Article pubs.acs.org/Langmuir
Repellency of the Lotus Leaf: Contact Angles, Drop Retention, and Sliding Angles C. W. Extrand* and Sung In Moon Entegris, Inc., 101 Peavey Road, Chaska, Minnesota 55318, United States ABSTRACT: Much of the modeling done on repellency and super hydrophobicity has focused on surfaces with rectilinear geometries, but their wetting behavior is simpler and can be quite different from that of repellent surfaces with curved features. In this study, we model the contact angles and sliding angles exhibited by the lotus leaf, accounting for the influence of curvature and pinning. Our estimates agree reasonably well with experimental observations.
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INTRODUCTION Liquid repellent surfaces, both natural and synthetic, continue to attract much interest. Excellent progress has been made in the last 20 years understanding the science of these surfaces. In parallel, the number of novel methods for producing them has exploded. There are numerous reports of both top-down and bottom-up approaches.1−6 Bottom-up approaches often employ some sort of lithography that yields rectilinear structures. Topdown approaches frequently produce curved surface features. Even though all super hydrophobic surfaces combine some level of inherent hydrophobicity with surface geometry, there can be significant differences in the behavior and functionality of rectilinear and curved features. Consider the sessile liquid drops shown in Figure 1. The drops are viewed from the side and are surrounded by a gas or
magnitude than any downward forces from gravity, inertia, Laplace curvature, etc. Otherwise, downward forces will drive liquid into the structure, completely wetting it, creating the socalled Wenzel state.8 Figure 2 depicts a sequence of events underneath the drops as downward pressure increases. If a liquid were deposited onto
Figure 2. Position of contact line on features with increasing pressure. (a) Rectilinear features. (b) Curvilinear features.
the surface with square pillars and the capillary forces were sufficiently large, the liquid would be suspended on top of pillars, Figure 2a. With modest pressure variations, the liquid would generally remain on top of the pillars.9−18 If the pressure were increased beyond some critical value, the liquid would collapse, displacing the air and completely wetting the surface. Until that critical pressure is exceeded, the position of the liquid on square pillars will not change much.15,16 With the curved features depicted in Figure 2b, the interaction is more complex. In the absence of pressure, liquids do not remain at the apex. As liquid spreads across curved features and establishes its advancing contact angle, it penetrates into the interstitial spaces.19−23 With increased pressure, liquid is pushed deeper into curved structures and
Figure 1. Depiction of water on two types of super hydrophobic surfaces. (a) Surface with rectilinear features. (b) Surface with curvilinear features.
vapor. The surfaces are covered with features that have the same base width and pitch. The features in Figure 1a are square or cylindrical pillars with vertical walls. On the other hand, the features in Figure 1b are hemispheroids. In both cases, the drops are suspended on structured, repellent surfaces that exhibit super hydrophobicity. This suspension is often referred to as the Cassie state.7 What’s holding them up? For these structured surfaces to impede intrusion, capillary forces acting around the features must be directed upward and of greater © XXXX American Chemical Society
Received: May 19, 2014 Revised: June 27, 2014
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eventually reaches the floor or collapses. In contrast to pillars, the position of the liquid on curved features varies with pressure, even in the superlyophobic Cassie state. Consequentially, so does the extent of contact. The relative extent of contact is one of the factors that determines repellency of structured surfaces. We previously analyzed the ability of the lotus leaf to repel intrusion of water.22 In this study, we examined the contact angles of the lotus leaf and its ability to retard liquid adhesion. We created a model surface with curved features that resembles the lotus leaf and estimated contact angles and sliding angles, and then compared those results to experimental observations on real lotus leaves.
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THEORY Description of the Model Surface. The surface of the lotus leaf is covered with protuberances that have structural hierarchy, Figure 3. The primary structure of these protuber-
Figure 4. Plan view of a liquid suspended on the model lotus leaf. The larger black circles represent the bases of the protuberances, the smaller blue circles show the contact lines of the suspended liquid. The perimeter contact line at the outer edge of the of the drop is depicted as straight blue lines connected to blue semicircles.
