# Correlation between surface morphology, superhydrophobicity, and icephobic behavior: a principal component analysis study

Louise Burdin, Anne-Catherine Brulez, Radoslaw Mazurczyk, Jean-Louis

Leclercq, Stéphane Benayoun

► To cite this version:

Louise Burdin, Anne-Catherine Brulez, Radoslaw Mazurczyk, Jean-Louis Leclercq, Stéphane Benayoun. Correlation between surface morphology, superhydrophobicity, and icephobic behavior: a principal component analysis study. Results in Surfaces and Interfaces, 2025, 21, pp.100642. 10.1016/j.rsurfi.2025.100642. hal-05350528

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# Correlation between surface morphology, superhydrophobicity, and icephobic behavior: a principal component analysis study

Louise Burdin<sup>a, *, b</sup>, Anne-Catherine Brulez<sup>a, b</sup>, Radosław Mazurczyk<sup>c</sup>, Jean-Louis Leclercq<sup>c</sup>, Stéphane Benayoun<sup>a</sup>

## ARTICLE INFO

Keywords:

Wetting

Superhydrophobic surfaces

PCA

Icephobic

Ice adhesion strength

## ABSTRACT

This study aimed to investigate the relationships between topographical parameters, wetting properties, and the icephobic behavior of textured surfaces. Principal component analysis (PCA) of the wetting data revealed a strong correlation between the slope of the patterns and the contact angle. However, because wetting states are not always reported with sufficient explanation, they were determined using the Extran model. In some cases, discrepancies with experimental results were observed, likely due to metastable states caused by droplet pinning on micro-roughness. A separate PCA on icing delay time (IDT) data indicated a correlation between slope, contact angle, and IDT, without requiring prior knowledge of the wetting state. In contrast, PCA on ice adhesion data revealed no clear correlation, highlighting a lack of standardization in the field that hinders comparisons. To refine the results, another PCA was conducted using the Extran-model-predicted wetting states, emphasizing the importance of accurately identifying the wetting regime to understand surface behavior. Given the challenges in correlating adhesion measurements, IDT emerges as a more relevant and accessible initial metric for evaluating icephobic properties. Finally, pattern slope appears to be a key topographical parameter. While other parameters showed no direct correlations, appropriate feature height and limited spacing are still critical to prevent complete droplet penetration.

## 1. Introduction

Ice accretion on exposed equipment, such as electrical wires [1], wind turbine blades [2], and even aircraft wings [3], in low temperature environments poses significant safety, efficiency, and operation cost challenges. For example, the crash of Flight 447 in 2009, which resulted in 228 fatalities, along with other incidents caused by the icing of pitot tubes [4], underscores the risks associated with ice formation. Active methods commonly employed to minimize ice formation and accretion. In aircraft icephobic systems, for instance, hot air is generated by converting electrical energy into thermal energy using heating resistors. The heated airflow is then directed to specific areas to remove accumulated ice. Chemical treatments [5] are another active strategy used to reduce ice formation and adhesion. However, these approaches are often expensive, energy-intensive, and potentially harmful to the environment. Consequently, there is a growing interest in passive strategies. Among such strategies are the use of superhydrophobic surfaces, which

have attracted attention owing to their ability to delay ice formation and reduce ice adhesion, making them promising candidates for icephobic applications [6–8]. The performance of such surfaces is strongly linked to the wetting behavior of water droplets, which can be described using classical models. In the Wenzel model [9], a liquid droplet fully penetrates asperities on rough surfaces, as illustrated in Fig. 1a. From interfacial energy considerations, the equilibrium contact angle $\theta_W$ can be determined using Eq. (1):

$$ \cos \theta_W = r_W \cos \theta_Y \qquad (1) $$

where $r_W$ is the ratio of the actual solid-liquid interface area to its projection on a flat surface, and $\theta_Y$ is the equilibrium contact angle on the corresponding flat surface.

In the Cassie-Baxter model [10], the liquid droplet resets on top of the surface asperities, as illustrated in Fig. 1b. In this case the equilibrium contact angle $\theta_{CB}$ is given by

<footnote><sup>a</sup> Ecole Centrale de Lyon, CNRS, ENTPE, LTDS, UMR5513, Ecully, 69130, France</footnote>

<footnote><sup>b</sup> ITECH, Ecully, 69130, France</footnote>

<footnote><sup>c</sup> Univ Lyon, CNRS, INSA Lyon, Ecole Centrale de Lyon, Université Claude Bernard Lyon 1, CPE Lyon, INL, UMR5270, Ecully, 69130, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: louise.burdin@ec-lyon.fr (L. Burdin).</footnote>
$$ \cos \theta_{CB} = -1 + \phi_s(\cos \theta_{Y+1}) \quad (2) $$

where $\phi_s$ is the area fraction of the solid-liquid interface.

Understanding these wetting states is critical for designing surfaces with enhanced icephobic performance, as they directly affect droplet mobility, icing delay time (IDT), and ice adhesion.

In studies of wetting behavior, superhydrophobicity is typically defined as a state in which the apparent contact angle exceeds 150° [11]. Here, $\Delta\theta$ is the difference between the advancing contact angle ($\theta_a$) and the receding contact angle ($\theta_r$), as illustrated in Fig. 1c.

The Cassie-Baxter state is particularly desirable because its low $\Delta H$ leads to optimal roll-off properties, making it a common target in the design of superhydrophobic surfaces. Nevertheless, transitions between the Cassie-Baxter and Wenzel states can occur under various conditions, including applied pressure, vibration, heating, surfaces geometry, or chemical properties, as investigated by Quéré et al. [12]. According to Callies et al. [13], droplets remain stable only when the solid fraction of textured surfaces is between 3 % and 8 %. Based on these observations and the Extrand model [14], it is possible to determine the optimal geometric parameters of designing surfaces that maintain a Cassie-Baxter state. The Extrand model predicts whether a liquid will remain suspended on the asperities of a surface (Cassie-Baxter state) or penetrate them (Wenzel state).

This model introduces two key parameters.

* Contact line density $\Lambda$: defined as the product of the asperity area density ($\delta$) and the asperity perimeter ($p$).

$$ \Lambda = p\delta \quad (3) $$

For a regular array of square pillars, as illustrated in Fig. 2, $\Lambda$ is given by:

$$ \Lambda = \frac{4D}{p^2} \quad (4) $$

where $D$ is the pillar diameter, and $P$ is the period between pillars (Fig. 2).

For circular pillars, $\Lambda$ can be expressed as follows:

$$ \Lambda = \frac{\pi D}{p^2} \quad (5) $$

* Critical contact line density ($\Lambda_c$): determined using the following equation:

$$ \Lambda_c = \frac{-\rho g V^{1/3} \left( \tan \frac{\theta_a}{2} \left( 3 + \left( \tan \frac{\theta_a}{2} \right)^2 \right) \right)^{2/3}}{\left( \left( 36 \pi \right)^{1/3} \gamma \cos \left( \theta_{a,0} + \omega - 90 \right) \right)} \quad (6) $$

where $\rho$ is the liquid density, $g$ is the gravitational constant, $V$ is the droplet volume, $\omega$ is the slope of the pattern (as depicted in Fig. 2), $\gamma$ is the surface tension, $\theta_a$ is the advancing contact angle on a textured surface and $\theta_{a,0}$ is the advancing contact angle on a smooth surface.

