Theoretical Explanation of the Lotus Effect: Superhydrophobic

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Theoretical Explanation of the Lotus Effect: Superhydrophobic Property Changes by Removal of Nanostructures from the Surface of a Lotus Leaf Minehide Yamamoto, Naoki Nishikawa, Hiroyuki Mayama, Yoshimune Nonomura, Satoshi Yokojima, Shinichiro Nakamura, and Kingo Uchida Langmuir, Just Accepted Manuscript • Publication Date (Web): 15 Jun 2015 Downloaded from http://pubs.acs.org on June 15, 2015

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Theoretical Explanation of the Lotus Effect: Superhydrophobic Property Changes by Removal of Nanostructures from the Surface of a Lotus Leaf Minehide Yamamoto,†Naoki Nishikawa,# Hiroyuki Mayama,*,‡ ¶ Yoshimune Nonomura, ┴ Satoshi Yokojima,§,║ Shinichiro Nakamura,║ and Kingo Uchida,*,†

†

Department of Materials Chemistry, Faculty of Science and Technology, Ryukoku University, Seta, Otsu 520-2194, Japan, Fax: +81-77-543-7483; Tel: +81-77-543-7462; E-mail; [email protected]

#

Mitsuboshi Belting Ltd., 4-1-21 Hamazoe-dori, Nagata-ku, Kobe 653-0024, Japan

‡

Research Institute for Electronic Science, Hokkaido University, N21, W10 Kita-ku, Sapporo 001-0021, Japan

┴

Department of Biochemical Engineering, Graduate School of Science and Engineering, Yamagata University, 4-3-16, Jonan, Yonezawa, Yamagata 992-8510, Japan

║

RIKEN Research Cluster for Innovation, Nakamura Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan

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§

School of Pharmacy, Tokyo University of Pharmacy and Life Sciences, 1432-1 Horinouchi, Hachioji, Tokyo 192-0392, Japan.

¶

Present address: Department of Chemistry, Asahikawa Medical University, 2-1-1-1 Midorigaoka–

higashi, Asahikawa, Hokkaido 078-8510, Japan

Abstract: Theoretical study is presented on the wetting behaviors of water droplets over a lotus leaf. Experimental results are interpreted to clarify the trade-offs among the potential energy change, the local pinning energy, and the adhesion energy. The theoretical parameters, calculated from the experimental results, are used to qualitatively explain the relations among surface fractal dimension, surface morphology, and dynamic wetting behaviors. The surface of a lotus leaf, which shows the superhydrophobic lotus effect, was dipped in ethanol to remove the plant waxes. As a result, the lotus effect is lost. The contact angle of a water drop decreased dramatically from 161° of the original surface to 122°. The water droplet was pinned on the surface. From the fractal analysis, the fractal region of the original surface was divided into two regions: a smaller-sized roughness region of 0.3 to 1.7 m with D of 1.48 and a region of 1.7 to 19 m with D of 1.36. By dipping the leaf in ethanol, the former fractal region, characterized by wax tubes, was lost, and only the latter large fractal region remained. The lotus effect is attributed to a surface structure that is covered with

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needle-shaped wax tubes, and the remaining surface allows invasion of the water droplet and enlarges the interaction with water.

Introduction The lotus leaf is well known for having a highly water-repellent, or superhydrophobic, surface, thus giving the name to the lotus effect.1,2 Water repellency has received much attention in the development of self-cleaning materials, and it has been studied in both natural and artificial systems.3-34 Barthlott et al. investigated the super-water-repellent and self-cleaning effect of the lotus leaf and attributed it to the double-roughness structure of the surface with micro- and nanostructures (trichomes, cuticular folds and wax crystals), together with the hydrophobic properties of the epicuticular wax.1,2 Lei Jiang et al. also showed the importance of the double roughness structure for the appearance of lotus effect.35, 36 Thanks to these structures, contaminating particles are carried away by water droplets, resulting in a cleaned surface (the lotus effect). Therefore, rough, waxy leaves are not only water-repellent but also anti-adhesive with respect to particulate contamination. On the other hand, some plants have different wetting properties. Rose petals and the leaves of garlic and scallions show superhydrophobicity, but the water droplets are pinned to the surface, even when the surface is upside down (the petal effect).9 The previous work explained that these superhydrophobic but water-adhesive surfaces were due to the existence of large cavities that water could penetrate. Recently, experimental studies on the lotus and petal

