Wetting on the Microscale: Shape of a Liquid Drop on a

May 11, 2012 - Marouen Ben Said , Michael Selzer , Britta Nestler , Daniel Braun , Christian Greiner , and Harald Garcke. Langmuir 2014 30 (14), 4033-...
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Wetting on the Microscale: Shape of a Liquid Drop on a Microstructured Surface at Different Length Scales Periklis Papadopoulos,† Xu Deng,†,‡ Lena Mammen,† Dirk-Michael Drotlef,† Glauco Battagliarin,† Chen Li,† Klaus Müllen,† Katharina Landfester,† Aranzazu del Campo,† Hans-Jürgen Butt,† and Doris Vollmer*,† †

Max Planck Institute for Polymer Research, Ackermannweg 10, D-55128, Mainz, Germany Center of Smart Interfaces, Technical University Darmstadt, D-64287 Darmstadt, Germany

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‡

S Supporting Information *

ABSTRACT: Describing wetting of a liquid on a rough or structured surface is a challenge because of the wide range of involved length scales. Nano- and micrometersized textures cause pinning of the contact line, reflected in a hysteresis of the contact angle. To investigate contact angles at different length scales, we imaged water drops on arrays of 5 μm high poly(dimethylsiloxane) micropillars. The drops were imaged by laser scanning confocal microscopy (LSCM), which allowed us to quantitatively analyze the local and large-scale drop profile simultaneously. Deviations of the shape of drops from a sphere decay at two different length scales. Close to the pillars, the amplitude of deviations decays exponentially within 1−2 μm. The drop profile approached a sphere at a length scale 1 order of magnitude larger than the pillars’ height. The height and position dependence of the contact angles can be understood from the interplay of pinning of the contact line, the principal curvatures set by the topography of the substrate, and the minimization of the air−water interfaces.

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θrec. The difference defines the contact angle hysteresis, Δθ = θadv − θrec. It quantifies the degree to which the macroscopic contact angle of a drop depends on its history rather than thermodynamic equilibrium. To improve insight into the interplay between the contact angle, hysteresis, and pinning, previous studies investigated substrates patterned with chemical stripes or topographic ridges.6,8,17,21 Asymmetric patterns can cause deformation of drops.18,21 Recent numerical studies calculated pinning points and contact angles with a resolution higher than the length scale of the roughness pattern, but at the expense of spatial extension.22,23 Also, experimental studies suffer from limited spatial resolution. To the best of our knowledge, the contact angles close to a pinning site and the three-dimensional drop shape have never been quantitatively measured simultaneously. However, this information is required to understand the relationship between the microscopic structure of a solid surface and the macroscopic contact angle. In most cases the contact line is studied by optical microscopy.24−27 Recently, confocal imaging experiments aimed at clarifying this discussion have been carried out.28,29 Wu et al. investigated the contact angle on a smooth substrate patterned with hydrophilic and hydrophobic patches. Using water dyed with rhodamine B, they visualized the contact line with a resolution of about 10 μm.29 However, rhodamine B

INTRODUCTION Wetting is of immense importance in technology and everyday life. It plays a key role in the morphology and stability of a liquid on a given surface.1,2 The wetting behavior controls the dynamics of spreading of drops on leaves or insect wings as well as the surface properties of a substrate after spray-coating or drop-casting.3 Some processes require fast and homogeneous wetting,4,5 whereas in other applications antiwetting or selfcleaning is required.6−10 Primarily, the wetting properties depend on the surface energy.11,12 The contact angle Θ on an ideally flat, homogeneous, and inert surface can be quantified by Young’s equation cos Θ = (γSV − γSL)/γLV. Here, γLV is the liquid−vapor, γSL is the solid− liquid, and γSV is the solid−vapor interfacial tensions.13 However, real surfaces are chemically inhomogeneous and rough.11,14 Wenzel accounted for roughness by introducing a roughness factor, defined as the ratio of the actual to the projected surface area.15 It has been shown that the contact angle of rough surfaces is only affected by the surface properties in the vicinity of the liquid−substrate−vapor interface, the socalled three-phase contact line.14,16−19 AFM measurements of nonevaporating drops (such as polymers)20 provide a contact angle with a resolution of a few nanometers. However, these studies are limited to low contact angles θ < 90°. Inhomogeneities and roughness, even of a few nanometers, lead to pinning of the contact line.6,8,17,21 Pinning prevents drops from reaching their global equilibrium shape. The macroscopic contact angle just before a droplet advances, θadv, exceeds the macroscopic contact angle just before it recedes, © 2012 American Chemical Society

