Bio‐Inspired Instability‐Induced Hierarchical Patterns Having Tunable Anisotropic Wetting Properties

This paper introduces a method for the bottom‐up fabrication of bio‐inspired hierarchical patterns having tunable anisotropic wetting properties. The method exploits the surface instability of bilayers comprising a gold nanofilm attached to a substantially prestretched elastomer substrate. Upon film formation, highly aligned wrinkles spontaneously form on the surface owing to the surface instability driven by the compressive residual stress in the film. Thereafter, uniaxial compressive strain is applied to the film by prestretch relaxation of the substrate, which generates an array of high‐aspect‐ratio ridges on the surface. Consequently, hierarchical patterns comprising unidirectionally aligned ridges covered with wrinkles are obtained. Water droplets placed on surfaces having the aforementioned hierarchical patterns show direction‐dependent contact angles, resulting in elongated shapes, which indicates the presence of anisotropic wetting properties. The magnitude of wetting anisotropy can be tuned by simple control of the applied compressive strain and film thickness.


Bio-Inspired Instability-Induced Hierarchical Patterns Having Tunable Anisotropic Wetting Properties
So Nagashima,* Ko Suzuki, Seishiro Matsubara, and Dai Okumura DOI: 10.1002/admi.202300039 been fabricated and exploited for versatile applications, including fog harvesting, self-cleaning, and microfluidic devices. [5] However, ordinary fabrication methods involve the use of top-down techniques such as photolithography and imprinting, which require expensive equipment and complex processes that are not readily accessible. Moreover, these techniques have limited capacity to control the magnitude of wetting anisotropy due to their inability to easily change the dimensions of the relevant patterns during creation. Therefore, new fabrication methods that overcome the limitations of conventional approaches are required.
Surface instability of bilayers comprising a thin film on a soft substrate is considered an attractive means of bottomup creation of nano-/microscale patterns. [6] This phenomenon occurs when the film is compressed beyond a critical level, allowing for the spontaneous formation of highly ordered surface patterns such as wrinkles and folds for a wide range of applications (e.g., controlled wetting, [7] flexible and stretchable sensors, [8] controlled friction, [9] tunable channels, [10] and nanomaterial manipulation. [11] ) Such instability-induced patterns have been exploited for the fabrication of hierarchical surfaces. For example, multiple cycles of film formation followed by mechanical compression generate wrinkles with spatially varying wavelengths and amplitudes, i.e., hierarchical wrinkles. [12] This approach is easy to implement in an ordinary laboratory environment. However, the resulting hierarchical wrinkles generally have low aspect ratios (amplitude/wavelength), thus exhibiting only a small effect on the wetting anisotropy. [13] In another example, surface instability is used to complement conventional top-down approaches to obtain complex high-aspect-ratio hierarchical patterns that are unattainable with a single approach. [14] However, such combined methods still require the aforementioned topdown techniques. Therefore, a new class of surface-instabilitybased methods that lack the need for top-down techniques is required to provide a low-cost and flexible route to the creation of high-aspect-ratio hierarchical patterns having anisotropic wetting properties.
Recently, instability-induced patterns developed through the formation of localized ridges have been shown to achieve high aspect ratios and possess unprecedented properties that cannot be attained using ordinary wrinkles, folds, or their derivatives. [15] In particular, hierarchical patterns comprising nanoscale wrinkles on microscale ridges that can be created by This paper introduces a method for the bottom-up fabrication of bio-inspired hierarchical patterns having tunable anisotropic wetting properties. The method exploits the surface instability of bilayers comprising a gold nanofilm attached to a substantially prestretched elastomer substrate. Upon film formation, highly aligned wrinkles spontaneously form on the surface owing to the surface instability driven by the compressive residual stress in the film. Thereafter, uniaxial compressive strain is applied to the film by prestretch relaxation of the substrate, which generates an array of high-aspect-ratio ridges on the surface. Consequently, hierarchical patterns comprising unidirectionally aligned ridges covered with wrinkles are obtained. Water droplets placed on surfaces having the aforementioned hierarchical patterns show direction-dependent contact angles, resulting in elongated shapes, which indicates the presence of anisotropic wetting properties. The magnitude of wetting anisotropy can be tuned by simple control of the applied compressive strain and film thickness.