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effects have been carried out from the viewpoint of material science and surface morphology. Artificial surfaces mimicking the lotus leaf were prepared and the wettability of the surfaces was analyzed. Meanwhile, theoretical studies to clarify the lotus effect have been also carried out. The wettability of such surfaces and these effects were fundamentally explained by Wenzel10 and Cassie-Baxter.11 They found that the wettability was strongly dependent not only on the free energy of the surfaces but also on the surface structures.12,13 The Wenzel state is a model that allows invasion of water droplets, and the Cassie state is a model that prevents invasion of water droplets by taking in air pockets. On a lotus leaf, water is prevented from penetrating the air pockets of the leaf by the nano-micro structure (Cassie state). Therefore, theoretical analysis of the lotus effects originated with the application of certain equations and the related studies could be categorized into three types: (1) experimental and theoretical studies on the wetting transition between the Wenzel and Cassie states,21-34 (2) theoretical studies on the Cassie state’s ability to maintain the lotus effect,37-41 and (3) quantitative and semi-quantitative analyses of various physical factors such as adhesion force.42,43 However, only a few studies on the lotus effect have considered sliding phenomena.26,34 In particular, the importance of the receding part on the sliding droplets has been suggested experimentally,28,29 but no comprehensive explanation of the lotus effect has incorporated this factor. In this paper, we adopted a multi-pin model that is mathematically convenient and relevant to understanding the lotus effect.

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Recently, we have reported photoinduced reversible wettability changes concomitant with topographical changes on the microcrystalline surface of diarylethene 1.14-16 By applying photocontrol of the type and size of the crystals, we could control the photoswitching between two types of water-adhesive superhydrophobic surfaces showing lotus and rose-petal effects. The observed dynamic wetting behavior was explained by a simple scenario that considers the trade-off between the surface-structure-dependent adhesion energy and the potential energy change.26 Here, we consider the superhydrophobic property of the natural lotus leaf theoretically. We compared the properties of the surface of a natural leaf having the double-roughness structures with those of the surface of a lotus leaf whose nano-structure was lost by dipping it in organic solvents. Consequently, we found a change in the dynamic wetting behavior from lotus effect to rose-petal effect due to the loss of wax crystals. We analyzed these surface structures by the box-counting method and interpreted the observed phenomena based on an extended theory of our previous one.26

EXPERIMENTAL Observation and characterization of lotus leaves. Lotus leaves were harvested on the Karasuma Peninsula in Lake Biwa. Contact angle (CA) measurement and scanning electron microscope (SEM) observation were carried out without any treatment of the leaves. Dried lotus leaf was prepared by simply storing the leaf in a room (temperature: 23±2°C, humidity: 70±10%) for five months. Removal of the wax-tubes on the leaves was carried out by dipping a piece of the fresh leaf (50×50

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mm) in ethanol for 20 min followed by drying by storage for one day long in the room. An SEM (KEYENCE VE-8800) was used to study the surface microstructures. Static CAs and SAs (sliding angles) using 1.5-L water droplets were measured with an optical contact angle meter (Kyowa Interface Science Co., Ltd., Drop Master 500). For the fractal analysis, a sample was set with conductive carbon tape on a cover glass on the electron microscope’s stage, and an Au-Pd alloy was evaporated onto the sample surface. The samples were set perpendicular to the stage for cross-section observation. The fractal dimension of a cross-section of each leaf’s surface was calculated from its trace curve by the box-counting method. A two-dimensional area containing these trace curves was divided using identical boxes of side-size r. The number of boxes containing trace curve N(r) was counted, and then side-size r was changed. The number of boxes was counted again with the new side-size r, and the above process was repeated. Based on the box-counting method, the fractal dimension could be calculated from the following relationship:

N r   r  D ,

(1)

where D is the fractal dimension of the cross-section, and the dimension of surface Ds is obtained approximately by Ds = D + 1.

