Biomimetic coating-free surfaces for long-term entrapment of air under wetting liquids

Trapping air at the solid–liquid interface is a promising strategy for reducing frictional drag and desalting water, although it has thus far remained unachievable without perfluorinated coatings. Here, we report on biomimetic microtextures composed of doubly reentrant cavities (DRCs) and reentrant cavities (RCs) that can enable even intrinsically wetting materials to entrap air for long periods upon immersion in liquids. Using SiO2/Si wafers as the model system, we demonstrate that while the air entrapped in simple cylindrical cavities immersed in hexadecane is lost after 0.2 s, the air entrapped in the DRCs remained intact even after 27 days (~106 s). To understand the factors and mechanisms underlying this ten-million-fold enhancement, we compared the behaviors of DRCs, RCs and simple cavities of circular and non-circular shapes on immersion in liquids of low and high vapor pressures through high-speed imaging, confocal microscopy, and pressure cells. Those results might advance the development of coating-free liquid repellent surfaces.


Supplementary Note 1: Calculations of cavity volume and capillary lengths of probe liquids
All the samples investigated in this study had an array of cavities with the primary dimension of D = 200 µm, pitch, L = 212 µm and depth of h ≈ 50 µm. We estimated the volume of the cavities by estimating its base area and multiplying by its depth, h, as shown in Supplementary Figure 2. For example, in the case of circular cavity, the volume is equal to, "#$ = ) ℎ/4 (1)

Supplementary Figure 2. A schematic representation of the cross-section of simple circular cavities.
A typical 2 µL water droplet with a 1 mm diameter could cover approximately 18 cavities of primary dimension of D = 200 µm, pitch, L = 212 µm. Since the ratio of the volume of a single cavity to a 2 µL liquid drop was ~1/1270, we could apply the Cassie-Baxter model (Supplementary Note 2).
Next, we calculate the capillary length, . , that characterizes the length scale at which interfacial tensions exceed inertial forces 1 : where 12 is the surface tension, r is density and g is the acceleration due to gravity. The diameters of the liquid drops employed in our experiments were smaller than the respective capillary lengths (Supplementary Table 1).

Supplementary Note 2: The Cassie-Baxter model
Since the volume of the cavities underneath the liquid drops of our microtextured silica surfaces were much smaller than the volumes of the drops themselves, we could employ the Cassie-Baxter model 7 to predict the apparent contact angles, cos ;< = 1> cos 7 − 12 where qPr is the apparent contact angle and qo is the intrinsic contact angle of the liquid on a smooth and flat surface (Young's contact angle) 1 . Here fLS = ALS/AH and fLV = ALV/AH are the ratios of real liquid-solid (ALS) and liquid-vapor (ALV) areas (Supplementary Figure 3A) compared to the projected horizontal area (AH) (Supplementary Figure 3B).

Supplementary
where D is the diameter of the cavity, L is the pitch, l is the height of the reentrant or doubly reentrant rim. We also note that LV ≥ 0 and ≥ LS ≥ 0 , where is the roughness of the microtexture, defined as the total surface area divided by the projected area. For further details on the derivation of Supplementary Equations 4, 5 and definitions of LV and LS , please refer the article by Kaufman and co-workers 8 . The receding contact angles for both water and hexadecane were less than 5° for all the microtextured surfaces. (Also see Table 1 in the main manuscript)

Supplementary Note 3: The effect of sharp edges on contact angles.
When a liquid is spreading over a flat surface with sharp 90° geometric turns, like our silica surfaces with arrays of simple cavities, there is a ~ 90° increase in the apparent contact angles at the edges of those features, known as the edge effect ( Figures 5A1,B1, C1) 9,10 . During immersion in water, as water spread over silica surfaces with arrays of simple circular cavities, the combination of intrinsic contact angle ( 7 ≈ 40°), primary dimension, D = 200 µm, and the edge effect enabled the entrapment of air in the cavities. In contrast, for hexadecane, lower intrinsic contact angle and surface tension, in comparison to water (Supplementary Table 1), led to the instantaneous filling of even simple circular cavities. Though, we consider that as the primary dimension of the circular cavities is reduced further, even hexadecane meniscus might trap air underneath due to the edge effect; this issue warrants further experimental investigation.
While modeling apparent contact angles on silica surfaces with arrays of simple cavities, that got filled instantaneously with wetting liquids, the predicted contact angles were corrected for the edge effect by adding 90° to ;< (Table 1). On the other hand, predictions of the Cassie-Baxter model (Supplementary Note 2) were higher than the observed apparent contact angles for the simple circular cavities with water (Table 1). We consider that it was due to the filling of cavities at the edge of the drop over time 8,[11][12][13] .

Supplementary Figure 5. Liquid imbibition along corners.
A schematic representation of imbibition of a wetting liquid along the corners of an intrinsically wetting capillary of square cross-section. Arc menisci, along the corners, rise faster and higher than the main terminal meniscus.

