The ferroin/ferriin ([Fe(phen)32+/3+]))-catalyzed Belousov−Zhabotinsky (BZ) reaction is the prototype oscillatory chemical reaction. In reaction mixtures in a Petri dish, with Br– initially added for production of bromomalonic acid, one sees the “spontaneous” formation of target patterns of concentric waves of oxidation (blue, high-ferriin) in a red/reduced/low-ferriin reaction medium, following an initiation period of several minutes in a red steady state. We report on a fifteen-year program of undergraduate research at Hofstra University and Bard College at Simon's Rock involving 40+ college students and several high school students into the dynamics of the apparently spontaneous generation of oscillatory (red/blue) pacemakers generating these target patterns. Both experimental and simulation methods were used; the latter using the Field−Körös−Noyes Oregonator model, a three-variable skeleton model of BZ kinetics and extensions involving the dynamics of bromination of malonic acid. Main results: The dynamics of pacemaker formation in the BZ reaction can be described by slow passage through a Hopf bifurcation from excitable to auto-oscillatory dynamics, in which an effective stochiometric factor including all bromide production serves as a bifurcation parameter. For the ferroin-catalyzed reaction, this Hopf bifurcation is subcritical, allowing a combination of heterogeneities and random fluctuations to initiate pacemakers. The transition between bulk oscillations in manganese (Mn2+/3+) catalyzed reactions and pattern formation in ferroin-catalyzed reactions can be understood by chemical interpolation using mixed catalysts. The Showalter-Noyes criterion for oscillations, that [H+][BrO3–] exceeds a critical value, arises because [H+][BrO3–] parametrizes the ratio of the time scale of fast HBrO2 dynamics to that of the slow redox dynamics of the catalyst. Open question: is the red/reduced low-ferriin reaction medium bistable at the time of pacemaker formation? Undergraduate research: The dynamics of the BZ reaction is an ideal area for undergraduate research because (1) getting started is relatively simple, (2) careful, replicable experimental practice is important because pacemaker initiation is sensitive to small perturbations, (3) a combination of experimental and simulation (stiff o.d.e.) techniques are used, 4) students learn about non-equilibrium kinetics, and (5) students can and have made important contributions to publications.

Onset of oscillations in the Beluosov-Zhabotinsky reaction: Undergraduate research experience

254th National Meeting (2017)

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