Figure 5. Side view of the lotus leaf model. (a) Water on the protuberances underneath the drop and at its advancing edge. (b) Receding edge. Curvature of the air−liquid interface is exaggerated to emphasize the liquid orientation and local inherent contact angle. The density of the secondary features is intentionally sparse to allow for clear depiction of the liquid orientation and the various parameters.
that globally, the air−liquid interface can be approximated as flat and horizontal. The model assumes the secondary features are densely packed such that most of the length of the contact line touches them.28 It also assumes that only the outmost portions of the secondary features interact with water. The sharp edges of these features pin the contact line29−31 and prevent intrusion into the hierarchical structure. The sharp edges also reorient the air− liquid interface in the vicinity of the contact line,13,29,30,32−38 increasing its apparent contact angle by 90°.21 Increasing pressure is expected to drive water downward between the rough hemispheres, where the contact line jumps from one secondary feature to the next. At each step, the liquid is pinned at the outermost edge. With a further increase in pressure, the process repeats. (In practice the incremental jumps from one secondary feature to the next are quite small, on the order of tens of nanometers. The density of the secondary features depicted in Figure 5 is intentionally sparse to allow for clear depiction of the liquid orientation and the various parameters.) The liquid advances with an inherent advancing contact angle of θa,0, which is reported to be 105° for water on the surface wax of the lotus leaf.1 Drop Profiles and Dimensions. In the latter part of the 19th century, Bashforth and Adams39 used iterative numerical methods to calculate sessile drop profiles from the Laplace equation40 for shape parameters ranging from β = 0.125 to 100. Here, we use their tabulated dimensionless results to determine profiles, dimensions, and volumes of sessile water drops sized according to their four smallest β parameters, 0.125, 0.25, 0.50,
Figure 3. Scanning electron micrograph of the top surface of the lotus (Nelumbo nucifera) leaf. The white scale bar is 20 μm long. Image kindly provided by Prof. Barthlott.
ances or papillae takes the form of prolate hemispheroids. The protuberances are covered with a secondary structure of wax crystalloids that project orthogonally outward, creating myriad of sharp edges. Figures 4 and 5 show the model of the lotus leaf employed in this study. The model surface consists of rigid hemispheres centered within a hexagonal array, Figure 4. The base diameter of the hemispherical protuberances is 2R. The unit cell dimension is 2y. The hemispheres have a secondary roughness that radiates orthogonally, Figure 5. In the model, each secondary feature effectively forms a continuous edge that extends around the entire circumference of the hemispheres, much like latitude lines on a globe. 2R extends to the tips of these secondary features. From Figure 3, 2R and 2y for the lotus leaf are estimated to be 11.0 ± 1.4 μm and 18.6 ± 3.3 μm, respectively, in agreement with previously reported values.24−26 (The measured value of 2R includes the secondary features which are about 1 μm long.27) Figure 5 also depicts the extent of intrusion of water into the interstitial spaces between the hemispheres, as described by the angle ϕ, which ranges from 0° for no intrusion to 90° for complete intrusion. While the orientation of the air−liquid interface at the contact line varies locally with ϕ, it is assumed B
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be approximated as a series of semicircles and straight segments,13 as depicted in Figure 4. The length of the perimeter contact line on each protuberance (lp) can be calculated as
and 0.75. Drop profiles can be traced out by connecting a series of dimensionless coordinates (x/b and z/b) that follow the air− liquid interface of the drop from its apex to the underlying solid surface. The point where the liquid meets the underlying solid determines the apparent contact angle (θ). The coordinates where this occurs are denoted (x/b)θ and (z/b)θ. Again, consider the small sessile drop on our model surface, as depicted in Figure 1b. The liquid has a surface tension of γ and a density of ρ. The height of the drops is h. The drops contact the structured surface with a base diameter of 2a. Its apex radius of curvature (b) can be calculated from the shape parameter, liquid surface tension, and density,39 ⎛ γ ⎞1/2 b = ⎜β ⎟ ⎝ ρg ⎠
