Multiscale modelling of diffusion and enzymatic reaction in porous electrodes in Direct Electron Transfer mode

This work is dedicated to a multi-scale modelling of coupled diffusion and reaction in a porous microelectrode operating in the Direct Electron Transfer mode. The pore-scale physico-electrochemical unsteady model is developed considering the oxygen reduction, catalyzed by an enzyme coating the pores of the electrode, coupled to the diffusion of oxygen and mass balance of enzymes. This model is formally upscaled to obtain an original closed unsteady macroscopic model operating at the electrode scale, together with the associated closure providing the effective diffusivity tensor. A validation of this model is carried out from a comparison with the solution of the initial 3D pore-scale governing equations considering the bilirubin oxydase as the catalyst. The relevance and accuracy of the macroscale model are proved allowing a considerable simulation speedup. It is further employed to successfully predict experimental voltammetry results obtained with porous gold electrodes functionnalized with a bilirubin oxidase mutant (BOD S362C). This model represents a breakthrough by providing an operational simple way of understanding and further optimizing porous electrodes functioning in DET mode.