<figure><img src="image_2.png" /><figcaption>Fig. 2. Side-view schematic of square pillar textures.</figcaption></figure>

If $\Lambda > \Lambda_c > 0$, the first criterion is satisfied, and the liquid droplet remains suspended above the surface texture, following the Cassie-Baxter wetting state. Conversely, if $\Lambda_c < 0$ or $\Lambda < \Lambda_c$, the system conforms to the Wenzel model.

However, Extrand’s first condition is necessary but not sufficient. The droplet meniscus between adjacent asperities must also be shorter than the texture height to maintain the Cassie-Baxter state. This leads to the second condition is $z > z_c$, where $z_c$ is the meniscus height, defined as follows:

$$ z_c = b \tan \left( \frac{\theta_{a,0} + \omega - 180}{2} \right) \quad (7) $$

Here, $2b$ represents the maximum distance between two adjacent pillars. For regular array of square pillars, $2b$ corresponds to the diagonal of the pillar network and is given by:

$$ 2b = \sqrt{2(P - D)} \quad (8) $$

Nevertheless, the literature remains divided on whether superhydrophobic surfaces consistently confer icephobic properties. These disparities are largely due to the lack of a standardized method for characterizing the icephobic performance of a surface. For instance, some studies have employed centrifuge-based apparatus to measure ice adhesion, while others have developed systems that push ice particles onto a surface using a force sensor positioned parallel to the ice-substrate interface, thereby measuring the force required to detach ice. Additionally, variations in the definition of ice adhesion varies across research groups further complicates comparisons.

In this study, principal component analysis (PCA) and the Extrand model are used to enhance understanding of the relationship between superhydrophobicity and icephobic performance. This study represents one of the first attempts to apply multivariate statistical analysis, specifically PCA, to systematically investigate correlations between surface topography, wetting properties, and icephobic performance. By doing so, it provides a structured framework to interpret heterogeneous datasets in the field, addressing the current fragmentation of studies on superhydrophobic icephobic surfaces and enabling more generalizable insights.

To this end, an initial PCA is conducted on surface topographical parameters and wetting properties. Icephobic behavior is then characterized using two approaches: IDT and ice adhesion strength. Separate

<figure><img src="image_3.png" /><figcaption>Fig. 1. Schematic representation of the Wenzel state (a), the Cassie-Baxter state (b), and the advancing and receding contact angle (c). A droplet is deposited on a solid substrate inclined at an angle $\alpha$.</figcaption></figure>
PCAs are performed for each method to elucidate the correlations between surface topography, wetting characteristics, and icephobic performance.

In this study, all PCAs are performed on textured surfaces composed of cylindrical or square pillars, as these structures can be readily fabricated using techniques such as laser texturing, injection molding, or photolithography. These patterns also allow for the quantification of wetting effects using theoretical models, such as the Extrand model, facilitating comparison across studies. Part of the dataset was compiled from the literature; however, due to an insufficient and number of samples, additional data was obtained experimentally. Few publications focus on the icephobic properties of textured pillar surfaces, and when they do, key information is often incomplete, complicating PCA analysis. A *Scopus* search comparing the number of studies on 'wetting micropillars' versus 'anti-icing micropillars' confirms this disparity (222 vs. 19 in March 2025). Moreover, Fig. 3 illustrates the number of studies published on these topics over the past five years, further highlighting the limited research addressing the icephobic properties of textured pillar surfaces.

Consequently, this paper also provides a critical analysis of studies on the characterization of icephobic properties, emphasizing the essential information that research on icephobic surfaces should include to be considered relevant and reliable.

## 2. Materials and methods

### 2.1. Dataset collection

**Wettability dataset** – Surface wettability has been extensively studied in the literature. As noted above, this study focuses specifically on textured pillars, either circular or square. From seven publications [15–21], 34 individual surfaces were extracted, and the key variables were recorded: pillar diameter (D), pillar height (z), pillar spacing (S), and pillar slope (ω), as illustrated in Fig. 2. Each of these variables was then correlated with the corresponding apparent contact angle (θ<sub>app</sub>) (see Appendix A). To expand this dataset, nine textured surfaces were fabricating by combining ultraviolet (UV) lithography, inductively coupled plasma (ICP) etching, and poly(dimethylsiloxane) (PDMS) replication. Among the various fabrication techniques available for producing nano- or micropatterned surfaces, these methods are widely used and relatively simple to reproduce.

**IDT dataset** – Eight individuals from four publications [22–25] were collected. As noted earlier, these represented textured surfaces with

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Number of studies on 'wetting micropillars' and 'anti-icing micropillars' published over the past five years, based on a *Scopus* search.</figcaption></figure>

square or circular pillars on which the IDT was measured. The recorded parameters included *D*, *z*, *S*, *ω*, θ<sub>app</sub>, and the IDT ratio. Because each research group employed different experimental conditions, the IDT ratio, defined as the ratio between the IDT on a textured surface and that on a smooth surface, was used to facilitate comparison across studies. However, for the purpose of a statistical study, the number of individuals from literature was insufficient to reliably identify correlations between surface morphology and superhydrophobic or iceohobic behavior. To address this limitation, 24 additional textured surfaces were fabricated using UV lithography (see Appendix B).

**Ice adhesion dataset** – This dataset comprises 20 individuals collected from five publications [21,25–28]. In these studies, ice adhesion on pillar-textured surfaces was measured by vertically pushing ice samples off the substrates. The recorded variables included *D*, *z*, *S*, *ω*, θ<sub>app</sub>, the adhesion reducing factor (ARF) [28], Δθ, and 1 + cos θ<sub>r</sub>. The ARF is defined as the ratio of ice adhesion on a smooth surface to that on a textured surface. Similar to IDT, no universal method exists for measuring ice adhesion, making this parameter valuable for comparing results across different studies. Furthermore, some research has shown that ice adhesion correlates linearly with Δθ and 1 + cos θ<sub>r</sub> [29,30]. One objective of this PCA analysis is to investigate whether these correlations are also observed in the current dataset.

### 2.2. Sample preparation

**Development of silicon molds** – As mentioned earlier, nine textured surfaces were experimentally fabricated by using PDMS replication to complete the dataset. The molds for replication were produced via standard UV photolithography and etching. A 1-µm-thick layer of silicon oxide was deposited on 4" silicon wafers using a plasma-enhanced chemical vapor deposition system. Subsequently, an approximately 1-µm-thick layer of AZ5214E photoresist (AZ Electronic Materials, Luxembourg, Luxembourg) was spin-coated onto the wafer, exposed, and developed in AZ 726 MIF (AZ Electronic Materials, Luxembourg, Luxembourg) following a classical positive procedure. The substrates were then etched using an ICP system (SI500, SENTENCH Instruments GmbH, Berlin, Germany) in two steps, as summarized in Table 1: first, the photoresist/SiO<sub>2</sub> mask pattern was transferred, and second, Cl<sub>2</sub>/O<sub>2</sub> deep etching of the silicon substrate was performed.

**PDMS replication** – Following the etching process, which included pattern transfer, photoresist mask removal, and surface cleaning, silicon wafers featuring circular holes of varying sizes were obtained and used to fabricate PDMS replica (all topographical parameters of the samples are listed in Appendix A). To facilitate demolding, a silanization step was first performed on the silicon molds. PDMS (Sylgard 184, Dow Corning Corporation, Midland, MI, USA) was mixed with a curing agent in a 10:1 ratio for 10 min at 1000 rpm. The mixture was then poured onto the prepared silicon wafers and placed in a vacuum chamber for 4 h to ensure optimal impregnation of PDMS into the textured surfaces. After two curing steps (24 h at 25 °C followed by 1.5 h at 80 °C), the PDMS replicas were demolded [31].

