A reversible Oregonator model has been used to simulate recent experimental measurements by Schmitz, Graziani, and Hudson of complicated oscillations by a Belousov–Zhabotinsky system in a stirred tank reactor. The experimental observations indicate chaotic behavior of the small amplitude oscillations occurring between major excursions, but our computer simulation with a small error parameter apparently generates a true limit cycle with six relative maxima before the pattern repeats. The differences between experiment and simulation suggest the chaotic behavior observed experimentally may result from fluctuations too small to measure in any other way. The computations also indicate that reversibility of the reaction of bromate with bromide is important in a continuously stirred tank reactor under conditions such that the (unstable) steady state has a very low concentration of bromide ion.

A modified Oregonator model exhibiting complicated limit cycle behavior in a flow system

A general and sensitive nonempirical protocol to determine the absolute configurations of erythro and threo diols, amino alcohols, and diamines is reported. Binding of diols to the porphyrin tweezer system is greatly enhanced by increasing the Lewis acidity of the metalloporphyrin. Supramolecular complexes formed between the porphyrin tweezer host and chiral substrates exhibited exciton-coupled bisignate CD spectra with predictable signs based on the substituents on the chiral center. The working model suggests that the observed helicity of the porphyrin tweezer is dictated via steric differentiation experienced by the porphyrin ring bound to each chiral center. A variety of erythro and threo substrates were investigated to verify this chiroptical method. Their absolute configurations were unequivocally determined, and thus a general mnemonic is provided for the assignment of chirality.

Fluorinated porphyrin tweezer: a powerful reporter of absolute configuration for erythro and threo diols, amino alcohols, and diamines.

Synthesis of 1,4‐bis(4‐pyridyl)butadiyne

Under appropriate conditions the cerium catalyzed oxidation of malonic acid by bromate in acid medium exhibits a numer of interesting phenomena, including sustained periodic the coexistence of alternative stable steady states,i4 nonperiodic (“chaotic”) oscillation^,^^^ and spatiotemporal waves of chemical Some insight into the mechanism that generates such diverse behavior can be gained by examining simple models of this reaction. Because of the wide separation of time scales, which occurs naturally in this problem, it is possible to derive analytic expressions in terms of system parameters for characteristic properties of models, such as the waveform and period of oscillations, the domain of existence of multiple steady states, and the conditions for periodic “echo” waves in an excitable medium.

Oscillations, bistability, and echo waves in models of the belousov‐zhabotinskii reaction*

The five‐step Oregonator model of the oscillatory Belousov–Zhabotinskii reaction has been expanded by taking into account the reversibility of the various steps. Forward and reverse rate constants have been assigned to four of the five steps by direct analogy to the detailed Field, Koros, and Noyes model of the Belousov–Zhabotinskii reaction. The rate constants and stoichiometry of the fifth step were parametrized and the stability of the steady state was investigated as a function of both of these parameters and the over‐all distance of the system from equilibrium. It was found that there is a critical distance from equilibrium which must be exceeded before the steady state becomes unstable. Numerical integration of the differential equations resulting from the model indicated that the system executes apparent limit cycle oscillations when the steady state is unstable. Introduction of reversibility into the Oregonator leads to a striking change in the range of values of the fifth step stoichiometric parameter over which oscillations will occur. This change is discussed in terms of the chemistry of the Belousov–Zhabotinskii reaction. Under some conditions the reversible Oregonator shows excitability such that a small finite perturbation of an infinitesimally stable steady state may be greatly amplified before the system returns to rest. An apparently analogous phenomenon appears in the Belousov–Zhabotinskii reaction itself.

Limit cycle oscillations in the reversible Oregonator

Oscillations in chemical systems. IX. Reactions of cerium(IV) with malonic acid and its derivatives

Kinetics and mechanism of the reactions between the oxygen-bonded complexes 4-, 3-, and 2-pyridinecarboxylatopentaamminecobalt(III) and aquopentacyanoferrate(II)

Intramolecular electron transfer from pentacyanoferrate(II) to pentaamminecobalt(III) mediated by various 4,4'-bipyridines

Oscillations in chemical systems. X. Implications of cerium oxidation mechanisms for the Belousov-Zhabotinskii reaction

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Oscillations in chemical systems. IX. Reactions of cerium(IV) with malonic acid and its derivatives

Kinetics and mechanism of the reactions between the oxygen-bonded complexes 4-, 3-, and 2-pyridinecarboxylatopentaamminecobalt(III) and aquopentacyanoferrate(II)

Intramolecular electron transfer from pentacyanoferrate(II) to pentaamminecobalt(III) mediated by various 4,4'-bipyridines

Oscillations in chemical systems. X. Implications of cerium oxidation mechanisms for the Belousov-Zhabotinskii reaction