Introduction
Anisotropic wetting is the directional dependence of surface wettability. This feature is ubiquitously observed on hierarchically textured directional surfaces present on insects and plants, such as butterfly wings, [1] water strider legs, [2] and rice leaves. [3] Wetting anisotropy plays an important role in enhancing certain functionalities of biological surfaces (e.g., drag reduction, thrust generation, and directional water collection), which are critical for promoting survival. Inspired by these functional surfaces in nature, researchers have devoted considerable effort to developing methods for creating multiscale hierarchical patterns based on top-down, bottom-up, and combined approaches. [4] Thus, a variety of hierarchically patterned surfaces having anisotropic wetting properties have www.advmatinterfaces.de depositing a stiff nanofilm on a highly prestretched elastomer substrate and subsequently relaxing the substrate have attracted much attention because the strong geometric confinement of the high-aspect-ratio patterns helps to facilitate directional motion of substances. [15a,c] Despite the attractive properties of such hierarchical patterns using ridges, several salient aspects remain unexplored. First, hierarchical patterns with characteristic lengths that exceed the single-micrometer scale have yet to be achieved, even though such large-scale hierarchical patterns are observed in nature. [16] Second, the alignment of the wrinkles on the ridges is uncontrollable, whereas biological surfaces generally show highly aligned patterns. [17] Finally, as a consequence of the aforementioned circumstances, anisotropic wetting on highly aligned, instability-induced hierarchical patterns with high aspect ratios remains unexplored. Addressing these issues would help to create fabrication opportunities for functional surfaces with tunable anisotropic wetting properties.
Here, we introduce a bottom-up method of fabricating bioinspired hierarchical patterns with tunable anisotropic wetting properties. This method exploits the surface instability of bilayers comprising a gold nanofilm attached to an elastomer substrate. Sputter coating of a substantially prestretched elastomer substrate with the gold nanofilm spontaneously forms highly aligned wrinkles (Figure 1a,b). Subsequent stretch relaxation of the substrate generates an array of high-aspect-ratio ridges with the wrinkles being retained, thus forming hierarchical patterns ( Figure 1c). This formation is a result of the combined effects of spontaneous compression due to the residual stress generated during the film coating and externally applied compression following the film coating. The ridge dimensions can be controlled by adjusting the magnitude of substrate prestretches and film thickness. Water droplets placed on surfaces having the aforementioned hierarchical patterns show directional dependency of contact angles resulting in elongated shapes, which demonstrate wetting anisotropy (Figure 1d). The magnitude of the wetting anisotropy can also be tuned by controlling the magnitude of substrate prestretches and film thickness.

Morphological Evolution of Surface Patterns
We first describe how structural hierarchy evolves on a surface. When a substrate that has been prestretched with a tensile strain of ε pre = 1.5 is sputter-coated with the gold film with a thickness of h ≈ 206 nm, unidirectionally aligned wrinkles with a wavelength of λ ≈ 3.3 µm spontaneously form on the surface (Figure 2a). The wrinkle formation is attributable to the surface instability driven by the compressive residual stress in the film, while the wrinkle alignment is presumably due to the constraints imposed on both ends of the substrate by the rigid stretcher. In the present study, the substrate surface subjected to the metal source reaches ≈55 °C in temperature when the film (h ≈ 206 nm) is deposited on the substrate, as measured using a temperature label. This increase in temperature causes the expansion of the substrate surface. Meanwhile, the substrate is firmly constrained by the stretcher at both ends ( Figure S1, Supporting Information). Thus, compressive thermal stress is created in the stretch direction, which causes unidirectionally aligned wrinkles to form. In contrast to the random wrinkles that appear when the film is simply deposited on the substrate on a glass slide (i.e., a stretcher-free substrate) ( Figure S2a, Supporting Information), such formation of aligned wrinkles is observed irrespective of the magnitude of substrate prestretches as long as the substrate is constrained by the stretcher ( Figure S2b-e, Supporting Information). These results suggest that this constraining plays a role in aligning the wrinkles.
According to the linear buckling theory, [18] the wavelength of the wrinkles formed under slight film compression is given by is the planestrain modulus with E being Young's modulus, ν Poisson's ratio, and the subscripts f and s denote the film and substrate, respectively. The equation above can be rewritten as where µ is the shear modulus. By using the values of µ f = 27 GPa, ν f = 0.44, µ s = 20 kPa, and ν s = 0.5, [15a] we obtain λ ≈ 464h. This equation suggests that the wavelength of the wrinkles formed upon completion of the sputter coating corresponds to a film thickness of h ≈ 7 nm. Given the total film thickness of h ≈ 206 nm, the wrinkle formation is assumed to occur at an early stage of sputtering due to the penetration and diffusion of metal atoms into the substrate surface. Meanwhile, the metal atoms produced following this time period are likely to be deposited on the wrinkles that have already formed because access to the substrate surface is prevented. Indeed, we experimentally observe that the wavelength of the wrinkles formed prior to relaxing the substrate prestretch remains nearly constant, i.e., λ ≈ 3 µm, irrespective of the total film thickness ( Figure S3, Supporting Information). These experimental observations