**Texturization of silicon wafer** – The samples for the IDT dataset were prepared using the same method employed for fabricating the silicon molds. In this case, a reversal procedure was performed to produce 12 silicon samples with circular plots of varying *D*, *z*, *S* and *ω*, rather than circular holes. This protocol was repeated once, and a fluorocarbon film was subsequently deposited onto the 12 samples via reactive-ion etching using CHF<sub>3</sub> plasma. The CHF<sub>3</sub> layer altered the surface chemistry, enabling the modification of the wetting properties of the textured silicon samples.

### 2.3. Characterization of topography, wettability, and IDT for experimentally obtained samples

The morphologies of the textured surfaces were characterized using a profilometer (Everest-K1, STIL, Aix-en-Provence, France) and an
<table><caption>**Table 1**
Etching parameters.</caption><thead><tr><th></th><th>ICP power (W)</th><th>RF power (W)</th><th>Pressure (Pa)</th><th>Ar flow (sccm)</th><th>CHF<sub>3</sub> flow (sccm)</th><th>H<sub>2</sub> flow (sccm)</th><th>Cl<sub>2</sub> flow (sccm)</th><th>O<sub>2</sub> flow (sccm)</th></tr></thead><tbody><tr><td>First etching</td><td>300</td><td>120</td><td>0.29</td><td>30</td><td>9</td><td>4</td><td>-</td><td>-</td></tr><tr><td>Second etching</td><td>100</td><td>143</td><td>0.29</td><td>-</td><td>-</td><td>-</td><td>22</td><td>4</td></tr></tbody></table>

interferometer (GT-K1, Bruker, Billerica, MA, USA). The resulting topographies of each texture were analyzed with MountainsMap software (version April 7, 8076, Digital Surf, Besançon, France) [32]. Surface wettability was assessed using a goniometer (DSA 30, Kruss, Hamburg, Germany). For each measurement, 3 µL of distilled water was gently deposited onto the surface, and the contact angle was determined using Drop Shape Analysis software (version 1.92.1.1, Kruss, Hamburg, Germany) with the tangent-2 method [33]. To ensure repeatability, measurements were performed three times for each sample.

Advancing contact angles were measured using the injection/absorption (sessile drop) method [34]. A 3 µL droplet of distilled water was gently deposited on the surface, and the needle was brought into contact with the top of the droplet. An additional 7 µL of water was then injected while monitoring the droplet's base diameter. The advancing contact angle was recorded when the base diameter began to increase. As with other measurements, three repetitions were performed to ensure repeatability.

The IDT of each sample was measured using homemade equipment. Each sample was placed on a cooling plate maintained at -20 °C, and a 5 µL droplet of distilled water was gently deposited on the surface. The droplet temperature was measured using an infrared camera (Xi 80, Optris, Berlin, Germany) until complete freezing occurred.

## 2.4. Principal component analysis

Visualizing multidimensional data becomes challenging when dealing with more than three variables. As noted earlier, the dataset in this study includes four topographical parameters along with the associated apparent contact angles. PCA [35] is therefore employed to identify potential correlations between each parameter and the contact angle. PCA is a multivariate statistical technique that reduces the dimensionality of a large set of potentially correlated variables while minimizing information. By simplifying the dataset in this way, the analysis becomes more manageable. The principal components (PCs) are derived from linear combinations of the original variables.

The correlation between each variable and the principal components can be interpreted using a correlation circle with a radius of one unit. Each vector in the circle represents a variable, and the closer a vector's tip is to the circumference, the stronger the correlation between the variables and the PCs. The correlation circle also allows for assessment of relationships between variables.

* If the angle between two vectors is small, the variables are positively correlated - when one increases, the other tends to increase as well.

* If the vectors form an angle of 180°, the variables are negatively correlated - when one increases, the other decreases.

* If the vectors are orthogonal, the variables are uncorrelated, indicating no linear relationship between them.

The objective of this analysis is to identify the PCs that most effectively represent the dataset.

## 2.5. Dataset centering and scaling

Large dataset often contain heterogeneous individuals, which was particularly evident for some of the studied variables, such as pillar diameter or spacing. To ensure that each variable contributed equally to the analysis the dataset was standardized prior to performing PCA.

PCA was carried out using R software (version 4.2.2, R Core Team,

Vienna, Austria) [36], specifically the *FactoMineR* package. This function automatically centers each variable and scales it to unit variance (Z-scoring), ensuring that variables with larger numeric scales do not dominate the analysis. The PCA output provided detailed information for each PC, including eigenvalues, variance, and cumulative variance (Table 2). Eigenvalues indicate the amount of variance explained by each PC, variance measures the information captured by a PC, and cumulative variance represents the total variance explained by multiple PCs considered together. PC with eigenvalues greater than one were extracted [37], as they explain more variance than an individual original variable. Factor loadings were also calculated to evaluate the contribution of each variable to the PCs. According to Hair et al., [38] for sample sizes between 60 and 70, factor loadings of 0.70 or higher are considered significant.

# 3. Results and discussion

## 3.1. PCA of the wettability dataset

The graphs in Fig. 4 illustrate the dispersion of each variable. Due to the diverse nature of the samples and the different experimental methods used, the dataset exhibited substantial heterogeneity.

The PCA produced two PC with eigenvalues greater than 1, which together account for 81.39 % of the total variability in the dataset. Although there is no universal criterion for determining the number of dimensions to retain, the first two PCs were selected to provide a clear and informative representation of the data. Factor loadings for each variable corresponding to these PCs are presented in Table 3. The first PC (PC1) exhibits the highest positive loading for pillar diameter (0.96), and a negative loading for apparent contact angle (-0.07). The second PC (PC2) shows the highest positive loading for pillar slope (0.87), and a negative loading for pillar period (-0.37). The correlation circle for this PCA is shown in Fig. 5.

Furthermore, as shown in the correlation circle (Fig. 5), the arrowheads lie close to the circumference, indicating that the variables are well represented by the PCA.

The PCA results reveal a strong correlation between $\theta_{app}$ and $\omega$. As the arrowheads for these two variables nearly overlap in the correlation circle, it can be inferred that larger slopes correspond to higher apparent contact angles. This findings align with studies indicating that surfaces with re-entrant textures are effective in achieving and maintaining a superhydrophobic state [19,39]. However, depending on the fabrication technique, creating textures with slopes greater than 90° may be impractical. For instance, in injection molding, slopes exceeding 90° prevent demolding, making such designs unfeasible.

Despite these insights, this PCA does not reflect the influence of pillar height, diameter, or period on the apparent contact angle. Furthermore, the analysis does not account for the wetting state of the surfaces. As

<table><caption>**Table 2**
Eigenvalues, explained variances, and cumulative variances for each principal components, corresponding to dimensions used to represent the dataset.</caption><thead><tr><th>Dimension</th><th>Eigenvalue</th><th>Variance (%)</th><th>Cumulative Variance (%)</th></tr></thead><tbody><tr><td>Dim. 1</td><td>2.25</td><td>45.03</td><td>45.03</td></tr><tr><td>Dim. 2</td><td>1.81</td><td>36.36</td><td>81.39</td></tr><tr><td>Dim. 3</td><td>0.48</td><td>9.66</td><td>91.06</td></tr><tr><td>Dim. 4</td><td>0.41</td><td>8.20</td><td>99.26</td></tr><tr><td>Dim. 5</td><td>0.04</td><td>0.74</td><td>100.00</td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Dispersion of the studied variables: N sample number, D pillar diameter, H pillar height, P pillar period, ω pattern slope, and θ<sub>app</sub> apparent contact angle. Light blue indicates the wettability dataset, while dark blue represents the icephobic dataset (IDT and adhesion).</figcaption></figure>