Supplementary Note 4: Confocal Microscopy
A Zeiss LSM710 upright confocal microscope was used to visualize cavity-filling mechanisms employing diluted 0.01 M solutions of Rhodamine B (Acros) as fluorescent dye for water experiments and Nile Red (Aldrich) for hexadecane. After fixing the sample at the bottom of a petri dish, the fluorescent solution was gently poured sideways until the sample was completely covered by a z ≈ 5 mm column of solution. A 20X immersion objective was then lowered to the working distance and the experiments where immediately started. Sequential images (1024px ×1024px) were taken in the Zstack mode, in which several confocal images were taken from the bottom of the cavities up to 100 microns above the top surface. The intensity of the laser was 0.2 mW for Rhodamine/water solution and 2 mW for Nile red/hexadecane solution for optimum imaging. Subsequently, using the Imaris v.8.1 software, by Bitplane, we were able to make 3D rendered surfaces and several cross sections to help visualize the wetting transition in our cavities. Figure 6. Effects of laser power and exposure intervals on tfailing of doubly reentrant cavities observed via confocal microscopy. Figures A and B demonstrate that due to the ultralow vapor pressure of hexadecane, increasing laser power from 2 mW to 20 mW did not affect tfailing. Contrastingly, the wetting transition was faster when the same samples were immersed in water. Figures C and D demonstrate cavity filling underwater, when we increase the laser power from 0.6 mW to 3 mW (a factor of 5), wetting transitions from partially-to fully-filled states reduced from 4.5 h to 40 minutes. Thus, our simple experiments demonstrate that for liquids with high vapor pressure, capillary condensation drives cavity filling, whereas for liquids with low vapor pressures, it is not a key mechanism.

Supplementary Note 5: Protocols for cleaning and storing the samples
After microfabrication we cleaned the SiO2/Si (silica) surfaces with fresh piranha solutions (H2SO4 : H2O2 = 4:1 at T = 388 K) for 10 min, blow-dried with a 99% pure N2 pressure gun and stored in glass petri dishes in a dedicated vacuum oven at T = 323 K, until the intrinsic contact angle of smooth SiO2/Si stabilized to, qo ≈ 40° (after 48 h).
Subsequently, the samples were stored in a N2 cabinet until needed for characterization.
We performed X-ray photoelectron spectroscopy (XPS) on silica samples (i) freshly cleaned by piranha solution, (ii) after 24 in vacuum, (iii) 48 h in vacuum, and (iv) 48 h in vacuum followed by one week of storage in a N2 cabinet (all stored in glass petri dishes), as shown in Supplementary Figure 12. We found no significant evidence of airborne hydrocarbon impurities or perfluorocarbon residues from the etching process. We concluded that the increase in the intrinsic contact angle of silica surfaces to the water/vapor system, 7 ≈ 0°→ 40°, was due to the partial dehydroxylation of such surfaces (Methods). Figure 12. X-ray photoelectron spectroscopy (XPS) characterization. XPS spectra on silica samples freshly cleaned by piranha solution, after 24 in vacuum, 48 h in vacuum and 48 h in vacuum followed by one week of storage in N2 cabinet in glass petri dish. S17

Supplementary Note 6: Pinning and depinning of bubbles
A simple comparison of the pinning forces at the mouths of doubly reentrant circular cavities, against the buoyancy of the bubble, gh7i~"#$ × ( 1 − j ) × (12) shows that buoyancy is insignificant at this length scale ( ;FG gh7i ⁄ ≈ 10 ) ), where e ≈ 40° and d ≈ 0° were the advancing and receding contact angles of water on silica 14 . The estimated pinning force experienced by the trapped bubble at the mouth of the cavity was significantly higher than buoyancy.
In the case of O2 plasma treated silica surfaces, the intrinsic contact angles of water in air were, 7 ≈ 0°. This was due to the highly hydroxylated surface of the silica after plasma activation (Methods). As a result, condensation of water led to formation of continuous films instead of discrete drops 15 . After the film spread across the cavity, the main meniscus collapsed inward asymmetrically, and the trapped bubble rose out of the cavity due to buoyancy and the absence of pining force (Supplementary Figure 13A

Supplementary Note 7: Calculation of Breakthrough Pressure
In this section we calculate the breakthrough pressure using ideal gas equation. Supplementary Figure 15 shows the liquid meniscus shapes under applied external pressure using home built pressure cell (Supplementary Figure 14). Since our cavity depth, h = D/4, the breakthrough occurred main meniscus touching the cavity floor. .#w = ) (3 u − ) 3 We used ideal gas equation to estimate the excess pressure (Pb= 116 kPa) inside the cavity at which breakthrough occurs; the geometrical dimensions of the cavity, i.e. depth (ℎ ≈ 50 µm), radius ( = 100 µm) and mean curvature of the intruding liquid meniscus ( u = 125 µm ). The volume of liquid that sags inside the cavity, .#w = 8.4 × 10 z (µm) s . Final trapped air volume at which breakthrough occurs ) = l − .#w = 7.2 × 10 z (µm) s .