Time-Dependent 3D Impedance Model of Mixed-Conducting Solid Oxide Fuel Cell Cathodes

A time-dependent three-dimensional (3D) impedance model of mixed ionic electronic conducting solid oxide fuel cell (SOFC) cathodes that considers the complex coupling of gas diffusion, surface exchange, ionic bulk-diffusion and electrolyte conductivity is presented. By using the finite element method, this model enables the time-dependent and space-resolved simulation of the physicochemical processes in a porous cathode microstructure. The developed model is used for a detailed analysis of the formation of a 'Gerischer-type' impedance. It is detected that the low-frequency part is dominated by the surface exchange reaction, whereas the typical 45° ramp of the Gerischer impedance is related to the ionic diffusion in the bulk. The capability of the time-dependent 3D impedance model is evaluated versus a well-established homogenized analytical model. For homogeneous 3D microstructures both models calculate impedance curves which are in excellent agreement. Further impedance simulations with microstructures containing features of high-performance SOFC cathodes clearly show that model separates and quantifies the contribution of the gas diffusion in a porous cathode layer. At an oxygen partial pressure of 0.21 atm the gas diffusion accounts for only 2% of the total polarization resistance, whereas a depletion of oxygen to 0.01 atm significantly increases this value to 38%.