Exploring Defect Height and Angle on Asymmetric Contact Line Pinning

ARTICLE pubs.acs.org/JPCC

Exploring Defect Height and Angle on Asymmetric Contact Line Pinning Renate Fetzer*,† and John Ralston* Ian Wark Research Institute, University of South Australia, Adelaide, SA 5095, Australia ABSTRACT: Wetting of structured surfaces is of great interest but is mainly studied for Cassie state wetting. To avoid trapping of air, surfaces structured with pyramid-shaped defects are manufactured rather than pillars. Wenzel state advancing and receding water contact angles are measured on these tailored rough surfaces. Asymmetric results are found for sessile drop and captive bubble configurations. These discrepancies are attributed to the contact line curvature and different pinning forces, which appear along the contact line, reflecting the geometry. An estimate for the effect of the surface topography on advancing and receding contact angles in both configurations is derived and compared with the experimental data.

’ INTRODUCTION The interplay between substrate roughness and wetting properties is a highly active field of research. It is known that roughness on the nanometer scale as well as topographical features in the micrometer range and larger affect the wettability of a substrate.1 Another wetting property that is without doubt influenced by the roughness of a solid surface is the pinning force at the three phase contact line along with the contact angle hysteresis. To quantify the impact of roughness on advancing and receding contact angles, surfaces with well-controlled topography offer the best preconditions. Extensive work has been published, for instance, on regular arrays of microsized pillars.2
7 When dealing with the wettability of rough surfaces, two distinct wetting states need to be distinguished. A liquid drop may rest on top of the surface features, with air trapped between the drop and the surface. This situation is referred to as the Cassie state, usually exhibits large contact angles and small contact angle hysteresis, and thus has extensive application in the field of superhydrophobic surfaces.1,3,8
12 On moderately hydrophobic materials or surfaces with moderate surface gradients, the socalled Wenzel state of wetting is often found: The liquid in a sessile drop penetrates into the structure, and no gas is trapped.13 For such cases, Wenzel's equation relates the equilibrium contact angle on a rough surface, θ*, to Young's contact angle θY on the respective smooth surface with the same inherent wettability, cos θ* = r 3 cos θY.14 The roughness factor r is defined as the ratio of the actual surface area (of the rough surface) to the projected area. Wenzel's description of thermodynamic equilibrium is wellestablished but usually fails to predict the large contact angle hysteresis found for Wenzel state wetting.6,15 Instead, consideration of local pinning forces, balanced with elastic forces, along the contact line seems to be promising in the case of single, individual defects.16
18 Despite the extensive body of work on the wetting r 2011 American Chemical Society

of rough and microstructured surfaces, contact angle hysteresis due to collective pinning for Wenzel state wetting is only poorly understood. Only a few groups have succeeded in quantifying advancing contact angles on surfaces densely packed with distinct microscopic features.5,7 These latter studies focused on advancing sessile drops and rectangular posts. In this investigation, we extend the discussion to receding contact angles and complement the investigation of contact angles with captive bubble measurements. We use surfaces decorated with pyramid-shaped defects, where the pinning strength of the individual defects can be varied systematically. To ensure that we achieve wetting situations in the Wenzel state, our studies are restricted to surfaces that do not involve steep side walls or overhangs that may give rise to air trapping. To manufacture such surface features, well-controlled and with tunable size and steepness, photolithography in combination with wet etching of the underlying glass substrate was used. A checkerboard pattern was imprinted in a coating of photoresist SU8. After wet acid etching of the supporting Pyrex substrates, pyramid-shaped defects were left on the sample. The height of these defects was tuned by adjusting the etching time. To customize the inherent surface wettability, the topographically structured substrates were then coated with thin layers of chromium and gold, and a self-assembled monolayer of alkane thiols was adsorbed. Advancing and receding contact angles on these surfaces were investigated, obtained from both sessile drop and captive bubble configurations, and compared with an analytical expression derived from a line average of local surface angles. Received: April 18, 2011 Revised: June 16, 2011 Published: June 20, 2011 14907

dx.doi.org/10.1021/jp203581j | J. Phys. Chem. C 2011, 115, 14907–14913

The Journal of Physical Chemistry C

ARTICLE

Figure 1. Optical micrographs of checkerboard pattern (periodicity 10 μm) in SU8 (a) and etched in glass (b). Scale bar in both images, 20 μm.

