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Advancing and Receding Motion of Droplets on Ultrahydrophobic Post Surfaces Christian Dorrer and Ju¨rgen Ru¨he* UniVersity of Freiburg, Department of Microsystems Engineering, Laboratory for the Chemistry and Physics of Interfaces, Georges-Ko¨hler-Allee 103, D-79110 Freiburg, Germany ReceiVed May 23, 2006. In Final Form: July 6, 2006 We have fabricated a range of silicon post surfaces where post width and spacing have been systematically varied. As one subset, we have generated surfaces where the post spacings in x and y assume different values. On these surfaces, the dynamic contact angles become anisotropic. A fluoropolymer monolayer is photochemically attached to the microstructured silicon, leading to the appearance of ultrahydrophobic properties. On one side, the advancing contact angles on these surfaces are not affected by variations in the geometric parameters. This furthers the conclusion that, during the advancing motion, a true contact angle of 180° is reached. On the other side, the receding angles are strongly influenced by the post size and spacing. We quantitatively analyze this dependence and relate variations in the receding angle to the shape and movement of the three-phase contact line. It is suggested that during the receding motion the meniscus successively dewets from one post at a time, with a step function running along the contact line until it has receded from a row of posts over its entire length.
Introduction The wetting of surfaces is of universal importance in many different areas as diverse as biology, microsystems engineering, and the painting of cars, ships, and buildings. Ultrahydrophobicity is at one extreme of the spectrum of wetting effects and describes a situation where water drops brought onto a surface show very high contact angles, typically in excess of 150°. Water drops roll around easily on these surfaces if the substrate is slightly tilted.1-4 In certain cases, drops rolling off the surface take loosely adherent dirt particles with them, thus giving rise to self-cleaning properties. Nature makes clever use of this effect, with the leaf of the lotus plant as a prominent, well-studied example.5 Interest in ultrahydrophobic surfaces is fueled by potential applications such as self-cleaning window panes and windshields, anti-graffiti coatings, and nonsoiling clothing. Surface roughness plays an important role in the appearance of ultrahydrophobic effects. The lotus plant, for example, combines roughness features on the micro- and nanometer scales.5 In general terms, the roughness size and topography have to be such that, for a given surface chemistry, drops are suspended on top of the roughness features, with air trapped underneath. A drop is then said to wet the surface in the Cassie or composite mode, and its static contact angle is derived from Cassie’s original equation6 as
cos θr ) φ cos θs + φ - 1
(1)
where φ is the fraction of the drop footprint in contact with a solid (as a consequence, 1 - f is the fraction of the drop footprint area spanning over the trapped air), θr is the contact angle on the rough surface, and θs is the contact angle on the smooth material. In contrast, a drop is said to be in the Wenzel mode * Corresponding author. E-mail:
[email protected].
(1) Chen, W.; Fadeev, A. Y.; Hsieh, M. C.; O ¨ ner, D.; Youngblood, J. P.; McCarthy, T. J. Langmuir 1999, 15, 3395. (2) Bico, J.; Marzolin, C.; Que´re´, D. Europhys. Lett. 1999, 47 220. (3) O ¨ ner, D.; McCarthy, T. J. Langmuir 2000, 16, 7777. (4) Richard, D.; Quere, D. Europhys. Lett. 1999, 48, 286. (5) Neinhuis, C.; Barthlott, W. Ann. Bot. 1997, 79, 667. (6) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546.
