Real-Space 3D Simulation of Cyclic Voltammetry in Carbon Felt Electrodes for Application in Vanadium Redox-Flow Batteries Based on a Combination of Micro CT Data, Digital Simulation and Convolutive Modelling

Cyclic voltammetry (CV) is the prevalently used technique for investigating the kinetic performance of carbon felt electrodes for application as porous electrocatalysts in vanadium redox-flow batteries. However, the theoretical treatment of internal diffusion-reaction phenomena of such electrodes, allowing for quantitative data evaluation, is still unexplored and mostly relies on diffusion domain approximations assuming the felt as an array of either planar, spherical or cylindrical microelectrodes in a randomly distributed and finite diffusion domain. With this study, we present a novel three-step strategy for real-space CV simulation of felt electrodes. By using micro x-ray tomography (CT) data of the felts, we obtain a locally resolved 3D template of the diffusion space making any diffusion domain approximations obsolete. CV simulation involving this real diffusion domain template is performed by combining the implicit Crank-Nicolson technique in 3D with convolutive modelling. At first, by utilizing the Crank-Nicolson method, we obtain the chronoamperometric current of the 3D porous network for Cottrell-like Dirichlet boundary conditions. Subsequently, the mass transfer functions, usually generated with the aid of Laplace integral transformation techniques, are calculated from these chronoamperometric currents. Then, CV simulation is performed on the basis of these mass transfer functions involving classical convolution integrals. This strategy offers three significant advantages. First, we avoid the difficulty of implementing non-Dirichlet boundaries in the matrices of the Crank-Nicolson scheme. Second, the difficulty of performing an inverse Laplace transformation is avoided since no direct Laplace transformation step is involved. Third, once the mass transfer functions are obtained the simulation can be done with significant savings in time since the 3D network is converted into a one-dimensional problem that can be solved via classical convolution integrals. Our simulation is supported by experimental data acquired for the VO2+-oxidation reaction underlining the validity of our approach. Figure 1