Uma Contribuição Usando Modelagem por Elementos Finitos para a Interpretação de Dados de Espectroscopia de Impedância Eletroquímica

Abstract

The technique of electrochemical impedance spectroscopy (EIS) has as one of its advantages to provide informations about the electrode/solution interface, allowing to investigate the structure of the electric double layer, adsorption and other interfacial phenomena. Normally, its modeling is based on the proposition of an equivalent electronic circuit, whose correspondence with the phenomenon is indirect. For this reason, we set out to model this technique using the partial differential equations that are already widely used in the description of electrochemical systems. We aim to provide subsidies for a direct interpretation with more physical meaning of the data obtained from this technique. The proposed models include hemispherical, rough and flat electrodes, the latter considers the presence of specific adsorption of anions. Since the set of equations that make up each model is broad and has coupled variables, the analytical solutions are not feasible, so they were solved using the finite element numerical method through the software Comsol Multiphysics in GNU Linux Ubuntu 16.04. In the simulations for the hemispherical electrode, it was possible to describe, with a one-dimensional model, microelectrodes and macroelectrodes. In the Nyquist diagrams for the microelectrode, we obtained a behavior for the diffusional part that differs greatly from that expected for the flat macroelectrode, for this reason, we deduce an expression for the Warburg element suitable for this geometry. It was observed that a zero charge potential change of 300 mV was sufficient to vary the estimated resistance of charge transfer by an order of magnitude, even when the carrier electrolyte concentration was 0, 1 molL−1. In the model for the rough electrode, a surface formed by identical peaks in shape and size and distributed according to a hexagonal arrangement was devised, in order to visualize what would be the effect of the roughness in the Bode diagrams, however, even when the simulated roughness were of the order of 20 nm, no interactions between the surface irregularities and the behavior of the diagrams were observed. In an attempt to describe a more realistic surface, the results of surface simulations with different roughness factors were combined, with this we obtained a behavior for the electric double layer consistent with that of a constant phase element whose value of the exponent tends to one with increasing ionic strength. In the model that considers the specific adsorption, the presence of a contaminant anion in the support electrolyte was allowed in a concentration of only 0, 1 mmolL−1 and 1 mmolL−1, with this it was found that even under these conditions there are significant distortions in the estimated capacitance for the electric double layer at different applied potentials. However, this model still needs refinements, since some experimental behaviors were not correctly described by it. Nevertheless, this model represents a step in the direction of describing more elaborated interfacial phenomena.