Minimizing the contact area between

Minimizing the contact area between liquid and solid is a widely used strategy to enhance superhydrophobicity; however, it results in fragile surface textures and poor resistance to wear20. Various approaches have been explored to address this problem—for example strengthening the bonding between the coating and the substrate by using an adhesion layer21,22, bearing the abrasion force by randomly introducing discrete microstructures23–26 and allowing abrasion by sacrificing the upper layers of a self-similar structure27–29—but these have resulted in only modest improvements in robustness (Supplementary Video 1). As an alternative strategy, we considered the features of mechanical durability and non-wettability separately and implemented them at two different length scales, fabricating nanostructures to impart water repellency and a microstructure to act as ‘armour’ to resist abrasion (Fig. 1a, Supplementary Fig. 1, Supplementary Video 2, Supplementary Discussion section 2.1). As the first feature of our design, the microstructure consists of an interconnected frame that prevents the nanostructures from being removed by abradants that are larger than the frame size (Fig. 1b, c). The interconnectivity also enhances mechanical robustness, as observed for various natural structures including springtail skin and honeycomb. Additional design features must also be considered to ensure that the non-wettability of the surface is not compromised. Here we explore the relationship between the liquid–solid contact fraction f, the Young’s contact angle θY and the apparent contact angle θ* using the Cassie–Baxter model: