Initial inhomogeneity-induced crazy-clock behavior in the iodate–arsenous acid reaction in a buffered medium under stirred batch conditions

Abstract

It is unambiguously demonstrated that in the case of an autocatalytic reaction, initial inhomogeneities induced by the imperfectly mixed part of the overall volume may result in a serious irreproducibility of the individual kinetic runs. A statistically meaningful number of repetitions, however, gives rise to a reproducible cumulative probability distribution curve often referred to as a support of the stochastic feature. The iodate-arsenous acid reaction being autocatalytic with respect to both iodide and hydrogen ions displays clock behavior. However, the time lag necessary for the appearance of iodine, even in buffered solution, varies in an apparently random manner. Careful analysis of the variation of the different parameters like stirring rate, overall volume, geometry of the reactor and the way of mixing the reactants led us to conclude that the fate of the individual samples is determined at the initial stage when the reacting system is per se inhomogeneous. The place, the size of the so-called ignition volume, where the reacting system is imperfectly stirred, as well as the residence time spent there by the imperfectly mixed reactants all seem to depend on external factors.

Imperfect mixing as a dominant factor leading to stochastic behavior: a new system exhibiting crazy clock behavior

“…10 It is therefore expected that a simpler real chemical system may facilitate the study of the theoretical background of the emergence of stochastic behavior. This expectation, along with the fact that the arsenous acid-iodate reaction exhibits crazy-clock behavior (CCB) as reported recently by our research group, 11 has led us to elucidate the comprehensive kinetic model of the arsenous acid-iodate system, 12,13 including the well-known Dushman 14 and Roebuck 15 reactions. Very recently, Pagnacco et al reported 16 that the state I (low iodide and iodine concentration) to state II (high iodide and iodine concentration) transition of the Briggs-Rauscher reaction 17 after leaving the strongly reproducible oscillatory state was found to be irreproducible as well.…”

“…This idea was supported by the fact that the increase of the overall volume significantly shortens the Landolt time, because the probability that random fluctuations produce more and more ignition places indeed increases. In our previous report when using the arsenous acid-iodate reactions to study the origin of CCB, 11 however, it was convincingly proven by systematically varying the stirring rate, the way of mixing, and the geometry of the reactor, that the fate of individual samples in this reaction is determined at the beginning stage-upon mixing the reactants-when the system is per se inhomogeneous. This study made it clear that even if random fluctuation at the later stage of an autocatalytic reaction cannot be entirely ruled out as a source of stochasticity, inherent inhomogeneity must play a crucial role in causing the serious irreproducibility of the individual samples performed ''under exactly the same experimental conditions''.…”

Exploding Chemical Gardens: A Phase‐Change Clock Reaction

“…[26] Our clock keeps reasonable but not perfect time.According to Figure 6c the system is ab etter timer at higher and lower concentrations of silicate than at intermediate concentrations.F luctuations in clock reaction dynamics have also been investigated, wherein chaotic and stochastic aspects (that is,both non-linear behavior and noise) of the dynamics can give rise to so-called crazy clocks where the lag time has av arying component. [27,28] We calculate two limits for the explosion time and plot them on the data in Figure 6c,and it is interesting to wonder about the jump between the two limits in the middle of the graph and its possible relationship with fluctuations in explosions times.I no ur case the trajectory escapes to infinity,b ut there might possibly be transient chaos,w hich would lead to as pread of explosion times for those concentrations.H owever,a ltering the initial conditions of the simulations shows that the results are quite robust;w edid not see any difference in the explosion time when changing the initial condition of non-dimensional pressure from 0t oa tl east 10, and initial condition of nondimensional concentration 0t o0 .4. Hence the experimental spread in explosion times at intermediate concentrations is likely to be as tochastic effect not present in our physical model.…”

“…Chemical-garden reactions in general have not previously been shown to have clock-reaction dynamics.H owever,c ement hydration is aw ell-known and commercially important precipitation reaction, and cement hydration is another example of chemobrionics closely linked to chemical gardens. [27,28] We calculate two limits for the explosion time and plot them on the data in Figure 6c,and it is interesting to wonder about the jump between the two limits in the middle of the graph and its possible relationship with fluctuations in explosions times.I no ur case the trajectory escapes to infinity,b ut there might possibly be transient chaos,w hich would lead to as pread of explosion times for those concentrations.H owever,a ltering the initial conditions of the simulations shows that the results are quite robust;w edid not see any difference in the explosion time when changing the initial condition of non-dimensional pressure from 0t oa tl east 10, and initial condition of nondimensional concentration 0t o0 .4. [25] It is clearly of significance to seek to apply the present results to the cement case,with the idea of achieving ab etter understanding of the mechanisms of hydration acceleration and retardation that would have wide industrial applicability.…”

Exploding Chemical Gardens: A Phase‐Change Clock Reaction

“…According to Figure c the system is a better timer at higher and lower concentrations of silicate than at intermediate concentrations. Fluctuations in clock reaction dynamics have also been investigated, wherein chaotic and stochastic aspects (that is, both non‐linear behavior and noise) of the dynamics can give rise to so‐called crazy clocks where the lag time has a varying component . We calculate two limits for the explosion time and plot them on the data in Figure c, and it is interesting to wonder about the jump between the two limits in the middle of the graph and its possible relationship with fluctuations in explosions times.…”