RESULTS AND DISCUSSION SEM images showing the surfaces of a natural lotus leaf, a leaf after dipping in ethanol for 20 min, and a dried lotus leaf are compared in Figure 1. Before dipping, the surface of the leaf is

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covered with projections having a diameter of ca. 10 m, and these are covered with nanostructures consisting of 0.1-m -sized plant wax tubes. The combined structure with 10- and 0.1-m levels of roughness is called a double-roughness structure. The main compound of the plant wax tubes is reported to be nonacosane-5,10-diol.27 The SEM images of the leaf after dipping in ethanol for 20 min did not show the wax tubes, while the dried leaf still had the tubes. SEM images of the cross-section of a natural lotus leaf’s surface were taken while changing the magnitude, and these are shown with trace curves in Figure 2. The corresponding SEM images and trace curves of a leaf dipped in ethanol and a dried leaf are shown in Figures. 3 and 4, respectively. In the low-magnification (× 300) images (a) of Figures 2-4, projections of ca. 10-m diameter were observed. In the higher-magnification images (c and e), the double-roughness structure, in which each projection was covered with nanostructures consisting of 0.1-m -sized wax tubes, is seen only on the surfaces of the natural and dried lotus leaves (Figures 2 and 4), but not on that of the dipped lotus leaf (Figure 3). These images show the loss of the wax tubes and the destruction of the double-roughness structure after dipping the leaf in ethanol.

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Figure 1. SEM images of the surfaces of natural lotus leaf (a) and (b), leaf after dipping in ethanol for 20 min (c) and (d), and dried lotus leaf (e) and (f). SEM images (a), (c), (e): × 1000, scale bar = 10.0 m; SEM images (b), (d), (f): × 7000, scale bar = 1.42 m

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Figure 2. SEM images of the cross-section of a natural lotus leaf (left) and corresponding trace curves (right): (a, b)×300, scale bar = 33.3 m; (c, d) ×2000, scale bar = 5.00 m; (e) ×20000, scale bar = 500 nm; Trace curve (f) corresponds to the area within the green oval in (e).

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Figure 3. SEM images of the cross-section of a lotus leaf after dipping in ethanol (left) and corresponding trace curves (right): (a, b)×300, scale bar = 33.3 m; (c, d) ×2000, scale bar = 5.0 m; (e, f) ×20000, scale bar = 500 nm.

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Figure 4. SEM images of the cross section of a dried lotus leaf (left) and corresponding trace curves (right): (a, b)×300, scale bar = 33.3 m; (c, d) ×2000, scale bar = 5.00 m; (e, f) ×20000, scale bar = 500 nm; Trace curve (f) corresponds to the area within the green oval in (e).