’ EXPERIMENTAL SECTION Sample Preparation and Characterization. Photolithography in combination with wet etching of the underlying glass (Pyrex) was used to manufacture surfaces with equally sized, homogeneously distributed topographical defects. To provide good adhesion of the photoresist, thoroughly cleaned glass (Pyrex) disks were coated with a 10
20 nm thick layer of chromium by thermal vapor deposition. After further degreasing with iso-propanol, the chromium-coated Pyrex disks were coated with a 7 μm thick layer of SU8, in a Class 100 UV-protected clean room. SU8 is an epoxy-based negative photoresist with excellent structural integrity and chemical resistance after hard bake (200 °C, 5 min).19 The SU8 monomer is an aromatic hydrocarbon with eight epoxy functional groups available for crosslinking.19 Using standard UV-lithography procedures, a checkerboard pattern of 5  5 μm2-sized squares was imprinted into the SU8 layer. Optical micrographs of the checkerboard structure developed in SU8 are shown in Figure 1a and confirm the good quality and homogeneity of the lithographic technique. Prior to wet acid etching of the samples, the now exposed chromium (uncovered by SU8) was removed by immersion in a potassium permanganate solution. The glass disks were then etched in 40% hydrofluoric acid for several seconds (15
30 s). Potential leftovers of SU8 were removed by sonication in nitric acid, and chromium remains were dissolved in the potassium permanganate solution. Optical microscopy was used to confirm the uniformity of the etching step, cf. Figure 1b. To achieve a specific inherent surface wettability, self-assembled monolayers of mixed alkane thiols were anchored to the surfaces. To do so, freshly cleaned samples (rinsed with ethanol and high purity water, dried under a stream of nitrogen, 1 min exposure to air plasma) were coated by thermal metal vapor deposition with thin layers of chromium (2 nm) and gold (5 nm). Film thicknesses of 2 and 5 nm were chosen to provide good optical transparency and contrast. Then, the surfaces were immersed for 2 h in a 10
3 molar ethanol solution of 11mercapto-1-undecanethiol and perfluorodecanethiol (>99%, both purchased from Sigma Aldrich and used without further purification) with the two thiols mixed in a molar ratio of 2:3 (40% of CF3terminated thiol). After immersion, the samples were thoroughly rinsed with fresh ethanol and dried under a nitrogen stream. After static and dynamic wetting studies were performed, the thiol layers on the samples were removed by exposure to an air plasma for 1 min. Then, alkane thiol layers of 100% perfluorodecanethiol were adsorbed on the samples in the same way as described above, and the wetting experiments were repeated. The efficacy of the cleaning and replacement procedures was verified by surface analysis. The topography of the samples was captured using tapping mode atomic force microscopy (AFM). Scans that were sized

Figure 2. AFM images, 20 μm2 in size, of two different samples. During the initial stage of etching (stage A), flat tops are left on the defects, while later (stage B) pyramid-shaped structures are obtained.

20  20 μm2 were performed on four different spots of each sample to obtain good statistics and confirm the uniformity of the pyramid-shaped structures. Small areas of 1 μm2 scan size between the defects were imaged to quantify the small-scale roughness of the surfaces. Contact Angle Measurements. To characterize the static wettability of the samples, advancing and receding contact angles of water were measured using the sessile drop and the captive bubble configuration (Dataphysics OCA-20). A droplet (or bubble, respectively) was formed at the end of a straight (Ushaped) needle, attached to a syringe, and carefully brought in contact with the sample. Once contact was established, the volume of the water droplet (air bubble) was slowly increased (at a rate of 0.06 μL/s). This process was recorded from a side view. Using automatic tracking of the contour line and fitting of ellipses to the drop (bubble) shapes, the advancing (receding) water contact angle was measured, while the contact line was slowly moving. Special care was taken to ensure that the liquid
air interface was tracked very well in the vicinity of the contact line to obtain accurate and consistent contact angle data. Then, the volume of the droplet (bubble) was reduced at the same rate, and the receding (advancing) water contact angle was measured using again automatic tracking. For all static contact angle measurements, the samples were aligned 45° to the checkerboard pattern, cf. Figure 1b. On each sample, advancing and receding contact angles for both sessile drops and captive bubbles were measured on at least three different spots. To check for consistent chemistry of the surface coating, water contact angles were also measured on the flat parts of each sample.

