Conductivity of porous materials with spheroidal pores

Models predicting the conductivity of porous materials with spheroidal insulating pores are summarized and a new model, based on our exponential relation, is proposed. Using the well-known single-inclusion solution for spheroids, Maxwell coefficients (“intrinsic conductivities”) are calculated in dependence of the pore aspect ratio for isotropic microstructures with randomly oriented spheroidal pores, and implemented into the three traditional effective medium approximations (Maxwell-type, self-consistent, differential) and our exponential relation. As expected, all models predict that prolate pore shape has a very small influence on the porosity dependence, while oblate pores affect the porosity dependence of conductivity significantly. However, the self-consistent predictions are linear and imply spurious percolation thresholds, whereas Maxwell-type and differential models (power-law relations) are known to provide predictions that are unrealistically high for the special case of spherical pore shape. Thus, our exponential relation seems to be currently the most suitable relation for implementing the single-inclusion solution for spheroids.