Fronts, Waves, and Stationary Patterns in Electrochemical Systems

Abstract

Oscillatory behavior has been observed for almost all electrochemical reactions in a certain, although sometimes small, range of external parameters. Only in the past ten years has it been possible, however, to find a common explanation for the occurrence of these temporal self-organization phenomena of chemically completely different electrochemical reactions. The breakthrough was achieved because new methods and concepts, which had been developed in nonlinear dynamics to describe the spontaneous formation of order in various disciplines, could be applied. This development in turn was only possible because the underlying laws are universal at a certain abstract level. Oscillations are only one possible manifestation of nonlinear behavior. Examples of other features that are often closely associated with temporal instabilities are spatial structures and waves. Initiated by the theoretical progress and the development of new experimental techniques, spatial pattern formation in electrochemical systems has been targeted for investigations in the past few years. Based on these investigations, it can be predicted under which conditions temporal or spatial pattern formation can be expected. Furthermore, the possibility of predicting the occurrence of instabilities indicates that it might be feasible to exploit nonlinear effects to increase, for example, the yield of electrocatalytic reactions. Here we discuss physicochemical mechanisms that lead to pattern formation in electrochemical systems. At the same time, we stress the generic principles that are responsible for self-structuring processes in many chemical and biological systems.

Origin of finite pulse trains: Homoclinic snaking in excitable media

“…Examples include biological sys tems [4,5], autocatalytic chemical reactions [6,7], electro chemistry [8], liquid crystals [9], nonlinear optics [10], semi conductors [11][12][13], and pipe flow [14]. A spatially extended system with a stable spatially uniform equilibrium state is called excitable when a large enough, spatially localized perturbation excites adjacent sites while the perturbation at the original location decays back to equilibrium.…”

Parameter estimation for a morphochemical reaction-diffusion model of electrochemical pattern formation

“…Given an experimental map M˚P R nˆm , the time integration interval r0, T s and the initial conditions pη 0 px, yq, θ 0 px, yqq in (4), FIND a suitable parameter set p˚P R r for the model (2) such that θpx, y, T q « M˚, where θ is the solution of the RD-PDE system (2)-(3)-(4).…”

“…In order to place our contribution in context, it is worth noting that mathematical models of Corresponding author Email: ivonne.sgura@unisalento.it electrochemical dynamics and of related pattern formation processes have been typically derived within the framework of activator-inhibitor mechanism in view of rationalising electrocatalytic processes [1,2,3]. As far as pattern formation in electrodeposition is concerned, instead, the focus has generally been on experimental aspects (e.g.…”

Self‐Organized Formation of Layered Nanostructures by Oscillatory Electrodeposition

“…The diffusion process can be flexibly controlled by changing the sizes and geometric arrangements of the electrodes in electrochemical cells. Recent theoretical studies explained rather elegantly the origin of the dynamic patterns and the patterns selection principle in electrochemical systems [131][132][133]. The modes, period, and amplitude of the spatiotemporal patterns can be tuned easily by changing the geometric arrangements of the electrodes and the applied potential or current.…”