Fabrication of nano-periodic structures and modification of the Wenzel model to estimate contact angle

The Wenzel model is widely accepted in understanding the roughness-induced hydrophobicity or hydrophilicity of a periodic structure. However, the present Wenzel model is insufficient for estimating the absolute value of the contact angle. In our recent work, we fabricated silicon test-pieces with nanometer scale periodic structures. The purpose of this paper is to enable us to quantitatively predict the contact angles on these periodic structures. The classical Wenzel equation was modified to extend it to 3-dimensional structures. Although the same material is used, the contact angle can be controlled over a range of more than 100° by changing the dimensions of the nano-periodic structures. The results for the contact angles calculated from the 3-dimensional Wenzel equation using a modified roughness factor agreed well with the results measured on the nano-periodic structures. We also clarified experimentally the threshold levels of the pitch and depth of these periodic structures for switching the wettability from hydrophobic to hydrophilic.