Oscillations in an array of bistable microelectrodes coupled through a globally conserved quantity

Abstract

The dynamical behavior of an array of microelectrodes is investigated under controlled current conditions during CO electrooxidation, a bistable electrochemical reaction with an S-shaped negative differential resistance (S-NDR) current-potential curve. Under these conditions, the total current constitutes a globally conserved quantity, thus coupling all microelectrodes globally. Upon increasing the total current, the microelectrodes activate one by one, with a single microelectrode being on its intermediate S-NDR current branch and the other ones being either on their passive or their active branches. When a few coupled microelectrodes are activated, the electrochemical system exhibits spontaneous potential oscillations. Mathematical analysis shows that oscillations arise already in a two group approximation of the dynamics, the two groups consisting of 1 electrode and n – 1 electrodes with n ≥ 3, respectively, with each group being described by a single evolution equation. In this minimal representation, oscillations occur when the single electrode is on the intermediate branch and the larger group is on the active branch.

Tuning Electrochemical Bistability by Surface Area Blocking in the Cathodic Deposition of Copper

“…4 As a result of these self-amplifying processes, a hysteretic profile arises, and consequently, chemical switches can be designed and finely tuned by the imposition of external perturbations. 5−9 For spatially extended systems, the appearance of collective switching between states has been based on the bistable nature of the individuals, 10−13 but it can also emerge from collective behavior even if the constituents are not bistable. 14 This co-existence of different steady states has been verified in homogeneous 15−19 and heterogeneous systems.…”

Collective oscillations of globally coupled bistable, nonresonant components

“…Another peculiar behavior, reported for an array of bistable electrodes [4,5] as well as for nanoparticulate Li-ion batteries [6][7][8][9][10], is that a slow parameter ramp leads to a sequential one-by-one passage of an individual element from one state-or phase-to the other one. Surprisingly, oscillations were also observed in such all-to-all connected ensembles of a few bistable components at fixed parameter values [11]. This finding was the motivation of the present study, where we derive a necessary condition for the occurrence of a Hopf bifurcaton in systems composed of all-to-all connected generic bistable components and demonstrate that oscillatory dynamics may also persist in the macroscopic limit.…”

“…As an example, we apply this result to a particular model, defined in Eqs. (30) and (31), that was derived from a more detailed model for CO electro-oxidation on Pt [11] (see Appendix C).…”

“…We derived our model from the following, more detailed model for the CO adsorption on a platinum microelectrode, which is described in detail in Ref. [11].…”

“…These sequential transitions might now occur in two different ways: In the simpler scenario, each individual electrode resumes one of the three steady states of the S-shaped current-potential curve, the voltage adopting correspondingly to a fixed value within the hysteretic region [5]. In the other scenario, the individual electrodes also split into two or three clusters, but the voltage as well as the partial currents undergo stable oscillations [11]. The oscillations were observed for a small number of electrodes and could be reproduced with a specific model.…”