lp = πR sin ϕ
and the length between them (lb) as
lb = 2y − 2R
λp = (1)
(2)
(3)
2γ b
(15)
θp,a = θa,0 + ϕ + 90◦
(5)
(16)
Combining eqs 13−16 produces an expression for the apparent contact angle on our model lotus leaf, θa = λp(θa,0 + ϕ + 90◦) + (1 − λp) ·180◦ = λp(θa,0 + ϕ − 90◦) + 180◦
(6)
(17)
Note that if θa,0 ≥ 90°, then effectively θa = 180° for all ϕ. As the contact line retreats, we assume that drops establish their inherent contact angle (θr,0) on the sides of the secondary features as depicted in Figure 5. If θr,0 ≥ 90°, then the receding angle on the protuberance (θp,r) is greater than the intrusion angle,
(7)
θp,r = θr,0 + ϕ − 90◦
(8)
(18)
Combining eqs 13−15 and 18 produces an equation for estimating the apparent receding angle,
Combining eqs 5−8 yields an expression that relates the intrusion angle to the various pressures in our system,
θr = λp(θr,0 + ϕ − 270◦) + 180◦
2Rγ sin ϕ cos(θa,0 + ϕ)
2γ + ρgh + =0 2 2 2 b (2 3 /π )y − R sin ϕ
(14)
Figure 5 shows the orientation of air-liquid interface under the drops as well as at the leading and retracting edges of the sessile drop. At the leading edge (i = a), the apparent advancing contact angle (θp,a) in our model surface depends on the inherent advancing contact angle, the extent of intrusion and the 90° reorientation of the air−liquid interface due to pinning on the secondary features,
(4)
and
ΔpL =
(13)
θ b = 180◦
The hydrostatic pressure (Δph) and Laplace pressure (ΔpL) are41,42 Δph = ρgh
(12)
where θp,i is the contact angle on the protuberance, θb is the contact angle between them and i = either a or r for advancing or receding contact lines. In all cases, we assume that
2Rγ sin ϕ cos(θa ,0 + ϕ) (2 3 /π )y 2 − R2 sin 2 ϕ
1 1 + (2/π )(y/R − 1) csc ϕ
θi = λpθp, i + λbθ b
The capillary pressure (Δpc) for our model surface is related to the intrusion angle (ϕ) by the following expression,21 Δpc = −
=
Apparent Contact Angles. If we approximate the apparent contact angles as simple linear averages, then the working equation takes the general form,13
Relation between Pressures and Intrusion Angle. In the absence of trapped or compressed gas, the ability of the lotus leaf to resist intrusion of liquid can be cast as a competition between the capillary pressure (Δpc) arising from interactions at the contact line and hydrostatic pressure (Δph) and Laplace pressure (ΔpL) of the drop, Δpc − Δph − ΔpL = 0.
lp + lb
λb = 1 − λp
The volume of the drop can be estimated from b and dimensionless volume (V/b3)θ, V = b3·(V /b3)θ
lp
and the linear fraction between them (λb) is
and their height (h) from the apex radius of curvature and the corresponding dimensionless vertical coordinate, h = b·(z /b)θ
(11)
Thus, the linear fraction (λp) of the contact line that resides on the protuberances is
where g is the acceleration due to gravity (g = 9.81 m/s2). The contact radius (a) of the drop comes from the product of apex radius of curvature and the dimensionless horizontal coordinate where the liquid and solid meet, 2a = 2b·(x /b)θ
(10)
(19)
Once this apparent receding contact angle is established, with further retraction, the receding liquid is expected to pinch onto the sides of the protuberances and rupture. The receding contact line jumps to the next protuberance and the process starts again. Sliding Angle. Sliding angles (α) can be measured experimentally using a simple inclined plane, where α = 0° is
(9)
Contact between the Liquid and the Protuberances. To estimate apparent contact angles on our model surface, we must determine the extent of contact between the intruding liquid and hemispherical protuberances. To do so, we assume that the shape of the contact line at the outer edge of drops can C
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Table 1. Estimates for Various Bashforth and Adams Shape Parameters (β): Drop Apex Radius of Curvature (b), Drop Base Diameter (2a), Drop Height (h), Drop Volume (V), Intrusion Angle (ϕ), Linear Fraction of the Contact Line on the Protuberances (λp), Apparent Advancing Contact Angle (θa), Apparent Receding Contact Angle (θr), Sliding Angle from Apparent Contact Angles (αa), Number of Capillary Bridges along the Receding Contact Line (n), and Sliding Angle from Capillary Bridge Rupture (αb) β
b (mm)
2a (mm)
h (mm)
V (μL)
ϕ (deg)
λp (deg)
θa (deg)
θr (deg)
αa (deg)
n
αb (deg)
0.125 0.25 0.50 0.75
0.959 1.36 1.92 2.35
0.496 0.907 1.57 2.10
1.71 2.24 2.83 3.18
