A Simple Method for Porosity Estimation at Nanoscale

Porous nanostructures have important applications in developing high-surface-area catalysts, sensors, and filters. It is difficult to accurately calculate porosity of nanomaterials using usual methods. Here, using the atomic force microscopy (AFM) topography, we introduce an interestingly simple method for calculating porosity of nanosized materials in three-dimensions based on the length correlation and average surface height difference. Computer simulations were used along with experimental results to test the validity of our proposed method. The porosity of the TiO2-nanowire-deposited silicon substrates was experimentally estimated from AFM-measured topography images. The corresponding computer simulations were carried out only for one crystallographic direction of the surface of the sample, for the surface is isotropic-there is no preferred direction at the surface-and we expect that simulations along an arbitrarily chosen cross section of the surface provide us with a full description of the entire surface. The results of the simulations were found to be in line with the results obtained by our proposed method from experimental data.