Surface roughness or asperities plays a detrimental role in the icephobicity of a surface. This could be in the form of overall surface roughness or imparting surface features that may aid to mitigate ice anchoring or encourage favourable wettability conditions to induce icephobic performance. First, overall surface roughness can be categorised into three ranges: (i) superhydrophobic roughness range of 50–100 μm ^[1][2][3][4][72,73,99,100] (referred to as rough surfaces or higher roughness), (ii) surfaces to avoid ice anchoring of roughness range <100 nm ^[5][6][7][71,101,102] (referred to as smooth surfaces or lower roughness), and (iii) surfaces to annihilate ice nucleation of roughness range <10 nm ^[6][8][9][34,35,101] (referred to as ultra-smooth or ultra-fine surfaces). Some researchers reported that there was no straightforward relationship between ice adhesion strength and hydrophobicity, while they also confirmed that ice adhesion increased with surface roughness ^[10][103]. Because of the mechanical interlock at the ice–solid interfaces, the ice adhesion on textured surfaces (with a certain surface roughness) could even be comparable to that on superhydrophilic surfaces ^[11][104]. A previous study also indicated the ice nucleation of supercooled water at surface defects, such as pits and grooves, on different substrates ^[12][105].

Second, the anti-icing and de-icing characteristics of certain surfaces induced by different surface morphological structures were further demonstrated. For example, a “honeycomb structure” showed better effectiveness, while an “island structure” behaved with stronger anti-icing stability ^[13][106]. Hou et al. ^[14][107] reported that microcubic arrays with different microspacing distances could entrap more air pockets underneath the water droplets and alter the actual solid/liquid contact fraction. Saito et al. ^[15][108] found that a reduction in ice adhesion strength is possible with high levels of roughness as it increases the number of air pockets presented between the interfacial ice–substrate contacts. However, surface roughness also increases the number of possible anchoring sites, which may lead to higher adhesion strengths in some instances ^[16][67].

Liu et al. ^[17][109] constructed modified nanosilica superhydrophobic coatings with micropillar array structures using a straightforward net embossing method. By controlling the width of the micropillar and further surface roughness, the anti-icing properties, corrosion resistance, and permeability resistance of the micropillar array structures were effectively improved, with the water contact angle (WCA) values above 150° and sliding angle (SA) less than 10°. This work indicates that surface roughness plays a crucial role in ice adhesion and changing the surface roughness and the restructuring of surfaces would be key in reducing ice adhesion strength ^[18][19][66,81].

In addition, there is a broader consensus on the role of surface roughness in delaying ice formation, and ice nucleation can be annihilated or immensely delayed by deploying surface roughness patterned close to or smaller than the critical ice nuclei size ^[20][21][110,111]. However, with lower surface roughness, the interfacial contact of ice is significantly enhanced compared to hydrophobic surfaces, and the material chemistry and properties play an important part ^[22][56]. In other words, ice adhesion could be sufficiently reduced by minimising ice anchoring points, but a synergetic effect of either low surface energy or a softer interface is required to induce a low ice adhesion. For example, remarkable freezing delays are expected on smoother, functionalised surfaces as it lowers the free energy barrier and favours homogeneous ice nucleation ^[23][112].

On the other hand, ice adhesion could be considerably enhanced if a surface has high surface energy or unfavourable conditions (surface impurities) that may promote the ice/surface interface bonding mechanisms ^[24][113]. There is a challenge to retain a smoother morphology under harsh environmental conditions, such as under rain erosion, which can significantly distort the microstructure and impart possible ice anchoring points (surface anomalies). Another advantage of smoother surfaces is that they are much easier to maintain, and a reliable icephobic performance is expected as the surface is not reliant on a certain roughness to induce hydrophobicity which could be damaged during ice shearing processes ^[25][114].

Zou et al. ^[26][115] studied the water contact angles of as-received aluminium (AR Al) and sandblasted aluminium (SB Al). The results predicted the Wenzel model and indicated that the hydrophilic properties of a surface can be enhanced by changing the surface roughness. Interestingly, higher water contact angles were determined on fluorinated carbon (FC)-film-coated samples due to the enhanced low surface energy imparted by the fluorine molecules, and a Cassie–Baxter state could be predicated. A slight increase in water contact angles was also noticed in the case of silicon-doped hydrocarbon-coated samples.