’ RESULTS Surface Topography. In Figure 2, AFM images of two qualitatively different surfaces are shown. The schematic in Figure 2 explains the respective stages of etching for these samples. Up to a certain etch depth, the defects grow in height and are left with flat tops, the areas of which shrink with increasing etching time (stage “A” in Figure 2). Once the flat tops are gone (stage “B”), upon further etching, the defects 14908

dx.doi.org/10.1021/jp203581j |J. Phys. Chem. C 2011, 115, 14907–14913

The Journal of Physical Chemistry C

ARTICLE

Figure 3. Geometry of surface defects and the contact line pinned to a row of defects in 45° orientation.

Table 1. Defect Characteristics etching stage A

defect

maximum

height H (nm) slope s (nm/nm) 1640 (40)

>2

a

line fraction

roughness

f = 2d/p

factor r

top: 0.20 (3)

1.14 (2)

B1

1040 (60)

0.81 (3)

bottom: 0.64 (3) 0.73 (2)

B2

940 (40)

0.75 (5)

0.73 (2)

1.028 (3)

B3

915 (25)

0.60 (2)

0.77 (2)

1.032 (4)

B4

630 (30)

0.50 (3)

0.63 (1)

1.020 (5)

1.04 (1)

Measurement limited by finite slope of AFM tip; standard deviation in brackets. a

decrease in height and slope. Eventually, the samples become flat again. From the AFM images, the height H of the defects, their maximum slope s (in 90° orientation, cf. Figure 3), and the line fraction f = 2d/p (in 45° orientation) at the base of the defects were determined. Table 1 shows respective values for all samples used in this study. The values were averaged over at least 15 individual defects, situated in four different areas of the sample; numbers in brackets give the standard deviation. Furthermore, the roughness factor r introduced by Wenzel (ratio of surface area to projected area) was determined from the AFM images and is given in Table 1. The rms roughness of the etched glass surface between the defects was 1.2 (2) nm, measured on 1 μm2-sized images. Wettability of Flat Samples. Advancing and receding water contact angles were measured on all topographically structured surfaces, coated with either a monolayer of perfluorodecanethiol (termed 100% CF3) or a layer of mixed alkane thiols (40% CF3). Results obtained at 45° orientation from both sessile drop (SD) and captive bubble (CB) experiments are shown in Figure 4, plotted against the maximum slope s of the defects on the respective sample. The data points at slope zero correspond to values measured on the flat part of each sample, averaged over all samples of the same surface coating. The small error bars of 3
4° shown for flat samples, representing the standard deviation on the various surfaces, indicate very good reproducibility for the surface coatings. Furthermore, on the flat parts of the samples, the contact angle values obtained from sessile drops coincide with those measured with the captive bubble technique. A contact angle hysteresis of 10 and 18°, respectively, was found on the flat 100% CF3 and 40% CF3 coatings. Wettability of Pyramid-Shaped Defects. Once topographical defects are introduced to the surface, advancing and receding contact angles start to diverge, thereby increasing the contact angle hysteresis. This effect becomes more prominent for increasing defect slopes. Although contact angle values obtained using the two different techniques SD and CB follow generally

Figure 4. Static advancing and receding contact angle data on (a) purely CF3-terminated thiol coatings and (b) mixed thiol coatings (40% molar ratio of CF3), obtained using the sessile drop (SD) and the captive bubble (CB) configuration.

