplitude. The experimental results are compared with the results obtained from a numerical analysis of the effects of similar perturbations on the oscillations for two model schemes of oscillating reactions.

Response of the Belousov–Zhabotinskii oscillating reaction to addition of either bromide or cerium(IV) ions

Analysis of the effects of solvent on the initial and transition states in the kinetics of reaction between tris(1,10-phenanthroline)iron(ii) cation and hydroxide ions in methanol- and acetone-water mixtures

David L. Roberts

Papers

Analysis of the dependence on temperature of the frequency of oscillation of the Belousov–Zhabotinskii reaction

Reactions of low-spin iron(II) complexes with hydroxide ion in aqueous methanol: the effect of ligand on rates of reaction

Analysis of the effects of solvent on the initial and transition states in the kinetics of reaction between tris(1,10-phenanthroline)iron(II) cation and hydroxide ions in methanol– and acetone–water mixtures

Response of the Belousov–Zhabotinskii oscillating reaction to addition of either bromide or cerium(IV) ions

Analysis of the effects of solvent on the initial and transition states in the kinetics of reaction between tris(1,10-phenanthroline)iron(ii) cation and hydroxide ions in methanol- and acetone-water mixtures