Tailoring re-entrant geometry in inverse colloidal monolayers to control surface wettability

Controlling the microscopic wetting state of a liquid in contact with a structured surface is the basis for the design of liquid repellent as well as anti-fogging coatings by preventing or enabling a given liquid to infiltrate the surface structures. Similarly, a liquid can be confined to designated surface areas by locally controlling the wetting state, with applications ranging from liquid transport on a surface to creating tailored microenvironments for cell culture or chemical synthesis. The control of the wetting of a low-surface-tension liquid is substantially more difficult compared to water and requires surface structures with overhanging features, known as re-entrant geometries. Here, we use colloidal self-assembly and templating to create two-dimensional nanopore arrays with tailored re-entrant geometry. These pore arrays, termed inverse monolayers, are prepared by backfilling a sacrificial colloidal monolayer with a silica sol-gel precursor material. Varying the precursor concentration enables us to control the degree to which the colloids are embedded into the silica matrix. Upon calcination, nanopores with different opening angles result. The pore opening angle directly correlates with the re-entrant curvature of the surface nanostructures and can be used to control the macroscopic wetting behavior of a liquid sitting on the surface structures. We characterize the wetting of various liquids by static and dynamic contact angles and find correlation between the experimental results and theoretical predictions of the wetting state based on simple geometric considerations. We demonstrate the creation of omniphobic surface coatings that support Cassie-Baxter wetting states for liquids with


Introduction
Colloidal particles can be self-assembled into ordered superstructures in two and three dimensions, giving access to materials with defined periodicities at the nanoscale by a simple bottom-up process. [1][2][3] Twodimensional colloidal crystals, commonly known as colloidal monolayers, are especially attractive as templates and masks to create large-area surface patterns with nanoscale dimensions by successive material deposition or removal steps. [4][5][6] Such surface coatings find applications in structural coloration, [7][8] light management in solar cells, 9 anti-reflective coatings, [10][11][12] or to impart self-cleaning and superhydrophobic properties. [13][14][15][16][17] Superhydrophobic surfaces typically mimic nature's famously self-cleaning lotus leaves. 18 Their repellent properties are based on the creation of a composite air/solid interface by introducing topographic features at the micro-and nanoscale to a surface bearing a chemical functionality that maximizes the contact angle with the liquid to be repelled. [19][20][21][22] Liquids with high surface tensions, predominantly water, can easily be prevented from infiltrating the roughness features; resting on a cushion of air and being in contact only with the tips of the structures, a situation that is known as the Cassie-Baxter state. 23 Superhydrophobic surfaces with efficient water shedding and self-cleaning properties result. [24][25] However, the design of surfaces that also repel low-surface-tension liquids such as oils is significantly more challenging. The challenge arises from the fact that regular surface features with vertical side walls only support a Cassie-Baxter wetting state with liquids having a contact angle of >90° on a flat surface. Even the most repellent surface functionalities (typically featuring long perfluorinated alkyl chains) do not support sufficiently high contact angles for low-surface-tension liquids such as hydrocarbon oils. Hence, these liquids will not be expelled from most surface features but infiltrate the structure and form a Wenzel wetting state. 26 It has been recognized that the design of an oleophobic coating requires the presence of re-entrant curvature, i.e. surface topography features that bend towards the substrate and form angles with the substrates below 90°. [27][28][29] If this angle is lower than the contact angle of the applied liquid, a convex meniscus shape results that pushes the liquid away from the sidewalls of the surface features and thus enables the creation of a metastable Cassie-Baxter state for low-surface-tension liquids. [27][28][29][30][31][32] Here, we use colloidal templating to prepare two-dimensional nanopore arrays known as inverse colloidal monolayers 33-35 as surface coatings that provide precisely adjustable re-entrant curvature without relying on complex fabrication protocols or hierarchical structure design. This simple nanoscale architecture enables us to rationally tailor the macroscopic wetting state, even for low-surface-tension liquids. The inverse monolayers are prepared by backfilling a colloidal monolayer with a sol-gel precursor. Upon calcination, the colloidal particles are combusted, creating arrays of nanopores with size and order reflecting the dimensions and quality of the colloidal monolayer. The inverse geometry provides several advantages over normal colloidal monolayers. First, the constituent material typically consists of oxides formed from the sol-gel process, which enables simple and versatile surface functionalization using silane chemistry. Second, the close-cell structure provides mechanical robustness since all features are interconnected and covalently bond to the substrate, rendering them much more resistant to abrasion and mechanical damage. 35 Finally, the inversion of the convex surface structure of the colloids provides concave surface features with overhang, 36 a prerequisite for controlling wettability of the surface features.
We prepare inverse colloidal monolayers over macroscopic areas by spin-coating of a silica sol-gel precursor solution onto a pre-assembled colloidal monolayer following an established protocol. 35 In brief, a colloidal monolayer is assembled at the air/water interface and manually transferred onto a solid substrate. 37 A mixture of tetraethylorthosilicate (TEOS), ethanol and hydrochlorid acid (0.1N) is hydrolyzed for one hour, added to the monolayer surface and spin-coated to solidify. After calcination to burn out the template colloids, the inverse monolayer architecture results ( Figure 1a). By controlling the concentration of the sol-gel precursor, we can tailor the pore opening: The template colloids are embedded more and more into the silica thin-film with increasing amount of added solid material (Figure 1b). The pore opening angle Ψ is the crucial parameter that determines the re-entrant geometry of the structures and is directly related to the diameter of the pore opening a and the pore diameter d (Figure 1c):