the same trend, they do not coincide any more. The disagreement seems to follow some systematic behavior: The advancing water contact angle measured at an increasing sessile drop, θSD adv, is consistently larger than θCB adv, that is, the contact angle obtained from a bubble that is decreasing in volume to allow the water contact line to advance. Similarly, the receding water contact angle measured when a captive bubble increases in volume, θCB rec , is systematically smaller than the receding contact angle of a sessile drop, θSD rec . This observation holds not only for the pyramid-shaped defects (maximum slope s < 1) but also for the pillarlike defects with flat tops (shown at s = 2). Wettability of Defects with Flat Tops. One peculiarity worth mentioning is that “real” (sticky) contact between a captive bubble and the surfaces with pillar-shaped defects (stage A) is not easily established. Once the bubble is brought in contact with such surfaces under water, dewetting of the water between bubble and surface does not take place spontaneously; the water contact angle stays at less than 10°, and the bubble can easily (with almost no adhesion) be detached from the surface. After nucleation of dewetting at the edge of the sample or a defect at the surface, however, “sticky” behavior of the bubble in contact with the surface is found, and consistent and reproducible values for both advancing and receding contact angles can be measured. These values are shown in Figure 4 at s = 2. Contact Area of Sessile Drops and Captive Bubbles. To elaborate on the previously mentioned discrepancies found in SD and CB measurements, top-view images of the droplets and bubbles were taken while advancing and receding on the topographically structured surfaces. As can be easily seen from the typical micrographs shown in Figure 5, the contact line is pinned to a row of defects only in the cases of an advancing contact line of a sessile drop or a receding contact line of a captive bubble. In both of these cases, the volume of the droplet or bubble, respectively, is increasing. During the opposite motions 14909

dx.doi.org/10.1021/jp203581j |J. Phys. Chem. C 2011, 115, 14907–14913

The Journal of Physical Chemistry C

ARTICLE

Figure 6. Evolution of the contact area of a droplet or a bubble.

Figure 5. Top-view images of the contact area between a droplet (left) or a bubble (right) and the topographically structured sample “B2” (left, 40% CF3; right, 100% CF3) on advancing (upper row) and receding (lower row) motion of the contact line.

(rec SD and adv CB), the volume of the droplet or bubble decreases while the measurements are taken. Here, the contact line is only weakly pinned to the defects but does not evolve a straight line over an extended length. Consequently, the contact area does not deviate substantially from a circular shape.

’ DISCUSSION Wenzel versus Cassie. Before discussing in more detail the contact angle data, it is important to know whether the droplets and bubbles are in the Wenzel or the Cassie state of wetting. In the Cassie state, air is trapped under the sessile drop, or liquid is left between the bubble and the surface. Thus, the droplet rests on a composite surface of solid and air, while the bubble contacts a surface composed of solid and water. The Wenzel state, however, refers to a uniform solid
liquid (solid
gas) interface between a drop (bubble) and a surface with no trapped air (water). As the height of the pyramid-shaped defects is gradually increased, the contact angle data start to deviate moderately from those determined on flat surfaces. There is no sudden change or discontinuity in contact angle values over the whole range of pyramid-shaped defects, which would indicate trapping of air (water). Furthermore, repeated expansion and shrinking of the drop (bubble) on the same spot does not change the observed contact angles as compared with the very first contact. From these observations, we conclude that all data on pyramidshaped defects shown in Figure 4 were captured in the Wenzel state. This was further confirmed by optical micrographs (Figure 5) of the contact areas of sessile drops and captive bubbles: No trapped gas or liquid was observed. Because no large slopes or overhangs and no sharp corners and wedges are present on the samples with pyramid-shaped defects, it is quite reasonable to expect the drops and bubbles to be in the Wenzel state. The situation changes dramatically for the defects with flat tops. As mentioned previously, “sticky” contact between a bubble and these samples was not established spontaneously. The nonadhesive state of the bubble corresponds to a Cassie situation, where a water film is trapped between a bubble and the surface. Dewetting of water only takes place on the flat tops of the pillarlike defects. However, because of the large surface slopes (s > 2), the contact line cannot penetrate into the structure. This is similar to superhydrophobic behavior observed on surfaces with tall and steep features; the latter prevent the liquid from penetrating into the structure. The Cassie state was found to be