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validate the mechanism of the wrinkle formation described above.
When ε = 0.04 is applied to the film by partially relaxing the substrate pre-stretch, distinct patterns called ridges [19] locally appear on the surface (Figure 2b). The ridges are evidently larger than the wrinkles shown in Figure 2a. Such formation of localized ridges results from the nonlinearity of the substrate produced by the substantial prestretch that induces a softer response for a local outward deflection than for an opposing inward deflection. [20] As the compressive strain further increases to ε = 0.10 and then to ε = 0.30, new ridges begin appearing around the ridges that have already been formed (Figure 2c,d), which results in the formation of more densely arrayed and sharper ridges. These outcomes demonstrate that the small wrinkles arising owing to surface instability induced by compressive residual stress are retained on large ridges resulting from surface instability driven by externally applied compressive stress. In this manner, hierarchical patterns comprising an array of ridges covered with highly aligned wrinkles are obtained (Figure 2e). Unlike the randomly oriented shallow wrinkles that are typically obtained when the film is simply deposited on an unstretched substrate ( Figure S4, Supporting Information), our method enables the formation of highly aligned, high-aspect-ratio hierarchical patterns (Figure 3).
We next describe the effects of the film thickness and applied compressive strain on the dimensions of the surface patterns. Figure 4a plots the wavelength λ of the ridges as a function of the film thickness h for a case in which the tensile strain is ε pre = 1.5. The wavelength increases from λ ≈ 4.5 to 65.4 µm as the film thickness increases from h ≈ 26 to   Figure 4b plots the wavelength λ and amplitude A of the patterns for various applied compressive strains ε when h ≈ 206 nm. Note that the values of λ and A for ε = 0.00 were measured using the random wrinkles obtained without any substrate prestretch ( Figure S4, Supporting Information). As the applied compressive strain increases from ε = 0.17 to 0.60, the wavelength decreases from λ ≈ 42.8 to 29.0 µm, while the amplitude increases from A ≈ 12.7 to 24.8 µm. Thus, the aspect ratio of the ridges increases from R ≈ 0.3 to 0.9 (Figure 4c). The resulting aspect ratio is significantly higher than that of ordinary wrinkles formed under slight film compression (i.e., R = 0.1−0.2). [21] The cross-sectional SEM images reveal that there is no delamination between the film and substrate. Numerical simulations in a previous study suggested that the aspect ratio of ridges is given by R ≈ 0.52ε pre + 0.23. [15a] Substituting ε pre = 1.5 into this equation yields R ≈ 1.0, which shows close agreement with the experimental value. Note that when the applied compressive strain is further increased by increasing the substrate prestretch, the surface becomes susceptible to undergoing a morphological transition from ridges to fold-like patterns, thereby suppressing further increases in the aspect ratio. Since the primary focus is on exploiting highaspect-ratio ridges, this study is hereafter restricted to the case of ε pre ≤ 1.5.