sin(Ψ) = �
Increasing the sol-gel concentration thus enables us to create surface structures with tailored re-entrant curvature. Figure 1e shows examples of structures with a pore opening angle ranging from 79° to 23°. Table 1 provides details of the structural parameters and preparation protocols. The high regularity and uniformity of these self-assembled surface structures is exemplarily shown in a low resolution SEM image in Figure 1d. We chose colloids with a diameter of 1060nm for the experiments since these enabled us to prepare inverse monolayer with a wide range of opening angles needed to establish their wetting properties in detail. While the methodology can be generally applied to smaller particle sizes, 35 adjustment of the opening angle becomes increasingly difficult due to the increasingly smaller differences in the silica film thickness required for different opening angles.  We use silane chemistry to functionalize the surface of the inverse monolayer structures with (1H,1H,2H,2H-tridecafluorooctyl)-trichlorosilane to maximize the contact angle formed with both water and hydrocarbon oils. Figure   Contrarily, if the contact angle Θ exceeds the re-entrant angle Ψ, the liquid forms a convex meniscus shape at the pore entrance, effectively preventing the liquid from filling the pore. 29 The wetting situation is analogous to liquid infiltration into three-dimensional pore arrays in inverse opal structures, with the notable difference that the inverse monolayer architecture enables tailoring of the involved angles. 38-39   or chemical synthesis in confinement; for example to fabricate metal-organic framework microsheets with tailored dimensions. 51 However, the spatial confinement of low-surface-tension liquids such as organic solvents is substantially more difficult because of their highly wetting behavior that has been shown so far to be prevented only by creating quite complex, lithographically defined surface structures. [52][53] In Figure 5, we demonstrate the use of micropatterning to locally define the surface functionalization of the inverse monolayer coatings. This enables us to tailor the wetting state of low-surface-tension liquids on macro-and microscopic areas with high accuracy and thus confine low-surface-tension liquids to designated areas of the substrate. Using photolithography, we can selectively expose defined surface areas which are subsequently fluorosilanized (indicated by an orange color in Figure 5a), while the parts of the surface blocked by the photoresist layer remain unfunctionalized (indicated as green color in Figure 5a).
After photoresist removal, we obtain an inverse monolayer that shows repellent properties only in the designated, fluorosilanized surface regions exposed by the patterning process. Tailoring the re-entrant geometry to enable Cassie-Baxter wetting in the surface-functionalized regions, a low-surface-tension liquid added to the surface will de-wet from the fluorinated areas and be confined to the nonfunctionalized areas. Figure 5b shows  In conclusion, we show how a simple colloidal templating process can be used to accurately predict and tailor the macroscopic wetting state of liquids with varying surface tensions. We create inverse monolayers by backfilling a two-dimensional colloidal crystal with a silica sol-gel precursor and are able to precisely tailor the opening angle of the individual pores via a variation of the precursor concentration.
This pore opening angle is the crucial parameter that characterizes the re-entrant curvature of the porous coating which, in turn, determines the wetting state of the liquid. If the pore opening angle is smaller than the contact angle of the liquid, pore infiltration is prevented, leading to a Cassie-Baxter wetting state. We prepare inverse monolayers with a wide range of pore opening angles and show that the macroscopic wetting properties of liquids with varying surface tensions can be controlled. We further locally pattern the surface functionality via photolithography which allows us to confine low-surface-tension liquids to designated areas of the surface with high accuracy. The ability to tailor wetting properties with high surface tension selectivity in a simple self-assembly process impacts various technologies and applications, from simplified tests of surface tension to separation membranes for low-surface-tension liquids or chemical reactions in spatially confined regions.

