Facile Fabrication of Superomniphobic Polymer ... - ACS Publications

Mar 2, 2017 - Hanmin Jang, Heung Soo Lee, Kwan-Soo Lee, and Dong Rip Kim*. School of Mechanical Engineering, Hanyang University, Seoul, 133-791, ...
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Facile Fabrication of Superomniphobic Polymer Hierarchical Structures for Directional Droplet Movement Hanmin Jang, Heung Soo Lee, Kwan-Soo Lee, and Dong Rip Kim ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b16015 • Publication Date (Web): 02 Mar 2017 Downloaded from http://pubs.acs.org on March 6, 2017

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Facile Fabrication of Superomniphobic Polymer Hierarchical Structures for Directional Droplet Movement Hanmin Jang1, Heung Soo Lee1, Kwan-Soo Lee1, and Dong Rip Kim1* 1

School of Mechanical Engineering, Hanyang University, Seoul, 133-791, Korea * Corresponding author. E-mail: [email protected]

Key Words: Superomniphobicity, Superhydrophobicity, Nano and Micro Structure, Hierarchical Structure, Directional Movement, Water Transport

ABSTRACT

We report the facile method to fabricate the polymer hierarchical structures, which are the engineered, ratchet-like micro-scale structures with nano-scale dimples, for directional movement of droplets. The fabricated polymer hierarchical structures with no surface modifier show hydrophobic, superhydrophobic, or omniphobic characteristics, depending on their intrinsic polymer properties. Further treatment with a surface modifier endows the polymer surfaces with superomniphobicity. The fabricated polymer substrates with no surface modifier enable the movement of the water droplet along the designed track at almost no inclination of the substrate.

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MANUSCRIPT

Engineering the surface structures in small scales, mimicking biological species, has been widely studied to endow the surface with new functionalities in terms of controlling droplet behaviors1-6. Such functional surfaces typically possess hierarchical structures which consist of both micro- and nano-scale structures7-8. Specifically, the conical spine of "Opuntia microdasys" have the different radius at both ends, and the microgrooves and sub-microgrooves are positioned on their surfaces, which results in the gradient of Laplace pressure for directional movement of fog droplets, thereby realizing their easy collection1. The leaves of “Ryegrass” have the slightly bent ratchet structures with a sharp tip on their surfaces2. While the slightly bent ratchet structures drive the anisotropic movement of water droplet, the sharp tip on the ratchet maximizes the liquid release force, which can enhance the directional water droplet repellency. Examples of controlling water droplets by surface structuring are not limited to plants. The wings of “Morpho Deidamia” also have hierarchical structures consisting of micro-scale ratchetlike triangular structures and nano-scale tips on their surfaces to effectively eliminate fog droplets by rolling off them from their wings3. Many studies have successfully demonstrated fabrication methods of bio-inspired surfaces to control the droplet behaviors due to their potentials to wide applications, such as water transport, drag reduction, anti-fogging, and frost retardation4,7,9-15. For example, superhydrophobic surfaces with hierarchical micro/nano-structures were realized by assembling silica nanoparticles onto microsphere-patterned plastic substrate and by subsequently modifying their surfaces with a low surface energy material9. The ratchet-like superhydrophobic surfaces were fabricated by coating micro/nano-structured porous polystyrene particles over the ratchet-

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like aluminum micro-structures for setting up a platform of directional motion of water droplet4. Moreover, superomniphobic mushroom-like hierarchical structures consisting of micropillars and nanoparticles were constructed by carrying out the epoxy molding process using the template filled with silica nanoparticles, followed by oxygen plasma etching and surface modification15. Albeit the successful demonstration of bio-inspired functional surfaces, the fabrication of those hierarchical structures still need more simplicity to be readily adopted to many applications. Here we demonstrate the facile method to fabricate polymer hierarchical structures for directional movement of droplets. Specifically, we utilize polymer molding process with the template of hierarchical structures, containing ratchet-like micro-scale structures and nano-scale spheres on top of them. The template is covered by tens of nanometer thick protecting layer, which enables the repeated molding process to fabricate the functional surfaces. As a result, the molded polymer shows good shape of hierarchical structures which are ratchet-like microscale structures with nano-scale dimples. The fabricated polymer surfaces show hydrophobic, superhydrophobic or omniphobic properties with no surface modifier, depending on the intrinsic properties of the polymers. Further modification of the molded polymer surfaces with selfassembled monolayer (SAM) results in superomniphobic properties of the surfaces. As such, various droplets with low surface tension like soybean oil can be directionally moved on the engineered surfaces, and the movements of water droplets can be controlled along the designed track at almost no inclination of the substrate without any additional external force like vibration. Figure 1 describes the schematic of our one-step molding process to fabricate the polymer hierarchical structures. First, the ratchet-like micro-structures were engraved onto an aluminum substrate by conventional machine tools (i.e., CNC lathe). The shape of the ratchet-