Received: January 28, 2012 Revised: May 10, 2012 Published: May 11, 2012 8392

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adsorbed at the air−liquid and solid−liquid interfaces and caused a reduction of the interfacial tension and pinning. Here, we employed a model substrate composed of an array of micropillars, in order to quantify drop shape variations at a resolution higher than the length scale of roughness. To investigate the shape of the liquid surface, we imaged water drops on smooth and microstructured hydrophobic surfaces with vertical resolution of 0.7 μm with a laser scanning confocal microscope (LCSM). The microstructured surface consisted of micropillars (5 μm radius, 5 μm height) arranged in a square lattice with 20 μm lattice distance. We mapped the drop contour surrounding a pinning point and simultaneously the macroscopic three-dimensional drop shape. These results are compared to conventional contact angle measurements on the same substrate.

Figure 2. (a) Hydrophobic N-(2,6-diisopropylphenyl)-3,4-perylenedicarboxylic acid monoimide (PMI) dye, used for labeling the PDMS substrate. (b) Absorption (dashed black) and fluorescence (solid red) spectra of PMI. Both spectra were measured in a PDMS film containing PMI at a concentration of ∼0.05 mg/mL. The absorption shows a maximum around 505 nm, whereas the emission maximum is around 525 nm. The absorption spectrum is measured with a PerkinElmer UV−vis spectrometer and the emission with the Leica TCS SP5 II confocal microscope by varying the spectral range in steps of 5 nm. (c) Chemical structure of N,N′-(2,6-diisopropylphenyl)-1,6,7,12-tetra(1-methylpyridinium-3-yloxy)perylene-3,4,9,10-tetracarboxylic acid diimide tetramethane−sulfonate (WS-PDI). This hydrophilic dye was used to label the water phase. (d). Absorption (black) and fluorescence (red) of WS-PDI. The spectra are obtained from a 0.05 mg/mL water solution of WS-PDI. The absorption and emission maxima are 545 and 590 nm, respectively. The roughness of the pillars’ surface and of the flat substrate was determined by AFM. Tapping-mode AFM imaging was performed with a Dimension 3100 CL (Digital Instruments) at 25 ± 2 °C using silicon AFM probes (OMCL-AC 240TS, Olympus, Japan) with a resonance frequency of about 70 kHz and a tip radius of less than 20 nm. Contact angle measurements were performed with a contact angle meter, Data Physics, OCA35. Static contact angles were measured depositing a liquid droplet of 10 μL on the surface. Advancing and receding contact angles were measured using a sessile droplet of 5 μL, with the needle in it, and then subsequently increasing and decreasing the liquid volume. Interfacial tension was measured following the Wilhelmy plate method, using a platinum plate cleaned with a Bunsen burner, with a DCAT11 tensiometer (DataPhysics Instruments GmbH). Confocal Microscopy. To visualize the 3D shape of a water droplet deposited on this microstructured surface by using LSCM, both the PDMS pillars and the water droplet had to be fluorescently labeled. A Leica TCS SP5 II - STED CW inverted confocal microscope with five detectors was employed. The spectral ranges could be freely varied, allowing the measurement of the emission from different dyes and the reflected light from the interfaces simultaneously. Hydrophobic perylenemonoimide dye (PMI, Figure 2a)30 was added to PDMS. For water, various hydrophilic dyes were tested. Most dyes tend to adsorb at the water−PDMS or water−air interface, changing the interfacial tensions. Water-soluble perylenediimide31 (WS-PDI, Figure 2c) was the most hydrophilic dye. The high efficiency of WSPDI in water arises from the diisopropylphenyl groups that hinder stacking and the high hydrophilicity of pyridinium salt. 0.1 mg/mL is sufficient to image the dyed water drop by laser scanning confocal microscopy. At these concentrations the dye hardly changes the surface tension γ of water. At a concentration of 0.1 mg/mL (0.06

