A Theoretical Study on Turing Patterns in Electrochemical Systems

Turing patterns modulation by chemical gradient in isothermal and non-isothermal conditions

Chemical gradients imposed through boundary conditions induce spatial symmetry breaking of Turing patterns in small systems.

Nanopatterning of transition metal surfaces via electrochemical dimple array formation

Nanoscale surface patterning is of great importance for applications ranging from catalysts to biomaterials. We show the formation of ordered nanoscale dimple arrays on titanium, tungsten, and zirconium during electropolishing, demonstrating versatility of a process previously only reported for tantalum. This is a rare example of an electrochemical pattern formation process that can be translated to other materials. The dimpled surfaces have been characterized with scanning electron microscopy, transmission electron microscopy, atomic force microscopy, and X-ray photoelectron spectroscopy, and electrochemical conditions were optimized for each material. While conditions for titanium and tungsten resemble those for tantalum, zirconium requires a different type of electrolyte. Given the appropriate electropolishing chemistry, formation of these patterns should be possible on any metal surface. The process is very robust on homogeneous surfaces, but sensitive to inhomogeneities in chemical composition, such as in the case of differentially etched alloys. An alternative process for some materials such as platinum is the coating of a dimpled substrate with a thin film of the required material.

Stationary spatial patterns during bulk CO electrooxidation on platinum

We present experimental studies and mathematical modeling on pattern formation during bulk CO electrooxidation on Pt ring electrodes. Profiles of the interfacial potential drop in front of the working electrode were recorded with a potential probe. Stationary self-organized potential patterns were observed under potentiostatic conditions in dilute acidic and basic supporting electrolytes. The amplitude and shape of these potential patterns can be modified by an appropriate local perturbation of the interfacial potential drop. A mathematical model of the formation of these patterns reveals that the homogeneous state becomes unstable through a subcritical Turing-like bifurcation and that several patterned electrode states coexist in wide parameter ranges.

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.

Breathing current domains in globally coupled electrochemical systems: a comparison with a semiconductor model

Spatio-temporal bifurcations and complex dynamics in globally coupled intrinsically bistable electrochemical systems with an S-shaped current-voltage characteristic under galvanostatic control are studied theoretically on a one-dimensional domain. The results are compared with the dynamics and the bifurcation scenarios occurring in a closely related model which describes pattern formation in semiconductors. Under galvanostatic control both systems are unstable with respect to the formation of stationary large amplitude current domains. The current domains as well as the homogeneous steady state exhibit oscillatory instabilities for slow dynamics of the potential drop across the double layer, or across the semiconductor device, respectively. The interplay of the different instabilities leads to complex spatio-temporal behavior. We find breathing current domains and chaotic spatio-temporal dynamics in the electrochemical system. Comparing these findings with the results obtained earlier for the semiconductor system, we outline bifurcation scenarios leading to complex dynamics in globally coupled bistable systems with subcritical spatial bifurcations.