Thermodynamic analysis of stable wetting states and wetting transition of micro/nanoscale structured surface

Superhydrophobicity of biological surfaces with micro/nanoscale hierarchical roughness has recently been given great attention and widely reported in many experimental studies due to the unique wettability. For example, the dual-scale structure of the lotus leaf not only shows high contact angle and low contact angle hysteresis but also presents good stability and mechanical properties. Though lots of experimental studies on the wettability of artificial hierarchical rough surface have been carried out, a thorough analysis on the contribution of micro- and nano-scaled roughness to the metastable wetting states and their transition is still lack. In this paper, a thermodynamic approach is applied to analyze all the wetting states (including four stable wetting states and five transition states) of a water droplet on a surface with micro/nanoscale hierarchical roughness, and the corresponding free energy expressions and apparent contact angle equations are deduced. The stable wetting states are confirmed by the principle of minimum free energy. And the calculated results by these state equations can fit well with the experimental results reported in the literature when compared with the previous models. Meanwhile, the influence of micro/nanoscale roughness on the stable wetting states and metastable-stable transition has been analyzed thermodynamically. It is found that there is a synergistic effect of micro and nanoscale roughness on wettability, which nlay result in many different wetting states. There are four wetting states during increasing relative pitch of a microscaled structure at a given nanoscaled structure, but two wetting states can be obtained as increasing relative pitch of nanoscaled structure at a given microscaled structure. The change of nondimensional energy and nondimensional energy barrier in the metastable-stable transition process of water droplet wetting micro and nanoscaled structure is quantitatively analyzed. Results indicate that the microscaled structure is never wetted in a special size range of the nanoscaled structure, and the special size range is of great significance to enhance superhydrophobic stability of the microscaled structure. Furthermore, the existence of microscaled structure decreases the transition energy barrier of water droplet wetting nanoscaled structure, which is helpful for understanding the experimental results reported in the literature. Finally, all possible stable wetting states of water droplet no a surface with micro/nanoscale hierarchical roughness are discribed in a wetting map. A design principle of superhydrophobic surface with micro/nanoscale hierarchical roughness is put forward, which is helpful to ensure the size of micro/nanoscale structure in the stable superhydrophobic region and to provide a theoretical guidance in the preparation of superhydrophobic surface.