A micromechanical model for effective conductivity in granular electrode structures

Optimization of composition and microstructure is important to enhance performance of solid oxide fuel cells (SOFC) and lithium-ion batteries (LIB). For this, the porous electrode structures of both SOFC and LIB are modeled as a binary mixture of electronic and ionic conducting particles to estimate effective transport properties. Particle packings of 10 000 spherical, binary sized and randomly positioned particles are created numerically and densified considering the different manufacturing processes in SOFC and LIB: the sintering of SOFC electrodes is approximated geometrically, whereas the calendering process and volume change due to intercalation in LIB are modeled physically by a discrete element approach. A combination of a tracking algorithm and a resistor network approach is developed to predict the connectivity and effective conductivity for the various densified structures. For SOFC, a systematic study of the influence of morphology on connectivity and conductivity is performed on a large number of assemblies with different compositions and particle size ratios between 1 and 10. In comparison to percolation theory, an enlarged percolation area is found, especially for large size ratios. It is shown that in contrast to former studies the percolation threshold correlates to varying coordination numbers. The effective conductivity shows not only an increase with volume fraction as expected but also with size ratio. For LIB, a general increase of conductivity during the intercalation process was observed in correlation with increasing contact forces. The positive influence of calendering on the percolation threshold and the effective conductivity of carbon black is shown. The anisotropy caused by the calendering process does not influence the carbon black phase.