Figure 1. Sketch of the fabrication of cylindrical PDMS pillars. (a) A SU-8 photoresist patterned wafer with cylindrical holes was used as template. (b) A 10:1 ratio of PDMS prepolymer and cross-linker (Sylgard 184, Dow Corning) labeled with the hydrophobic PMI dye was poured on the template. Care was taken that the thickness of the PDMS film did not exceed 30 μm. Excess material is allowed to drain slowly. Finally, a thin (140 μm) glass slide is placed on the PDMS film (blue). (c) After the PDMS film is cured at 100 °C for 1 h the glass slide is removed slowly, so that the square lattice of cylindrical pillars remains undamaged on the glass slide. The total thickness is about 170 μm.

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MATERIALS AND METHODS

Soft Lithography. The microstructures consisted of cylindrical PDMS pillars arranged in a square lattice on glass (Figure 1). The PDMS pillars were prepared by soft-molding of poly(dimethylsiloxane) (PDMS, Sylgard 184, Dow Corning) on SU-8 patterned templates that were hydrophobized with (1H,1H,2H,2H)perfluorooctyltrichlorosilane. The flat-top cylindrical pillars had a radius of R = 5 μm, height H = 5 μm, and center-to-center distance P = 20 μm. PDMS was fluorescently labeled with PMI dye (Figure 2a,b) that was mixed with PDMS and the cross-linker (0.05 mg/mL). The morphology of the substrate was characterized by scanning electron microscopy (SEM) with a LEO 1530 Gemini (Zeiss, Oberkochen, Germany) at low operating voltages (0.5−1.4 kV). The samples were not modified before measurement. 8393

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mM) in water, the surface tension of the solution was 71 mN/m, only slightly lower than that of pure water, γLV = 72 mN/m (γ = 72 mN/m at 0.05 mg/mL and γ = 70 mN/m at 0.2 mg/mL). The emission maximum of PMI in PDMS is at λPMI = 525 nm (Figure 2b) and for WS-PDI in water at λWS‑PDI = 590 nm (Figure 2d), i.e., well above that of PMI, so the overlap in fluorescence from dyed PDMS and water was minimal. To excite the dyes, two wavelengths were used: PMI was excited using the argon line at 488 nm; WS-PDI was excited using the 561 nm wavelength of a DPSS laser. Fluorescence from water (Figure 3c) and PDMS (Figure 3d), as well as the reflected light from the interfaces (Figure 3e), were

air interface sharply bends upward. The intensity of reflected light depends on the differences of the refractive indices and the angle of incidence (Figures S1 and S2). The reflection from the PDMS−water interface was barely measurable, due to the similarity of refractive indices (nH2O = 1.33 and nPDMS = 1.45), in contrast to the strong reflection at the PDMS−air interface (nair = 1.0). If the interface is not horizontal, only part of the reflected light is collected by the objective (Figure S2). Superposition of the fluorescence and reflection images accurately depicts the morphology of all three interfaces (Figure 3e). Figure S1 shows images where the water was not dyed, verifying that low concentration of dye did not affect the drop shape within experimental accuracy. The absence of reflection on top of the pillars, supported by the fluorescence images of the water−PDMS interface, proved that the pillars were completely wetted by water, without trapped air. Here we define the contact angle θLSCM obtained by LSCM images (Figure 4). The angle determined by normal optical

Figure 3. Fluorescently labeled substrate and water drops. (a) Scanning electron microscope image of a square lattice of cylindrical PDMS pillars, prepared by soft-molding. Inset: magnification of a single pillar. The root-mean-square roughness (rms) on top of and in between the pillars was determined by AFM on an area of 1 × 1 μm2 and calculated to be 5 ± 2 nm. SEM images were taken without modifying the pillars’ surface. (b) Schematic side view of a water droplet placed on the pillar array. (c) Fluorescence image of a section of a water droplet dyed with WS-PDI in contact with PDMS pillars and air. The PDMS substrate is labeled with PMI and is not visible because the wavelengths of PMI and WS-PDI are well separated. (d) Fluorescence image of a section of a dyed PDMS microstructured substrate. (e) Superposition of the simultaneously recorded confocal images of water (cyan), PDMS (yellow), and light reflected at the PDMS−air interface (magenta).

