Chaotic pH Oscillations in the Sulfur(IV)−Hydrogen Peroxide−Marble Flow System

Abstract

A self-accelerating oxidation of sulfur(IV) by hydrogen peroxide in an unbuffered aqueous solution in the presence of solid marble has been utilized to develop an oscillatory system in a continuous-flow stirred tank reactor. First, a model was constructed from the component reactions: (1) H2O2 + HSO3 - → H+ + SO4 - + H2O; (2) CaCO3 + H+ → Ca2+ + HCO3 -; (3) HSO3 - ↔ H+ + SO3 2-; (4) CO2(aq) + H2O ↔ H+ + HCO3 -; (5) CO2(aq) → CO2(gas). Simulations based on the kinetics of reactions 1−5 predicted regular pH oscillations, bursting, and chaotic responses. Most of the simulated phenomena were found experimentally in the vicinity of the predicted conditions. The parameters of the experimental oscillations also agree well with their calculated counterparts.

Discovery of Novel Bromate−Sulfite pH Oscillators with Mn2+ or MnO4- as a Negative-Feedback Species

“…The scheme was summarized in an abstract model and was successfully utilized as a guiding principle for the systematic design of novel pH oscillators. , Spatial pattern formation − and photoresponse − were studied for a number of pH oscillators. Recently, the idea of simultaneous employment of two negative-feedback species led to the discovery of chaotic pH oscillations, − for which photoinduced bifurcation to chaos was demonstrated for the first time . Although most of the studies of the pH oscillators reported so far have been more or less kinetics-oriented, practical applications of the pH oscillators to the temporally controlled drug delivery system − and to the control medium for the rhythmically pulsatile mechanical motion of a polymer hydrogel system emulating muscular tissue have also been suggested.…”

Kinetic Role of CO2 Escape in the Oscillatory H2O2−HSO3-−HCO3- Flow System

“…Another difficulty is that the reproducibility of the clock-type curves is poor. 1 All in all, at this point we tend to accept the higher value k 1 ) 7.0 for further considerations. Reaction 1 with a two-term rate law is considered in the erl model that represents mechanistic steps F2 and F3.…”

“…Second, the value of k 1 ) 7.0 M -1 s -1 in the erl is 2-fold higher than in the mechanism (see constant for reaction F2). To obtain as simple a model as possible, we neglect F1 because it seems to 1.48 × 10 7 6.5 × 10 6 k2 s - 1 3.0 × 10 3 1.0 × 10 3 k-2 M -1 s -1 5.0 × 10 10 1.0 × 10 10 k3 s -1 4.3 × 10 -2 1.1 × 10 -2 k-3 M -1 s -1 9.6 × 10 4 2.5 × 10 4 a Apparent activation energies for the rate constants were used with values available at 25.0°C to calculate values for 4.0°C.…”

“…1 We have found this reaction system to exhibit either periodic or chaotic pH oscillations depending on conditions. Here, marble provides the necessary negative feedback for oscillations as it removes H + when the reaction mixture becomes acidic as a result of the H + -producing oxidation of the hydrogen sulfite ion.…”

Tracking unstable steady states and periodic orbits of oscillatory and chaotic electrochemical systems using delayed feedback control

“…General application of this method is troublesome 29 in chemical systems. Although chaotic behavior can be represented by one-dimensional return maps in many chemical systems ͑e.g., in the BZ reaction, 30 electrochemical systems, 31 pH oscillators, 32 combustion reactions, 15 and biochemical systems 33 ͒, the perturbation of a control parameter can increase the dimensionality of the system. Methods do exist to overcome this problem, 12,29,34 however, the tracking algorithms become complicated again.…”