if it is fully impaled on the roughness features. Over the past decade, there has been strong interest in artificial ultrahydrophobic surfaces.1-4,6-14 Among these, surfaces with regular patterns of post structures have gained importance as model systems.2,3,7,8,15,16 The roughness of these surfaces is lithographically defined in size and topography, allowing a precise calculation of parameters such as the roughness factor r and the solid fraction φ. O ¨ ner et al. have investigated in detail the size scale of the posts necessary to achieve ultrahydrophobic behavior.3 The characterization of an ultrahydrophobic surface is never complete without a determination of the dynamic contact angles.9 The advancing angle is measured as the drop is expanded, and the receding angle is determined as the drop recedes over the surface. Generally speaking, the advancing of liquid is associated with the wetting of additional surface area, and the receding motion is related to the dewetting from parts of the surface. An important parameter describing the wetting properties of a surface is the contact angle hysteresis, given by the difference between the advancing and the receding value. On truly ultrahydrophobic surfaces, the contact angle hysteresis becomes small, which is in turn associated with a low roll-off angle.17 Whereas Cassie’s original theory allows an estimation of the static contact angle, its use for the prediction of the dynamic angles is problematic. Several authors have emphasized that the stability of the threephase contact line is a critical quantity in determining how easily the meniscus is displaced.1,3,9 This means that even for a constant solid fraction, the dynamic contact angles are a function of the topography of the surface. In their work on post surfaces, O ¨ ner (7) Yoshimitsu, Z.; Nakijima, A.; Watanabe, T.; Hashimoto, K. Langmuir 2002, 18, 5818. (8) He, B.; Patankar, N. A.; Lee, J. Langmuir 2003, 19, 4999. (9) Youngblood, J. P.; McCarthy, T. J. Macromolecules 1999, 32, 6800. (10) Morra, M.; Occhiello, E.; Garbassi, F. Langmuir 1989, 5, 872. (11) Miwa, M.; Nakajima, A.; Fujishima, A.; Hashimoto, K.; Watanabe, T. Langmuir 2000, 16, 5754. (12) Shibuichi, S.; Onda, T.; Satoh, N.; Tsujii, K. J. Phys. Chem. 1996, 100, 19512. (13) Onda, T.; Shibuichi, S.; Satoh, N.; Tsujii, K. Langmuir 1996, 12, 2126. (14) Abdelsalam, M.; Bartlett, P.; Kelf. T.; Baumberg, J. Langmuir 2005, 21, 1753. (15) Extrand, C. W. Langmuir 2002, 18, 7991. (16) Patankar, N. Langmuir 2003, 19, 1249. (17) Furmidge, C. G. L. J. Colloid Sci. 1962, 17, 309.
10.1021/la061452d CCC: $33.50 © 2006 American Chemical Society Published on Web 08/08/2006
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et al. observed a dependence of the dynamic angles on the post size and shape.3 They attributed these changes to the varying structure and continuity of the contact line. Extrand suggested a dependence of the dynamic angles on what he called the fractional contributions along the contact line.15 At present, the quantitative topography and size-scale dependence of the dynamic angles and the contact line dynamics on composite surfaces are still unclear. In this work, we have fabricated a number of silicon-based ultrahydrophobic post surfaces where post width d and post spacing s have been systematically varied. The bare silicon surface was coated with a thin film of a hydrophobic fluoropolymer. A simple photochemical process permits the covalent attachment of the polymer film to the substrate and thus allows for the easy fabrication of model surfaces. The dynamic contact angles on these surfaces have been measured. In the analysis of our data, we were interested in investigating the influence of the surface geometry on the advancing and receding angles and in relating these changes to the motion of the contact line.
Figure 1. Schematic of a quadratic post surface. The geometric parameters are post width d and post spacing s. The unit cell is indicated.
Experimental Section Silicon Micromachining. Using lithographic techniques (AZ1518 photoresist) and reactive ion etching, a pattern of quadratic shapes was transferred from a photomask into a low-temperature oxide layer on 4 in. (110)-orientation silicon wafers (silicon wafers were from Silicon Quest Int.). The oxide acted as a masking layer in a subsequent anisotropic etching step, where the actual 3D post structure was fabricated. The wafers coming out of the clean room were diced and cleaned in deionized water, 2-propanol, and acetone. (Solvents were from Fluka.) Surface Modification. For the chemical surface modification, a benzophenone-based silane (4-(3′-chlorodimethylsilyl)propyloxybenzophenone) was first synthesized and immobilized at the surface according to a procedure published previously.18,19 A thin film of poly(3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,10-heptadecafluorodecylacrylate)-co-4-methacryloyloxybenzophenone (PFA-co-MABP, synthesis described previously19,20) was then deposited onto the surface in a dip-coating step. The film was UV exposed at 265 nm for 5 min. During irradiation, the polymer layer was simultaneously cross linked and covalently attached to the substrate. As has been shown, this procedure results in thin films with thickness on the order of 10-15 nm.19,20 Effects on the geometry of the surface can therefore be neglected. Smooth PFA shows dynamic contact angles of θadv/θrec ) 120°/71° against water. Contact Angle Measurements. The contact angles were determined optically with an OCA20 system from Dataphysics using deionized, filtered Millipore water. For the dynamic measurements, liquid was pumped into/sucked from the drop with a syringe pump. The transient behavior of the contact angle was recorded and found to plateau as the advancing/receding value was reached. Each angle was measured multiple times, resulting in an average value with a standard deviation in the range of around 2°.