<table><caption>**Table 3**

Factor loadings of each variable on the first (PC1) and second (PC2) principal components from PCA.</caption><thead><tr><th>Variable</th><th>PC1</th><th>PC2</th></tr></thead><tbody><tr><td>D</td><td>0.96</td><td>0.06</td></tr><tr><td>H</td><td>0.73</td><td>0.43</td></tr><tr><td>P</td><td>0.88</td><td>-0.37</td></tr><tr><td>◆</td><td>0.10</td><td>0.87</td></tr><tr><td>θ<sub>app</sub></td><td>-0.07</td><td>0.85</td></tr><tr><td>Eigenvalue</td><td>2.25</td><td>1.82</td></tr><tr><td>Variance percent (%)</td><td>45.03</td><td>36.36</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Correlation circle of the PCA for the wettability dataset.</figcaption></figure>

shown in Table 4, the studies from which the data were drawn do not use a model to justify the wetting state and rely solely on measured contact angles. However, droplets are not always in an ideal wetting state and may exist in a metastable configuration. Therefore, accurately determining the wetting state is essential for proper characterization of surface properties.

To address this, models such as the one proposed by Extrand can be employed to determine the wetting state. Accordingly, Λ and Λ<sub>c</sub> were calculated for each sample to identify the wetting state and compute the corresponding contact angle, θ<sub>CB</sub> or θ<sub>w</sub>. This procedure first requires calculating the Cassie-Baxter and Wenzel model parameters, φ<sub>s</sub> and r<sub>w</sub>, using the following equations:

$$ \phi_s = \frac{\pi \left(\frac{D}{2}\right)^2}{P^2} \qquad (9) $$

$$ r_w = \frac{P^2 + \frac{\pi \text{HD}}{\sin \omega} (1 - \cos \omega) + \frac{\pi \text{H}^2}{\sin \omega \tan \omega} (1 - \cos \omega)}{P^2} \qquad (10) $$

where φ<sub>s</sub> represents the solid fraction and r<sub>w</sub> denotes the surface roughness.

These parameters were calculated using the geometrical data obtained either from the literature or experimentally. For each sample, the corresponding θ<sub>CB</sub> or θ<sub>w</sub> was determined based on the Extrand model predictions. This approach resulted in two populations: samples in the

<table><caption>**Table 4**

Summary of the wettability dataset information on surface wetting states and the use of models for their determination (✓: information provided; x: information not provided).</caption><thead><tr><th>Reference</th><th>Wetting state</th><th>Model used</th></tr></thead><tbody><tr><td>[15]</td><td>✓</td><td>Extrand model</td></tr><tr><td>[16]</td><td>✓</td><td>x</td></tr><tr><td>[17]</td><td>✓</td><td>Surface Evolver modeling</td></tr><tr><td>[18]</td><td>✓</td><td>x</td></tr><tr><td>[19]</td><td>✓</td><td>x</td></tr><tr><td>[20]</td><td>✓</td><td>x</td></tr><tr><td>[21]</td><td>✓</td><td>Sag criterion</td></tr></tbody></table>
Cassie-Baxter state and those in the Wenzel state. For each population, the calculated $\theta_{CB}$ or $\theta_{W}$ was then compared with the apparent contact angle reported in the literature or measured experimentally (Fig. 6).

Fig. 6 compares the contact angles obtained experimentally with those predicted by the Extrand model for both wetting states. For the Wenzel state, the relative deviation between predicted and experimental contact angles ($|\frac{\theta_M - \theta_{Exp}}{\theta_{Exp}}|$), where $\theta_M$ is the Extrand-model-predicted contact angle and $\theta_{Exp}$ is experimentally measured one) ranges from 0 to 53 %. In contrast, for the Cassie-Baxter state, the relative deviation ranges from 1 to 8 %. As shown in Fig. 6, the Extrand model tends to underestimate contact angles in the Wenzel state, whereas it slightly overestimates them for the Cassie-Baxter state. This discrepancy can be attributed to the fact that the Extrand model assumes regular, truncated pillars and neglects the asperities on the tops and walls of the pillars. As illustrated in Fig. 7, some literature sample exhibit wavy walls. In such cases, water droplets can become pinned to these asperities, resulting in a metastable configuration. The droplet does not fully wet the surface asperities and therefore behaves more like a Cassie-Baxter state than a Wenzel state.

These findings are also reflected in the PCA conducted for the

Extrand-model-predicted wetting states (Fig. 8). For such cases in the Cassie-Baxter state, a positive correlation between $\omega$ and $\theta_{app}$ is expected, which is indeed observed in Fig. 8b. For surfaces in the Wenzel state, a decrease in $\omega$ reduces the roughness ($r_W$), so a positive correlation with the contact angle would also be anticipated. However, this trend is not evident in Fig. 8a. This discrepancy may be explained by the fact that the droplet is not truly in a Wenzel state and external factors such as pinning effects can influence the results. Therefore, accurately determining the wetting state is essential for fully understanding surface behavior. In this context, the Extrand model offers a relevant approach, provided that its predictions are carefully compared with experimental observations.

<figure><img src="image_7.png" /><figcaption>Fig. 7. Schematic illustration of a droplet pinned on a wavy-wall texture.</figcaption></figure>

## 3.2. PCA of the IDT dataset

As previously noted, icephobic properties can be characterized by measuring either the IDT or ice adhesion. Potential correlations between topographical parameters, wetting properties, and IDT were first investigated using the IDT dataset presented in Appendix B. A PCA was performed using the following parameters: P,D, $\omega$, and the IDT ratio. The resulting correlation circle is shown in Fig. 9. The arrowheads lie close to the circumference, indicating that the variables are well represented by this PCA. The analysis revealed, a positive correlation between $\theta_{app}$ and $\omega$. Consequently, if superhydrophobic surfaces delay freezing, $\omega$ is expected to correlate positively with the IDT ratio. This expectation is confirmed by the correlation circle in Fig. 9, which shows that indeed both $\theta_{app}$ and the IDT ratio are positively correlated with $\omega$. In other words, higher contact angles correspond to longer IDTs, supporting the use of superhydrophobic surfaces to delay ice formation. Although this PCA does not explicitly account for the wetting state, it is likely, as previously discussed, that droplets become pinned to micro-roughness and reside in a metastable configuration that is closer to the Cassie-Baxter state than the Wenzel state. This behavior may explain why a positive correlation is still observed.

However, the PCA did not reveal correlations with other topographical parameters. Nevertheless, appropriate dimensions remain crucial for achieving icephobic behavior. Nguyen et al. [25] demonstrated that textured surfaces with nanopillars having a very small top diameter (30–90 nm) can maintain a metastable Cassie-Baxter state and delay freezing. A small top diameter also reduces the contact area between the droplet and the substrate. Another key parameter is the spacing between pillars. Studies by Mouterde et al. [40] and Zhang et al. [41] indicate that the pillar spacing should be minimized to prevent droplet penetration. If the distance between pillars is too large, the droplet’s weight can force it into asperities, increasing the contact area

<figure><img src="image_8.png" /><figcaption>Fig. 6. Comparison of apparent contact angles obtained experimentally with those predicted using the Extrand model, following the Wenzel model (a) and the Cassie-Baxter model (b). N is the sample number; light blue indicates experimental contact angles ($\theta_{Exp}$) and dark blue represents contact angles predicted by the Extrand model ($\theta_M$)).</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 8. Correlation circles from PCA for surfaces predicted to be in a Wenzel wetting state (a) and a Cassie-Baxter wetting state (b).</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 9. Correlation circle from PCA conducted on the IDT dataset.</figcaption></figure>

and triggering a transition from the Cassie-Baxter state to the Wenzel state, thereby compromising icephobic performance. Finally, the pillar height must be sufficient so that the droplet meniscus does not reach the bottom of the texture.