Surface Wettability
The anisotropic wetting of liquid droplets placed on a unidirectionally grooved surface can be described by evaluating the i) difference between contact angles of the droplets measured perpendicular to the groove direction and those parallel to such direction and ii) extent of the droplet distortion measured using the length of the major axis and width of the minor axis of the droplet baseline. [22] Therefore, we describe in the following sections how the contact angles and baseline shape of water droplets change according to the applied compressive strain and film thickness.

Water Contact Angles
The contact angles of water droplets measured perpendicular (perpendicular contact angle, θ ⊥ ) and parallel (parallel contact angle, θ ∥ ) to the groove direction (Figure 5a) are plotted as a function of the applied compressive strain ε in Figure 5b. Note that the contact angles for the random wrinkles (ε = 0.00, Figure S4, Supporting Information) were measured from the longitudinal and transverse directions of the substrate, which are denoted by θ ⊥ and θ ∥ , respectively. When ε = 0.00, the contact angles remain nearly constant, irrespective of the direction from which the droplets are observed, which indicates that the surface wettability is isotropic. The contact angles θ for the

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low-aspect-ratio wrinkles can be characterized by the Wenzel equation expressed by cos θ = rcos θ 0 , where θ 0 is the contact angle measured on a flat surface, and r ( > 1) is the roughness factor defined as the ratio of the actual surface area to the projected area. Using the experimentally measured value of θ 0 ≈ 77° and an estimate of r ≈ 1.02 (see the Supporting Information), the contact angle is calculated to be θ ≈ 77°, which is in reasonable agreement with the experimental values presented in Figure 5b.
As the applied compressive strain increases to ε = 0.09, the perpendicular contact angle measures θ ⊥ ≈ 97°, while the parallel contact angle remains at θ ∥ ≈ 78°. These changes of the contact angles demonstrate that the surface wettability becomes anisotropic. When the applied compressive strain further increases to ε = 0.60, the perpendicular contact angle reaches θ ⊥ ≈ 112°, while the parallel contact angle decreases to θ ∥ ≈ 68°.
To quantitatively understand the effect of the applied compressive strain on the wetting anisotropy, the values of contact angle difference Δθ = θ ⊥ − θ ∥ are plotted as a function of the compressive strain ε in Figure 5c. As the applied compressive strain increases from ε = 0.09 to 0.60, the contact angle difference increases from Δθ ≈ 19° to 44°. These results suggest that the magnitude of wetting anisotropy can be tuned by controlling the applied compressive strain. Furthermore, the greatest magnitude of wetting anisotropy can be attained when the applied compressive strain of ε = 0.60 is employed.
We now discuss the mechanism of the increase of the perpendicular contact angles by considering the case of h ≈ 206 nm. Contact angles of liquid droplets placed on surfaces with high-aspect-ratio patterns can generally be estimated using the Cassie-Baxter equation given by cos θ = fcos θ 0 + f − 1, where f is the fraction of the solid-liquid interface. Substituting Figure 5. Water contact angles. a) Schematic illustration of a water droplet placed on surfaces with hierarchical patterns, where the contact angles are measured perpendicular (θ ⊥ , colored orange) and parallel (θ ∥ , colored blue) to the groove direction. b,c) Contact angles θ ⊥ and θ ∥ b) and their differences Δθ = θ ⊥ − θ ∥ c) as a function of the applied compressive strain ε (h ≈ 206 nm), where the insets in (b) show the images of the water droplets (2 µL each) placed on the surfaces for ε = 0.00 and 0.60. d,e) Contact angles θ ⊥ and θ ∥ d) and their differences Δθ = θ ⊥ − θ ∥ e) as a function of the film thickness h ( ε pre = 1.5). the experimentally measured values of θ ≈ 112° and θ 0 ≈ 77° into this equation yields f ≈ 0.5. Here, we assume that the surface geometry of the hierarchical patterns can be represented by an array of trapezoids ( Figure S5, Supporting Information). By considering the geometric characteristics and experimentally obtained values, the penetration depth d of the water droplet measured from the top of the trapezoids is calculated to be d ≈ 6.6 µm (see the Supporting Information). Since the amplitude of the hierarchical patterns is A ≈ 24.8 µm (Figure 4b), the estimate suggests that the water droplet partially wets the hierarchical patterns disposed on the surface, while air is trapped beneath the droplet.