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Next, we carried out box-counting fractal analysis of these surfaces, and the results are summarized in Figure 5. All surfaces have a fractal region. The natural and dried surfaces have a fractal region of 0.3 to 19 m, which is divided in two regions at 1.7 m. Here, 1.7 and 19 m are the characteristic lengths of the diagonal lines of the wax tubules and large roughness (projections), respectively, as shown in Figures S5-S7. In principle, length of characteristic scales in periodic patterns can be found in an ideal fractal system by the box-counting method; however, the lengths of diagonal lines in disordered patterns are detected as averaged characteristic lengths in a real fractal system. Therefore, we adopted 19 and 1.7 m as the characteristic lengths and analyzed fractal dimensions in two scale ranges between 0.3 and 1.7 m and between 1.7 and 19 m in Figure 5a, c. The 1.7 and 19 m values correspond to the diameter of the top of the projections and the diagonal length of the projections, respectively. The 0.3 and 1.7 m values correspond to the diameter of the top of the nanotubes and the diagonal length of the nanotubes, respectively. The cross-sectional fractal dimension D for the region of 0.3 to 1.7 m was 1.48. After removal of the wax tubes, the fractal region between 0.3 to 1.7 m disappeared, and only the larger region remained, indicating the removal of the plant wax tubes. This D value was reduced to 1, with no changes observed for the 1.7- to 19-m region. The fractal dimensions of the dried surface were almost the same as those of the natural surface in both regions. The fractal region of 0.3 to 1.7 m corresponds to the area of wax tubes, and that of 1.7 to 19 m corresponds to the projections. The insets in Figure 5 show the dependence of the differentiation 𝑑(log𝑁)⁄𝑑(log 𝑟) = −𝐷 on scale. In Figure 5(a, c),

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𝑑(log𝑁)⁄𝑑 (log𝑟) is ~ -1 in the ranges of r < 0.3 and > 19 m, while it is ~ -1.4 in r = 0.3 ~ 19 m. In Figure 5(b), 𝑑(log𝑁)⁄𝑑(log 𝑟) is ~ -1.3 in r = 1.9 ~ 19 m and ~ -1 in the ranges of r < 1.9 and > 19 m.

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Figure 5. Fractal analysis of lotus leaves. N(r) vs. r plot for the trace curves of the surfaces of the lotus leaves. (a) Natural surface of the lotus leaf, (b) surface after dipping in ethanol, (c) surface of a dried lotus leaf. The insets show the dependences of d(log N)/d(log r) (= -D) on r. 1.7 and 19 m are characteristic scales of wax tubules and large roughness, respectively (See, SI).

The CAs of a water droplet on the natural, dipped, and dried surfaces of the lotus leaf were 161°, 122°, and 161°, respectively (Figure 6). The lotus effect was observed for the natural and dried surfaces. The results indicate that the roughness size in the region between 0.3 and 1.7 m plays an important role in the appearance of the lotus effect. The SAs before dipping and after drying were 2.7° and 2.3°, respectively, while this was not determined after dipping. Such superhydrophobic lotus effect was also observed other 17 kinds of lotus in Japan, and the SEM images of their fresh surfaces, the CAs, and SAs are summarized in Figs. S9, S10 and Table S2 in the Supporting Information. The surface of a rose petal is known to be superhydrophobic (CA: 154°) with a high adhesive property. Therefore, a water droplet is pinned to the surface, even when the surface is upside down.20 Bhushan et al. reported that the wetting property of rose petals changes by drying. Drying the cells caused the specimen to shrink and water to easily penetrate into the specimen, thus decreasing the CA of the water droplet while increasing the CA hysteresis and adhesive property.26 This explanation also matches the finding of our research. Removal of the wax tube also increases the space between the projections on a lotus leaf, allowing water to penetrate into the space.

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Figure 6. Water droplets on a natural lotus leaf (a), a lotus leaf after dipping in ethanol (b), and a dried lotus leaf (c). The contact angles of the water droplet for (a), (b), and (c) are 161°, 122°, and 161°, respectively. The sliding angles for (a), (b), and (c) are 2.7°, none, and 2.3°, respectively.

Theory of lotus and petal effects As shown above, we found that the lotus effect was observed on the surface before dipping the leaf in ethanol and after drying without dipping, while the petal effect appears on the surface after dipping. As stated in Introduction, the theoretical studies on the lotus effect have mainly focused on the wetting transition between the Cassie and Wenzel states,21-34 the Cassie state’s ability to maintain

