Simulation of Electrical Conductivity of Porous Composite Electrodes for Solid Oxide Cells Using a Monte Carlo 3D Equivalent Electronic Circuit Networks
Authors: Budac Daniel , Milos Vojtech , Carda Michal , Paidar Martin , Bouzek Karel 
Published: August 2024

Solid oxide cells (SOCs) show high potential in energy conversion applications necessary for the decarbonization of the economy. Their advantage consists in ability to operate at high temperatures, reaching up to 900 °C. Firstly, it results in accelerated electrode reactions kinetics, secondly, in favorable thermodynamic conditions decreasing the equilibrium voltage of the water splitting. As a result, SOCs are attractive candidates for both efficient electrolysis and fuel cell applications, offering a robust solution in the pursuit of clean energy. However, the elevated operational temperature also introduces material challenges that hinder the competitiveness of SOCs.
Porous gas diffusion electrodes are used to accomplish the desired electrode reactions. Considering conventional exclusively electron-conductive electrode materials, triple phase boundary (TPB) is required for the reactions to take place – a simultaneous contact of electron-conductive, ion-conductive and gaseous phase. While the electrode and electrolyte phases are solid, the gaseous phase is represented by open porosity in the electrode body. TPB is located exclusively at the contact area of electrode and electrolyte components in the case of single-phase electrodes, limiting the electrode electrocatalytic performance. To avoid the limitation by TPB length, composite electrodes are frequently used. Due to the involvement of the ionically conductive phase, they exhibit improved electrocatalytic capabilities.
Electrolyte phase, however, usually exhibits 4 orders of magnitude lower electrical conductivity than the electron-conductive phase, while gaseous phase is electrically non-conductive. Thus, an improper phase composition and morphology of the composites can lead to a significant drop in their electrical conductivity and thus in the cell performance. Simple and reliable method for the conductivity value prediction is up to now missing. At the same time, experimental determination is both expensive and time-consuming. The goal of this study was to develop simple, fast and reliable method for prediction of electrical conductivity of the porous electron-ion conductor composites.
The key feature of the presented approach lies in the minimal requirements for input parameters. Only electrode phase composition and bulk electrical conductivity of each phase are required. Based on the input composition, the model generates a 3D artificial specimen, a domain discretized into cubic voxels each assigned randomly to a specific phase. The resulting structure is substituted with an equivalent circuit network with electric elements corresponding to the electrochemical properties of the material components: specific resistivity of electrical conductors and polarization resistance / capacitance of electrochemical reaction at material interface. In-silica electrochemical impedance spectroscopy measurement is performed by solving charge balance following Kirchhoff’s current law for multiple frequency values. Resulting impedance spectrum is fitted in order to obtain Ohmic and polarization resistance and the capacitance of the artificial specimen. This procedure is averaged over a large number of artificial specimens in a Monte Carlo manner.
Conventionally used oxygen electrode composite material lanthanum strontium manganite (LSM) mixed with yttria-stabilized zirconia (YSZ) was used to produce validation dataset. LSM:YSZ powder mixtures of compositions between 1:0 and 0:1, chosen to produce samples of various degree of LSM percolation, were homogenized. The mixtures were fired at 1150 °C. Electrical conductivity of the pellets was determined at temperatures between 600 and 800 °C using electrochemical impedance spectroscopy.
Experimental data obtained were confronted to the model results. The model demonstrated very good accuracy for a porosity value of up to 55%. Significant error was observed in the porosity range between 55% and 68%. Finally, the model failed to generate an artificial specimen with a porosity of 75%. As it was found, the limited applicability of the model for the materials characteristic for high porosity was caused by the coalescence of the void phase. This shortcoming of the model was solved by implementing morphological parameter describing degree of void phase coalescence in the electrode structure. Due to this modification, model allows to gain valuable information on the microstructure of the studied composite material on the base of the experimentally determined conductivity data.
This work introduces a novel modelling approach with minimal amount of input parameters, streamlining the prediction of electrical conductivity of porous electron-ion conductor composites. This simplified yet effective methodology holds great promise for efficiently characterizing and optimizing materials for energy conversion applications, offering a valuable tool for advancing research in the field.
This publication was supported by the project "The Energy Conversion and Storage", funded as project No. CZ.02.01.01/00/22_008/0004617 by Programme Johannes Amos Commenius, call Excellent Research.