### 3.3. PCA of the ice adhesion dataset

A new PCA was also performed on the ice adhesion dataset (Appendix C). As shown in Fig. 10, the variables are well-represented, with the arrows lying close to the circumference of the correlation circle. One might reasonably expect a positive correlation between the ARF and $\theta_{app}$, assuming that superhydrophobic surfaces reduce ice adhesion. However, this trend is not evident in Fig. 10, preventing any definitive conclusions about correlations among the variables. This finding is consistent with the conflicting reports in the literature regarding the effect of superhydrophobicity on ice adhesion. For example, Bharathidasan et al. [42] reported an ARF of 43.2 on a surface with a contact

<figure><img src="image_11.png" /><figcaption>Fig. 10. Correlation circle from PCA conducted on the ice adhesion dataset.</figcaption></figure>

angle of only 105°, whereas for a surface with a contact angle of 158°, the ARF decreased by a factor of 10. Conversely, Zou et al. [43] observed that ice adhesion increases with surface roughness, corresponding to higher contact angles.

The results shown in Fig. 10 also highlight the lack of a standardized procedure for characterizing of ice adhesion. As summarized in Table 5, each research group uses its own testing equipment and experimental conditions. Factors such as temperature, motor velocity, and water volume can significantly affect the wetting state and the actual contact area between ice and the substrate. Additionally, the quality of the water used to form ice samples must be considered, as impurities can influence the results. Consequently, differences in evaluation methods make it difficult to compare ice adhesion measurements across studies.

To explore potential correlations between ice adhesion and wetting properties, the PCA was refined by determining the wetting state of each sample using the Extrand model. A new PCA was performed using the parameters $\theta_{CB}$, $\theta_{W}$, $ARF_{CB}$, and $ARF_{W}$, with the corresponding correla-
<table><caption>**Table 5**
Experimental conditions used to measure ice adhesion in various studies (shaded boxes indicate information not specified) [21, 25–28].</caption><thead><tr><th>Reference</th><th>Temperature (°C)</th><th>Volume of water</th><th>Type of water</th><th>Waiting time for complete freezing</th><th>Velocity</th></tr></thead><tbody><tr><td>[24]</td><td>-15</td><td>1 mL</td><td></td><td>1 h</td><td>5 mm/s</td></tr><tr><td>[25]</td><td>-15</td><td>1 mL</td><td></td><td>5 h</td><td>0.5 mm/s</td></tr><tr><td>[19]</td><td>-10</td><td>10 µL</td><td></td><td>1-2 min</td><td>0.5 mm/s</td></tr><tr><td>[23]</td><td>-20</td><td>5 µL</td><td>Deionized water</td><td></td><td>50 µm/s</td></tr><tr><td>[26]</td><td>-15</td><td>2 mL</td><td>Reverse osmosis water</td><td>2 h</td><td>0.5 mm/s</td></tr></tbody></table>

tion circle shown in Fig. 11. If superhydrophobic surfaces effectively reduce ice adhesion, a positive correlation between $\theta_{CB}$ and $ARF_{CB}$ and a negative correlation between $\theta_{W}$ and $ARF_{W}$ would be expected. The results show a strong correlation between $\theta_{CB}$ and $ARF_{CB}$, whereas no correlation is observed between $\theta_{W}$ and $ARF_{W}$. As noted previously, this lack of correlation may be due to the droplet not being in a true Wenzel state, which could explain the observed discrepancy. These findings further emphasize the importance of accurately identifying the wetting state when analyzing surface icephobic properties.

## 4. Conclusion

This study focused on textured pillar surfaces, obtained both experimentally and from the literature, with the primary goal of understanding correlations between topographical parameters and surface wettability, and assessing whether these correlations extend to icephobic properties.

A first PCA on the wettability dataset revealed a strong correlation between $\omega$ and $\theta_{app}$. However, because this analysis did not account for the wetting states of the surfaces, the Extrand model was used to predict these states. The results showed that the predicted wetting states were not always consistent with experimental observations, as droplets can become pinned on micro-roughness, resulting in a metastable configuration rather than clearly defined Wenzel or Cassie-Baxter states.

A second PCA using the IDT dataset demonstrated a positive correlation between $\omega$, $\theta_{app}$, and the IDT ratio, without requiring prior knowledge of the wetting states. A third PCA was conducted on ice adhesion dataset, which initially revealed no clear correlations, highlighting the lack of standardization in ice adhesion testing and challenges in comparing results across studies. By incorporating wetting states predicted by the Extrand model, the analysis was refined. These findings emphasize the importance of accurately identifying the wetting state to fully understand surface-related properties. The Extrand model provides a useful tool for this purpose when key parameters ($D$, $H$, $P$, $\omega$, $\theta_{app}$, $\theta_{a}$, $\theta_{app,0}$, and $\theta_{a,0}$) are known. Moreover, due to the complexity of adhesion dataset, IDT measurements may serve as a more practical first indication of a surface's icephobic performance.

The PCA further highlighted slope as a critical topographical parameter for designing icephobic surfaces. However, slope should not be considered in isolation, as its effectiveness depends on its interplay with other geometric descriptors. For instance, while reducing the liquid-solid contact area is desirable, excessive pillar spacing can lead to full droplet impregnation, accelerating ice nucleation. Similarly, pillar height must be sufficient to prevent the droplet meniscus from reaching the bottom of the texture. These interactions underscore the need to balance multiple design parameters, rather than relying solely on slope.

Overall, these findings provide a systematic framework for guiding the design of superhydrophobic surfaces with enhanced icephobic performance. By linking surface topography and wettability to icephobic behavior, this study offers insights that can help standardize assessments and support the rational development of passive icephobic strategies for practical applications.

<figure><img src="image_12.png" /><figcaption>**Fig. 11.** Correlation circle from PCA incorporating the predicted wetting states of the surfaces.</figcaption></figure>

### CRediT authorship contribution statement

**Louise Burdin:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Anne-Catherine Brulez:** Writing – review & editing, Supervision, Resources, Project administration, Methodology, Funding acquisition, Conceptualization. **Radosław Mazurczyk:** Writing – review & editing, Supervision, Project administration, Methodology, Conceptualization. **Jean-Louis Leclercq:** Writing – review & editing, Supervision, Resources, Project administration, Funding acquisition, Conceptualization. **Stéphane Benayoun:** Writing – review & editing, Validation, Supervision, Resources, Project administration, Methodology, Funding acquisition, Conceptualization, Formal analysis.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

This project was carried out within the framework of TextuPol
project from the CNRS IngéLyse research federation (FR-CNRS 3411).