3.4 8.7 21 33
3.6 2.8 2.4 2.2
0.125 0.102 0.086 0.079
180 180 180 180
158 162 165 166
3.3 1.6 0.8 0.6
42 77 133 177
11 6.3 3.8 3.0
pipettes (Eppendorf Reference Series 2000, 2−20 μL and 10−100 μL). For advancing angles, an image was captured immediately after deposition and then the profile of the drop was fit with various Bashforth and Adams profiles to determine its apparent advancing contact angle (θa). For receding angles, we deposited a drop and allowed evaporation to retract the contact line. When it had shrunk to one of BA volumes, an image was captured and fit with various BA profiles to determine its apparent receding contact angle (θr). Sliding angles (α) were measured with a 30 cm lever. A piece of leaf was attached near the fulcrum of the lever with two-sided tape, a water drop was deposited on the leaf and the lever slowly lifted. The length of the lever (L) and the lift distance (d) that initiated sliding were used to estimate α,
horizontal and α = 90° is vertical. We estimate the sliding angle from first-principles using two different approaches. In the first approach, we use apparent contact angles. Here the global capillary force acting around the perimeter contact line is equated to the body force acting on the mass of the drop.43 The working equation for sliding angle takes the following form44−47 γ ·a sin αa = k (cos θr − cos θa) ρgV (20) where k depends on the shape of the drop. If the drop has a circular contact patch, then k = 48/π3.47 In the second approach, we assume that the retention force arises from capillary bridges on the back half of the drop.15−17,48−50 For the drop to roll forward, capillary bridges along the receding contact line must rupture. The retention force (f r) resisting movement is the product of the number of capillary bridges (n) and the rupture force for each individual bridge ( f i). fr = n·fi
sin α =
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The number of bridges can be approximated from the length the receding contact line (πa) and the protuberance spacing (2y), πa n= 2y (22)
RESULTS AND DISCUSSION Estimates from the Proposed Model. We can use results from Bashforth and Adams’ numerical computations39 along with the equations derived here to estimate contact and sliding angles for water drops on our model lotus leaf. We start by calculating b values for various shape parameters (β = 0.125, 0.25, 0.50, and 0.75) with eq 1. Assuming that drops deposited on the surface of our model lotus leaf produce apparent advancing contact angles of θa = 180°, we next estimate contact radii, heights, and volumes for the drops using eqs 2−4. Values of β, b, h, 2a and V are listed in Table 1. With β = 0.125−0.75, these sessile drops are small and of the size typically used for contact angle measurements. Their dimensions ranged from a fraction of a millimeter for the contact diameter to several millimeters for their height; volumes were 3.4 to 33 μL. Having determined the critical dimensions of our water drops, we then estimated intrusion angles, fractional contact, contact and slide angles, which also are listed in Table 1. Intrusion angles for the various drops came from eq 9. In general, penetration of water into our model lotus leaf is expected to be quite shallow, only a few degrees. Values of ϕ were greatest for the smallest drop, ϕ = 3.3°. As V increased, ϕ declined. As shown later, these drops all resemble spheres with flattened bottoms. With significant curvature in the upper half, Laplace pressure was dominant. For the smallest drops, curvature generated 90% of the downward pressure. Even though hydrostatic pressure grew with drop height, for the largest drops, the Laplace pressure still constituted 66% of the downward pressure.
The rupture force for each individual bridge (f i) is roughly (23)
Substituting eqs 22 and 23 into 21 and balancing against the body force ( f b) acting on the drop, fb = ρgV sin α
(24)
yields an alternative equation for estimating the angle of inclination required to dislodge a sessile drop from a lotus leaf, sin αb =
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π 2γ ·aR sin ϕ ρgVy
(26)
All measurements were performed at 25 ± 1 °C. Initially we were concerned that aging of the lotus leaves would affect our measurements. During the first several weeks lotus leaves were refrigerated in plastic bags containing a small amount of water. Measurements made immediately after harvesting the leaves were not significantly different from those made later.
