Chemical Complexity by Alexander S. Mikhailov & Gerhard Ertl

Author:Alexander S. Mikhailov & Gerhard Ertl
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Finally, synchronization phenomena in large populations of coupled chemical BZ oscillators were also explored. In 2009, A. Taylor et al. [35] performed experiments with a colloid system where porous catalytic particles were suspended in the catalyst-free BZ reaction mixture. The sizes of the particles varied from 50 to 250 m, with the average of about 100 m. Typically, about 100,000 such particles were present in the reaction volume; the number density of particles could be varied in the experiments. The reactor was stirred so that the the reactants were well mixed and the system was uniform.

In this system, the reaction took place only within the catalytic particles but intermediate reaction products could be freely transported from one particle to another. The reaction was in the oscillatory regime and thus every catalytic particle effectively represented an individual oscillator. The exchange of reaction products through the solution resulted in interactions—or coupling—between the oscillators. Because of persistent stirring, such coupling was global, i.e. not dependent on spatial positions of the oscillatory microparticles or distances between them.

As shown in Chap. 5, the Kuramoto theory predicts that synchronization in populations of globally coupled oscillators can take place when the strength of interactions between them is increased. The synchronization transition is characterized by an order parameter that yields the collective oscillation amplitude. This order parameter vanishes if oscillations are asynchronous and increases according to Eq. (5.​24) above the transition point. For globally coupled electrochemical oscillators, the predicted dependence could be verified in 2002 by I. Kiss, Y. Zhai and J. L. Hudson [36] (Fig. 5.​12). This could be however done only for a relatively small system with 64 individual oscillators.

Fig. 7.9 a Synchronization transition in a population of globally coupled BZ oscillators. b Distribution of frequencies of individual oscillators.

Adapted with permission from [35]

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