Analysis of the Bromate−Sulfite−Ferrocyanide pH Oscillator Using the Particle Filter: Toward the Automated Modeling of Complex Chemical Systems

Abstract

This study was aimed at identifying a quantitatively accurate reaction model of the bromate-sulfilte-ferrocyanide (BSF) pH oscillator by using the simulation-based model estimation algorithm known as the particle filter. The Rbai-Kaminaga-Hanazaki (RKH) model proposed for the BSF system was extended by adding the protonation equilibrium of SO42-, for which the particle filter analysis was carried out to optimize the rate constants involved with reference to the measured pH oscillation data. The extended RKH model with the optimized rate constants almost completely reproduced the measured pH oscillations and the state diagram, showing the validity of the present analysis. Chemical oscillators such as the BSF system show drastic switching of the dominant reaction path, which strongly disturbs the convergence of the rate constants if the objective function is defined in a conventional manner to reflect only a single time step datum. In this study, the objective function was defined as the residual sum of squares with respect to pH taken over an interval longer than one oscillatory period, so that all of the relevant reaction steps can contribute to the objective function. This is the first report which exemplifies the effectiveness of the particle filter in the analysis of real complex chemical systems.

Modulation of spatiotemporal dynamics in the bromate–sulfite–ferrocyanide reaction system by visible light

“…During simulation, the rate constants of (M1) , (M2) , (M4) , (M5) was obtained from ref. 32 . And others were fitted according to our experimental results.…”

Self-Oscillating Membranes with Polymer Interface Synchronized with Chemical Oscillator to Reproduce Lifelike Pulsatile Flow

“…The BSF pH oscillator mechanism has been reported by Rabai, Kaminaga and Hanazaki (RKH) (reactions 1−5; Table 1), 40 (reaction 6). 41 When the SO 3 2− species are present, reactions 1 and 3 predominate and the stoichiometric balance shows a stable and low concentration of H + . The pH of the oscillator is then at its highest.…”

“…To implement the self-oscillating behavior, the pH-sensitive hybrid membrane is then mounted into a filtration setup and coupled with a pH oscillator system in a solution (bromate–sulfite–ferrocyanide, BSF) (Figure b). The BSF pH oscillator mechanism has been reported by Rábai, Kaminaga and Hanazaki (RKH) (reactions 1–5; Table ), further extended by Sato et al by adding the protonation equilibrium of SO 4 2– (reaction 6) . When the SO 3 2– species are present, reactions 1 and 3 predominate and the stoichiometric balance shows a stable and low concentration of H + .…”

Pulse-density modulation control of chemical oscillation far from equilibrium in a droplet open-reactor system

“…We investigated the controllability of chemical reaction dynamics far from equilibrium using a droplet open-reactor system through bromate–sulfite–ferrocyanide (BSF) pH oscillation 33 34 35 (details are given in the Methods section, Supplementary Note 2 and Supplementary Table 1 ). This reaction consists of a time-delay negative feedback loop of the autocatalytic production of H + and the consumption of H + at low pH.…”

“…The following is a simple reaction model of the BSF reaction that is called the Rabai–Kaminaga–Hanazaki model 34 35 :…”