## Appendix A. Wettability dataset

<table><thead><tr><th>Reference</th><th>N</th><th>D (μm)</th><th>H (μm)</th><th>P (μm)</th><th>◆ (°)</th><th>θapp (°)</th><th>Λ (m-1)</th><th>Λc (m-1)</th><th>2b</th><th>zc (μm)</th><th>Predicted state</th><th>rw</th><th>φs</th><th>θW (°)</th><th>θCB (°)</th></tr></thead><tbody><tr><td>a</td><td>1</td><td>2,97</td><td>4,82</td><td>49</td><td>48</td><td>113</td><td>3886,10</td><td>-881,43</td><td>-</td><td>-</td><td>Wenzel</td><td>1,02</td><td>-</td><td>114</td><td>-</td></tr><tr><td>a</td><td>2</td><td>3,21</td><td>5,18</td><td>58,8</td><td>53</td><td>115</td><td>2916,76</td><td>-1403,35</td><td>-</td><td>-</td><td>Wenzel</td><td>1,02</td><td>-</td><td>114</td><td>-</td></tr><tr><td>a</td><td>3</td><td>3,11</td><td>5,3</td><td>73,4</td><td>49</td><td>115</td><td>1813,50</td><td>-1044,89</td><td>-</td><td>-</td><td>Wenzel</td><td>1,01</td><td>-</td><td>114</td><td>-</td></tr><tr><td>a</td><td>4</td><td>5,65</td><td>5,65</td><td>48,95</td><td>53</td><td>115</td><td>7407,86</td><td>-1565,59</td><td>-</td><td>-</td><td>Wenzel</td><td>1,04</td><td>-</td><td>115</td><td>-</td></tr><tr><td>a</td><td>5</td><td>5,39</td><td>3,91</td><td>59</td><td>55</td><td>115</td><td>4864,46</td><td>-2001,10</td><td>-</td><td>-</td><td>Wenzel</td><td>1,01</td><td>-</td><td>114</td><td>-</td></tr><tr><td>a</td><td>6</td><td>5,45</td><td>6,05</td><td>73,25</td><td>55</td><td>118</td><td>3191,03</td><td>-1989,66</td><td>-</td><td>-</td><td>Wenzel</td><td>1,02</td><td>-</td><td>114</td><td>-</td></tr><tr><td>a</td><td>7</td><td>9,45</td><td>5,03</td><td>49,07</td><td>43</td><td>117</td><td>12329,62</td><td>-682,77</td><td>-</td><td>-</td><td>Wenzel</td><td>1,04</td><td>-</td><td>115</td><td>-</td></tr><tr><td>a</td><td>8</td><td>11,4</td><td>6,25</td><td>59</td><td>50</td><td>118</td><td>10288,47</td><td>-1121,94</td><td>-</td><td>-</td><td>Wenzel</td><td>1,04</td><td>-</td><td>115</td><td>-</td></tr><tr><td>a</td><td>9</td><td>11,74</td><td>5,62</td><td>73,35</td><td>46</td><td>134</td><td>6855,16</td><td>-827,13</td><td>-</td><td>-</td><td>Wenzel</td><td>1,02</td><td>-</td><td>114</td><td>-</td></tr><tr><td>[15]</td><td>10</td><td>22,1</td><td>9,8</td><td>99,9</td><td>62</td><td>115</td><td>6956,83</td><td>-1277,00</td><td>-</td><td>-</td><td>Wenzel</td><td>1,05</td><td>-</td><td>95</td><td>-</td></tr><tr><td>[15]</td><td>11</td><td>19,9</td><td>10,1</td><td>100,5</td><td>59</td><td>112</td><td>6189,72</td><td>-1191,03</td><td>-</td><td>-</td><td>Wenzel</td><td>1,05</td><td>-</td><td>102</td><td>-</td></tr><tr><td>[15]</td><td>12</td><td>21,1</td><td>10</td><td>100,5</td><td>59</td><td>116</td><td>6562,97</td><td>-5483,81</td><td>-</td><td>-</td><td>Wenzel</td><td>1,05</td><td>-</td><td>113</td><td>-</td></tr><tr><td>[15]</td><td>13</td><td>19,4</td><td>15,1</td><td>100,3</td><td>63</td><td>129</td><td>6058,29</td><td>-2032,90</td><td>-</td><td>-</td><td>Wenzel</td><td>1,08</td><td>-</td><td>95</td><td>-</td></tr><tr><td>[15]</td><td>14</td><td>20,4</td><td>15,3</td><td>100,2</td><td>65</td><td>144</td><td>6383,29</td><td>-7314,26</td><td>-</td><td>-</td><td>Wenzel</td><td>1,08</td><td>-</td><td>102</td><td>-</td></tr><tr><td>[15]</td><td>15</td><td>18,2</td><td>16,9</td><td>100,4</td><td>65</td><td>131</td><td>5672,23</td><td>-1682,97</td><td>-</td><td>-</td><td>Wenzel</td><td>1,09</td><td>-</td><td>95</td><td>-</td></tr><tr><td>[15]</td><td>16</td><td>17,6</td><td>17,6</td><td>100,4</td><td>68</td><td>142</td><td>5485,23</td><td>-23850,29</td><td>-</td><td>-</td><td>Wenzel</td><td>1,09</td><td>-</td><td>102</td><td>-</td></tr><tr><td>[16]</td><td>17</td><td>25</td><td>75</td><td>50</td><td>90</td><td>149</td><td>31415,93</td><td>21190,50</td><td>45,71</td><td>1,68</td><td>Cassie-Baxter</td><td>-</td><td>0,20</td><td>-</td><td>144</td></tr><tr><td>[16]</td><td>18</td><td>25</td><td>75</td><td>62,5</td><td>90</td><td>154</td><td>20106,19</td><td>21190,50</td><td>-</td><td>-</td><td>Wenzel</td><td>2,51</td><td>-</td><td>97</td><td>-</td></tr><tr><td>[16]</td><td>19</td><td>25</td><td>75</td><td>75</td><td>90</td><td>158</td><td>13962,63</td><td>21190,50</td><td>-</td><td>-</td><td>Wenzel</td><td>2,05</td><td>-</td><td>96</td><td>-</td></tr><tr><td>[17]</td><td>20</td><td>5</td><td>3</td><td>15</td><td>90</td><td>160</td><td>69813,17</td><td>1448,02</td><td>16,21</td><td>2,68</td><td>Cassie-Baxter</td><td>-</td><td>0,09</td><td>-</td><td>162</td></tr><tr><td>[17]</td><td>21</td><td>1</td><td>3</td><td>3</td><td>90</td><td>160</td><td>349065,85</td><td>1406,21</td><td>3,24</td><td>0,54</td><td>Cassie-Baxter</td><td>-</td><td>0,09</td><td>-</td><td>162</td></tr><tr><td>[17]</td><td>22</td><td>3</td><td>7</td><td>12</td><td>90</td><td>161</td><td>65449,85</td><td>1649,79</td><td>13,97</td><td>2,31</td><td>Cassie-Baxter</td><td>-</td><td>0,05</td><td>-</td><td>167</td></tr><tr><td>[17]</td><td>23</td><td>3</td><td>3</td><td>12</td><td>90</td><td>161</td><td>65449,85</td><td>1366,29</td><td>13,97</td><td>2,31</td><td>Cassie-Baxter</td><td>-</td><td>0,05</td><td>-</td><td>167</td></tr><tr><td>[17]</td><td>24</td><td>3</td><td>1,5</td><td>12</td><td>90</td><td>162</td><td>65449,85</td><td>1426,87</td><td>13,97</td><td>2,31</td><td>Cassie-Baxter</td><td>-</td><td>0,05</td><td>-</td><td>167</td></tr><tr><td>[17]</td><td>25</td><td>3</td><td>1,1</td><td>12</td><td>90</td><td>160</td><td>65449,85</td><td>1469,67</td><td>13,97</td><td>2,31</td><td>Cassie-Baxter</td><td>-</td><td>0,05</td><td>-</td><td>167</td></tr><tr><td>[18]</td><td>26</td><td>3</td><td>7,2</td><td>4,5</td><td>90</td><td>149</td><td>465421,13</td><td>2300,73</td><td>3,36</td><td>0,56</td><td>Cassie-Baxter</td><td>-</td><td>0,35</td><td>-</td><td>144</td></tr><tr><td>[18]</td><td>27</td><td>3</td><td>7</td><td>6</td><td>90</td><td>156</td><td>261799,39</td><td>2619,31</td><td>5,49</td><td>0,91</td><td>Cassie-Baxter</td><td>-</td><td>0,20</td><td>-</td><td>153</td></tr><tr><td>[18]</td><td>28</td><td>3</td><td>7</td><td>9</td><td>90</td><td>154</td><td>116355,28</td><td>2278,75</td><td>9,73</td><td>1,61</td><td>Cassie-Baxter</td><td>-</td><td>0,09</td><td>-</td><td>162</td></tr><tr><td>[18]</td><td>29</td><td>3</td><td>7</td><td>12</td><td>90</td><td>156</td><td>65449,85</td><td>2489,11</td><td>13,97</td><td>2,31</td><td>Cassie-Baxter</td><td>-</td><td>0,05</td><td>-</td><td>167</td></tr><tr><td>[19]</td><td>30</td><td>2,7</td><td>7</td><td>6</td><td>90</td><td>157</td><td>235619,45</td><td>3335,72</td><td>5,79</td><td>0,69</td><td>Cassie-Baxter</td><td>-</td><td>0,16</td><td>-</td><td>153</td></tr><tr><td>[19]</td><td>31</td><td>2,7</td><td>7</td><td>6</td><td>90</td><td>152</td><td>235619,45</td><td>1513,56</td><td>5,79</td><td>1,84</td><td>Cassie-Baxter</td><td>-</td><td>0,16</td><td>-</td><td>164</td></tr><tr><td>[19]</td><td>32</td><td>2,7</td><td>7</td><td>6</td><td>90</td><td>156</td><td>235619,45</td><td>3454,57</td><td>5,79</td><td>0,67</td><td>Cassie-Baxter</td><td>-</td><td>0,16</td><td>-</td><td>153</td></tr><tr><td>[19]</td><td>33</td><td>2,6</td><td>9</td><td>6</td><td>90</td><td>152</td><td>226892,80</td><td>3835,62</td><td>5,89</td><td>0,68</td><td>Cassie-Baxter</td><td>-</td><td>0,15</td><td>-</td><td>154</td></tr><tr><td>[19]</td><td>34</td><td>3</td><td>5</td><td>6</td><td>90</td><td>151</td><td>261799,39</td><td>3129,20</td><td>5,49</td><td>0,63</td><td>Cassie-Baxter</td><td>-</td><td>0,20</td><td>-</td><td>149</td></tr><tr><td>[20]</td><td>35</td><td>42</td><td>33</td><td>105</td><td>90</td><td>152</td><td>11967,97</td><td>20481,56</td><td>-</td><td>-</td><td>Wenzel</td><td>1,39</td><td>-</td><td>94</td><td>-</td></tr><tr><td>[20]</td><td>36</td><td>42</td><td>33</td><td>132</td><td>90</td><td>161</td><td>7572,71</td><td>9573,74</td><td>-</td><td>-</td><td>Wenzel</td><td>1,25</td><td>-</td><td>94</td><td>-</td></tr><tr><td>[20]</td><td>37</td><td>42</td><td>33</td><td>147</td><td>90</td><td>160</td><td>6106,11</td><td>22760,79</td><td>-</td><td>-</td><td>Wenzel</td><td>1,20</td><td>-</td><td>93</td><td>-</td></tr><tr><td>[20]</td><td>38</td><td>42</td><td>33</td><td>162</td><td>90</td><td>157</td><td>5027,70</td><td>17079,87</td><td>-</td><td>-</td><td>Wenzel</td><td>1,17</td><td>-</td><td>93</td><td>-</td></tr><tr><td>[21]</td><td>39</td><td>20</td><td>10</td><td>40</td><td>90</td><td>112</td><td>39269,91</td><td>-603,11</td><td>-</td><td>-</td><td>Wenzel</td><td>1,39</td><td>-</td><td>53</td><td>-</td></tr><tr><td>[21]</td><td>40</td><td>20</td><td>10</td><td>50</td><td>90</td><td>103</td><td>25132,74</td><td>-519,48</td><td>-</td><td>-</td><td>Wenzel</td><td>1,25</td><td>-</td><td>57</td><td>-</td></tr><tr><td>[21]</td><td>41</td><td>20</td><td>10</td><td>60</td><td>90</td><td>98</td><td>17453,29</td><td>-470,24</td><td>-</td><td>-</td><td>Wenzel</td><td>1,17</td><td>-</td><td>59</td><td>-</td></tr><tr><td>[21]</td><td>42</td><td>20</td><td>10</td><td>70</td><td>90</td><td>95</td><td>12822,83</td><td>-467,30</td><td>-</td><td>-</td><td>Wenzel</td><td>1,13</td><td>-</td><td>60</td><td>-</td></tr><tr><td>[21]</td><td>43</td><td>20</td><td>10</td><td>80</td><td>90</td><td>96</td><td>9817,48</td><td>-478,22</td><td>-</td><td>-</td><td>Wenzel</td><td>1,10</td><td>-</td><td>61</td><td>-</td></tr></tbody></table>

