Well-defined porous membranes for robust omniphobic surfaces via microfluidic emulsion templating

Durability is a long-standing challenge in designing liquid-repellent surfaces. A high-performance omniphobic surface must robustly repel liquids, while maintaining mechanical/chemical stability. However, liquid repellency and mechanical durability are generally mutually exclusive properties for many omniphobic surfaces—improving one performance inevitably results in decreased performance in another. Here we report well-defined porous membranes for durable omniphobic surfaces inspired by the springtail cuticle. The omniphobicity is shown via an amphiphilic material micro-textured with re-entrant surface morphology; the mechanical durability arises from the interconnected microstructures. The innovative fabrication method—termed microfluidic emulsion templating—is facile, cost-effective, scalable and can precisely engineer the structural topographies. The robust omniphobic surface is expected to open up new avenues for diverse applications due to its mechanical and chemical robustness, transparency, reversible Cassie–Wenzel transition, transferability, flexibility and stretchability.


Supplementary
. Ultraviolet-visible transmittance spectra of a glass slide and a PVA porous membrane coated glass. The solid fraction of the test omniphobic surface is f s = 21%. For light wavelength in the visible spectra ranging from 380 to 780 nm, the transparency of the omniphobic surface coated glass is reduced by ~20% compared to that of the bare glass substrate. The reduction in transparency results from the absorption of light by PVA (with the thickness ranging from tens to hundreds of micrometers) and reflection of light on the curved air-PVA interface on the micro-cavities. We anticipate that higher light transmittance is possible by further reducing the solid fraction of the omniphobic surfaces. Figure 4. Immersion of the PVA porous membrane in water and soybean oil. The shiny white part in the middle of the petri dish indicates the air pocket trapped inside the micro-cavity when the porous membrane is immersed in both water and soybean oil. The air cushion observed in the picture is similar to that identified in springtail immersion test.

Supplementary
Supplementary Figure 5. The breakthrough pressure in two sagging scenarios. (a) Breakthrough pressure P h in the case that the liquid front contacts the bottom substrate. r is the radius of the opening, h is the height of the structure, and R f is the radius of the sagging interface. In this case, angle θ is essentially smaller than the advancing angle θ a . (b) Breakthrough pressure P θ in the case of contact line depinning. Depending on the value of θ a -φ mnin , three possibilities may occur for the depinning: case 1 (red dashed line) where θ a -φ mnin < 90°, case 2 (blue solid interface) where θ a φ mnin = 90°, and case 3 (olive dashed line) where θ a -φ mnin > 90°. (a) Schematic of the cross-section profile of a droplet deposit during evaporation. θ r is the receding angle of the liquid, and R base is the base radius of the liquid deposit. (b) Series of images displaying water and DMC droplets evaporation on the porous omniphobic surface. (c) Image of a droplet during evaporation. Both the apparent contact angle θ and base radius R base are time dependent. (d) The plot of apparent contact angle and normalized base radius versus normalized time for water and DMC evaporation. The base radius is normalized by the initial value when the droplet is deposited at time t = 0. The time is normalized by droplet lifetime T 0 , 2229 s for water and 210.8 s for DMC. (e) Variation of Laplace pressure P drop (symbol) during water and DMC droplets evaporation. P drop is always smaller than the breakthrough pressure P break (dashed line) for the entire lifetime of both water and DMC droplets. (f) A hexagonal pattern of an ink residual after water evaporation. The residual is situated atop the porous surface, as demonstrated in the right two magnifications, where the left one is focused on the top layer of the surface, while the right one is focused on the bottom. The edge of the residual pattern is sharp and clear in the left magnification (black box) but dim in the right one. . The yellow arrow indicates the transmitted light and the orange arrow denotes reflection on the air-water interface. The width of the arrow represents the luminous intensity. The absorption of light by the medium is not displayed. Owing to the reflection and refraction of light on the air-water interface, the focal plane should be adjusted in the range between the top to the bottom layer for a clear visualization of the wetting process. (b) Snapshots of the reversible wetting process at different instants. At the pressurizing stage, the air is compressed so that the air-water interface lowers with the increasing pressure. In this case, the focal plane is correspondingly lowered. So at 0 s (top left image, before pressurizing), the focal plane is on the top layer, where the light part denotes the narrow opening of the micro-cavity, and the dark part represents the solid polymer structure. At 11 s (top middle image), the focal layer is lowered to the middle plane, where the light part is water phase and the dark part is the compressed air because of the reflection on the air-water interface. At 24 s (top right image), the focal plane is at the bottom layer of the membrane, where the circular boundary between micro-cavities is clear. In this case, the light part still stands for water and the dark part for air. In the process of depressurizing, the focal plane is tuned inversely from the bottom to the top layer. Finally, at 63 s, the system restores the non-wetting state, and the light circle indicates the top narrow opening. In this case, the solid material is deformed by the imposed strains, as indicated by the dashed red box where buckling of the sidewall is observed. The deformation of the solid material is also manifested in the relation of (1 + ε x )(1 + ε y ) > 1, and the product of (1 + ε x ) and (1 + ε y ) increases with the strain. This type of deformation is, therefore, irreversible.

Supplementary Figure 16. Liquid immersion test. (a) Experimental setup for the liquid immersion test.
The sample is placed in a sealed chamber that is pre-filled with the test liquid. A syringe stored a specific volume of air is connected to the chamber by a microtubing. The pressure of the liquid is elevated by compressing the air stored in the syringe using a syringe pump. The whole process of the immersion test is observed under an inverted optical microscope, and recorded by a high-speed CCD camera that is connected to a computer. (b) Schematic of the detailed connection between the syringe and liquid-filled chamber.

