Nonlinear Dynamics in Alloy Electrodissolution: Modeling and Simulations
Authors: Miranda Renan Carneiro Cavalcante de , Parma Eduardo , Pereira dos Santos Caio Guilherme , Nagao Raphael 
Published: July 2021

The formation of spatiotemporal patterns on electrochemical systems during the electrodissolution of metals depends on the nature of the metal constituent of the electrodes and can present regions with different behaviors, such as bistability and oscillations, for a set of physical-chemical parameters under potentiostatic control. The understanding of the influence of the parameters that govern the dynamics of the electrodissolution system in the emergence of spatiotemporal patterns has already been well studied taking into account its geometry and arrangement of the reference electrode, usually simplifying or neglecting the kinetics of reaction in the counter-electrode. This study aims to expand the complexity of the problem by considering the nature of the metal, changing the composition of the electrodes using metal alloys. The modelling of metal electrodissolution was based on previous works in the literature, in which the potential and the hydronium activity are considered as dependent and representative variables of the system. In this electrochemical system, the following geometries are adopted for the system: the electrochemical cell is cylindrical and the working electrode and counter-electrode are one on each side of this cylinder, having a ring or disc shape and the reference electrode is considered as a point belonging to the system.
The activation-passivation transition that occurs in the working electrode is described by a smooth function Heaviside dependent on the Flade potential, as a consequence on the hydronium activity, and double-layer potential. Therefore, the total current density is the sum of two terms: one faradic current density, that is represented by this transition and the other assuming the existence of a capacitive current. In the mass transport of the hydron ions near the electrode we consider a linear diffusional term and a migratory one. The kinetics of the counter-electrode potential has a parameter that depends on the nature of the metal or alloy, from which the electrodes are made, and provides a novel approach to this study.
The model takes advantage of the given geometric arrangement and its symmetries to reduce the spatial dimensionality by placing the reference electrode on the cylinder wall. In the case of ring electrodes geometry, it can be imposed that the radial derivative is null on this surface, reducing the evaluation of three spatial variables for cylindrical system: radius (r), angle (θ) and height (z), respectively, to s and z, where s is the arc of circumference. The simulations start with a working electrode entirely passive, and a section of the working electrode is disturbed, calculating the potentials of the system by numerical integration for each time step. A rectangular grid of points was used, and the time integration was done using a Runge-Kutta fourth order method. The disturbance in the initial condition is done considering a small section as activated. This disturbance is reproduced experimentally by scratching away a small portion of a passivating oxide layer. Several assumptions were made regarding the different metal potential in the counter-eletrode kinetics, comparing pure metal and these different ratio of metals in alloys, looking for three different responses to the temporal evolution of the potentials in the system due to these initial conditions: a totally active state, a totally passive state, and a partial active state.
In future works, it is intended to validate the model using experimental data during the electrodissolution of alloy electrodes, so that can be applied as a guide in the search for desired spatiotemporal patterns.

Figure 1