Figure 4. Fitting of the contact angle θLSCM, as defined in the text. (a) The fluorescence image (Figure 3c) is corrected for attenuation due to spherical aberration (dry objective, dye in water), by normalizing the intensity of each line. Areas of about 7 μm high and 50 μm width are taken to calculate the contact angle “on the pillars”. Heights z are measured with respect to the plane at the top of pillars (dashed line). (b) 3D representation of the intensity of the selected part. The intensity of the pixels is plotted as height. (c) The selection is fitted with a 2D step function with arbitrary boundaries.

measured simultaneously. After deposition the substrate was slightly vibrated to allow the drop to approach its equilibrium shape. Immediately after deposition, a cap was placed over the drop to suppress evaporation. The 3D image stacks were recorded by scanning subsequent xy planes at different heights z and processed with the ImageJ software. In order to ensure that the coordinates of the water− air interface, which is the main interest of this work, are measured accurately, a dry objective with high NA and a correction ring was employed (40×/0.85). In this case all distances are correct, when the light path is in air. However, this causes a progressive decrease of intensity from dyed water, as height increases. For some xy images, where high vertical resolution was not necessary, a low magnification 10×/0.3 objective was used.

microscopy on a 0.1 mm to 1 mm length, more than 1 order of magnitude longer than the roughness, is referred to as the “macroscopic” contact angle θm. In order to compare the angles directly, vertical sections (xz) through the drop are evaluated to calculate the contact angle θLSCM. If not stated otherwise, water fluorescence image areas of about 7 μm height and 50 μm width are fitted with a suitable step function, as shown in Figure 4. In some cases the sections were shifted vertically to investigate the influence of height z on the measured values. For a flat PDMS substrate θLSCM was compared with θm measured with a commercial contact angle measurement device (Figure 5). The drop shape was fitted assuming a sessile drop profile giving values for θm = 109 ± 3° (Figure 5a). Within experimental accuracy, this value agreed with θLSCM = 107 ± 1° (Figure 5b). Accuracy was limited only by image noise. The advancing and receding contact angles for flat PDMS were 115° and 75°, respectively. For contact angles close to 90°, the fluorescence intensity near the water−air interface was low. Reflection and refraction allowed only a small fraction of the emitted light to reach the objective (Figure 5b and Figure S2). On microstructured surfaces water drops formed static macroscopic contact angles of θm = 142° and θLSCM = 138°

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RESULTS AND DISCUSSION For fluorescence imaging of the water−PDMS and water−air interfaces, the labeled water droplet was deposited on the microstructured surface (Figure 3a,b). A confocal image of a sessile water drop on PDMS pillars is shown in Figure 3c. This 2D cross-section in the xz plane shows water in contact with PDMS pillars and air with a resolution of about 0.25 and 0.7 μm in the horizontal and vertical directions, respectively. Water sitting on the PDMS substrate follows the topography of the pillars, reflected in a periodic step profile. The small height to distance ratio favors the Wenzel state, i.e., complete wetting of the pillars’ surfaces. At the three-phase contact line the water− 8394

