THE MODELING OF MIXED-MODE AND CHAOTIC OSCILLATIONS IN ELECTROCHEMICAL SYSTEMS

We develop a simple but general three-variable model skeleton to describe complex nonlinear behaviors in electrochemical processes taking place at either a hanging mercury drop electrode (HMDE) or a rotating-disk electrode (RDE). We apply our formalism to the reduction of indium(III) at a HMDE in the presence of thiocyanate, a reaction known to exhibit complex mixed-mode and chaotic oscillations. Besides the role of the negative Faradaic impedance in destabilizing the electrochemical system, mass transport appears to be crucial as the model explicitly takes into account, in a truncated fashion, the time-dependent relaxation of the concentration profile. We study in detail the nonlinear dynamic behavior of our model of the indium/thiocyanate system and a RDE model. The models support mixed-mode sequences that appear either as incomplete Farey sequences or as periodic-chaotic sequences, which we discuss in terms of an incomplete homoclinic scenario whose definition and properties are worked out here. Our results compare very well to the experimental observations in the indium/thiocyanate system and the electrodissolution of a rotating copper disk in phosphoric acid. This satisfactory agreement strongly suggests that diffusion relaxation is an important phenomenon in electrochemical oscillations and could be the essential third variable in many dynamical electrochemical processes.