Electrochemical reaction dynamics: a review

Traveling fronts of copper deposition

We report the experimental observation of traveling fronts during the electroless deposition of copper on passive steel substrates. The low-carbon steel samples are passivated in nitric acid prior to the plating experiment, thus creating a thin, protective oxide layer on the steel surface. The deposition experiments are carried out from slightly acidic (pH 3.2) copper sulfate solution and copper nitrate solution with the latter showing front propagation only in the presence of chloride ions. For up to 30 s, fronts propagate with constant velocities in the range from 0.5 to 5 mm/s depending on the experimental conditions. This phase of constant-speed propagation gives way to accelerating fronts and very rapid, spatially unstructured deposition. Front-mediated plating is observed over a wide range of cupric ion concentration and constitutes a striking and unexpected example for pattern formation in electrochemical systems.

Theory of electrochemical pattern formation

The spatial coupling in electrochemical systems is mediated by ion migration under the influence of the electric field. Since field effects spread very rapidly, every point of an electrode can communicate with every other one practically instantaneously through migration coupling. Based on mathematical potential theory we present the derivation of a generally applicable reaction-migration equation, which describes the coupling via an integral over the whole electrode area. The corresponding coupling function depends only on the geometry of the electrode setup and has been computed for commonly used electrode shapes (such as ring, disk, ribbon or rectangle). The pattern formation observed in electrochemical systems in the bistable, excitable and oscillatory regime can be reproduced in computer simulations, and the types of patterns occurring under different geometries can be rationalized. (c) 2002 American Institute of Physics.

Evolution of spatiotemporal patterns during the electrodissolution of metals: Experiments and simulations

Spatiotemporal patterns including accelerating fronts, rotating waves, and homogeneous oscillations evolve during the electrodissolution of metals like cobalt and iron that exhibit passivity under potentiostatic control. The nature of the patterns is determined by long-range (nonlocal) coupling through the electric field which in turn is influenced by the geometry of the electrochemical cell, the applied potential, and the conductivity of the electrolyte. A two-variable model in a three-dimensional geometry is presented which is able to simulate the essential features of the experimental system.(c) 2002 American Institute of Physics.

Spatiotemporal Patterns on a Disk Electrode: Effects of Cell Geometry and Electrolyte Properties

Spatiotemporal patterns on a disk electrode are simulated with a model for the electrodissolution of a metal that exhibits passivity; a 3-dimensional geometry with a point reference electrode is used. The two variables of the model are the potential drop across the electric double layer and the proton concentration near the surface of the working electrode. Non-local coupling among reaction sites is through the electric field. Several patterns seen previously in experiments are reproduced in the simulations and the dependence of transitions among them on system geometry, electrolyte conductivity and double layer capacitance are explored. For example, a state with an inhomogeneous oscillation is changed to one with a rotating wave as the reference electrode is moved closer to the working electrode and negative coupling develops; under other conditions the negative coupling produces anti-phase oscillations.

Avalanche behavior in the dynamics of chemical reactions

Sudden bursts of chemical activity, displaying avalanche-like behavior, have been observed in reactions between metals and liquid electrolytes by measuring the time-dependent chemomagnetic fields with a high-T(c) SQUID. The observed intermittent chemomagnetic field pulses exhibit power-law behavior in the distributions of peak sizes, noise spectra, and return-time distributions. Such power-law behavior provides evidence for self-organized criticality occurring in the form of "chemical avalanches" over a wide range of size and time scales.

Phase synchronization and suppression of chaos through intermittency in forcing of an electrochemical oscillator

External periodic forcing was applied to a chaotic chemical oscillator in experiments on the electrodissolution of Ni in sulfuric acid solution. The amplitude and the frequency (Omega) of the forcing signal were varied in a region around Omega=omega(0), where omega(0) is the frequency of the unforced signal. Phase synchronization occurred with increase in the amplitude of the forcing. For Omega/omega(0) near 1 the signal remained chaotic after the transition to the phase-locked state; for Omega/omega(0) somewhat farther from 1 the transition was to a periodic state via intermittency. The experimental results are supported by numerical simulations using a general model for electrochemical oscillations.

Spatiotemporal patterns and symmetry breaking on a ring electrode

A series of experiments on a ring electrode with changes in a parameter, the applied potential, are described. Spatiotemporal patterns are investigated in a region of parameter space in which relaxation oscillations occur. The simplest state is a period 2Pi oscillation that has full O(2) symmetry so that at each instant the pattern is unchanged by rotations or reflections of the ring. With change in parameter a spatiotemporal period doubling occurs to period 4Pi. This is followed by a symmetry breaking to another state with period 4Pi and subsequently by a second period doubling to period 8Pi. Proper orthogonal decomposition is used as an aid in elucidating the nature of the transitions.

Modeling maps by using rational functions

Rational functions are not very useful for obtaining global differential models because they involve poles that may eject the trajectory to infinity. In contrast, it is here shown that they allow one to significantly improve the quality of models for maps. In such a case, the presence of poles does not involve any numerical difficulty when the models are iterated. The models then take advantage of the ability of rational functions to capture complicated structures that may be generated by maps. The method is applied to experimental data from copper electrodissolution.