From Excitatory to Inhibitory Connections in Networks of Discrete Electrochemical Oscillators

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

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.

Spatially distributed current oscillations with electrochemical reactions in microfluidic flow cells

The formation of spatiotemporal patterns is investigated by using a chemical reaction on the surface of a high-aspect-ratio metal electrode positioned in a flow channel. A partial differential equation model is formulated for nickel dissolution in sulfuric acid in a microfluidic flow channel. The model simulations predict oscillatory patterns that are spatially distributed on the electrode surface; the downstream portion of the metal surface exhibits large-amplitude, nonlinear oscillations of dissolution rates, whereas the upstream portion displays small-amplitude, harmonic oscillations with a phase delay. The features of the dynamical response can be interpreted by the dependence of local dynamics on the widely varying surface conditions and the presence of strong coupling. The patterns can be observed for both contiguous and segmented metal surfaces. The existence of spatially distributed current oscillations is confirmed in experiments with Ni electrodissolution in a microfluidic device. The results show the impact of a widely heterogeneous environment on the types of patterns of chemical reaction rates.

Synchronization of electrochemical oscillators with differential coupling

Experiments are presented to describe the effect of capacitive coupling of two electrochemical oscillators during Ni dissolution in sulfuric acid solution. Equivalent circuit analysis shows that the coupling between the oscillators occurs through the difference between the differentials of the electrode potentials. The differential nature of the coupling introduces strong negative nonisochronicity (i.e., phase shear, strong dependence of the period on the amplitude) in the coupling mechanism with smooth oscillators (under conditions just above a Hopf bifurcation point). Because of the negative nonisochronicity, asymmetrically coupled oscillators exhibit anomalous phase synchronization in the form of frequency difference enhancement. At strong coupling bistability is observed between in-phase and antiphase synchronized states. With relaxation oscillators, in contrast to the resistive coupling where antiphase synchronization can occur, the typical system response with weak coupling is out-of-phase synchronization. When the capacitance is applied on the individual resistors attached to the electrodes the oscillators exhibit weak positive nonisochronicity; this is in contrast with the strong negative nonisochronicity obtained with cross coupling. The proposed coupling configurations reveal the importance of the nonisochronicity level of oscillations for the experimentally observed synchronization patterns and also provide efficient ways of tuning the nonisochronicity level of the oscillations. This latter feature can be exploited to design synchronization features with a combination of resistive (difference) and capacitive (differential) coupling.

Dynamics of electrochemical oscillators with electrode size disparity: asymmetrical coupling and anomalous phase synchronization

Experiments are carried out in dual electrode oscillatory Ni electrodissolution in which the two electrodes have different surface areas. The transition to phase synchronization is analyzed as asymmetrical coupling strength, induced by placing a cross resistance between the electrodes, is varied. It is shown that because of nonisochronicity (phase shear, i.e., strong dependence of period on amplitude) of the oscillators, anomalous phase synchronization effects can be observed: advanced/delayed synchronization and, to a lesser extent, frequency difference enhancement. The type of synchronization is strongly affected by the underlying heterogeneities of the oscillators; in the experiments with a slow driver (large surface area) electrode the synchronization is advanced, with a fast driver electrode the synchronization is delayed with respect to symmetrical coupling. The findings thus reveal that the interplay of asymmetrical coupling with the types of inherent heterogeneities plays an important role for the interpretation of size effects in the dynamical behavior of a nonlinear chemical reaction.

Synchronized Current Oscillations of Formic Acid Electro-oxidation in a Microchip-based Dual-Electrode Flow Cell

We investigate the oscillatory electro-oxidation of formic acid on platinum in a microchip-based dual-electrode cell with microfluidic flow control. The main dynamical features of current oscillations on single Pt electrode that had been observed in macro-cells are reproduced in the microfabricated electrochemical cell. In dual-electrode configuration nearly in-phase synchronized current oscillations occur when the reference/counter electrodes are placed far away from the microelectrodes. The synchronization disappears with close reference/counter electrode placements. We show that the cause for synchronization is weak albeit important, bidirectional electrical coupling between the electrodes; therefore the unidirectional mass transfer interactions are negligible. The experimental design enables the investigation of the dynamical behavior in micro-electrode arrays with well-defined control of flow of the electrolyte in a manner where the size and spacing of the electrodes can be easily varied.

Spatiotemporal coding in an electrochemical oscillatory network

A network consisting of N relaxation electrochemical oscillators, mutually coupled by all-to-all inhibitory connections, can have (N-1) ! coexisting out-of-phase states, each state being a permutation of a periodic spiking sequence. The modification of the out-of-phase states by shots of laser pulse perturbations is shown. In such networks the phase relation of the oscillators is stored as a coded pattern. The ability of the network to function as a rewritable memory of (N-1) ! different spatiotemporal patterns is demonstrated experimentally for N=4.