Susoff et al. ^[18][66] studied superhydrophobic plates by immersing the plates in water and found that the force required to peel off the ice was multiple times higher than that of pristine plates. They concluded that even if the surface behaves superhydrophobic, ice adhesion significantly depends on surface roughness or the structure of the surface. Additionally, surface roughness along with other parameters strongly depends on the effective surface area of the sample (i.e., the mean interfacial area) ^[18][66]. Furthermore, Janjua et al. ^[16][67] concluded that with an increase in contact angle hysteresis, ice adhesion decreases, and this trend is valid when CAH is higher than 92° and the higher CAH is coupled with a high surface roughness. Hao et al. ^[27][92] found that by controlled nucleation and effective heat transfer, the freezing process on rough surfaces could be delayed, and such results required the surface roughness to be in a controlled pattern, and the void or interval of a pattern should be smaller in size than the critical ice nuclei. Following this procedure, a pre-superhydrophobic surface with controlled surface textures demonstrated superhydrophobic capabilities, together with efficient ice removal and anti-icing capabilities ^[27][92]. Poulikakos and co-workers ^[8][28][34,95] prepared nanometre-scale roughness grooves on hydrophilic surfaces and interestingly showed a longer droplet freezing delay. The magnitude of the freezing delays was at least one order greater than a traditional superhydrophobic surface with low wettability and higher surface roughness. Chen et al. ^[29][90] reported that a liquid-fused coating surface showed rough morphology with a R_a of 0.536 nm in the air. When the coating was submerged in the water, the surface became smoother with a R_a of 0.264 nm. The results indicated that a liquid-like layer was formed when the coating was submerged, and this thin layer would induce icephobicity by minimizing the interfacial contact area of the formed ice. For smoother surfaces, the results indicated a one order of magnitude reduction in ice adhesion, and for rougher surfaces, a three-fold increase in the magnitude of ice adhesion strength was reported in comparison to pristine substrates under similar conditions ^[29][90]. To further understand the role of surface roughness, the type of formed ice also matters when considering icephobicity. For example, impact glaze and rime ice form a hard bond with the texted surfaces, while bulk-formed glaze ice demonstrates a lower ice adhesion strength ^[30][31][116,117]. Impact glaze and rime ice are normally formed by fast-incoming supercooled droplets, such as during icing fog or rain conditions. These microdroplets will penetrate the void valleys or textures of the rough surfaces or pores and anchor with the solid surface ^[32][33][76,118]. According to another study, when a layer of polytetrafluoroethylene (PTFE) was applied on rough coatings, the ice adhesion of bulk-formed ice was reduced. However, no significant reduction in ice adhesion was observed for impact glaze ice ^[34][119].

2. The Role of Surface Roughness on Ice Nucleation and Thermodynamics

Physical mechanisms such as electrostatic interaction, hydrogen bonding, and van der Waals forces are primarily responsible for ice adhesion on surfaces ^[28][35][36][10,95,123]. Ice adhesion is significantly reduced on materials/surfaces with a lower surface energy ^[37][38][65,124]. The science behind their impressive icephobic performance is the weaker molecular interaction between the coating surface and the water/ice interfaces ^[39][40][125,126]. Another factor influenced by the surface energy is the droplet freezing delay, and it is reported that droplet freezing delay can be altered or controlled by a predefined surface roughness. The formation of ice crystallites starts with nucleation, which can be achieved in either homogeneous or heterogeneous ice nucleation. In homogenous nucleation, the nucleation is induced by thermal fluctuations, and larger nuclei are only formed after overcoming the free energy barriers within the surrounding liquid. Whereas, in heterogeneous nucleation, crystallites are formed with the help of heterogeneous ice seeds, such as on a solid surface (roughness asperities) ^[41][42][127,128], dust, impurities, or other ice crystals, as they reduce the activation energy ^[43][32]. Jung et al. ^[8][44][45][34,129,130] reported that a one order of magnitude longer freezing delay was observed with a surface having higher wettability and nanoscale roughness. The results suggested that the surface roughness had a strong influence on ice nucleation and its growth. In the experiments, they used samples with different surface roughness values, e.g., from a few nanometres to several micrometres. Smoother samples showed a remarkable freezing delay, and the droplets were in an unfrozen condition for 150 times longer than the other samples ^[8][34]. This significant delay in freezing can be attributed to the low roughness values or roughness values comparable to the radius/size of the critical ice nuclei ^[5][71]. The samples, having a similar surface roughness but variable surface energies, showed a strong dependence on surface energy, and the surfaces with a lower surface energy demonstrated a longer freezing delay. The theory of classical heterogeneous ice nucleation states that surface roughness and wettability (hydrophobicity) are two main factors that decide the freezing probability, i.e., the rate of critical nuclei generation in the droplet ^[7][102]. The dependence of freezing delay on surface roughness was also studied, and it was assumed that the freezing delay rose with lower surface roughness, and a longer freezing delay was expected on surfaces with a lower surface energy ^[5][71]. In terms of the thermodynamics for the homogeneous ice nucleation of a supercooled water droplet on a solid surface, the free energy barrier ΔG is higher than that of heterogeneous nucleation ^[7][102]. The theory suggests that the critical size 𝑟_𝑐 must be reached for the formation of stable ice nuclei at a given temperature, which can be calculated using Equation (1) ^[7][102]: $${\mathrm{r}}_{\mathrm{c}}=\raisebox{1ex}{$2·{\mathsf{\gamma }}_{\mathrm{IW}{}_{}\raisebox{1ex}{$\Delta {\mathrm{G}}_{\mathrm{f},\mathrm{v}{}_{}\raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.}$}\!\left/ \!\raisebox{-1ex}{$$}\right.}$}\!\left/ \!\raisebox{-1ex}{$$}\right.$$ where Δ𝐺_𝑓,𝑣 is the volumetric free energies between water–ice interfaces per unit volume, and 𝛾_𝐼𝑊 is the interfacial water–ice energy. At a temperature of −25 °C, the critical size of ice nuclei was determined experimentally to be r_c ≈ 1.7 nm. These results suggest that the radius of curvature of roughness should be close to the critical size of ice nuclei to suppress the icing effects and prevent the formation of stable ice nuclei. Thus, the classical theory identifies a strong bearing of the roughness radius of curvature on the freezing delay mechanism ^[9][35]. Therefore, it is reasonable to assume that the maximisation of the free energy barrier for the development of ice embryos (lower surface energy) and the minimisation of the effective interfacial contact area (smoother or lower surface roughness) of the supercooled droplet will significantly increase the icing/freezing delay. However, the formation of ice nuclei is not a simple function of the surface roughness ^[9][35]. Thus, effective strategies need to be identified and deployed. One such strategy could be the application of nanostructuring, which has been debated in anti-icing coatings. It was reported that nanostructured substrates with 0.17–173 nm RMS roughness demonstrated a remarkable freezing delay, i.e., a three-order increase in magnitude ^[9][35]. It suggested that the values of curvature should be less than ten times the critical radius to mitigate icing nucleation/formation. The interface between ice/water and superhydrophobic surfaces with low ice adhesion strength is dominated by van der Waals forces ^[46][131], and the thickness of depletion layers increases with the increase of water contact angles ^[47][48][49][132,133,134]. The adhesion strength, in this case, can be calculated using Equation (2) ^[46][131]: $${\mathsf{\tau }}_{\mathrm{a}}=\frac{\mathrm{U}}{6{\mathsf{\pi }\mathrm{D}{3}^{}\frac{}{}}^{}}$$ where the thickness of depletion layers is denoted by D (normally in the range of 0.1–1 nm), and the Hamaker constant is U, bearing a value of 10~19 J. Typically, the adhesion strength of ice reduces and D increases with an increase in water contact angles. A fluoro-based polyhedral oligomeric silsesquioxane/poly(ethyl methacrylate) surface will have a depletion layer thickness in the order of 1 nm, and the highest intrinsic hydrophobicity values are measured on these surfaces ^[50][135].

