Mechanistic study of oscillations and bistability in the Briggs-Rauscher reaction

A ten-step mechanism has been developed for the Briggs-Rauscher system which contains iodate, hydrogen peroxide, malonic acid, and manganese(I1) in acidic solution. The model is qualitatively identical with, though it differs quantitatively from, that proposed independently by Noyes and Furrow. It also bears strong similarities to the mechanistic suggestions of Cooke. Extensive numerical simulations of the reaction in a flow reactor show that the model predicts the observed topology of the "cross-shaped phase diagram" in which both bistability and oscillations appear as the input flows of the reactant species are varied. The observed hysteresis in the steady-state iodine concentration as a function of I2 flow and a variety of other dynamic behavior are also calculated in agreement with experiment. The remaining discrepancies between theory and experiment appear to result from an overestimation in the model of the stability of the nonradical steady state. A possible remedy for this problem is suggested. The Briggs-Rauscher (BR) reaction,' in which the acidic ox- idation of malonic acid by a mixture of hydrogen peroxide and iodate is catalyzed by manganous ion, is best known as the most visually impressive of the chemical oscillators. Under appropriate conditions and with the addition of a starch indicator, at room temperature a stirred batch solution goes through 15 or more cycles of colorless-gold-blue before expiring as a purplish solution with a strong odor of iodine. The BR reaction, however, exhibits a far richer collection of nonlinear dynamic phenomena than simple oscillation. In a flow reactor, complex oscillations* as well as multiple stable states3 accompanied by a variety of bifurcation and hysteresis phenomena have been obse~ed.~.~ The BR system was discovered some 8 years ago and is a hybrid of two other chemical oscillators, the Belousov-Zhabotinskii (BZ)5 and the Bray-Liebhafsky (BL) reactions,6 for which detailed mechanisms have been proposed and numerically evaluated.'~~ It is therefore surprising that until quite recently there had been no quantitative and very little qualitative discussion of the mechanism of the BR reaction. Cookeg has studied the BR and related systems experimentally and has made a number of mechanistic suggestions based on his results. No quantitative comparison between theory and exper- iment was carried out. More recently, Furrow and Noyes'O have conducted a systematic study of the reaction, investigating the kinetics of the reacting species taken two and three at a time. These authors have proposed a skeleton mechanism and have estimated rate constants for the elementary steps in that mech- anism. They have also reported a single numerical simulation1& with their model which shows that it can indeed give rise to oscillations. In this paper, we use a broad range of experimental data ob- tained mainly, but not exclusively, under flow conditions, to guide the construction of a mechanism for the BR reaction. Although we approach the problem from a rather different point of view, we have independently arrived at a mechanism similar to that of Cooke and nearly identical with that of Furrow and Noyes. We have carried out extensive calculations with our mechanism in an attempt to simulate not only the oscillatory behavior, but the multistability, hysteresis, and bifurcation phenomena as well. We find qualitative agreement with nearly all of the observed phe- nomena and quantitative agreement with some. Most of the discrepancies which remain between our calculations and the experimental results can be attributed to a single weakness of the model-its exaggeration of the stability of the nonradical steady state of the system. We suggest how the mechanism might be augmented to correct this failing. Modifications of the BR system in which malonic acid is re- placed by related organic specie^^^^*'^ are also known to oscillate. In particular, Furrow" has carried out a careful study of the BR reaction with methylmalonic acid and has found a significant lengthening of the oscillation period over that of the malonic acid system. By introducing Furrow's experimentally determined rate parameters for the methylmalonic acid-iodine reaction at the appropriate point in our model, we show that it indeed predicts the observed increase in the period of oscillation.