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 Δ
G is higher than that of heterogeneous nucleation
[7][102]. The theory suggests that the critical size
𝑟𝑐 must be reached for the formation of stable ice nuclei at a given temperature, which can be calculated using Equation (1)
[7][102]:
where
Δ𝐺𝑓,𝑣 is the volumetric free energies between water–ice interfaces per unit volume, and
𝛾𝐼𝑊 is the interfacial water–ice energy. At a temperature of −25 °C, the critical size of ice nuclei was determined experimentally to be
rc ≈ 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]:
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].