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contact line were completely wetted (Figure 6b). This is confirmed by the absence of reflections at the top of the pillars. Thus, the contact angle results from interplay of the different boundary conditions: on the bottom and the side of the pillars, θ was fixed to the value for flat PDMS. However, the pillar sides tended to induce a curvature in the horizontal direction. The interplay of the different principal curvatures set by the contact line gave rise to both convex and concave regions (in the xzplane) of the drop shape (Figure 6d). Because of pinning, the macroscopic contact angle depends on the orientation of pinning as well as on the vertical distance from the substrate. Different cases are shown in Figure 7. In case of pinning of the contact line along the diagonal of the square lattice (Figure 7a−d) the large pillar−pillar distances caused variations of θLSCM at z = 0 by up to 20° (Figure 7c, black dots). In the middle between the pillars θ LSCM approached the value measured on a flat substrate, θLSCM = 107°. The contact angle θLSCM increased toward 132° close to vertical sides and the rim of the pillars’ top. The amplitude of the periodic variation decayed with increasing vertical distance from the pillars’ surface and was already less than 5° at z = 10 μm (Figure 7c, red dots). In contrast, when the contact line was pinned along the main axis (Figure 7e−h), θLSCM reached 141° due to the shorter interpillar distance (Figure 7g). The amplitude of the periodic variation of the contact angle was lower and superimposed on a continuous increase. Local maxima are caused by the vertical sides. Minima correspond to the interpillar valleys and the flat areas on top of the pillars. At the rim of the pillars’ top the contact angle can be varied within a broad range, according to the Gibbs criterion. The superimposed continuous increase of the contact angle hints that large-scale constraints intervene with the local constraints, resulting from the shape and distance of the pillars. This interplay will be discussed in the context of Figure 8. Not only θLSCM but also the macroscopic contact angle θm varied between 128° and 142°, depending on the direction of the light path of the camera with respect to the underlying substrate (Figure 7d,h). This dependence on details of roughness and the angle of view caused the reported variations in θm on rough surfaces.27 In contrast, on a flat PDMS substrate (Figure 7i−l) the variation in θLSCM was less than 2° (Figure 7k). The tiny hump, at y = 18 μm, was caused by a submicrometer sized dust particle, sticking to the substrate (Figure S3). The pronounced variations of the contact angle θLSCM are in contrast to the nearly spherical macroscopic drop shape,

Figure 5. Contact angles at different length scales. (a) Static contact angle of water drops (∼10 μL) on a flat PDMS surface measured by optical microscopy, θm, and (b) LSCM, θLSCM. (c, d) Respective images for a water drop on a PDMS pillar square. The drop profile in the xz-plane is analyzed to obtain θLSCM (Figure 4).

(Figure 5c,d), when the drops were viewed from a direction parallel to the main axis of the square pillar lattice. As expected, these values were between, but closer to the advancing (θm,adv = 148°) compared to the receding contact angle (θm,rec = 60°).11 An increase of the contact angle on the wetted pillar lattice was expected from the Wenzel model, cos θW = r (γSV − γSL)/γLV, because of the additional solid−liquid and solid−vapor interface.15 Here, γLV is the liquid−vapor, γSL the solid−liquid, and γSV the solid−vapor interfacial tension, and r defines the ratio of the actual surface area to the projected area. In this case r = 1 + 2πRH/P2 = 1.39, giving a Wenzel angle of θW = 114°. Both θm and θLSCM were higher than the calculated Wenzel angle, confirming that the model is inadequate. This is in line with previous observations because the Wenzel equation does not take pinning and hysteresis into account.14,16−19 In order to reveal details of contact line pinning and variations of the contact angle, 3D images of the drop were taken. Lowmagnification images of the drop revealed that the contact line was preferably pinned at the pillars along the main axes of the square lattice or diagonally (PD = √2P = 28 μm, Figures 3a and 6a). Between the PDMS pillars the contact line segments were convex. The lengths of the straight and curved segments depend on details of how the drop was deposited and handled to approach local equilibrium. This includes the kinetic energy the drop gains while detaching from the needle and the amplitude and vibration of the drop after deposition on the substrate. High-resolution imaging of the water profile and PDMS substrate show that the top surfaces of the pillars at the

Figure 6. 3D images of a sessile water drop on a square lattice of PDMS pillars. (a) Horizontal section (10×) of a fluorescently labeled sessile water drop just above the pillars. The drop is preferably pinned along the main axes and the diagonal of the square lattice. (b) 3D image (40×) of a section of the drop, showing pinning along the main axis of a PDMS pillar square lattice. This section is indicated with a white square in (a). The angle θLSCM is marked. (c) Magnified section of (b) showing the varying curvature of the water−air interface. (d) Contact line of a wetted pillar (red line). The gray part is wetted with water; the yellow region is in contact with air. 8395