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like structure has a critical role to enhance the internal driving force of droplets, which can be optimized by the following equation3-4. F =  |cos . +  | − |cos . +  |

(1)

, where F is the internal driving force per the length of two ratchet-like micro-structures,  is the surface tension of liquid, . and . refer to the advancing and receding contact angles of a droplet with respect to the hypotenuse of a triangular shape of ratchet structure, respectively, and  and  are the base angles of a triangular shape of the ratchet structure. We designed the ratchet-like triangular structure that had a height of 200 µm and a width of 400 µm with base angles of about 27° and 90° to increase the internal driving force of droplets. Second, silica (SiO2) nano-spheres with a diameter of 600 nm were deposited on top of the ratchet-like micro surfaces by using Langmuir-Blodgett coating, followed by spin coating the protecting layer with a thickness of about 50 nm (spin-on-glass (SOG), UP Chemical) and curing the substrate at 450℃ for 10 min. The templates were used to fabricate polymer hierarchical structures by using simple molding process with a variety of polymers, including ethylene vinyl acetate (EVA, SigmaAldrich), polypropylene (PP, Sigma-Aldrich), and polytetrafluoroethylene (PTFE, Daikin). Specifically, we used a hot press machine tool for molding process (molding temperatures of EVA, PP, and PTFE were 180℃, 230℃, and 340℃, respectively, and molding pressures were about 30 MPa for all the polymers for 10~30 minutes. As a result, molded polymer hierarchical structures were shaped as ratchet-like micro-structures with nano-dimples. Further surface modifications over the molded PTFE substrates were carried out by SAM coating. First, oxygen plasma (a power of 300W, and a frequency of 13.56 MHz) was applied for 10 min over the molded PTFE substrates to form hydroxyl (OH-) group on their surfaces. Second, the PTFE

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substrates were immersed into the 0.1 vol% perfluorodecyltrichlorosilane (PFDTS, SigmaAldrich) in n-hexane solution for 10 min, followed by heating the substrates on a hot-plate at 130℃ for one hour. The surface morphologies were characterized by using scanning electron microscope (SEM, Hitachi, S-4800), and the static contact angles were measured by placing an 8 µl droplet of each solution on the substrates (Surface Electro Optics, Phoenix-10). The dynamic droplet behavior was monitored by using a high speed camera at 50 frames per second after dropping a 10 µl droplet from the height of about 45 mm. Figure 2 shows the surface morphologies of the template and the molded polymers. The hierarchically structured template consists of ratchet-like triangular micro-structures and 600 nm diameter silica nano-spheres, covered by a very thin silica protecting layer (a thickness of about 50 nm) (Figure 2a). The silica nano-spheres and protecting layer on top of aluminum ratchet-like substrates effectively maintains the original shape of the template during the repeated molding process at high temperature and high pressure. The molding process well forms the hierarchical structures using a variety of polymers (EVA, PP, and PTFE) (Figure 2b-d). The molded polymer hierarchical structure shows the opposite surface patterns to the template, which has the hierarchical structures of the ratchet-like triangular shape with nano-dimples. Figure 3a to 3d show the wettability of the molded polymer hierarchical structures by measuring the static contact angles (C.A.) and sliding angles (S.A.) with various liquid droplets, such as, water (a surface tension of 72.1 mN/m)16, glycerol (a surface tension of 64.0 mN/m) 17, ethylene glycol (a surface tension of 47.3 mN/m)18, and soybean oil (a surface tension of 27.6 mN/m)19. First, the molded polymer hierarchical structures effectively increase their surface roughness to reduce the solid-liquid contact areas, thereby increasing the static contact angles of