Supplementary Note 1: Determining the breakthrough pressure
The Cassie-Wenzel transition occurs when the pressure difference across the liquid-vapor interface exceeds a critical value, denoted as the breakthrough pressure P break . The wetting transition is induced by either the liquid front making contact with the substrate (Supplementary Fig. 5a) or depinning of the three-phase contact line ( Supplementary Fig. 5b).
In the scenario of Supplementary Fig. 5a, P break = P h = 2γ/R f , where R f is the radius of the liquid front, and γ is the liquid surface tension. To determine R f , we have the following geometric relationship (Supplementary Fig. 5a): (1 cos ) According to Supplementary Equations (1) and (2), R f is determined to be R f = (h 2 + r 2 )/2h. As such, the breakthrough pressure is calculated to be In the scenario of Supplementary Fig. 5b, R f is determined by the advancing angle of the liquid θ a . Here, we consider arbitrary minimum geometric angle φ min , and R f is expressed of the form R f = r/sin(θ a -φ min ). The minimum value of R f is r when θ a φ min ≥ 90°. The breakthrough pressure is determined by the minimum R f during the wetting transition. In case 1 (shown in Supplementary Fig. 5b) where θ a -φ min < 90°, the breakthrough pressure is simply written as P break = P θ = 2γ/R f = 2γsin(θ a -φ min )/r. The critical membrane height h c is the depth of the liquid front, h c = R f (1cos(θ aφ min )) = r(1cos(θ a -φ min ))/sin(θ a -φ min ) = rsin(θ a -φ min )/(1 + cos(θ a -φ min )). In cases 2 and 3, where θ a -φ min ≥ 90°, the breakthrough pressure is determined by the moment when R f = r. As such, P break = P θ = 2γ/R f = 2γ/r. Now, the critical membrane height h c is of the form h c = r.
In summary, we determine the breakthrough pressure P break depending on the relative difference between θ a -φ min and 90° as follows: for θ a < 90° + φ min , (5)

Supplementary Note 2: Height of the porous membrane
The height of the porous membrane is determined by the deformation of droplet templates. For most cases, droplets self-assemble into dense-packed hexagonal arrays, and deform into pancake-like shape during membrane fabrication. Considering the extreme case that all spherical droplets of radius R deform into prisms with hexagonal cross-section and height h, as shown in Supplementary Figs. 6a and 6b hR   that sets a lower limit for the height of the membrane. Therefore, the height of the porous membrane fabricated by the MET method inherently has In very limited cases, we observe that droplets are arrayed in a rhombus pattern, as shown in Supplementary Figs. 6c We see that in any of the two cases, the membrane height is larger than the radius of the spherical droplet, thereby larger than the critical height h c (h > R > r > h c ).

Supplementary Note 3: Persistence of the Cassie state during droplet evaporation
The robustness of the micro-cavity structure (high P break ) is also manifested in the persistence of the Cassie state during droplet evaporation. During droplet evaporation, the elevated Laplace pressure is a result of the shrinkage of the droplet radius R drop . Basically, R drop is related to the base radius of the droplet R base in the form of R drop = R base /sinθ r , where θ r is the receding angle of the liquid (Supplementary Fig. 7a). The Laplace pressure is then determined to be P drop = 2γ/R drop = 2γsinθ r /R base . Since R base is essentially larger than the radius of the opening r, P drop ≤ 2γsinθ r /r. To preserve the Cassie state, the condition of P drop < P break should be met. By comparing P drop ≤ 2γsinθ r /r and P break given in Supplementary Equations (4) and (5) Considering that φ min ≤ 0° for any liquid deposits, we anticipate that droplet sustains the Cassie state throughout the evaporation process owing to θ r < θ Y < 90° and θ r < θ a < θ a -φ min for all the test liquids. To confirm this, we examined, for example, water and DMC droplets evaporating on the PVA omniphobic surface ( Supplementary Fig. 7b). After extracting the transient contact angle θ and base radius R base (Supplementary Figs. 7c and 7d), the calculated P drop (R drop = R base /sinθ) is found to be always smaller than P break for both liquids ( Supplementary Fig. 7e), indicating a sustained Cassie state for the entire droplet lifetime. Furthermore, by filming the evaporation process under an optical microscope, we have confirmed this speculation in the main context ( Fig. 3d and 3e), except that several cavities are sparsely wetted by DMC (Fig. 3e), probably due to defects at the rims of the corresponding openings (resulting in φ min > 0°). It is remarkable to note that, in contrast to pillar-like arrays where sideways spreading of liquids may occur along with the wetting transition, the wetted micro-cavities are solitary and prevented from propagating by the impermeable sidewalls. As maintained in the Cassie state, the residual of a solution would sit atop the porous membrane after solvent evaporation, as shown in Supplementary Fig. 7f (see also Supplementary Movie 3). The hexagonal shape of the ring-like pattern, as a result of the hexagonal-arrayed openings, may offer new opportunities for liquid-based printing and biosensing applications.

Supplementary Note 4: Apparent contact angle on deformed omniphobic surfaces
In the Cassie state, the apparent contact angle is predicted by the Cassie-Baxter model. We therefore have * cos (cos 1) 1 In terms of surface deformation ( Supplementary Fig. 14), we consider the one-dimensional solid fraction f s = (Lr)/L along the deformational direction, where r is the radius of the opening, L is the characteristic length scale of the hexagonal cell. (13) by applying (1 + ε x )(1 + ε y ) = 1.