Results and Discussion Figure 1 shows the unit cell for a surface with quadratic posts as used in this work. The surface is characterized by three parameters: post width d, post spacing s, and post height h. The fraction of the solid surface in contact with a drop (solid fraction) is given by
φ)
d2 (s + d)2
(2)
(18) Toomey, R.; Freidank, D.; Ru¨he, J. Macromolecules 2004, 37, 882. (19) Samuel, J. D. J.; Ru¨he, J. Langmuir 2004, 20, 10080. (20) Mock, U.; Michel, T.; Tropea, C.; Roisman, I.; Ru¨he, J. J. Phys.: Condens. Matter 2005, 17, 595.
Figure 2. Schematic depiction of the anisotropic post surfaces used in this study. The post spacing in the x direction, sx, is different from the spacing in the y direction, sy. The posts are quadratic with a width of d.
Figure 3. Drop of water resting on an ultrahydrophobic post surface. Note that light can be seen under the drop, indicating that the surface is wet in the Cassie mode.
While d and s were independently varied between 4 and 32 µm in four steps, h was held constant at 40 µm, a height sufficient to ensure a Cassie contact at all values of d and s. Additionally, anisotropic post surfaces were fabricated. On these surfaces, the post spacings were different in the x and y directions (Figure 2), resulting in an anisotropy of the dynamic contact angles. Because the dynamic angles were always measured parallel to a row of posts, the influence of the post spacing parallel (s|) and perpendicular (s⊥) to the direction of contact line motion could be determined separately. On the anisotropic surfaces, d and sx were 8 µm, and sy was varied between 8 and 32 µm. Figure 3 shows a drop of water resting on a surface with posts 16 µm wide and at a 32 µm spacing. Light can be seen under the drop, indicating that the surface is wet in the Cassie mode. Overexposure was necessary to resolve the post structure underneath the drop; this is why the area next to the drop appears white. Advancing Contact Angles. The advancing contact angles (θadv) remain independent of d and s, as shown in Figure 4a. θadv lies in a narrow band around 156°; deviations are within the error bars of the measurement. To put these results into context, we compare our data to O ¨ ner’s measurements on a series of hexagonally arrayed post surfaces where post size and post spacing were varied simultaneously.3 It is interesting to note a few similarities: On the basis of O ¨ ner’s results, no clear dependence
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Figure 5. Advancing motion of the contact line shown schematically. (a) The advancing contact line has reached the far side of a post. (b) The contact line is pinned at the corner, and the meniscus bulges forward as the drop is expanded. (c) To touch down on the next post, the contact angle approaches ∼180° per definitionem.
Figure 4. (a) The variation of the advancing contact angle as a function of the post spacing s is shown. (b) The receding contact angles decrease with post width d. (c) An increase in the receding angle is observed with increasing post spacing s. (a, c) d ) 4 (9), 8 (0), 16 (b), and 32 µm (O); (b) s ) 4 (9), 8 (0), 16 (b), and 32 µm (O).
