Thermodynamic analysis of the effect of the hierarchical architecture of a superhydrophobic surface on a condensed drop state.

Condensed drops usually display a Wenzel state on a superhydrophobic surface (SHS) only with microrough architecture, while Cassie drops easily appear on a surface with micro-nano hierarchical roughness. The mechanism of this is not very clear. It is important to understand how the hierarchical structure affects the states of condensation drops so that a good SHS can be designed to achieve the highly efficient dropwise condensation. In this study, the interface free energy (IFE) of a local condensate, which comes from the growth and combination of numerous initial condensation nuclei, was calculated during its shape changes from the early flat shape to a Wenzel or Cassie state. The final state of a condensed drop was determined by whether the IFE continuously decreased or a minimum value existed. The calculation results indicate that the condensation drops on the surface only with microroughness display a Wenzel state because the IFE curve of a condensed drop first decreases and then increases, existing at a minimum value corresponding to a Wenzel drop. On a surface with proper hierarchical roughness, however, the interface energy curve of a condensed drop will continuously decline until reaching a Cassie state. Therefore, a condensed drop on a hierarchical roughness surface can spontaneously change into a Cassie state. Besides, the states and apparent contact angles of condensed drops on a SHS with different structural parameters published in the literature were calculated and compared with experimental observations. The results show that the calculated condensed drop states are well-coordinated with experimental clarifications. We can conclude that micro-nano hierarchical roughness is the key structural factor for sustaining condensed drops in a Cassie state on a SHS.