The different tendency between the contact angles θ ⊥ and θ ∥ with respect to the applied compressive strain ε illustrated in Figure 5b is attributable to energy barriers that are imposed on the droplet by the hierarchical patterns. [7] The three-phase contact line perpendicular to the groove direction is pinned around the pattern peaks owing to the energy barriers. Even though the pattern amplitude increases with increasing compressive strain, the contact line should remain pinned because the energy barriers become greater. Meanwhile, no energy barriers are imposed on the droplet parallel to the groove direction, thereby allowing the contact line to easily move along the pattern peaks until the contact angle attains an equilibrium value. Therefore, the perpendicular contact angle θ ⊥ increases with increasing compressive strain. By contrast, the parallel contact angle θ ∥ slightly decreases as the applied compressive strain increases, which can be ascribed to the roughnessenhanced wetting that is characterized by the Wenzel equation.
As described above, the water droplets placed on surfaces with the aforementioned hierarchical patterns are considered to be in the Cassie-Baxter state. In particular, the high-aspect-ratio ridges are assumed to considerably reduce the area fraction of the solid-liquid interface and increase the area fraction of the air-liquid interface, which enhances the surface hydrophobicity. Let us consider a water droplet that comes into contact with surface patterns with inclined walls. The Laplace pressure Δp at the solid-liquid interface, which plays a crucial role in maintaining the Cassie state, is written as where γ, θ, R 0 , β, and h are the surface tension of water, contact angle, half width of the base edges of the two adjacent inclined walls, inclination angle, and height of the water meniscus, respectively ( Figure S6, Supporting Information). [23] This equation indicates that the Laplace pressure increases as the inclination angle of the sidewalls decreases. Consequently, the air entrapment beneath the droplet is more likely to occur. In the present study, cross-sectional SEM images of the hierarchical patterns reveal that the inclination angle of the ridge walls becomes smaller with increasing compressive strain ( Figure S7, Supporting Information). Therefore, the air entrapment is expected to be enhanced for larger values of ε, which causes the increase in perpendicular contact angle θ ⊥ (Figure 5b).
When the applied compressive strain is fixed at ε = 0.60, the perpendicular contact angle increases from θ ⊥ ≈ 102° to 112° as the film thickness increases from h ≈ 26 to 206 nm, while the parallel contact angle decreases from θ ∥ ≈ 74° to 68° (Figure 5d). When the film thickness further increases to h ≈ 413 nm, the perpendicular and parallel contact angles increase to θ ⊥ ≈ 115° and θ ∥ ≈ 73°, respectively. Figure 5e plots the values of the contact angle difference Δθ as a function of the film thickness h. As the film thickness increases from h ≈ 26 to 206 nm, the contact angle difference increases from Δθ ≈ 28° to 44°. Further increase in the film thickness to h ≈ 413 nm results in a slight decrease of the contact angle difference. This decrease is primarily due to the decrease of the parallel contact angle that occurs when the film thickness increases from h ≈ 206 to 413 nm (Figure 5d). These results show that the magnitude of wetting anisotropy can be controlled by adjusting the film thickness. Furthermore, within the film thickness range tested in the present study, the wetting anisotropy is most enhanced by setting the film thickness at h ≈ 206 nm when the applied compressive strain is fixed at ε = 0.60.

