A numerical investigation of the effect of external resistance and applied potential on the distribution of periodicity and chaos in the anodic dissolution of nickel.

The oscillatory electrodissolution of nickel is one among several reactions utilized as a model-system to study the emergence of oscillations and pattern formation in electrochemical interfaces, in addition to frequently providing experimental proofs for theoretical predictions in synchronization engineering. The reaction was modeled in 1992 by Haim and co-workers [J. Phys. Chem. 1992, 96, 2676] and since then the model has been used with great success. Although some numerical studies have been done in this regard, there is apparently no detailed investigation of the effect of control parameters on the complex dynamics of nickel dissolution. Here, we provide a well-detailed and rigorous analysis of the effect of the external resistance and applied potential by simulating high-resolution phase diagrams based on the calculation of Lyapunov exponents and isospike diagrams. Our findings clearly indicate a strong dependence of the self-similar periodic islands, the so-called shrimps (i.e., periodic islands within chaotic domains in the parameter space), with the control parameters. Overall, we have observed a low density of periodic structures in the phase diagrams, being completely suppressed for large values of resistance and potential. The shrimp-like structures become gradually elongated with an increase of the control parameters to the point where only diagonally aligned periodic bands intertwined with chaotic domains are present. Interestingly, period-doubling cascades were observed not only on the shrimps but also on the periodic bands. The detailed distribution of chaos and periodicity of oscillatory electrodissolution reactions in resistance-potential phase diagrams can bring, for instance, important information to experimentalists to set a desired dynamic behavior and, therefore, to create novel nanostructured self-organized materials.

Quasiperiodic behavior in the electrodeposition of Cu/Sn multilayers: extraction of activation energies and wavelet analysis.

Living systems are one of the many examples in which self-organizing systems yield more intricate structures than those that can be achieved using a "step-by-step" approach. This phenomenon can be observed in electrochemical organic synthesis, oscillating metal deposition and in chemical clocks. There is a plenitude of temporal instabilities during self-organization, from ordinary period-one oscillations, going through quasiperiodicity, to the onset of chaos. Here, we describe the emergence of quasiperiodic behavior during the oscillatory electro-deposition of Cu/Sn. The time-series were characterized using a continuous wavelet transform in order to extract the oscillation frequency of the process with changes in temperature, and to calculate the apparent activation energies. Two different energy ranges are presented, and these are attributed to an activation barrier (∼50 kJ mol-1) which is closely related to a fast time-scale of the feedback loops responsible for the current oscillations and a diffusional process (∼20 kJ mol-1), connected to the slow modulations of the oscillation amplitude, giving rise to quasiperiodic dynamics. This kinetic information might provide information on the self-organized synthesis of Cu/Sn metallic multilayers which are kept far from the thermodynamic equilibrium. As self-organization in chemical systems is rapidly developing into a powerful strategy for designing new functional materials, the availability of kinetic parameters is of major interest in rational design.