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their planar substrates20. The water contact angles of the polymer hierarchical structures (about 133° for EVA, 153° for PP, and 158° for PTFE) significantly increase, compared to those of planar substrates (about 93° for EVA, 99° for PP, and 108° for PTFE). It should be noted that the wettabilities of the molded polymer substrates are solely from the rough hierarchical surfaces without any surface modifiers, showing excellent implementation of template surface morphologies to polymer through molding process. Second, in spite of similar surface morphologies, the molded polymer hierarchical structures exhibit different wettabilities, such as hydrophobic, superhydrophobic, and omniphobic, in terms of the type of polymers. Specifically, EVA, PP, and PTFE hierarchical structures in Figure 3a, 3b, and 3c show hydrophobic, superhydrophobic, and omniphobic properties, respectively. The different wettabilities of the molded polymer hierarchical structures qualitatively follow the intrinsic properties of polymers, because under the same surface morphologies, low intrinsic surface energies of the polymers lower the effective surface energies of the polymer hierarchical structures. EVA, PP, and PTFE have an intrinsic surface energy of 38.6 mJ/m2

21

, 30.0 mJ/m2 22 and 20 mJ/m2 23, respectively.

It should be noted that EVA has relatively high intrinsic surface energy due to the hydrophilic properties of vinyl acetate (CH3CO2CHCH2) in the polymer21. We further carried out the surface treatment over the omniphobic PTFE hierarchical structures with a surface modifier (perfluorodecyltrichlorosilane, PFDTS) in Figure 3d. As a result, this surface modified PTFE hierarchical structures effectively repel even the soybean oil droplets, performing the superomniphobic properties. This is attributed to the combined effects of the rough surfaces of PTFE hierarchical structures and the low surface energy of PFDTS. We further tested the repeatability of our fabrication method by creating the polymer hierarchical structures with three different materials using the same molding template (Figure 3e). Twenty

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repeated molding process per each material (a total of sixty fabrication repetitions with the molding template) generate the hierarchically-structured polymer surfaces with a similar degree of wettabilities for the identical polymers. Hydrophobic EVA, superhydrophobic PP, and omniphobic PTFE hierarchically-structured surfaces perform the static contact angle of 131.7° ± 1.7°, 153.4° ± 0.9°, and 157.2° ± 0.8° for water droplets, respectively. Moreover, SEM image of the template surface after sixty fabrication repetitions reveals the robustness of the template surface (Supporting Information, Figure S1). This not only indicates the repeatable process of our proposed method, but also the durable molding templates with ultra-thin protecting layer, which acts as the main cost-saving factor for wide applications to many industrial products. We also investigated the dynamic droplet behavior of polymer hierarchical structures, because water transport can occur in dynamic circumstances rather than in static environments. Specifically, we measured the rebounding height of the droplet which was dropped at the same height, while capturing the images using high speed camera (Figure 4 and Table 1). On the superhydrophobic PP hierarchically-structured surfaces, the rebounding height of a water droplet is about three times higher than that on the planar PP surfaces, while the rebounding height of an ethylene glycol droplet was about 1.5 times higher than that on the planar PP surfaces. The superhydrophobic PP hierarchical structures can also maintain higher static contact angles of water and ethylene glycol droplets after rebounding processes. Similarly, both water and ethylene glycol droplets rebound from the omniphobic PTFE hierarchically-structured surfaces about 1.6 times higher than the planar PTFE surfaces. The higher rebounding height of the droplets on the hierarchically-structured surfaces, showing better liquid repellency, results from the existence of many air traps on hierarchical structures, when the droplet dynamically contacts with the surface24. Additionally, we measured the rebounding height of PFDTS-modified

