Experimental Strategy for Characterization of Essential Dynamical Variables in Oscillatory Systems: Effect of Double-Layer Capacitance on the Stability of Electrochemical Oscillators

Delayed feedback induced multirhythmicity in the oscillatory electrodissolution of copper

Occurrence of bi- and trirhythmicities (coexistence of two or three stable limit cycles, respectively, with distinctly different periods) has been studied experimentally by applying delayed feedback control to the copper-phosphoric acid electrochemical system oscillating close to a Hopf bifurcation point under potentiostatic condition. The oscillating electrode potential is delayed by τ and the difference between the present and delayed values is fed back to the circuit potential with a feedback gain K. The experiments were performed by determining the period of current oscillations T as a function of (both increasing and decreasing) τ at several fixed values of K. With small delay times, the period exhibits a sinusoidal type dependence on τ. However, with relatively large delays (typically τ ≫ T) for each feedback gain K, there exists a critical delay τcrit above which birhythmicity emerges. The experiments show that for weak feedback, Kτcrit is approximately constant. At very large delays, the dynamics becomes even more complex, and trirhythmicity could be observed. Results of numerical simulations based on a general kinetic model for metal electrodissolution were consistent with the experimental observations. The experimental and numerical results are also interpreted by using a phase model; the model parameters can be obtained from experimental data measured at small delay times. Analytical solutions to the phase model quantitatively predict the parameter regions for the appearance of birhythmicity in the experiments, and explain the almost constant value of Kτcrit for weak feedback.

Experimental assessment of the sensitiveness of an electrochemical oscillator towards chemical perturbations

In this study we address the problem of the response of a (electro)chemical oscillator towards chemical perturbations of different magnitudes. The chemical perturbation was achieved by addition of distinct amounts of trifluoromethanesulfonate (TFMSA), a rather stable and non-specifically adsorbing anion, and the system under investigation was the methanol electro-oxidation reaction under both stationary and oscillatory regimes. Increasing the anion concentration resulted in a decrease in the reaction rates of methanol oxidation and a general decrease in the parameter window where oscillations occurred. Furthermore, the addition of TFMSA was found to decrease the induction period and the total duration of oscillations. The mechanism underlying these observations was derived mathematically and revealed that inhibition in the methanol oxidation through blockage of active sites was found to further accelerate the intrinsic non-stationarity of the unperturbed system. Altogether, the presented results are among the few concerning the experimental assessment of the sensitiveness of an oscillator towards chemical perturbations. The universal nature of the complex chemical oscillator investigated here might be used for reference when studying the dynamics of other less accessible perturbed networks of (bio)chemical reactions.

Electrochemical Oscillations of Nickel Electrodissolution in an Epoxy-Based Microchip Flow Cell

We investigate the nonlinear dynamics of transpassive electrodissolution of nickel in sulfuric acid in an epoxy-based microchip flow cell. We observed bistability, smooth, relaxation, and period-2 waveform current oscillations with external resistance attached to the electrode in the microfabricated electrochemical cell with 0.05 mm diameter Ni wire under potentiostatic control. Experiments with 1mm × 0.1 mm Ni electrode show spontaneous oscillations without attached external resistance; similar surface area electrode in macrocell does not exhibit spontaneous oscillations. Combined experimental and numerical studies show that spontaneous oscillation with the on-chip fabricated electrochemical cell occurs because of the unusually large ohmic potential drop due to the constrained current in the narrow flow channel. This large IR potential drop is expected to have an important role in destabilizing negative differential resistance electrochemical (e.g., metal dissolution and electrocatalytic) systems in on-chip integrated microfludic flow cells. The proposed experimental setup can be extendend to multi-electrode configurations; the epoxy-based substrate procedure thus holds promise in electroanalytical applications that require collector-generator multi-electrodes wires with various electrode sizes, compositions, and spacings as well as controlled flow conditions.

Frequency of negative differential resistance electrochemical oscillators: theory and experiments

An approximate formula for the frequency of oscillations is theoretically derived for skeleton models for electrochemical systems exhibiting negative differential resistance (NDR) under conditions close to supercritical Hopf bifurcation points. The theoretically predicted omega infinity (k/R)1/2 relationship (where R is the series resistance of the cell and k is the rate constant of the charge transfer process) was confirmed in experiments with copper and nickel electrodissolution. The experimentally observed Arrhenius-type dependence of frequency on temperature can also be explained with the frequency equation. The experimental validity of the frequency equation indicates that 'apparent' rate constants can be extracted from frequency measurements of electrochemical oscillations; such method can aid future modeling of complex responses of electrochemical cells.

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

Experimental results are presented on successful application of delayed-feedback control algorithms for tracking unstable steady states and periodic orbits of electrochemical dissolution systems. Time-delay autosynchronization and delay optimization with a descent gradient method were applied for stationary states and periodic orbits, respectively. These tracking algorithms are utilized in constructing experimental bifurcation diagrams of the studied electrochemical systems in which Hopf, saddle-node, saddle-loop, and period-doubling bifurcations take place.