Determination of the Wenzel roughness parameter by the Power Spectral Density of functional Alumina surfaces

• Wenzel roughness parameter and Power Spectral Density are theoretically linked.
• The formula is tested for Alumina surfaces with distinct roughnesses.
• The formula agrees with the experimental data from Atomic Force Microscopy.
• The proper contribution of topography in surface wetting can be ascertained.

The Wenzel roughness parameter of isotropic Gaussian surfaces is analytically described in terms of the Power Spectral Density function without the smooth surface approximation. This Wenzel roughness parameter — Power Spectral Density link was examined for distinct roughnesses of Aluminum-oxide thin films. The Power Spectral Density functions of the surfaces were determined in a wide spatial frequency range by combining different scan areas of Atomic Force Microscopy measurements. The calculated results presented a good agreement with the Wenzel roughness parameter values obtained directly from the topography measured by Atomic Force Microscopy. Finally, wetting behavior was ascertained through determination of water contact angles, including superhydrophobic behavior. This approach, together with an empirical procedure based on a structural parameter, can predict the wetting properties of a surface by taking all its relevant roughness components into account.