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the lotus effect,37-41 and quantitative and semi-quantitative analysis of both states,42,43 while the importance of the receding part has been suggested by experimental findings.28,29 However, few theoretical studies have attempted to understand the sliding phenomena.26,34 Here, we discuss an extended theory focusing on the sliding phenomena based on related studies26,44 and experimental findings.28,29 Figure 7 shows schematic representations of the ideal situations discussed here. Figure 7a illustrates the CB state of a small droplet on a multi-pillar surface22, while Figure 7b shows the CB state on a multi-pillar surface with double-roughness and Figure 7c shows the Wenzel state in which the droplet penetrates into the spacing between surface structures; we assume that the initial states are the CB and Wenzel states, respectively. To focus on the sliding behaviors or wetting dynamics, we do not discuss the wetting mechanism of the CB and Wenzel states on the rough surfaces here. To discuss semi-quantitatively, we adopt the multi-pillar surface which allows us to estimate wetting area easily. This simplification is allowed because there is no significant difference in the size of wetting area on multi-pillar surface and surface covered by round shaped structures as observed in lotus leaves. Under this situation, we will develop the theoretical discussion on the level of energy because we have found that it is easy to understand the physical meanings of the equilibrium contact angle (the Young’s relation) and pinning effect in wetting phenomena by free-energy arguments,44 where it is impossible to discuss the pinning effect on the level of surface tension, especially. In other words, the discussion based on energy enables us to estimate the orders of some dominant factors in the wetting and sliding phenomena, to compare their magnitudes, and to

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discuss their magnitude correlation to understand the mechanism as discussed in our previous study.26 Now, we pay an attention to three factors related to the level of energy: the change in potential energy ∆𝑈 due to the change in height of the droplet’s center of mass in the gravitational field, the local pinning energy 𝐸local pin due to the physical and chemical defects, and the adhesion energy 𝐸ad in the solid-liquid interface. In this theoretical discussion, we consider these factors. In particular, 𝐸ad is considered in addition to our previous study26 instead of the pinning of the receding part.28 Here, we discuss these energy factors’ competitive relationship based on the sliding conditions and the characteristic dimensions of the surface structures. Before further discussion, let us clarify sliding conditions of the small droplets. Although sliding occurs when ∆𝑈 is equal to or larger than 𝐸local pin and 𝐸ad , it should be noted that there are theoretically three modes of sliding. In the first, the front and back parts of the contact line slide simultaneously when 𝐸local pin is equal to 𝐸ad . This would occur on an ideal surface. In the second mode, the front part advances before the back line slides when 𝐸local pin is smaller than 𝐸ad , and in the third, the back part advances before the front line slides when 𝐸ad is smaller than 𝐸local pin . No sliding occurs if ∆𝑈 is much smaller than 𝐸local pin or 𝐸ad . The differences among the sliding modes have not yet received sufficient attention. Here, we also point out that sliding always occurs if the droplet size is more than several mm because ∆𝑈 is proportional to cubed droplet size, while 𝐸local pin and 𝐸ad are proportional to squared droplet size.26, 45 Next, we apply this scenario to the sliding of small droplets on tilting superhydrophilic and

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superhydrophobic surfaces. In wetting on super-hydrophilic surfaces, it is well-known that wicking film forms around the contact line and decreases 𝐸local pin in the front part. This would make the sliding of the front line easier. On the other hand, there is no wicking film in the front part on super-hydrophobic surfaces. Therefore, the local pinning effect remains in the front line26 and adhesion exists in the back part, which inhibits the sliding. We elaborate upon ∆𝑈, 𝐸local pin and 𝐸ad in the following discussion. Change in potential energy ∆𝑼26 First, ∆𝑈 in sliding is described as ∆𝑈 = 𝑚𝑔ℎ,

(2)

where 𝑚, 𝑔 and ℎ are mass of a droplet, gravitational acceleration, and the change in height of a droplet’s center of mass, respectively. ℎ is related to the surface roughness through the spacing between the defects 𝑝 and sliding angle 𝜙 as follows. ℎ=

𝑝sin𝜙 2

.