metastable; once dewetting of the water in the structure is nucleated at some surface defect, the bubble switches to the Wenzel state, where it rests stably and contact angles may be measured in the usual way. A metastable Cassie state was also found for sessile drops resting upon pillarlike defects coated with the 100% CF3terminated thiol. In this case, air was trapped between the drop and the surface, which resulted in a superhydrophobic behavior. Decreasing the size of the droplet, however, was enough to force the system into the stable Wenzel state. Wenzel’s Equation. Recall from above that Wenzel's equation correlates the equilibrium contact angle on a rough surface, θ*, to Young's contact angle θY on a smooth surface of same inherent wettability, cos θ* = r 3 cos θY. For the structured surfaces investigated here with roughness factors r mostly below 1.1 (cf. Table 1), there is hardly any influence of the roughness on wettability predicted by Wenzel's equation. This is illustrated by the dashed lines in Figure 4, which show the predicted impact of roughness on advancing and receding contact angles using Wenzel's equation. Although Wenzel's equation seemed to successfully describe advancing and receding contact angles in some cases reported previously,6 the significant deviation of contact angle values observed on the structured surfaces does not really surprise: Advancing and receding contact angles do not represent situations in thermodynamic equilibrium as considered by Wenzel. It is therefore not appropriate to apply Wenzel's description equation a priori to advancing and receding contact angles. For a quantitative description of contact angle hysteresis, one rather needs to consider local capillary and pinning forces at a contact line that is in nonequilibrium. To estimate such local forces, we first require some knowledge about the geometry of the contact line. Contact Area of Sessile Drops and Captive Bubbles. The contact angle data were obtained at 45° orientation, cf. Figure 1, where some asymmetry between the sessile drop and the captive bubble measurements was found, both in terms of contact angle values (Figure 4) as well as the shape of the contact area (Figure 5). For decreasing drop or bubble volume (θCB adv and θSD rec ), circular contact areas are observed, and the contact line does not appear extensively pinned. In the case of an expanding CB process (θSD adv and θrec ), however, the contact line is pinned to rows of defects over extended lengths. To elaborate on the different mechanisms identifying this different behavior, we now consider the same initial condition, where sections of the contact line rest along rows of defects (solid line in Figure 6). First, the volume of the droplet or bubble expands, the parts of the contact line that experience least resistance, that is, the smallest pinning force, start to move. This corresponds to the sections of lowest defect density, that is, the parts not yet pinned along rows of defects. As indicated by the open arrows, this contact line motion leads to an increase in the length of the pinned sections (dashed line in Figure 6). At the same time, the water contact angle along these rows increases (or decreases, respectively, in the case of 14910

