Inferring fractal dimension of rough/porous surfaces—A comparison of SEM image analysis and electrochemical impedance spectroscopy methods

There are many methods for analysis and description of surface topographies that rely on analysis of surface images obtained by various methods such as SEM or AFM. However, they can seldom provide quantitative topographical information. Such information can be obtained by fractal analysis of the images resulting in a characteristic fractal dimensions. The advantage of fractal approach to surface characterization is that it is insensitive to the structural details, and the structure is characterized by single descriptor, the fractal dimension D. On the other hand, it is well established that electrochemical impedance spectroscopy (EIS) is convenient method often used to infer the fractal dimension of porous or rough surfaces–electrodes. Here we present and discuss the results of comparison of two methods for the determination of topological fractal properties of porous/rough surfaces: electrochemical impedance spectroscopy and SEM gray-scale image analysis. We have established that in most cases there is a good correlation between the fractal dimensions inferred from EIS measurements (DEIS) and those obtained from fractal analysis of gray-scale SEM images (Dg). However, the fractal dimension inferred from gray-scale SEM images Dg seems to be a better descriptor of surface topology than the fractal dimension inferred from CPE exponent α of EIS measurements, since the latter may be influenced by other parameters beside pure geometrical surface roughness or porosity. This conclusion is supported with recent finding of good correlation of Dg and relevant different profilometric parameters.