(21)
fi = 2πRγ sin ϕ
d L
(25)
EXPERIMENTAL DETAILS
Fresh lotus leaves were obtained from the Como Park Conservatory in St. Paul, MN. Small pieces (approximately 1 cm2) were cut from the leaves. The contact liquid was deionized water, which has a density of ρ = 998 kg/m3 and a surface tension of γ = 72 mN/m.51 Measurements of both contact and sliding angles were made using sessile drops that had volumes (V) associated with specific Bashforth and Adams shape parameters, β = 0.125, 0.25, 0.50, and 0.75. For contact angle measurements, a piece of leaf was attached to the stage of a drop shape analyzer (Krüss DSA10) with two-sided tape. Sessile drops of water of were deposited with adjustable volume D
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Using the intrusion angles from eq 9, fractional contact (λp) was estimated with eq 12. Values of λp were around 0.1, which implies that most of the liquid in the vicinity of the contact line was suspended between protuberances. From eq 17, it is anticipated that the apparent advancing contact angles will effectively be θa = 180°, regardless of their size or extent of intrusion. On the other hand, apparent receding angles, estimated from eq 19 by assuming that θ r,0 = 95°, ranged from θr = 158° to 166°. Finally, we can predict sliding angles (α). By plugging the apparent advancing and receding contact angles in eq 20, we estimated that sliding angles should range between 3° for the smallest drop and α = 0.6° for the largest. On the other hand, estimates from eq 25 for capillary rupture gave larger sliding angles, between 3° and 11°. We expect α to vary with V on all types of surfaces, but the effect was more pronounced for larger drops on our model surfaces, where the Laplace pressure and subsequent intrusion were less. As an aside, we also made the same types of estimates, assuming model surfaces consisted of smooth hemispheres without secondary features. Everything else being equal, water would be expected to penetrate deep into the interstitial spaces between the smooth hemispheres (∼75°), exhibit much lower receding contact angles (∼110°) and much greater sliding angles (10−30°). These estimates assume that drops maintain a Cassie state. If the liquid did completely wet the solid, the hysteresis and sliding angles would be even greater. Comparison with Experiments. Advancing contact angles on the lotus leaf previously have been measured with sessile drops by goniometer and reported to be approximately θa = 160°.52,53 It has been well documented that precise measurement of very high contact angles can be quite challenging, due to experimental difficulties.13,54−56 Figure 6 shows an image of
Figure 7. Advancing water drops on the surface of a lotus leaf. (a) V = 3.4 μL, β = 0.125; (b) V = 8.7 μL, β = 0.25; (c) V = 21 μL, β = 0.50; (d) V = 33 μL, β = 0.75. The curves represent theoretical profiles of Bashforth and Adams for θa = 180°: (a) β = 0.125, (b) β = 0.25, (c) β = 0.50, and (d) β = 0.75.
agreed well with the profiles of Bashforth and Adams and with our prediction of θa = 180°. We also tried measuring θa values using our drop shape analyzer with its Laplace sessile drop fitting function. This algorithm requires setting the baseline manually and then initiating the software. The algorithm fits a Bashforth and Adam profile to the drop image and then estimates a contact angle from the intersection of the profile and baseline. Because the surface of the lotus leaf is rough, the apparent location of the baseline can vary across the contact patch by as much as 50 μm. Very small differences in position of the baseline produced large differences in contact angles. For example, our initial positioning of the baseline for a drop with V = 21 μL gave θa = 160°. By moving the baseline down just one pixel or approximately 15 μm, θa increased to 171°. One more pixel caused θa to jump to 425° (effectively 180°). We believe that the apparent advancing contact angle on the lotus leaf (and other superhydrophobic surfaces) is effectively 180°, regardless of the extent of flattening.13 For the contact line to advance, the liquid must bulge to transverse the air space between features.13,32,54,57−59 Dorrer and Rühe have argued that, by definition, this process constitutes an advancing contact angle of 180°.54 The surface of our lotus leaves were not perfectly nonwetting. We were able to demonstrate hysteresis and a receding contact angle of θr < 180° by bringing a small pendant drop of water into contact with the leaf surface and pulling it away. The drop exhibited pinning as it retracted, and upon liftoff, its air−liquid interface vibrated. Figure 8 shows liquid drops that were placed on the surface of a lotus leaf and allowed to evaporate until their volume equaled one of the values listed in Table 1, V = 3.4, 8.7, 21, and 33 μL. Their shapes were similar to the advancing drops. Images of the drops were fit with Bashforth and Adams profiles for θr = 180° and 160°. Also, we fit the largest receding drop with a half-profile for 150°. The uncertainty again is quite large for many of the same reasons stated above. While the profile for θr = 150° did not fit well, with some confidence, we can conclude that the receding angles fell somewhere between 160° and 180°. Thus, our experimental θr values generally agree with our predictions.