dx.doi.org/10.1021/jp203581j |J. Phys. Chem. C 2011, 115, 14907–14913

The Journal of Physical Chemistry C captive bubbles) until at some critical moment, the contact line in one particular spot gets depinned, moves on, and gets repinned at the next row of defects. This local movement nucleates an almost instantaneous zipperlike motion of the whole previously pinned section of the contact line; the contact line “jumps” to the next row of defects where the process starts again. Second, we now consider shrinking droplets and bubbles at the same initial condition; that is, sections of the contact line are pinned along rows of defects. As the volume of the drop or bubble decreases, again, these parts of the contact line with the lowest defect density start to move, this time toward the center of the contact area (indicated by the gray filled arrows in Figure 6). This motion induces zipperlike depinning of the sections of the contact line pinned to the rows of maximum defect density (dotted line). The depinning process propagates at moderate speed from the edges toward the center of the pinned sections, which was indeed observed in our experiments; no jumplike behavior occurs as was observed in the first case described above. The mechanisms of contact line pinning and depinning described above depend on the strength of the pinning sites (i.e., in our case, on the steepness of the defects).2 For more shallow defects as compared with the sample B2 shown in Figure 5, pinning might not be strong enough to distort the contact line significantly from its circular shape upon increasing of the contact area. Hence, no or shorter straight sections of the contact line pinned to rows of defects might occur, as was indeed observed on samples B3 and B4 (see Table 1). For taller defects (samples A and B1, see Table 1) with stronger pinning, however, upon increasing the contact area, the contact line was found to adopt straight lines along rows of defects, not only at 45° orientation but also at 90° orientation. In the case of decreasing drop or bubble volume, one might also expect some differently shaped contact areas for strong pinning as compared with weak pinning sites. On our samples, however, we could not find any significant deviation from the circular contact areas upon decreasing of the drop or bubble volume, even for samples A and B1. In extreme cases where the contact line is completely pinned to surface features (θSD rec = 0), however, such deviations might be found.5 Theoretical Description for Increasing SD (CB) Volume. In the following, we concentrate on increasing drop and bubble volumes where the contact line is pinned to rows of pyramidshaped defects (Figure 5). To quantitatively estimate the impact of surface topography along these rows, the coordinate system shown in Figure 3 is used: The (average) surface lies in the x
yplane, and the contact line may be located along the y-axis, that is, at x = 0. The height of the surface structure h(x, y) is considered to be much smaller than the typical height scale of water contact angles. Because h(x, y) is also much smaller than the periodicity of the surface structure, p, the contact line periodicity is estimated by p. The mean or apparent contact angle θ on a heterogeneous surface, far away from local undulations, is determined by averaging the local interfacial tension forces along the contact line7,18,20,21 Z p cos θ ¼ cos θðyÞ dy=p ð1Þ

ARTICLE

Figure 7. Data from Figure 4, together with the “exact estimate” eqs 1
3 (solid lines), and an approximated estimate eq 4 (dotted lines) for pinning along rows of pyramid-shaped defects.

θðyÞ ¼ θflat þ RðyÞ with RðyÞ ¼
arctanð∂h=∂xjx f 0( Þ

Note that for advancing contact lines (moving in the positive xdirection), the water contact angle on the flat surface corresponds to the advancing contact angle, θflat = θadv flat , and for the calculation of the surface angle R(y) via eq 2, x = 0 has to be approached from positive values, x f 0+. This becomes important along corners and edges of the surface. Accordingly, for receding contact lines, the limit x f 0
needs to be considered in eq 2, and the receding contact angle on flat surfaces becomes relevant, θflat = θrec flat. In the next step, an expression for the topography of the defects is required to quantify the surface angle R(y). Assuming perfect walls of the SU8 coating and isotropic etching of Pyrex in hydrofluoric acid during the fabrication of the samples, the surface of each pyramid-shaped defect is represented by four intersecting cylinders. For instance, for the calculation of R(y), y ∈ [0, d] and advancing contact lines (limit x f 0+), the cylindrical surface indicated by the hatched area in Figure 3 is relevant qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3Þ hðx, yÞ ¼
R 2
ðx
yÞ2 =2 with the etch depth R given by R = (2H2 + d2)/4H. Combining eqs 1
3 leads to an elliptic integral, a very good approximation of which is given by cos θ ¼ ð1
f Þ cos θflat þ f cos½θflat ( arctanðH=dÞ ð4Þ

0

The local water contact angle θ(y) on a structured or locally inclined surface may be estimated by the sum of the inherent water contact angle measured on the respective flat surface, θflat, and the local surface angle, R(y)18,20