(3)

On the other hand, 𝐸ad is a competing factor against ∆𝑈 in the present study. In our previous study,22 we mentioned the local pinning energy 𝐸local pin as a competing factor to explain the dynamic wetting behaviors on diarylethene microcrystalline surfaces with superhydrophobicity under the situation shown in Figure 7a since the microcrystalline is a needle-shaped physical defect that enhances pinning. First, we calculate ∆𝑈 using eqs. (2) and (3). 𝑚 is calculated from the volume and density. To

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distinguish between the lotus and petal effects, the sliding distance p on the surfaces should be the same before and after dipping. Here, we assume p = 10 m from the SEM images and that 𝜙 = 2.7° and 2.3° for the sliding angle before dipping and after drying without dipping, respectively, while 𝜙 = 90° after dipping. As a result, we obtain ∆𝑈 = 6.92 × 10−12 and 5.90 × 10−12 J before dipping and after drying without dipping, respectively, and ∆𝑈 = 1.47 × 10−10 J after dipping. The theoretical values are shown in Table 1. Local pinning energy 𝑬𝐥𝐨𝐜𝐚𝐥 𝐩𝐢𝐧 26,44 Next, 𝐸local pin can be approximated on the basis of full pinning energy 𝐸full pin : 𝑤

𝐸local pin = 2𝜋𝑅 𝐸full pin ,

(4)

where 𝑅 and 𝑤 are radius of the solid-liquid interface (wetting area) and diameter of the smallest defect. Although here we skip the details of 𝐸local pin , essentially this means the increase in the air-liquid interfacial energy. 𝐸local pin is due to the local pinning by a defect at the lowest part of the contact line of the droplet on a slope, and we roughly assume that its magnitude is proportional to the ratio of 𝑤 to the length of contact line 2𝜋𝑅. We next estimate 𝐸full pin to further discuss 𝐸local pin . In line with the calculations in the supporting information of a previous work26, we obtain 𝐸full pin = 3.64 × 10−8 J before dipping and after drying without dipping, and 𝐸full pin = 1.78 × 10−6 J after dipping. R in eq. 4 is 𝑅 = (2−3 cos 𝜃

4

3 eq +cos 𝜃eq

1/3

)

𝑟0 sin𝜃eq .

(5)

Here, 𝑟0 = 7.10×10-4 m from the volume of a droplet 𝑉 = (4⁄3)𝜋𝑟03 = 1.5 μL. When 𝜃eq =

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161° and 122°, we obtain 𝑅 = 2.31 × 10−5 m before the rinsing and after the drying and 6.33 × 10−4 m after the rinsing from eq. (5). Next, we estimate 𝐸local pin using eq. (4). From SEM images, we assume that 𝑤 ~ 30 nm before dipping and after drying without dipping and that 𝑤 ~10 m after dipping. The reason why the former is obtained is attributed to the area of adhesion energy. As a result, we obtain 𝐸local pin = 7.51 × 10−13 J before dipping and after drying without dipping, and 4.48 × 10−9 J after dipping. Theoretical values are summarized in Table 1. We found that ∆𝑈 ≥ 𝐸local pin before dipping and after drying without dipping is one of the minimum conditions, as well as ∆𝑈 < 𝐸local pin after dipping. These relations explain the reason why the lotus and petal effects appear without and with dipping, respectively. Adhesion energy 𝑬𝐚𝐝 26 It has been reported that the strength of adhesion plays a significant role in dynamic wetting behaviors28. We tried to estimate 𝐸ad in this study. 𝐸ad can be discussed from the viewpoint of the equilibrium contact angle 𝜃eq on a flat surface, the surface tension of liquid 𝛾L , and actual adhesive area 𝑆.45 𝐸ad = 𝛾L (1 + cos 𝜃eq,flat )𝑆,

(6)

where 𝜃eq.,flat is the equilibrium contact angle on a flat surface, assumed to be 110° on typical wax,46 𝛾𝐿 = 72 mN/m and 𝑆 is actual wetting area reflecting the wetting state as discussed below. Actually, the total wetting area is directly correlated with the surface fractal dimension, but the following discussion shows that the wetting area in the minimum receding part is particularly