of θadv on the post geometry can be established. In particular, θadv remains unaffected as the post shape is varied. Before proceeding with the analysis, we would like to comment on a few practical aspects of the measurement of the advancing angles on these ultrahydrophobic surfaces. Results obtained by different groups for different surfaces range from ∼156° (in our case) to ∼170-175° for other authors,3 which is a considerable variation considering the rather similar surface structure. It should be explicitly noted that the values obtained in our contact angle measurements were very reproducible. However, the absolute values should be taken with caution because the measurement software, which is using drop shape analysis, will in this extreme situation tend to give slightly lower values than could be observed upon visual inspection of the micrograph image. It is thus entirely
possible that our results do not reflect the true value of θadv. We suggest that in such a situation the commonly employed optical measurement methods generally reach their limitations. High contact angles mean that the meniscus will come very close to the surface before making contact at the three-phase contact line. This in turn means that the region around the three-phase contact line will, with increasing contact angle, become more and more difficult to resolve properly. The interface appears to be blurred. As outlined above, this certainly caused problems in our case. It could be seen on the micrograph image that the software was unable to obtain a fit that precisely described the shape of the drop on the ultrahydrophobic surface. For the same reason, a manual extraction of the contact angle from the micrograph via a tangent leaning method was not practicable. The measurement was further complicated by the fact that on these rough surfaces the movement of the meniscus is not continuous but much more a series of jumping events. The contact line will not advance homogeneously over its entire length, as is detailed below. This in turn means that the contact angle will not be the same over the entire length of the contact line, leading to an additional blurring of the image in the region around the contact line. Looking at the droplet from the side, we will observe some kind of average value that could deviate considerably from the true value for θadv. It is not known at the moment what influence these aspects have on the contact angle measurements on different systems or with different fitting algorithms. Therefore, as far as the comparison with the results of other authors is concerned, comparing absolute values is difficult and might be totally misleading; however, a comparison should be possible for trends in the data. We start the analysis of the advancing motion on a post surface by looking at a situation where the meniscus is resting on the far side of a post as shown in Figure 5a. Because the advancing contact angle of the surface coating, θadv,s, is >90°, the contact line is pinned at the corner. As the drop is expanded, the meniscus bulges forward (Figure 5b). At this stage, θadv,s < θ < 180°, where θ is the contact angle of the meniscus relative to the horizontal. Just before the meniscus touches the next post (Figure 5c), the contact angle reaches 180° per definitionem. The contact line has to “traverse” a part of the composite surface that is “composed of air”. It can only do so once the contact angle is 180°. In fact, this mechanism of motion is very similar to what
Droplets Motion on Ultrahydrophobic Post Surfaces
Figure 6. Receding motion of the contact line from post row i to row i + 1 illustrated schematically. (a) The meniscus dewets from post i. (b) The contact line falls back to row i + 1.
was proposed by other authors.9,15,21 This idea is also supported by the fact that drops on ultrahydrophobic surfaces roll rather than slide, as Quere et al. found.4 Now, in accordance with the condition of constant Laplace pressure within the drop, the curvature of the meniscus is generally assumed to be much larger than the dimension of the posts. Even if we allow for an elliptical deformation of the drop close to the surface, an ∼180° contact angle means that the meniscus will remain nearly horizontal for a considerable length. In such a situtation, the influence of the post spacing should then be negligible. As a side remark, an elliptical deformation of the drop is actually inevitable because reaching an advancing angle of close to 180° while retaining the drop in the shape of a spherical cap is not possible without a gigantic increase in volume. Receding Contact Angles. The receding angles (θrec) show a pronounced dependence on both the post width d and the post spacing s. On one side, θrec decreases strongly with increasing post width, reaching a value of 79° for the surface where d ) 32 µm and s ) 4 µm (Figure 4b). On the other side, a marked increase in θrec is observed with increasing post spacing (Figure 4c). For the surfaces where d ) 16 µm, θrec changes from 90 to 133° as s is increased from 4 to 32 µm, resulting in a corresponding decrease in the contact angle hysteresis from 66 to 23°. The latter surface is thus closer to the ideal ultrahydrophobic surface in the sense that drops roll off easily, whereas on the first, pinning is observed. We again compare our results to O ¨ ner et al.’s data.3 In their case as well, θrec depends much more strongly on the size and shape of the posts than does θadv. This fact becomes especially apparent for the n-octyldimethylchlorosilane-modified surfaces, where θrec decreases from 141 to 132° as the post size is decreased from 2 to 32 µm. However, the variation of the receding angles in O ¨ ner’s case is much less pronounced than for our surfaces. We attribute this to the geometry of the post surface that was hexagonal in their case versus quadratic in our case. The movement of a drop over a surface is associated with a movement of the three-phase contact line. On an ideally smooth surface, this movement would be continuous. In contrast, on a structured surface, the receding contact line has to jump from feature to feature in discrete motions, going through a series of metastable states separated by energy barriers. Figure 6 illustrates this mechanism for a post surface: In Figure 6a, the receding contact line is still resting on post i. The meniscus then dewets from post i and falls back to post i + 1, reaching the next metastable state (Figure 6b). At any given time, the shape of the contact line is a function of the different interfacial energies involved. On one hand, the footprint of the drop is deformed from the ideal circular shape by the underlying pattern of posts (Figure 7). This deformation will propagate into the z direction and is thus associated with an increase in the liquid-air interfacial area (21) Gao, L.; McCarthy, T. J. Langmuir 2006, 22, 2966.