Baseline Shape
The length of the major axis and width of the minor axis of the droplet baseline, which are denoted by l and w, respectively (Figure 6a), are plotted as a function of the applied compressive strain ε in Figure 6b. When the film is simply deposited on the substrate without any prestretch (i.e., ε = 0.00), the values of l and w are approximately the same as 2.1 mm, which indicates that the baseline shape is nearly a perfect circle, and the surface wettability is isotropic. As the applied compressive strain increases to ε = 0.60, the length increases to l = 2.6 mm, while the width decreases to w = 1.5 mm. Figure 6c plots the ratio of the length to width (i.e., l/w) as a function of the applied compressive strain ε. When ε = 0.00, the ratio measures l/w ≈ 1.0, which clearly shows the wetting isotropy. Meanwhile, the ratio increases from l/w ≈ 1.3 to 1.8 as the applied compressive strain increases from ε = 0.09 to 0.60.
In particular, a sharp increase of the ratio is observed when the applied compressive strain is increased from ε = 0.38 to 0.55. This trend is consistent with the marked increase in contact angle difference observed when the applied compressive strain increases from ε = 0.38 to 0.55 (Figure 5c). Both increases are probably caused by the remarkably increased aspect ratio of the ridges that plays a critical role in imposing enhanced geometric confinements on the droplet (Figure 4c). As described in the previous section, the contact line perpendicular to the groove direction is assumed to be pinned around the ridge peaks. Since the wavelength of the ridges decreases with increasing compressive strain (Figure 4b), the width should decrease accordingly. Meanwhile, the length could increase as the applied compressive strain increases because the contact line can readily move along the peaks. These possible behaviors are a reasonable cause for the increased values of l/w with increasing compressive strain ε. Figure 6d plots the length l and width w of the droplet baseline as a function of the film thickness h. As the film thickness increases from h ≈ 26 to 206 nm, the length increases from l ≈ 2.1 to 2.6 mm, while the width decreases from w ≈ 1.7 to 1.5 mm. When the film thickness further increases to h ≈ 413 nm, the length decreases to l ≈ 2.5 mm, while the width remains nearly unchanged at w ≈ 1.5 mm. Figure 6e plots the ratio l/w as a function of the film thickness h. As the film thickness increases from h ≈ 26 to 206 nm, the ratio increases from l/w ≈ 1.3 to 1.8. Further increase of the film thickness to h ≈ 413 nm leads to a slight decrease of the ratio (i.e., l/w ≈ 1.7). This decrease results from the decrease of the length l when the film thickness increases from h ≈ 206 to 413 nm (Figure 6d). These results demonstrate that the magnitude of wetting anisotropy can also be tuned by adjusting the film thickness. In particular, the wetting anisotropy with the greatest magnitude is achieved when the film thickness is adjusted to h ≈ 206 nm under the condition of ε pre = 1.5. Taken together, our results suggest that the wetting anisotropy on the hierarchical patterns can be finely tuned by simply adjusting the applied compressive strain and film thickness.

Future Directions
As the surface roughness is increased by introducing hierarchical patterns, the solid-liquid interface can be replaced by the liquid-air and solid-air interfaces. This phenomenon causes the Laplace pressure to increase, thereby enhancing the surface hydrophobicity. In the present study, the Laplace pressure induced by the hierarchical patterns is considered much higher than the pressure required to facilitate the transition from the Cassie state to the Wenzel state. [24] Therefore, the hierarchical patterns show the hydrophobicity when measured perpendicular to the groove direction, even though the gold nanofilm is intrinsically hydrophilic. Although the partial penetration of the space between the ridges by water is assumed (see section on Water Contact Angles), it remains unclear how the wrinkles on the ridges affect the wettability. Direct observations of the interface between the water droplet and the hierarchical patterns disposed on the surface under an environmental scanning electron microscope would be of great help. Furthermore, the hydrophobicity could be further enhanced by coating the Figure 6. Baseline shape of the droplet. a) Schematic illustration of the top view of a water droplet placed on a surface upon which hierarchical patterns are disposed, where the length of the major axis (l, colored pink) and width of the minor axis (w, colored green) of the droplet baseline are measured to evaluate the extent of droplet distortion. b,c) Length l and width w b) and their ratio l/w c) as a function of the applied compressive strain ε (h ≈ 206 nm), where the insets in (b) show the top-view images of the water droplets (2 µL each) placed on the surfaces for ε = 0.00, 0.17, and 0.60. d,e) Length l and width w d) and their ratio l/w e) as a function of the film thickness h ( ε pre = 1.5).

