Oregonator Scaling Motivated by the Showalter–Noyes Limit

Science, serendipity, coincidence, and the Oregonator at the University of Oregon, 1969-1974

This historical review of the development of the Oregonator model of the Belousov-Zhabotinsky reaction is based on a lecture Dick Field presented during IrvFest2015-Celebrating a founding father of chaos!, a meeting in commemoration of Irving R. Epstein's 70 th birthday. For Dick's 80 th birthday festschrift, we focus here on the five papers in the series named "Oscillations in chemical systems," published in 1972 [Noyes et al., J. Am. Chem. Soc. 94, 1394-1395 (1972); Field et al., J. Am. Chem. Soc. 94, 8649-8664 (1972); Field and Noyes, Nature 237, 390-392 (1972)] and 1974 [Field and Noyes, J. Chem. Phys. 60, 1877-1884 (1974); Field and Noyes, J. Am. Chem. Soc. 96, 2001-2006 (1974)].

Measurements and Simulations of the Acidity Dependence of the Kinetics of the Iron-Catalyzed Belousov-Zhabotinsky Reaction: Proton-Catalysis in the Electron Transfer Reaction Involving the [Fe(phen)3]3+ Species

The acidity dependence of the iron-catalyzed bromate-malonic acid Belousov-Zhabotinsky reaction was studied in the range 0.36 M < [H₂SO₄]₀ < 1.20 M, and the temporal evolutions of the oscillation patterns were analyzed. The experimental results show that the period times PT _i decrease exponentially with increasing acidity and that the period times parallel the decrease of the reduction times RT with increasing acidity. Simulations using the reactions of the commonly accepted core reaction mechanism failed to match the measurements even in a qualitative fashion. However, we found that compelling agreement between the experiments and the simulations can be achieved over the entire range with the inclusion of second-order proton-catalysis of the oxidation of bromomalonic acid (BrMA) by the [Fe(phen)₃]³⁺ species in the reaction identified in this paper as reaction 9 (R9), and this [H⁺] dependence is informative about the species involved in the outer sphere electron transfer reaction. The trication [Fe(phen)₃]³⁺ species is stabilized by ion pairing and solvation, and one may anticipate the presence of [Fe(phen)₃(HSO₄) _n(H₂O) _m]^{(3- n)+} species ( n = 0-3). Our results suggest that the removal of aggregating HSO₄^- ions by protonation creates a better oxidant and facilitates the approach of the reductant BrMA, and the second-order [H⁺] dependence further suggests that BrMA is primarily oxidized by a doubly charged [Fe(phen)₃(HSO₄)₁(L) _k]²⁺ species. Considering the complexity of the BZ system and the uncertainties in the many reaction rate constants, we were somewhat surprised to find this high level of agreement by (just) the replacement of R9 by R9'. In fact, the near-quantitative agreement presents a powerful corroboration of the core reaction mechanism of the BrMA-rich BZ reaction, and the replacement of R9 by R9' extends the validity of this core reaction mechanism to acidities above and below the typical acidity of BZ reactions ([H⁺] ≈ 1 M).

On Emulation of Flueric Devices in Excitable Chemical Medium

Flueric devices are fluidic devices without moving parts. Fluidic devices use fluid as a medium for information transfer and computation. A Belousov-Zhabotinsky (BZ) medium is a thin-layer spatially extended excitable chemical medium which exhibits travelling excitation wave-fronts. The excitation wave-fronts transfer information. Flueric devices compute via jets interaction. BZ devices compute via excitation wave-fronts interaction. In numerical model of BZ medium we show that functions of key flueric devices are implemented in the excitable chemical system: signal generator, and, xor, not and nor Boolean gates, delay elements, diodes and sensors. Flueric devices have been widely used in industry since late 1960s and are still employed in automotive and aircraft technologies. Implementation of analog of the flueric devices in the excitable chemical systems opens doors to further applications of excitation wave-based unconventional computing in soft robotics, embedded organic electronics and living technologies.