Figure 6. Side view image of a 3.4 μL water drop on the surface of a piece of lotus leaf.
a 3.4 μL water drop on a piece of lotus leaf. The surface is visibly rough due to the protuberances, but also from the macroscopic contours of the leaf, which were not completely flattened when attaching the leaf to a glass substrate. This roughness hampers precise placement of the base and tangent lines used to estimate contact angles. Gravitational sagging also can impair precise placement of lines and can lead to erroneous assumptions regarding the extent of spreading. Thus, previously reported θa values may have been underestimated. How do the results from the proposed lotus leaf model compare with our experimental observations? Figure 7 shows advancing water drops with volumes of V = 3.4, 8.7, 21, and 33 μL on the surface of a lotus leaf. These volumes correspond to β values of 0.125, 0.25, 0.50, and 0.75, respectively. All drops were distorted by gravity. For the smaller drops, distortion was localized to the bottom portion of the drop. Conversely, for the larger ones, sagging was more global. Bashforth and Adams drop profiles for θa = 180° are overlaid on the images. Within experimental error, the shape and dimensions of these drops E
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(3) Genzer, J.; Efimenko, K. Recent Developments in Superhydrophobic Surfaces and Their Relevance to Marine Fouling: A Review. Biofouling 2006, 22 (5), 339−360. (4) Extrand, C. W. Super Repellency. In Encyclopedia of Surface and Colloid Science; Somasundaran, P., Ed.; Taylor & Francis: New York, 2006; pp 5854−5868. (5) Zhang, X.; Shi, F.; Niu, J.; Jiang, Y.; Wang, Z. Superhydrophobic Surfaces: From Structural Control to Functional Application. J. Mater. Chem. 2008, 18 (6), 621−633. (6) Quéré, D. Wetting and Roughness. Annu. Rev. Mater. Res. 2008, 38, 71−99. (7) Cassie, A. B. D.; Baxter, S. Wettability of Porous Surfaces. Trans. Faraday Soc. 1944, 40 (21), 546−551. (8) Wenzel, R. N. Resistance of Solid Surfaces to Wetting by Water. Ind. Eng. Chem. 1936, 28 (8), 988−994. (9) Thorpe, W. H.; Crisp, D. J. Studies on Plastron Respiration. I. The Biology of Aphelocheirus [Hemiptera, aphelocheiridae (naucoridae)] and the Mechanism of Plastron Retention. J. Exp. Biol. 1947, 24 (3,4), 227−269. (10) Dettre, R. H.; Johnson, R. E., Jr. Contact Angle Hystereisis Porous Surfaces. Society of Chemical Industry: London, 1967; Vol. 25, p 144−163. (11) Ö ner, D.; McCarthy, T. J. Ultrahydrophobic Surfaces. Effects of Topography Length Scales on Wettability. Langmuir 2000, 16 (20), 7777−7782. (12) Yoshimitsu, Z.; Nakajima, A.; Watanabe, T.; Hashimoto, K. Effects of Surface Structure on the Hydrophobicity and Sliding Behavior of Water Droplets. Langmuir 2002, 18 (15), 5818−5822. (13) Extrand, C. W. Model for Contact Angles and Hysteresis on Rough and Ultraphobic Surfaces. Langmuir 2002, 18 (21), 7991− 7999. (14) Patankar, N. A. Mimicking the Lotus Effect: Influence of Double Roughness Structures and Slender Pillars. Langmuir 2004, 20 (19), 8209−13. (15) Papadopoulos, P.; Deng, X.; Mammen, L.; Drotlef, D.-M.; Battagliarin, G.; Li, C.; Müllen, K.; Landfester, K.; del Campo, A.; Butt, H.-J.; Vollmer, D. Wetting on the Microscale: Shape of a Liquid Drop on a Microstructured Surface at Different Length Scales. Langmuir 2012, 28 (22), 8392−8398. (16) Papadopoulos, P.; Mammen, L.; Deng, X.; Vollmer, D.; Butt, H.