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important to understand the lotus and petal effects. Figure 8a, b illustrates model multi-pillar surfaces corresponding to double-roughness surfaces before dipping/ after drying without dipping and after dipping, respectively. 𝑆 is the sum of the cross-sectional area of the pillar heads in the apparent solid-liquid interfacial area in the CB state in the minimum de-adhesion area, while it is actual solid-liquid interfacial area in the Wenzel state in the minimum de-adhesion area. In the CB state, we assume that the diameter of a pillar head is ca. 30 nm from the SEM images. This is evaluated from the contacting width between tangential lines and the wax tubes as shown in the inset of Figure 8a. We also assume that the average distance between the wax tubes is 500 nm on large roughness approximated as pillars with 5-m diameter and 18-m height, and the average distance between pillars is 20 m. According to these rough assumptions, the apparent adhesive area in unit area is estimated to be 1.94 × 10−12 m2 in a 20×20-m area before dipping and after drying without dipping, while it is 6.83 × 10−10 m2 after dipping. In this way, we could estimate the adhesive area in unit surface structure. Next, let us discuss 𝑆 based on this. As shown in Figure 9a, the contact line on a multi-pillar surface can slide uniformly in a step-by-step way. Besides 𝐸local pin , another minimum condition of sliding is the de-adhesion energy needed to induce the step-wise sliding of the back part. Figure 9b shows the geometry to calculate the minimum de-adhesion area. From the geometry, the de-adhesion area 𝑆 is 𝑆=

𝑅2 2

(2𝜑 − sin 2𝜑),

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(7)

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where 𝑅 is obtained from eq. (5), 𝑝 is the pitch as shown in Figure 7, and 𝜑 is the angle from the 𝑥-axis. This is determined from

cos 𝜑 =

𝑅−𝑝 𝑅

.

(8)

As a result, we obtain 𝑆 =1.23×10-11 m2 and 𝐸ad = 5.84 × 10−13 J before dipping and after drying without dipping, while 𝑆 = 7.24 × 10−9 m2 and 𝐸ad = 3.42 × 10−10 J after dipping. The theoretical results are summarized in Table 1.

Relationship between ∆𝑼, 𝑬𝐥𝐨𝐜𝐚𝐥 𝐩𝐢𝐧 and 𝑬𝐚𝐝

Here, we compare the obtained values of ∆𝑈, 𝐸local pin and 𝐸ad . Before dipping and after drying without dipping, the orders are the same, but ∆𝑈 is slightly larger than the others. This semi-quantitatively explains why the lotus effect appeared. In other words, the fine wax tubes significantly decrease 𝐸local pin and 𝐸ad . On the other hand, 𝐸local pin is ca. 10 times larger than ∆𝑈 and 𝐸ad after dipping. This semi-quantitatively explains the petal effect after dipping in which 𝐸local pin governs. Although we discussed 𝐸local pin and 𝐸ad based on the wetting states, the relationships among 𝐸local pin , 𝐸ad , and the CB and Wenzel states,47 on the basis of characteristic dimensions, remain unclear. This issue should be clarified in further studies.

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Figure 7. Schematic representations of the CB state on multi-pillar surface (a), the CB state on that with double-roughness (b) and the Wenzel state (invasion into surface structure of multi-pillar surface occurs) (c). Initial states are shown by thick solid shapes, while a transient state and the final state are depicted by thin dashed and solid shapes, respectively. Local pinning in the front part and adhesion in the back part are indicated as thick dashed circles.



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Figure 8. Assumed situations of the adhesion areas (shaded areas) in a unit surface area of double roughness surface (20 × 20 m in size) together with typical dimensions in the CB state before dipping and after drying without dipping (a) and in the Wenzel state after dipping (b). The inset in (a) illustrates how the actual wax tubes are approximated. The small pillar heads are the adhesive parts in the CB state, while a large pillar head, the column wall, and the substrate composes the adhesive part in the Wenzel state.

