# A Review on Ultrafast Laser Enabled Excellent Superhydrophobic Anti-Icing Performances
## 2 Ultrafast Laser-Fabricating Micro-Nanostructured Superhydrophobic Surfaces  
### Wettability and Superhydrophobicity  
Surface wettability represents the ability of liquids to spread on surfaces. When the spreading reaches the equilibrium, droplets statically rest on surfaces and form an angle, namely, contact angle \(\theta\) (CA). From thermodynamics, CA is the characterization of three-phase interfacial free energies. Back in 1805, the relationship between them has been well described by [PERSON]'s equation [83], as shown in Figure 4a:  
\[cos\theta=(\gamma_{sv}-\gamma_{ls})/\gamma_{l\upsilon} \tag{1}\]  
where \(\gamma_{sv}\), \(\gamma_{ls}\) and \(\gamma_{l\upsilon}\) denote the interface tensions of solid-vapor, liquid-solid, and liquid-vapor, respectively. Although [PERSON]'s equation establishes the qualitative relationship  
Figure 3: Flow chart describing the arrangement and order of each part in this review.  
between interfacial energies and wettability, it is not appropriate for describing rough surfaces in the real world. [PERSON] et al. introduced the roughness factor r and took the apparent contact angle \(\theta^{*}\) to characterize surface wettability [84], as shown in the following equation:  
\[cos\theta^{*}=r\cdot(\gamma_{sv}-\gamma_{ls})/\gamma_{lv}=r\cdot cos\theta \tag{2}\]  
where the roughness factor r is the ratio of the actual solid-liquid contact area to the nominal contact area. However, the model is limited to the occasion that liquids completely penetrate micro-nano valleys and cannot explain some common wetting phenomena in nature such as the rolling droplets on lotuses. [PERSON] and [PERSON] further introduced the contact fractions of liquid-solid \(f_{ls}\) and liquid-vapor \(f_{lv}\) to describe the mixed triple-phase interfaces [85]. Considering \(f_{ls}+f_{lv}=1\), the Cassie-Baxter equation is expressed by:  
\[cos\theta^{*}=f_{ls}\cdot cos\theta-1+f_{ls} \tag{3}\]  
Generally, droplets on superhydrophobic surfaces show a large CA and low adhesion strength. Contact angle hysteresis is one of the most common evaluation standards of droplet adhesion. The maximum and minimum static CAs are defined as the advancing angle \(\theta_{adv}\) and receding angle \(\theta_{rec}\), respectively. The difference between \(\theta_{adv}\) and \(\theta_{rec}\) is the contact angle hysteresis (CAH), as shown in Figure 4a. Smaller CAHs mean smaller adhesion forces exist between interfaces so that droplets can move on surfaces more easily. In this case, surfaces have better liquid-repellency [86; 87]. In nature, superhydrophobic phenomena exist widely. For example, luxviariant micropapillae covered by low-surface-energy epicuticular wax endow lotuses with excellent superhydrophobic and anti-fouling properties [88] (Figure 4(d1,d2)), and needle-shaped micro-nano setae combined with wax make water striders walk on rivers freely [89] (Figure 4(e1,e2)). Meanwhile, diverse micro-nanostructure arrangements also bring about many unique superhydrophobic properties, such as the high droplet adhesion on rose petals enabled by single-tier microstructures (Figure 4(f1,f2)) [90], directional adhesion on rice leaves [88] and butterflies enabled by directional microgrooves [91] (Figure 4(g1,g2,h1,h2)), and the anti-fogging properties on mosquito eyes enabled by elaborate nanonipples [92] (Figure 4(i1,i2)).