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.