ð2Þ

valid for small defect heights H/d. The plus sign accounts for advancing and the minus sign for receding contact lines, respectively, which sense maximum pinning at around the same location, cf. Figure 5 for experimental confirmation. Equation 4 14911

dx.doi.org/10.1021/jp203581j |J. Phys. Chem. C 2011, 115, 14907–14913

The Journal of Physical Chemistry C is motivated by the fact that H/d corresponds to the average slope of the pyramid-shaped defects in 45° direction. Note that eq 4 has some similarity to a Cassie type average of contact angles on a composite surface, weighted by the respective line fractions instead of area fractions. The importance of line fraction was pointed out previously for advancing sessile drops on rectangular pillars7 and on random arrays of chemical defects.21 Comparison Theory—Experiment. In Figure 7, contact angle data obtained on samples B1
B4 (pyramid-shaped defects without flat tops) are compared with the theoretical predictions. The circular symbols refer to cases of shrinking droplets and CB bubbles, that is, θSD rec and θadv, where the contact area was found to be circular without significant pinning to rows of defects. Squares refer to an increasing drop or bubble volume (θSD adv and θCB rec ), in which cases the contact line is extensively pinned to rows of defects. For the latter situations, the estimated impact of the surface topography, eqs 1
3, is shown by the solid lines. The approximation eq 4, represented by the dotted lines, follows the numerical solution of eqs 1
3 closely in the range of investigated defect heights. However, none of the curves mimics the experimentally obtained contact angle values successfully. For receding contact angles (open squares in Figure 7), the impact of the surface topography is overestimated for all defect sizes. For advancing contact lines (filled squares), however, the theory eqs 1
3 overestimates the impact of topography only for small defects but underestimates the pinning effects of larger defects. These deviations might be caused by several factors. First of all, the real topography of the defects deviates from the idealized one given in eq 3. The patterning of SU8 via lithography does not result in perfectly smooth side walls. Upon wet etching of the underlying glass, the small undulations along the SU8 walls are replicated in the glass surface. This leads to streaks running down the sides of the defects, cf. the 3D AFM image shown in Figure 2. Furthermore, the corners of the SU8 squares are not expected to be perfectly sharp. This flaw propagates into the etched glass in terms of rounded edges, which is expected to decrease pinning. Also, there might be some nonisotropy in the etching process, which could result in further rounding/softening of edges and of the tips of pyramid-shaped defects. Apart from the nonideal defect topography, the height of the defects—which was neglected in eq 1—might have some considerable influence on pinning forces and on the location and propagation of the contact line due to line tension or the elasticity of the contact line, cf. the theoretical descriptions of pinning on individual defects.16,18 Furthermore, the curvature of the surface in the y-direction (along the contact line) might influence the propagation of the contact line (termed wedge wetting). These curvature effects become more pronounced for increasing defect heights. Finally, the length of the contact line sections pinned to rows of surface features could well impact on the measured contact angle: The longer the pinned section is, the stronger the impact of collective pinning is. As discussed above, we indeed found that the lengths of the straight sections on advancing drops increase with the height of the defects. The calculations should give the upper limit of an infinitely long pinned contact line. Other Orientations. Contact angles measured at orientations other than 45° with respect to the checkerboard pattern show less impact of the topographical defects as compared with those at 45° orientation. The circular shape of the contact line is also less distorted upon increasing the SD (CB) volume. At 90° orientation, for instance, the contact line is detectably pinned to a

ARTICLE

row of defects only for the tallest pyramid-shaped defects of sample B1. Using the same approach described by eqs 1 and 2 to this case, the contact angles are expected to deviate by only 3° from the inherent contact angle on the flat surface, that is, much less than at 45° orientation, where both the change and the sensitivity to topography are greatest. The results at 90° orientation thus qualitatively confirm the insights gained from studying contact line pinning at 45° orientation.

’ CONCLUSION Advancing and receding water contact angles were studied on regularly structured surfaces with varying defect heights and angles, using both the sessile drop and the captive bubble configuration. Asymmetries in terms of contact angle values and the shape of the contact area were found between these two well-established methods. For expanding drops and bubbles (adv SD and rec CB), the contact line was found to be pinned to rows of defects, while upon shrinking (rec SD and adv CB), the contact area did not deviate significantly from a circular shape, independent of the strength of pinning sites. These asymmetries can be attributed to the curvature of the contact line and, hence, the different mechanisms of depinning (nucleated jumplike motion vs continuous depinning from the sides). Quantitative estimates for the effect the defects might have on advancing and receding contact angles in both cases were derived based on pinning forces and local surface angles along the contact line. In most cases, these calculations were found to overestimate the impact. The deviations may be caused by the simplifications used in the calculations, including the finite lengths of the pinned section of the contact line. Approaches assuming thermodynamic equilibrium such as Wenzel's equation are not applicable to advancing and receding contact angles, and their predictions deviate strongly from the experimental data. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (R.F.) or John.Ralston@unisa. edu.au (J.R.). Present Addresses †