3. Nanostructured Surfaces and Surface Texturing

Controlling roughness asperities to the nanolevel to annihilate ice nucleation before it grows heterogeneously is a sensible strategy for icephobic materials. Kim et al. ^[51][68] fabricated nanostructured slippery liquid-infused porous surfaces (SLIPSs) using aluminium plates as the substrates. They deposited highly textured polypyrrole layers on the as-received aluminium substrates by electrodeposition. The coatings were then fluorinated, and a lubricant was infiltrated into the pores of the coatings using a heat treatment method ^[51][68]. They reported an ice adhesion reduction factor of 87, and a reduced ice adhesion of 15.6 kPa. Interestingly, similar results were demonstrated even under high humidity conditions at −10 °C, which was very impressive considering the high humidity environments. The results may suggest a reduction in microcondensation due to smoother morphology ^[51][68]. In order to control the roughness asperities, samples with nanosize structures such as honeycombs, pillars, and brick patterns, etc., have been produced to study surface superhydrophobicity and ice freezing delay. Mishchenko et al. ^[1][72] prepared highly ordered and nanosized structures bearing high aspect ratios on various substrates by the Bosch process to create hydrophilic, hydrophobic, and superhydrophobic surfaces, respectively. The hydrophilic surfaces were as-received aluminium plates, the hydrophobic surfaces were silane-functionalised smooth silicon wafers, and the superhydrophobic surfaces were nanostructured and silane-functionalised silicon wafers. Ice formed on the hydrophilic surfaces in a few seconds, while the hydrophobic surfaces showed an approximate 1 min delay in icing at −10 °C. Furthermore, the nanostructured superhydrophobic surfaces showed no ice accreditation over a period of approximately 30 min, and similar results were obtained at the temperature range of −25~−35 °C. Eberle et al. ^[9][35] fabricated various hydrophilic and hydrophobic surfaces with different nanoscaled roughnesses from 0.17 nm to 176 nm (RMS), while some surfaces were of a plain grain structure, and some were of a hierarchical type. Various nanoscaled roughnesses were achieved by polishing aluminium with silicon oxide nanoparticles, followed by an etching process using cryogenic ICP (inductively coupled plasma). Furthermore, the hierarchical structures were achieved using photolithography ^[9][35]. The surfaces were rendered hydrophobic by depositing a perfluorochemical (PFC) monolayer on top of the etched or lithographed surfaces. It was demonstrated that the nanopits on the surface greatly reduced the ice nucleation rate and resisted heterogonous ice growth. The samples also exhibited long freezing delays, and a remarkable icing delay of approximately 25 h was observed on ultrafine (R_a ≈ 0.17 nm) hydrophobic surfaces with hierarchical structures. These freezing delays are some of the longest reported in anti-icing research to date ^[9][35].