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Figure 7. Variation of θLSCM along the contact line. (a−h) Contact lines and angles (θLSCM) of water drops deposited on a microstructured substrate and (i−l) on flat PDMS. (a) Section of a 3D fluorescence image, where a drop is pinned along the diagonal of the lattice (Figure 6a). The value of θLSCM at y = 0 and z = 0 is added. (b) Horizontal (xy) cross section of the water air interface at the bottom of the substrate (z = −5 μm). The contact angle at the pillars’ side is indicated (white circle). (c) Variation of the respective contact angle θLSCM along the contact line, evaluated at z = 0 (black points) and z = 10 μm (red points). (d) Macroscopic contact angle measured by optical microscopy. The drop is viewed at 45° with respect to the lattice. (e) The same drop is pinned along the square lattice main axis (Figure 6a). (f) Respective xy cross section (z = −5 μm), (g) contact angle values, and (h) optical microscopy image at 0°. (i−l) Respective images for a drop on a flat pillar lattice. The volume of the drop on the PDMS substrate was about 30 μL. In all other cases drop volume was about 15 μL. The length scale in each row is fixed.

Figure 8. Water drop on a microstructured surface. (a) Vertical (xz) section of the drop along the part of the contact line pinned at 45° (Figure 6a). (b) Horizontal (xy) section on top of the pillars (z = 0), denoted by “1” in (a). The white line shows the curvature on and between the pillars. (c) Section normal to the water−air interface at the top of the pillars, denoted by “2” in (a). The peak-to-peak amplitude of the deviation from the plane is denoted by A. (d) Similar section 2 μm higher in the z-direction, denoted by “3” in (a). (e) Scaled peak-to-peak deviation amplitude A/P as a function of scaled height z/P. The contact line is pinned at 0° (black points) or 45° (red points), and the respective pitch P is 20 and 28 μm (Figure 6a). The black line is a fit with exponential decay.

is the peak-to peak amplitude, P the pitch of periodically pinned contact line, and b a constant. Regardless of the pinning direction (Figure 6a), this coefficient is equal to b = 17.3 ± 0.5. Already at z = 5 μm the sinusoidal deviations of the water−air interface essentially vanished. Therefore, the contact angles estimated in Figures 4 and 7 at z = 10 μm may be considered as “macroscopic” angles. Despite this fast decay of the water−air interface fluctuations close to the pillars surface, long-range deviations of the water− air interface from its spherical shape persist. They are attributed

apparent when imaging the drop from the side or top at low resolution (Figure 7d,h,l).27 To quantify the height at which the drop takes a spherical shape, the variations of the contact angle were analyzed at length scales of z = 0.1−5 μm and z = 5−400 μm above the pillar’s top surface. Close to the substrate the local deviations of the water−air interface from a smooth plane are caused by the surface’s microstructure (Figure 8). These deviations have a nearly sinusoidal form (Figure 8c,d) and decay exponentially with height (Figure 8e). They can be fitted with the function d = (A/2) sin(2πy/P) exp(−bz/P), where A 8396

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contact angle is greater than for pinning along the diagonal (Figures 7a,e and 9d). These local variations need to be flattened because the minimization of the air−water interfacial energy of the macroscopic drop prefers a fixed contact angle. Therefore, the interfacial tension exerts a large-scale force on the shape of the water−air interface close to the substrate. This leads to the continuous variation of the contact angle between the maxima and minima set by the direction of pinning, as sketched in Figure 9d. For demonstration of the interplay between the microscopic and macroscopic constraints, the section shown in Figures 6b and 7e−h was off-centered. Thus, deviations from a spherical shape of a drop exist on different length scales, precluding the assignment of a single macroscopic contact angle to the drop. From the conceptual point of view and for large drops on a flat homogeneous surfaces, a core region around the threephase contact line and a more macroscopic region have been distinguished.32 In the core region, which extends to typically 10 nm away from the solid/liquid interface, surface forces, such as van der Waals and electrostatic double-layer forces, influence the shape of the liquid surface. In the macroscopic region, Young’s contact angle describes the slope of the liquid surface. As discussed above, from the experimental point of view and for microstructured surfaces, it would be more appropriate to indicate the length scale over which the slope of the liquid surface near the three-phase contact line is measured. In that sense, one could discriminate between a nanoscopic contact angle, as measured by atomic force microscopy or scanning electron microscopy, on the length scale of 10−100 nm, a microscopic contact angle, as determined by LSCM, on the 1− 10 μm scale, and a macroscopic contact angle measured by other optical techniques on the >10 μm scale.

to the noncircular shape of the contact line. For a quantitative analysis, horizontal sections at different heights z were considered. Directly above the pillars (z = 0), the horizontal cross section resembled a square with rounded edges (Figure 9a). Moving further up, it became more circular (Figure 9b).

