Simulated impedance of diffusion processes in tomographically derived microstructures

Impedance spectroscopy is a powerful and widely used technique for characterising processes in electrochemical devices, such as batteries and fuel cells. The performance of these devices is closely related to their 3D microstructures; however, the elements used for representing them are typically either zero dimensional (resistors, capacitors etc.) or occasionally 1D. The most commonly used 1D elements are Warburg diffusion elements, which are particularly useful as they have analytical solutions and so can be easily incorporated into standard EIS fitting algorithms. However, the transport processes that these elements are used to represent are inherently 3D, and so Warburg diffusion elements must capture transport phenomena with bulk parameters such as tortuosity factors and porosities. Details of the geometry of porous electrodes have recently become routinely available using microtomography. This technique typically represents the geometry as an array of cuboid volume elements (voxels) that must be segmented from greyscale to a phase labelled volume. In 2016, the authors published an open-source software package, TauFactor, which allows for the rapid calculation of tortuosity factors from segmented tomography data. An updated version of the software is here presented to efficiently calculate diffusive impedance spectra in the frequency domain, directly from segmented tomography data. Numerical results show that the diffusion impedance may significantly deviate from the Warburg analytical solution for structures showing an inhomogeneous distribution of pores. In particular, multiple peaks may appear in the high-frequency region in the complex plane, which may be misinterpreted as separate electrochemical processes in real impedance data (see fig.1 for a simple 2D example). Two classes of structures, namely with increasing or decreasing porosity distribution, can be identified from the analysis of diffusion impedance. Thus, the software can be used to overcome the limits of conventional equivalent circuit analysis in modelling transport phenomena in porous electrodes.