Scaling relationship for oscillating electrochemical systems: dependence of phase diagram on electrode size and rotation rate.

Dynamics of oscillations in electrochemical systems are affected by both chemical and physical properties of the systems. Chemical properties include the type of electrochemical reaction, the electrode material, the composition of the electrolyte, etc., while physical properties include the solution resistance, the cell constant, the electrode size, the rotation rate, the external resistance, etc. Earlier, we proposed the application of cell-geometry-independent phase-diagrams to characterize the oscillatory regions in the electrode potential vs. external resistance parameter plane. In this report, we investigate how this type of phase diagram changes with the surface area (electrode radius) and the rotation rate of an electrode. Based on linear stability analysis of a general, two-variable model for negative-differential resistance (NDR) type electrochemical oscillators we propose a scaling relationship. It predicts that all scaled data points derived from the critical values of parameters (resistance and potential) characterizing the onset of oscillations should fall - independently of the size of the electrode and the rotation rate - on a single plot. The analytical predictions are tested in both numerical simulations and experiments with copper electrodissolution in phosphoric acid.

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.

Experimental strategy for characterization of essential dynamical variables in oscillatory systems: effect of double-layer capacitance on the stability of electrochemical oscillators.

An experimentally accessible algorithm for changing the time scale associated with a dynamical variable is proposed. In general, a differential controller can be applied to (a) identify the essential species in oscillatory systems and (b) explore their role in the feedback loops. Here, we report on classifying electrochemical oscillators by changing the time scale over which the electrode potential varies; the type of different electrochemical oscillators is identified based on whether the controlled modification of pseudo-capacitance induces or suppresses current oscillations.