The Model of “Minimal Oscillator” Derived from the Kinetic Mechanism of the H₂O₂-NaSCN-NaOH-CuSO₄Dynamical System

Abstract

Dissipative chemical reactions, which involve oscillatory variations of the concentrations of the intermediates in time, are usually characterized with complicated kinetic mechanisms. However, the essential source of the oscillations can often be reduced to only a few reaction steps providing the alternative domination of the positive and negative feedback loops. In an extreme case such a reduction leads to the so-called "minimal oscillator," the concept used in the past for the well-known Belousov-Zhabotinsky (BZ) reaction. In the present work, we construct such a minimal system for the (discovered by M. Orbán) H 2 O 2 -NaSCN-NaOH-CuSO 4 homogeneous oscillator, in which instabilities originate from kinetic mechanism substantially different from that proposed for the BZ system. The methodology involves intuitive analysis of the reaction mechanism, supported by numerical calculations and spectrophotometric measurements. We show how the actual, only three-variable model evolves from our previously elaborated: nine-and five-variable mechanisms and prove that its further reduction to two-variable one is not possible. Thus the present work is a final step in our searches for the "minimal Orbán oscillator". C 2015 Wiley Periodicals, Inc. Int J Chem Kinet 47: [795][796][797][798][799][800][801][802] 2015

Mechanism of the oscillating chemiluminescence reaction in the luminol‐H2O2‐KSCN‐CuSO4‐NaOH system

“…The reaction Cu21 is taken from Refs. 16,20–22. The reactions Cu22 (red letters), T31 (red dotted arrow), and T32 (red solid arrow) are incorporated in the present work [Color figure can be viewed at wileyonlinelibrary.com]…”

“…16 The drop in Pt electrode potential was also observed by Takayama et al 18 For the oscillating chemiluminescence reactions, it was indicated that the superoxide anion O 2 ⋅ − promotes cycloaddition, followed by the detachment of nitrogen molecules that were incorporated into the phthalate dianion. 3,19 Previous theories 3,20 have suggested that intermittent intense fluorescence was due to the reaction of luminol with the hydroperoxyl radical HO 2 ⋅.…”

“…Wiśniewski et al 16 calculated the potential and [Cu(OH) 3 − ]/[Cu(OH) 2 − ] ratio, and the concentration of HO 2 Cu(OH) 2 − , which was compared with the experimental absorbance at 375 nm 21,22 . Jędrusiak et al 20 calculated the concentration of HO 2 Cu(OH) 2 − , − OS(O)CN, and HO 2 ·. Recently, Cervellati et al 23,24 also carried out a detailed calculation for the Orbàn‐Epstein reaction system.…”

Oscillatory chemical reaction as a sensor of Cu(II)–EDTA complex formation and ligand degradation in copper ion‐catalyzed oxidation of thiocyanate ions with hydrogen peroxide

“…Also, this reaction can generate luminescent spatiotemporal patterns of novel type (thermokinetic kinematic/phase waves) 17,18 . In further studies, we also proposed the stepwise reduction of the original kinetic mechanism to the core explaining only oscillations in terms of ten, 16 five, 19 and finally three dynamical variables, 20 composing the minimal oscillator, meaning that the latter mechanism cannot be further reduced to two variables without a loss of the oscillatory instabilities.…”

Oscillating chemiluminescence reaction in the L‐012–H2O2–KSCN–CuSO4–NaOH system

“…Jędrusiak et al. calculated the concentration of HO 2 Cu(OH) 2 − , − OS(O)CN, and HO 2 · 8 . Recently, Cervellati et al.…”