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patterns with a hydrophobic material. These aspects remain to be explored in future work.
The magnitude of the wetting anisotropy of a patterned surface can also be altered via surface chemistry. [25] In particular, surface hydrophilicity enhances the elongation of water droplets placed on unidirectionally aligned patterns. [26] Using the hierarchical patterns that have been made hydrophilic with oxygen plasma treatment, we indeed observe significant increases in the values of l/w ( Figure S8a,b, Supporting Information). Furthermore, the degree of droplet elongation on the hydrophilic surface changes depending on the droplet volume ( Figure S8c, Supporting Information). Meanwhile, isotropic wettability of the random wrinkles (Figure 6b) is retained even after oxygen plasma treatment ( Figure S8d, Supporting Information). These preliminary results suggest that future work could be focused on precise control of the chemical compositions of the hierarchical patterns to attain desired anisotropic wetting properties for designated volumes of water droplets. Regarding technological applications, the hierarchical patterns could be exploited to fabricate functional surfaces for fog harvesting and water collection when they are combined with appropriate chemical compositions; [27] the small wrinkles may play a role in the nucleation and growth of water droplets, while the large ridges may facilitate directional transport of the grown droplets ( Figure S8e,f, Supporting Information). Detailed investigations of such functions would be exciting research directions.

Conclusion
We have shown that hierarchical patterns comprising an array of ridges covered with highly aligned wrinkles can be obtained by exploiting the surface instability of bilayers comprising a gold nanofilm deposited on a substantially prestretched elastomer substrate. Upon film formation, highly aligned wrinkles spontaneously form on the surface. When the substrate prestretch is subsequently relaxed, the surface develops an array of high-aspect-ratio ridges, while retaining the aligned wrinkles. Consequently, a structural hierarchy appears on the surface. The wavelength and amplitude of the hierarchical patterns can be controlled by adjusting the compressive strain applied to the film and film thickness. Accordingly, the magnitude of anisotropic wetting can be tuned in a highly controlled manner. Our method would help create fabrication opportunities for functional surfaces with tunable anisotropic wetting properties.

Experimental Section
Pattern Formation: An elastomer substrate with a thickness of 1 mm and an initial length L 0 (VHB4910, 3 M Inc.) was prestretched with uniaxial tensile strains of ε pre = 0 − 2.0 using a custom-built stretcher. The surface was subsequently sputter-coated with a gold film (HSR-522, Shimadzu Corp.). For the film coating, a gold target (99.99%, Shimadzu) was used as the source. The film thickness h was controlled within a range of ≈26-413 nm by adjusting the duration of film coating. Thereafter, the prestretch imposed on the substrate was relaxed to apply nominal compressive strain ε = {(1 + ε pre )L 0 − L}/{(1 + ε pre )L 0 } to the film, where L ( > L 0 ) is the released length of the substrate. Unless otherwise noted, ε pre was fully released to apply ε = ε pre /(1 + ε pre ) to the film.
Surface Characterization: Surface morphological changes were characterized with respect to ε under an optical microscope (BX51M, Olympus Corp.) and a scanning electron microscope (ETHOS NX5000, Hitachi High-Tech Corp.) equipped with focused ion beam. Prior to imaging, the samples were coated with platinum to prevent any possible alteration of the surface morphology and any potential damage resulting from gallium ion irradiation. The wavelength and amplitude of the patterns were measured based on the top-view and cross-sectional microscope images. The surface wettability was evaluated by measuring the contact angle θ, length l, and width w of water droplets (2 µL each) placed on the surfaces. The measurements were performed using software ImageJ. The water droplets were observed using a goniometer (LSE-ME3, NiCK Corp.) and a digital camera (LPE-07 W, Sanwa Supply Inc.) in ambient air. The substrate temperature during the film deposition was measured using a temperature label (THERMO LABEL, NiGK Corp.).
Statistical Analysis: The wavelength and amplitude were measured for 10 wrinkles or ridges. The contact angles were measured at 7 different locations on the surface. The baseline width and length were measured for 5 droplets prepared on the surface. For each case, the results are expressed as the mean and the corresponding standard deviation.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.