-J. How Superhydrophobicity Breaks Down. Proc. Natl. Acad. Sci. U.S.A. 2013, 110 (9), 3254−3258. (17) Paxson, A. T.; Varanasi, K. K. Self-similarity of Contact Line Depinning from Textured Surfaces. Nat. Commun. 2013, 4, 1492. (18) Gauthier, A.; Rivetti, M.; Teisseire, J.; Barthel, E. Finite Size Effects on Textured Surfaces: Recovering Contact Angles from Vagarious Drop Edges. Langmuir 2014, 30 (6), 1544−1549. (19) Bán, S.; Wolfram, E.; Rohrsetzer, S. The Condition of Starting of Liquid Imbibition in Powders. Colloids Surf. 1987, 22 (2), 291−300. (20) Shirtcliffe, N. J.; McHale, G.; Newton, M. I.; Pyatt, F. B.; Doerr, S. H. Critical Conditions for the Wetting of Soils. Appl. Phys. Lett. 2006, 89 (9), 094101. (21) Extrand, C. W. Repellency of the Lotus Leaf: Resistance to Water Intrusion under Hydrostatic Pressure. Langmuir 2011, 27 (11), 6920−6925. (22) Extrand, C. W.; Moon, S. I. Intrusion Pressure To Initiate Flow through Pores between Spheres. Langmuir 2012, 28 (7), 3503−3509. (23) Badge, I.; Bhawalkar, S. P.; Jia, L.; Dhinojwala, A. Tuning Surface Wettability using Single Layered and Hierarchically Ordered Arrays of Spherical Colloidal Particles. Soft Matter 2013, 9 (11), 3032−3040. (24) Wagner, P.; Furstner, R.; Barthlott, W.; Neinhuis, C. Quantitative Assessment to the Structural Basis of Water Repellency in Natural and Technical Surfaces. J. Exp. Bot. 2003, 54 (385), 1295− 1303. (25) Zhang, J.; Sheng, X.; Jiang, L. The Dewetting Properties of Lotus Leaves. Langmuir 2009, 25 (3), 1371−1376. (26) Sheng, X.; Zhang, J. Air Layer on Superhydrophobic Surface Underwater. Colloids, Surf. A 2011, 377 (1−3), 374−378.
Figure 8. Receding water drops on the surface of a lotus leaf. (a) V = 3.4 μL, β = 0.125; (b) V = 8.7 μL, β = 0.25; (c) V = 21 μL, β = 0.50; (d) V = 33 μL, β = 0.75. The curves represent theoretical profiles of Bashforth and Adams for θr = 180° (blue), 160° (red) and 150° (yellow).
Tilt or sliding angles (α) that we observed experimentally were several degrees or less but were difficult to quantify precisely for the reasons discussed aboveworking surfaces are never perfectly flat, and the leaves have macroscopic contours that introduce inherent tilt angles. Nevertheless, our estimates were in general agreement with these experimental observations and earlier reports that tilt angles for lotus leaves are α < 5− 10°.2,52
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CONCLUSIONS We anticipate that the wetting behavior of the lotus leaf will depend not only on liquid properties but also on drop size and shape. Smaller drops are expected to create more downward pressure, which increases penetration, contact, and retention. Our estimates of contact and sliding angles from modeling agree reasonably well with experimental observations, accounting for the influence of surface curvature and pinning.
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AUTHOR INFORMATION
Corresponding Author
*Tel: 1-651-999-1859. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank M. Acevedo, C. Giesen, T. Edlund, J. McDaniel, L. Monson, J. Pillion, and B. Powell for their support and their suggestions on the technical content and text. The image of the surface of the lotus leaf was kindly provided by Prof. W. Barthlott. Finally, we are grateful to P. Kruth of Como Park Conservatory for generously providing us with fresh lotus leaves.
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REFERENCES
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dx.doi.org/10.1021/la5019482 | Langmuir XXXX, XXX, XXX−XXX