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Figure 9. Schematic representation of adhesion area along the back part due to sliding (a) and the detailed geometry (b).

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Table 1. Theoretical results for surface before dipping, after drying without dipping, and after dipping. After drying without

Treatment

Before dipping

𝑉 (L)

1.5

1.5

1.5

𝑟0 (m)

7.10×10-4

7.10×10-4

7.10×10-4

CA (deg)

161

161

122

dipping

After dipping

𝑅 (m)

2.31×10

2.31×10

𝑤 (m)

10-7

10-7

10-5

𝑝 (m)

2.0×10-5

2.0×10-5

2.0×10-5

𝜙 (deg)

2.7

2.3

90

𝛥𝑈 (J)

6.92×10-12

5.90×10-12

1.47×10-10

𝐸local pin(J)

7.51×10-13

2.5×10-12

4.48×10-9

𝑆 (m2)

1.23×10-11

1.23×10-11

7.24×10-9

𝐸ad (J)

5.84×10-13

5.84×10-13

3.42×10-10

Relation

Δ𝑈 > 𝐸local pin > 𝐸ad

Δ𝑈 > 𝐸local pin > 𝐸ad

𝐸local pin > 𝐸ad > Δ𝑈

Effect

Lotus effect

Lotus effect

Petal effect

-4

-4

27

6.33×10-4


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CONCLUSION The surface of a lotus leaf showing the superhydrophobic lotus effect was dipped in ethanol to remove the plant waxes. Consequently, the lotus effect was lost, and the contact angle of a water drop decreased dramatically from 161° on the original surface to 122°, and the water droplet was pinned to the surface. From the fractal analysis, the fractal region of the original surface was divided into two regions: a smaller-sized roughness region of 0.3 to 1.7 m with a fractal dimension D of 1.48 and a region of 1.7 to 19 m with D of 1.36. By dipping the leaf in ethanol, the former fractal region corresponding to wax tubes was lost, and only the latter fractal region remained. The lotus effect is attributed to a surface structure that is covered with needle-shaped wax tubes, and the lost surface allows invasion of the water droplet and enlarges the interaction with water. The observed differences in wetting behaviors are explained by an extended theory that considers the trade-offs among the potential energy change, the local pinning energy, and the adhesion energy. Rough estimation of the theoretical parameters calculated from the experimental results semi-quantitatively explains the relations among surface fractal dimension, surface morphology and dynamic wetting behaviors.

Corresponding Authors:

Kingo Uchida (Prof. Dr.)

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Address: Department of Materials Chemistry, Faculty of Science and Technology, Ryukoku University, Seta, Otsu 520-2194, Japan. Telephone: +81-77-543-7462. Fax: +81-77-543-7483. E-mail: [email protected]

Hiroyuki Mayama (Dr.) Address: Department of Chemistry, Asahikawa Medical University, 2-1-1-1 Midorigaoka–higashi, Asahikawa, Hokkaido 078-8510, Japan. Telephone: +81-166-68-2726. Fax: +81-166-68-2782. E-mail: [email protected]

Acknowledgement This work was supported by the Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) as a Supported Program for the Strategic Research Foundation at Private Universities and by a Grant-in-Aid for Scientific Research on Innovative Areas “Photosynergetics” (No. 26107008). HM and YN were supported by a Grant-in-Aid for Scientific Research (C) (nos. 26390001 and 26400424) from the Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT).

ASSOCIATED CONTENT Supporting Information

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SEM images of a lotus (Nelumbo nucifera) leaf were taken after removal of the plant wax by dipping in various solvents, showing the contact angles of a water droplet on the lotus leaf after removal of the plant wax, and the surface structures of lotus leaves, CAs and SAs of 17 kinds of lotus in Japan. This material is available free of charge at http://pubs.acs.org.

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Theoretical Explanation of the Lotus Effect: Superhydrophobic

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