Institute of Condensed Matter and Nanosciences-Bio & Soft Matter, Université Catholique de Louvain, Croix du Sud 1 box 4, 1348 Louvain-la-Neuve, Belgium.
Langmuir. 2010 Dec 7;26(23):17798-803. doi: 10.1021/la104282q. Epub 2010 Nov 8.
We show experimentally and analytically that for single-valued, isotropic, homogeneous, randomly rough surfaces consisting of bumps randomly protruding over a continuous background, superhydrophobicity is related to the power spectral density of the surface height, which can be derived from microscopy measurements. More precisely, superhydrophobicity correlates with the third moment of the power spectral density, which is directly related to the notion of Wenzel roughness (i.e., the ratio between the real area of the surface and its projected area). In addition, we explain why randomly rough surfaces with identical root-mean-square roughness values may behave differently with respect to water repellence and why roughness components with wavelength larger than 10 μm are not likely to be of importance or, stated otherwise, why superhydrophobicity often requires a contribution from submicrometer-scale components such as nanoparticles. The analysis developed here also shows that the simple thermodynamic arguments relating superhydrophobicity to an increase in the sample area are valid for this type of surface, and we hope that it will help researchers to fabricate efficient superhydrophobic surfaces based on the rational design of their power spectral density.
我们通过实验和分析表明，对于由随机凸起的凸起物组成的单值、各向同性、均匀、随机粗糙表面，如果表面高度的功率谱密度可以从显微镜测量中得出，则超疏水性与表面高度的功率谱密度有关。更确切地说，超疏水性与功率谱密度的三阶矩相关，而三阶矩与 Wenzel 粗糙度的概念直接相关（即表面实际面积与投影面积之比）。此外，我们解释了为什么具有相同均方根粗糙度值的随机粗糙表面在疏水性方面可能表现不同，以及为什么波长大于 10 μm 的粗糙度分量不太可能重要，或者换句话说，为什么超疏水性通常需要亚微米级组件（如纳米粒子）的贡献。这里开发的分析还表明，将超疏水性与样品面积增加相关联的简单热力学论点对于这种类型的表面是有效的，我们希望它将帮助研究人员基于其功率谱密度的合理设计来制造高效的超疏水性表面。