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Figure 7. The footprint of the drop is deformed from the ideal circular shape by the underlying pattern of posts.
compared to the ideal spherical shape, corresponding to an increase in the free energy given by γLV(Aactual - Aspherical). Let us call this energy difference ∆Gdef. We cannot quantify ∆Gdef for the moment without knowing the exact shape of the drop surface. On the other hand, the total energy of the drop is influenced by the interaction of the liquid with the individual posts. More specifically, during the receding motion, the meniscus remains pinned on a row of posts until the receding angle is reached. The magnitude of the pinning effect should be a direct function of the area of contact between the meniscus and the posts just about to be dewetted by the meniscus. Extrand expressed θrec as a linear combination of the receding angle on the solid surface and the receding angle on air15
θrec ) λPθrec,s + (1 - λP)θair
(3)
where he defined λP as “the linear fraction of the contact line on the asperities”. This hypothesis can be tested by selecting the appropriate surfaces from our data. Because we now deal with (interfacial) energies, we look at cos θ rather than θ. For the surfaces where d ) s, λP is constant at 0.5. Still, a pronounced increase in cos θrec is observed (Figure 8a). In the next step, to eliminate the influence of post spacing in the direction of motion, s|, we select the pair of surfaces where d ) 4 µm, s⊥ ) s| ) 8 µm and d ) 8 µm, s⊥ ) 16 µm, s| ) 8 µm. For this ensemble, λP is again constant, as is now s. However, a 7° difference in θrec is found (138 vs 131°), an observation that again underlines that λP does not sufficiently characterize the surface for predicting θrec. In our opinion, the reason for this is the following: It is improbable that a length of contact line will dewet over its entire length at once (Figure 9a), as is implicitly assumed by the concept of fractional contributions. On the contrary, it would be energetically preferable for the meniscus to jump from one post at a time. The receding motion would thus be split into a series of jumping events, resulting in a step function running along the contact line (Figure 9b). Schwartz and Garoff predicted a similar effect for heterogeneous surfaces.22,23 On one side, in this model, the energy barrier for such a mechanism of motion would now be a function not so much of λP but of the area of contact between the meniscus and an individual post and thus of the post width d. On the other side, the post spacing perpendicular to the direction of contact line motion, s⊥, now simply determines how often this energy barrier has to be overcome for the contact line to recede over its entire length. The behavior of cos θrec with increasing d and constant s⊥ ) s| ) s is shown in Figure 8b. Cos θrec increases strongly. However, in this case, the post pitch (i.e., the number of posts per unit length) is not constant. For the pair of surfaces where (i) d ) s| ) 8 µm, s⊥ ) 16 µm and (ii) d ) 16 µm, s⊥ ) s| ) 8 µm, the post pitch is constant, as is s|. θrec decreases significantly (from 131 to 110°) as d is doubled. Finally, the influence of the post density (i.e., the post pitch) perpendicular (22) Schwartz, L. W.; Garoff, S. J. Colloid Interface Sci. 1985, 106, 422. (23) Schwartz, L. W.; Garoff, S. Langmuir 1985, 1, 219.
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Figure 8. (a) Dependence of cos θrec on the post size scale. For this set of surfaces, the post width d is equal to the post spacing s. (b) cos θrec increases as a function of d (s ) 4 (9), 8 (0), 16 (b), and 32 µm (O)).
Dorrer and Ru¨he
Figure 10. (a) cos θrec plotted as a function of the post spacing perpendicular to the direction of contact line motion. d and s| are constant at 8 µm. (b) cos θrec as a function of the post spacing parallel to the direction of contact line motion. In this case, d and s⊥ are constant at 8 µm.
Figure 9. (a) Contact line dewetting from a row of post at once over its entire length. (b) Contact line receding by dewetting from one post at a time, with a jumping front proceeding along the contact line.