a: Samples obtained experimentally.

## Appendix B. IDT dataset

<table><thead><tr><th>Reference</th><th>N</th><th>D (μm)</th><th>H (μm)</th><th>P (μm)</th><th>◆ (°)</th><th>θapp (°)</th><th>Ratio IDT</th></tr></thead><tbody><tr><td>[22]</td><td>1</td><td>10</td><td>20</td><td>50</td><td>90</td><td>150</td><td>1,68</td></tr><tr><td>[23]</td><td>2</td><td>55</td><td>90</td><td>85</td><td>90</td><td>160</td><td>1,72</td></tr><tr><td>[24]</td><td>3</td><td>2,93</td><td>3,33</td><td>5,43</td><td>90</td><td>157</td><td>3,58</td></tr><tr><td>[25]</td><td>4</td><td>0,03</td><td>0,3</td><td>0,15</td><td>75</td><td>169</td><td>2,72</td></tr><tr><td>[25]</td><td>5</td><td>0,05</td><td>0,3</td><td>0,15</td><td>75</td><td>160</td><td>2,11</td></tr><tr><td>[25]</td><td>6</td><td>0,07</td><td>0,3</td><td>0,15</td><td>75</td><td>154</td><td>2,06</td></tr><tr><td>[25]</td><td>7</td><td>0,09</td><td>0,3</td><td>0,15</td><td>75</td><td>151</td><td>1,83</td></tr><tr><td>[25]</td><td>8</td><td>0,145</td><td>0,3</td><td>0,15</td><td>75</td><td>132</td><td>1,44</td></tr><tr><td>a</td><td>9</td><td>6,49</td><td>5,16</td><td>30</td><td>77</td><td>35</td><td>0,50</td></tr><tr><td>a</td><td>10</td><td>3,09</td><td>5,15</td><td>40</td><td>66</td><td>32</td><td>1,00</td></tr><tr><td>a</td><td>11</td><td>6,55</td><td>5,12</td><td>50</td><td>78</td><td>42</td><td>1,00</td></tr><tr><td>a</td><td>12</td><td>3,59</td><td>5,11</td><td>60</td><td>63</td><td>41</td><td>1,00</td></tr><tr><td>a</td><td>13</td><td>11,43</td><td>5,18</td><td>30,2</td><td>77</td><td>36</td><td>1,00</td></tr><tr><td>a</td><td>14</td><td>10,9</td><td>5,17</td><td>40,05</td><td>79</td><td>36</td><td>1,00</td></tr><tr><td>a</td><td>15</td><td>10,9</td><td>5,17</td><td>50,1</td><td>77</td><td>44</td><td>1,50</td></tr><tr><td>a</td><td>16</td><td>8,25</td><td>5,12</td><td>60</td><td>58</td><td>39</td><td>1,00</td></tr><tr><td>a</td><td>17</td><td>18,5</td><td>5,11</td><td>30,2</td><td>76</td><td>37</td><td>1,00</td></tr><tr><td>a</td><td>18</td><td>18,55</td><td>5,16</td><td>40,1</td><td>77</td><td>72</td><td>2,00</td></tr><tr><td>a</td><td>19</td><td>16,3</td><td>5,15</td><td>49,8</td><td>67</td><td>38</td><td>2,00</td></tr><tr><td>a</td><td>20</td><td>16,95</td><td>5,04</td><td>74,9</td><td>60</td><td>37</td><td>1,50</td></tr></tbody></table>