Figure 9. Variation of 2D horizontal cross sections (10×) of a water drop (15 μL) with increasing vertical distance z from the microstructured substrate. (a) Just above the substrate (z = 0). The asymmetry of the contact line, ξ, is defined as the ratio of radius R1 to the shortest distance from the center R2, ξ = R1/R2. The contact angle took its minimum value, θmin, at the center of the diagonal and its maximum value, θmax, at the center of the main axis. (b) With increasing distance z from the substrate the asymmetry of the contact line decreased, until finally, the water cross section became almost circular. (c) Asymmetry factor, ξ, of horizontal cross sections through a drop, calculated at different distance to the substrate. An exponential fit is indicated by the red line. Inset: superposition of an image of a drop taken by optical microscopy along the main axis (cyan) and diagonal (blue), showing that the asymmetry persisted well above the surface. (d) Sketch of the variation of the macroscopic contact angle along the contact line. These large-scale variations need to be distinguished from the local variations of the contact angle, caused by the shape of a single pillar and the pillar−pillar distance (e.g., Figure 7c). The red rectangles show the measurement ranges in Figures 7a−d and 7e−h, respectively. The latter is deliberately slightly off the maximum.

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CONCLUSIONS LCSM images of wetting of a hydrophobic microstructured substrate on micrometer-length scale illustrate the origin of the variations of the contact angle. Depending on the length scale probed, the shape and arrangement of asperities, and the largescale constraints set by a spherical drop shape, different contact angles are reported. By using LSCM, pinning can be quantitatively studied as a function of the size, shape, and chemistry of the substrate asperities. Similar information can be obtained for all transparent substrates and liquids. In particular, LSCM will provide a complementary technique to assist the development of superhydro- and superamphiphobic coatings,33 and it will offer new insight into capillary bridges, dominating the rheological properties of wet (nano)particles, colloids, or granular matter.34 The method’s flexibility opens new ways for dynamic studies of wetting which have not been explored yet but are of high scientific and technological interest.

Asymmetry was quantified by the ratio ξ of the radii of the outer (R1) and inner (R2) bounding circle (Figure 9a). The ratio decreased from ξ = 1.15 at z = 0 to 1.05 at z = 200 μm, 10 times the interpillar distance and 40 times their height (Figure 9c). It also decays nearly exponentially as ξ = ξ0 − c exp(−z/L), where ξ0 = 1.03 ± 0.01, c = 0.12 ± 0.01, and L = 104 ± 5 μm. Therefore, the observed superimposed continuous increase of the contact angle on the local variations (Figure 7g) results from the interplay of the (i) microscopic boundary conditions set by the shape of the pillars and the interpillar distance with (ii) the large-scale constraints set by the minimization of the air−water interfaces. The latter favors a spherical calotte. The dependence of the contact angle on the interpillar distance sets a 4-fold symmetry. If the pinning is along the main axis, the

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ASSOCIATED CONTENT

S Supporting Information *

Detailed discussion on avoiding artifacts in confocal microscopy measurements. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected], Tel +49 6131 379 113, Fax +49 6131 379. 8397

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Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to A. Kaltbeizel and J. O. Morsbach for their technical support. We thank J. Ally, D. Quéré, J. Yeomans, and C. Semprebon for fruitful discussions. Financial support is gratefully acknowledged from the Deutsche Forschungsgemeinschaft, via SPP 1420 (H.J.B.), SPP 1486 (D.V.), and DFGTR6 (P.P).

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dx.doi.org/10.1021/la300379u | Langmuir 2012, 28, 8392−8398