Figure 11. To follow the overall spherical shape of the drop, the contact line crosses from one row of posts to the next. We speculate that a larger post spacing s2 will destabilize the meniscus.
to the direction of contact line motion, s⊥, is isolated on the anisotropic surfaces where s| ) d ) 8 mm. Here, the number of posts per unit length decreases with increasing s⊥; in agreement with the model, cos θrec decreases (Figure 10a). In the previous section, we have isolated the effects of d and s⊥ on the receding angle. We now look at a variation in s| while keeping d and s⊥ constant. As can be seen in Figure 10b, cos θrec decreases as a function of s|. We argued above that the receding motion is a series of jumping events proceeding along the contact line. Where would such a motion be preferentially started? We speculate that this is likely to be the case in those regions where the contact line crosses from one row of posts to the next to follow the overall spherical shape of the drop (Figure 11). In those regions, the deformation of the drop from the spherical shape is the most extreme. It is probable that this will lead to energy concentrations that facilitate the dewetting from the outermost post in a row, with a dependence on s| as illustrated in Figure 11.
To summarize, we have shown that the receding contact angle of water on microstructured, fluorinated surfaces is a complicated function of several geometric parameters (i.e., the size of the roughness features and their spacing parallel and perpendicular to the direction of the contact line motion). Following the original Cassie theory, calculations of the receding angle based on the solid fraction (the fraction of the drop footprint in contact with the solid vs with air) have often been attempted. Deviations from this behavior have been observed before.8,15 We have studied this aspect systematically and have found that for identical solid fractions but different surface geometries, realized through surfaces where post size and post width were varied simultaneously in such a way that the solid fraction remained constant, the receding angle varies strongly. We explain this dependence by looking at the receding motion of the contact line across the post structure. In particular, we put forward the hypothesis that the liquid meniscus successively jumps from one post at a time,
Conclusions
Droplets Motion on Ultrahydrophobic Post Surfaces
with the jumping front proceeding along the contact line. This model leads to the conclusion that the energy barrier that has to be overcome for the meniscus to dewet from a row of posts is mainly a function of the area of contact between the drop and an individual post (i.e., the post width). We speculate that, similar to a nucleation event, the receding motion is likely to be started in those areas where energy is concentrated because of the deformation of the drop interface from the ideal spherical shape by the underlying surface roughness. On rectangular surfaces, a multitude of such “nucleation sites” should always be present because the rectangular grid is essentially incompatible with the circular footprint that the drop tries to assume. These considerations emphasize that, next to the shape of the contact line, the detailed shape of the free surface forming the liquid-air interface is of prime importance in determining exactly how the motion of the meniscus will take place. An exact prediction and quantification of the receding angle will thus be possible only once both shapes are known. In contrast to the receding angles, it is found in our experiments that the advancing angles remain relatively unaffected by changes in the surface geometry (i.e., unaffected by both post spacing and post width). We argue that during the advancing motion the contact line is pinned on the post corners. The meniscus bulges forward, reaching a contact angle approaching 180° before touching down onto the next posts. It thus remains parallel to the surface for a considerable length. We believe that this principle is valid not only for the system in question here but that, in
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general, for surfaces wet in the Cassie mode, the advancing angle is in fact independent of the exact roughness size and topography (provided that the pinning effects are strong enough). Changes in the contact angle hysteresis would then be caused only by variations in the receding angle. This view is supported by experiments on entirely different surfaces. Dettre and Johnson, for example, prepared ultrahydrophobic surfaces by heat treatment of a TFE-methanol telomer wax as early as in the 1960s.24 Interestingly, they observed θadv to be constant as the degree of roughness was varied, while θrec showed a strong variation. The same phenomenon can be seen in Morra’s contact angle data for plasma-treated PTFE surfaces.10 Both experimental series are thus in good agreement with the findings of our study discussed here. There are a number of other interesting aspects as far as the wetting of these microrough surfaces is concerned, such as the stability of the Cassie state in comparison to the Wenzel state. Our method of surface preparation allows for the easy variation of the surface free energy of the post structure by applying different polymer coatings. The results of further studies on these additional surfaces will be the subject of a subsequent paper. Acknowledgment. We thank Achim Trautmann and Patrick Ruther for help with the silicon micromachining. LA061452D (24) Dettre, R. H.; Johnson, R. E. AdV. Chem. Ser. 1964, 43, 136.
