Understanding the Impedance of Mesoporous Oxides: Reliable Determination of the Material-Specific Conductivity.

The unique architecture of ordered mesoporous oxides makes them a promising class of materials for various electrochemical applications, such as gas sensing or energy storage and conversion. The high accessibility of the internal surface allows tailoring of their electrochemical properties, e.g., by adjusting the pore size or surface functionalization, resulting in superior device performance compared to nanoparticles or disordered mesoporous counterparts. However, optimization of the mesoporous architecture requires reliable electrochemical characterization of the system. Unfortunately, the interplay between nanocrystalline grains, grain boundaries, and the open pore framework hinders a simple estimation of material-specific transport quantities by using impedance spectroscopy. Here, we use a 3D electric network model to elucidate the impact of the pore structure on the electrical transport properties of mesoporous thin films. It is demonstrated that the impedance response is dominated only by the geometric current constriction effect arising from the regular pore network. Estimating the effective conductivity from the total resistance and the electrode geometry, thus, differs by more than 1 order of magnitude from the material-specific conductivity of the solid mesoporous framework. A detailed analysis of computed impedances for varying pore size allows for the correlation of the effective conductivity with the material-specific conductivity. We derive an empirical expression that accounts for the porous structure of the thin films and allows a reliable determination of the material-specific conductivity with an error of less than 8%.