A Dynamic Mechanistic Model of an Electrochemical Interface

Abstract

We propose a dynamic mechanistic model, based on nonequilibrium thermodynamics and electrodynamics, describing the transient response to current perturbations of an electrochemical double layer at the metal/electrolyte interface in the presence of electrochemical reactions. As an example of application, we have simulated the hydrogen oxidation reaction taking place in a polymer electrolyte fuel cell anode. The model is composed of ͑i͒ a 0-D inner layer submodel describing the composition of the metallic phase surface where water and reactant can be adsorbed, and the generated electric potential difference between the metal and the electrolyte phases; and ͑ii͒ a 1-D diffuse layer submodel in the electrolyte constituted by spatially moving ions and counterions, describing the ionic transport by migration-diffusion, based on the coupling of a Nernst-Planck's equation with a Poisson's equation. At the interface, the reaction kinetics depending on the potential difference is coupled with the inner-layer model through the charge conservation law. The numerical model allows dynamic simulation of the evolution of the local electric potentials ͑ionic and electronic͒ and concentrations inside the interface, and the influence of the working conditions on the impedance spectra characteristics.

A Multi‐Scale Dynamic Mechanistic Model for the Transient Analysis of PEFCs

“…Other authors [3] derive analytical expressions of the impedance dependence with nominal current, supposing simple electrochemical mechanisms in the electrodes: the analytical expressions obtained are not reusable (they have to be recalculated if one changes a mechanism or couple it with other physicochemical phenomena); furthermore, analytical computations of complex impedances become impossible for more complicated mechanisms. In this paper we propose a multi-scale mechanistic Membrane-Electrodes Assembly (MEA) dynamic model [6][7][8] based on the distributed-parameter Bond Graph language [8][9][10][11][12][13][14] (irreversible thermodynamics and electrodynamics) and depending on the internal physical parameters. Our model is composed of an anodic and cathodic electrodes and an membrane electrolyte mechanistic submodels (the electrodes of some micrometers thickness are separated by a 20 to 100 micrometer thick membrane).…”

“…2). The multiscale model results of the coupling of a microscale proton and electron transport description through the electrode thickness, a spatially distributed microscale model of the reactant (H 2 in the anode, O 2 in the cathode) diffusion through the Nafion ® layer, and a spatially distributed nanoscopic model of the Pt/CNafion ® interface, introduced by Franco et al elsewhere [15]. The last one is constituted of a diffuse layer and a compact layer.…”

Electrochemical mechanism of ion current rectification of polyelectrolyte gel diodes

“…The ionic groups of polyelectrolyte gels are essentially immobile (and thus are treated as uniform fixed charges), and, in contrast, their counterions freely diffuse in the entire volume of the system; our model thus extends the treatments of these ions that have been developed in soft matter physics [17][18][19][20][21][22][23] to electrochemical systems. Analogous models are used to treat electrolyzers [13][14][15]24,25 and fuel cells [26][27][28] that use polymer electrolyte membranes. We treat the cases in which counterions are not the reactants or products of electrochemical reactions.…”

“…Our theory predicts the following experimentally accessible predictions: first, voltages are mostly distributed to the interfaces between the two gels for reverse voltages and to the surfaces of the electrodes for forward voltages. This prediction may be accessible by using experimental techniques that measure local electric fields, for example, electric field-induced second harmonic generation 32 , and/or techniques that capture the signature of redistribution of counterions, for example, cyclic voltammetry, fluorescence microscopes with charged probes 10 and electrochemical impedance spectroscopy 28 . Second, the asymmetry of electric currents increases (forward currents increase and reverse currents decrease) with decreasing values of k f l 0 ðn 3=2 f Þ, see Fig.…”

“…We treated hydrogen and hydroxide ions as symmetric ions; this is to highlight the roles played by the electric charges of polyelectrolyte gels and their counterions in the ion current rectification of PGDs. D hyd is the diffusion constant of hydrogen and hydroxide ions (this constant depends on the volume fraction and the density of the ionic groups of polyelectrlyte gels for the cases in which these parameters are relatively large 22 and thus should be measured by separate experiments or predicted by using multiscale modelling [24][25][26][27][28] Poisson equation. Electrostatic potentials are generated by the electric charges of hydrogen ions, hydroxide ions, the polyelectrolyte gels and their counterions and are derived by using the Poisson equation that has the from @ 2 @z 2 cðzÞ ¼ À 4pl B n H ðzÞ À n OH ðzÞ þ n pol ðzÞ þ n c þ ðzÞ À n c À ðzÞ…”