Optimal thickness of porous micro-electrodes operating a single reduction reaction
Résumé
In the recent decades, porous electrodes with high specific surface, which are of major interest for the design of miniaturized electro-devices such as bio-batteries, have received a lot of attention both from modeling and experimental points of view. Such electrodes may provide much higher electrical current than classical flat electrodes of the same size [1]. Despite considerable progress in porous electrode manufacturing, effective tool for predicting the optimal thickness of such electrodes have not been developed in the literature. To fill this gap, this work aims at developing a thorough approach to estimate the optimal thickness of a porous electrode operating a single reduction reaction. This is achieved by making use of a macroscopic model formally derived from the microscopic coupled diffusion and electrochemical reaction model operating at the pore scale using an upscaling procedure [2] relying on the volume averaging method [3]. The solution of this macroscopic model was successfully compared to the solution of the microscale original model obtained from direct numerical simulations on the one hand and to experimental data on the other hand, validating our theoretical macroscale model. The macroscopic model is subsequently used in the steady-state regime (a situation which is of wide practical interest) to derive an analytical solution for the concentration profile of the dilute species allowing to express the current intensity available at the electrode. On this basis, an optimization procedure is finally proposed to estimate the effective electrode thickness which is defined as the crossover value of two asymptotic regimes characterizing the volume current density dependence upon the electrode thickness. This yields an analytical expression of the optimal thickness that is general for a cylindrical porous electrode, regardless the type of microstructure of the electrode material. An illustration is provided for the type of electrode used in the experiments reported in this work.