Materials
All materials were purchased from Sigma Aldrich and used without further purification, except for styrene which was distilled at reduced pressure to remove the inhibitor.

Colloidal synthesis and assembly into monolayers
Colloids were synthesized by surfactant-free emulsion polymerization with acrylic acid as comonomer as described elsewhere. 54 Self-assembly was performed using the air/water interface as a template following a protocol from literature. In brief, the colloidal dispersion was diluted with ethanol (50% by volume) and added to the air/water interface via a hydrophilic glass slide immersed into the water subphase at an angle of approximately 45°. At the three phase contact line, the colloids assemble into a close-packed monolayer. Addition was continued until the entire air/water interface was covered by a monolayer.
Subsequently, a substrate was immersed into the subphase and withdrawn under a shallow angle to transfer the monolayer.

Inverse monolayer preparation
Tetraethylorthosilicate, hydrochloric acid (0.1N) and ethanol were mixed with ratios specified in Table 1 and stirred for 1h at room temperature for prehydrolysis. The solution was diluted with ethanol to control the pore opening (values specified in Table 1) and added onto the monolayer-coated substrate (10µl/cm 2 ).
The solution was uniformly spread onto the substrate by tilting and subsequently spincoated at 3000rpm for 30s. Calcination was performed at 500°C (heating from 23°C to 500°C for 5h, temperature kept constant for 2h, cooling for 5h to 23°C). All samples were characterized by scanning electron microscopy on a Zeiss Ultra SEM.

Photolithography
A positive tone photoresist (S1818, Shipley) was spincoated (4000 rpm, 60 s) onto the inverse monolayer substrate and illuminated with UV light as specified by the manufacturer (irradiation dose: 200 mJ cm -2 ).
Afterwards, the pattern was developed by immersion into a commercial developer solution (Shipley, Developer) for 60s. The patterned substrate was plasma-treated (O 2 plasma, 100W, 5sccm flow) for 5min and then surface-functionalized following the protocol described above. Finally, the resist was removed from the surface (Remover PG 1165, Shipley), leaving the uncovered surface areas without fluorinated surface groups.

Contact angle measurements
Contact angles were measured at room temperature without control of humidity. Droplets with a volume of 3µl were added to the substrate via a syringe and the droplet profile was analyzed with the software provided by the manufacturer (Krüss GmbH). Advancing and receding contact angles were measured by increasing and decreasing the droplet volume while taking screenshots. All values for contact angles given in the main text were averaged over at least 10 different measurements.