Karlsruhe Institute of Technology, Institute for Pulsed Power and Microwave Technology, D-76021 Karlsruhe, Germany.

’ ACKNOWLEDGMENT Valuable discussions with Craig Priest and experimental support by Marta Krasowska are warmly acknowledged. The financial support of the Australian Research Council Linkage Scheme, AMIRA International, and State Governments of South Australia and Victoria is gratefully acknowledged. ’ REFERENCES (1) Quere, D. Annu. Rev. Mater. Res. 2008, 38, 71–99. (2) Cubaud, T.; Fermigier, M. Europhys. Lett. 2001, 55, 239–245. (3) Dorrer, C.; Ruhe, J. Langmuir 2006, 22, 7652–7657. (4) Kusumaatmaja, H.; Yeomans, J. M. Langmuir 2007, 23, 6019–6032. (5) Dorrer, C.; Ruhe, J. Langmuir 2008, 24, 1959–1964. (6) Yeh, K.-Y.; Chen, L.-J.; Chang, J.-Y. Langmuir 2008, 24, 245–251. 14912

dx.doi.org/10.1021/jp203581j |J. Phys. Chem. C 2011, 115, 14907–14913

The Journal of Physical Chemistry C

ARTICLE

(7) Forsberg, P. S. H.; Priest, C.; Brinkmann, M.; Sedev, R.; Ralston, J. Langmuir 2010, 26, 860–865. (8) Zhang, X.; Jin, M.; Liu, Z.; Tryk, D. A.; Nishimoto, S.; Murakami, T.; Fujishima, A. J. Phys. Chem. C 2007, 111, 14521–14529. (9) Bahadur, V.; Garimella, S. V. Langmuir 2009, 25, 4815–4820. (10) Gao, N.; Yan, Y. J. Bionic Eng. 2009, 6, 335–340. (11) Vrancken, R. J.; Kusumaatmaja, H.; Hermans, K.; Prenen, A. M.; Pierre-Louis, O.; Bastiaansen, C. W.; Broer, D. J. Langmuir 2010, 26, 3335–3341. (12) Bormashenko, E.; Pogreb, R.; Whyman, G.; Bormashenko, Y.; Erlich, M. Appl. Phys. Lett. 2007, 90, 201917. (13) Peters, A. M.; Pirat, C.; Sbragaglia, M.; Borkent, B. M.; Wessling, M.; Lohse, D.; Lammertink, R. G. H. Eur. Phys. J. E 2009, 29, 391–397. (14) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988–994. (15) Spori, D. M.; Drobek, T.; Z€urcher, S.; Ochsner, M.; Sprecher, C.; M€uhlebach, A.; Spencer, N. D. Langmuir 2008, 24, 5411–5417. (16) Joanny, J. F.; de Gennes, P. G. J. Chem. Phys. 1984, 81, 552–562. (17) Ramos, S.; Tanguy, A. Eur. Phys. J. E 2006, 19, 433–440. (18) de Gennes, P. G. Rev. Mod. Phys. 1985, 57, 827–863. (19) Feng, R.; Farris, R. J. J. Micromech. Microeng. 2003, 13, 80–88. (20) Shuttleworth, R.; Bailey, G. L. J. Discuss. Faraday Soc. 1948, 3, 16–22. (21) Cubaud, T.; Fermigier, M. J. Colloid Interface Sci. 2004, 269, 171–177.

14913

dx.doi.org/10.1021/jp203581j |J. Phys. Chem. C 2011, 115, 14907–14913