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(continued)

<table><thead><tr><th>Reference</th><th>N</th><th>D (μm)</th><th>H (μm)</th><th>P (μm)</th><th>◆ (°)</th><th>θapp (°)</th><th>Ratio IDT</th></tr></thead><tbody><tr><td>a</td><td>21</td><td>7,53</td><td>4,94</td><td>32,55</td><td>79</td><td>142</td><td>1,25</td></tr><tr><td>a</td><td>22</td><td>7,36</td><td>5,57</td><td>41,78</td><td>76</td><td>144</td><td>1,25</td></tr><tr><td>a</td><td>23</td><td>7,7</td><td>5,51</td><td>52,06</td><td>77</td><td>145</td><td>1,50</td></tr><tr><td>a</td><td>24</td><td>7,8</td><td>5,84</td><td>62,01</td><td>78</td><td>145</td><td>1,75</td></tr><tr><td>a</td><td>25</td><td>7,5</td><td>9,39</td><td>29,27</td><td>77</td><td>139</td><td>0,75</td></tr><tr><td>a</td><td>26</td><td>7,42</td><td>9,86</td><td>37,6</td><td>76</td><td>143</td><td>1,50</td></tr><tr><td>a</td><td>27</td><td>7,5</td><td>10,19</td><td>47,18</td><td>76</td><td>144</td><td>0,75</td></tr><tr><td>a</td><td>28</td><td>7,74</td><td>10,4</td><td>57,32</td><td>76</td><td>143</td><td>1,25</td></tr><tr><td>a</td><td>29</td><td>7,44</td><td>14,4</td><td>33,04</td><td>67</td><td>145</td><td>0,75</td></tr><tr><td>a</td><td>30</td><td>7,49</td><td>14,53</td><td>43</td><td>67</td><td>144</td><td>1,00</td></tr><tr><td>a</td><td>31</td><td>7,78</td><td>14,78</td><td>53,05</td><td>69</td><td>144</td><td>1,00</td></tr><tr><td>a</td><td>32</td><td>7,68</td><td>15,51</td><td>67,24</td><td>68</td><td>146</td><td>2,75</td></tr></tbody></table>

a: Samples obtained experimentally.

## Appendix C. Ice adhesion dataset

<table><thead><tr><th>Reference</th><th>N</th><th>D (μm)</th><th>H (μm)</th><th>P (μm)</th><th>◆ (°)</th><th>θapp (°)</th><th>ARF</th><th>ΔH</th><th>1+cosθr</th></tr></thead><tbody><tr><td>[26]</td><td>33</td><td>15</td><td>10</td><td>20</td><td>90</td><td>145 to 163</td><td>2,46</td><td>14</td><td>0,20</td></tr><tr><td>[26]</td><td>34</td><td>15</td><td>10</td><td>30</td><td>90</td><td></td><td>1,54</td><td>14</td><td>-</td></tr><tr><td>[26]</td><td>35</td><td>15</td><td>10</td><td>45</td><td>90</td><td></td><td>1,21</td><td>14</td><td>-</td></tr><tr><td>[26]</td><td>36</td><td>15</td><td>10</td><td>60</td><td>90</td><td></td><td>1,01</td><td>14</td><td>0,06</td></tr><tr><td>[27]</td><td>37</td><td>5</td><td>5</td><td>10</td><td>90</td><td>128</td><td>0,14</td><td>14</td><td>0,42</td></tr><tr><td>[27]</td><td>38</td><td>5</td><td>5</td><td>15</td><td>90</td><td>119</td><td>0,29</td><td>14</td><td>0,56</td></tr><tr><td>[27]</td><td>39</td><td>5</td><td>5</td><td>25</td><td>90</td><td>115</td><td>0,45</td><td>14</td><td>0,61</td></tr><tr><td>[27]</td><td>40</td><td>5</td><td>5</td><td>45</td><td>90</td><td>112</td><td>0,58</td><td>14</td><td>0,67</td></tr><tr><td>[21]</td><td>41</td><td>20</td><td>10</td><td>40</td><td>90</td><td>112</td><td>1,54</td><td>13,8</td><td>0,78</td></tr><tr><td>[21]</td><td>42</td><td>20</td><td>10</td><td>50</td><td>90</td><td>103</td><td>1,35</td><td>15,7</td><td>0,92</td></tr><tr><td>[21]</td><td>43</td><td>20</td><td>10</td><td>60</td><td>90</td><td>98</td><td>1,32</td><td>15,2</td><td>0,99</td></tr><tr><td>[21]</td><td>44</td><td>20</td><td>10</td><td>70</td><td>90</td><td>95</td><td>1,48</td><td>14,3</td><td>0,98</td></tr><tr><td>[21]</td><td>45</td><td>20</td><td>10</td><td>80</td><td>90</td><td>96</td><td>1,17</td><td>18,8</td><td>1,04</td></tr><tr><td>[25]</td><td>46</td><td>0,05</td><td>0,3</td><td>0,15</td><td>90</td><td>160</td><td>57,64</td><td>14</td><td>0,07</td></tr><tr><td>[25]</td><td>47</td><td>0,07</td><td>0,3</td><td>0,15</td><td>90</td><td>154</td><td>35,15</td><td>14</td><td>0,12</td></tr><tr><td>[25]</td><td>48</td><td>0,09</td><td>0,3</td><td>0,15</td><td>90</td><td>151</td><td>14,70</td><td>14</td><td>0,14</td></tr><tr><td>[25]</td><td>49</td><td>0,145</td><td>0,3</td><td>0,15</td><td>90</td><td>132</td><td>1,65</td><td>14</td><td>0,36</td></tr><tr><td>[28]</td><td>50</td><td>34,7</td><td>59,7</td><td>93,2</td><td>90</td><td>-</td><td>0,66</td><td>6</td><td>0,13</td></tr><tr><td>[28]</td><td>51</td><td>60,9</td><td>60,7</td><td>122,7</td><td>90</td><td>-</td><td>0,65</td><td>8</td><td>0,16</td></tr><tr><td>[28]</td><td>52</td><td>40,9</td><td>94,1</td><td>106,5</td><td>90</td><td>-</td><td>0,6</td><td>9</td><td>0,17</td></tr><tr><td>[28]</td><td>53</td><td>85,1</td><td>93,8</td><td>142</td><td>90</td><td>-</td><td>0,75</td><td>8</td><td>0,15</td></tr></tbody></table>

## Data availability

Data will be made available on request.

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