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superomniphobic PTFE hierarchically-structured surfaces, which shows 1.5 times and 1.3 times higher rebounding height of water and ethylene glycol droplets than the control planar surfaces, respectively. It should be noted that the control planar surfaces are chemically modified with PFDTS under the identical process to the hierarchically-structured surfaces. Compared to the dynamic droplet behavior of the PTFE surfaces without the coating of surface modifiers, as shown in Table 1, the PFDTS-modified PTFE surfaces do not exhibit significant differences in the dynamic droplet behavior even for soybean oil (Figure S2). This means that, although the surface modifier (PFDTS) effectively lowers the surface energy of the PTFE, the air gaps generated by surface roughness and morphology are of importance to rebound the droplets dynamically25-26. Our hierarchically-structured polymer surfaces are designed to move the droplet directionally. To see the potency of the directional movement of various droplets using the fabricated surfaces, we tested the droplet movement on the hierarchically-structured PTFE surfaces with no chemical modifier by placing droplets, as shown in Figure 5. The ratchet-like micro-structures in the substrates are designed to uni-directionally move the droplet from left to right. The working principle is that the formation of the advancing contact angle of the droplet toward the direction and the receding contact angle of the droplet on the opposite side generates the effective driving force of "the caterpillar-like crawling" directional movement of the droplet4. Consequently, even though there is no additional external force like vibration, the water droplet on the functional surface is driven to the right with the speed of water droplet as about 1.9 cm/s at the inclination of the substrate of about 1.5° (Figure 5a). The liquid droplets with lower surface tension, such as glycerol and ethylene glycol, require the higher degree of the substrate inclination (glycerol: about 6.2°, ethylene glycol: about 9.2°) to realize the directional movement

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of droplets (Figure 5b and 5c). It should be noted that if such droplets are placed on the planar substrate, the droplets are pinned on the substrate without any rolling movement even in higher inclination. The measured velocities of the droplet are highly related to the surface tension and viscosity of the liquid. The droplet of glycerol is slowly moved on the substrate at the velocity of about 1.5 cm/s. Although the higher gravity force in the more inclination of the substrates is exerted on the droplet of glycerol to move, glycerol has lower surface tension (64.0 mN/m) and higher kinematic viscosity (498.3 cSt) than water (a surface tension of 72.1 mN/m and a kinematic viscosity of 1.0 cSt)27, which results in the lower velocity of glycerol droplet. On the other hand, the droplets of ethylene glycol (a droplet velocity of about 4.8 cm/s) move much faster than those of water and glycerol. Although the surface tension of ethylene glycol is lower than that of water or glycerol, the kinematic viscosity of ethylene glycol (1.9 cSt)28 is similar with water, and the increased gravity force associated with higher inclination mainly increases the droplet velocity of ethylene glycol. The droplet movement of soybean oil, requiring the superomniphobic properties of the surfaces, was tested on the PFDTS-modified hierarchicallystructured PTFE surfaces. The soybean oil droplet moves in a direction with the velocity of 0.8 cm/s at the inclination of 9.8° (Figure 5d). The low velocity of the soybean oil droplet is responsible to low surface tension (27.6 mN/m) and high viscosity (50.1 cSt)29 of the soybean oil, albeit the higher inclination of the substrate. We confirmed that the directional movements of droplets arose from the ratchet-like micro-structures in our study by comparing the droplet movement along and against force-generating direction of the ratchet-like micro-structures (Figure S3) and by monitoring the growth behavior of water droplet on the superhydrophobic surfaces with random structures and with ratchet-like micro-structures under slow injection of water through a needle (Figure S4 and S5).

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In addition, we demonstrate the utilization of the fabricated polymer substrates, enabling the directional movement of droplets, by constructing the S-shaped and U-shaped tracks, which means that the droplet movement can be controlled in two-dimensional domain. Both tracks were assembled by cutting the hierarchically-structured PTFE substrates in the narrow shape and by attaching those substrates together after bending. It should be noted that no surface modifier was applied to those substrates. As shown in Figure 6a and 6b, the water droplet successfully moved along the S-shaped and U-shaped tracks. Specifically, the droplets move with the velocity of 4.8 cm/s at the substrate inclination of about 2.0° along the S-shaped track with the curvature radius of 12.9 cm (Figure 6a), and they also move with the velocity of 5.5 cm/s at the substrate inclination of about 3.0° along the U-shaped track with the even smaller curvature radius of 6.4 cm (Figure 6b). Remarkably, the water droplets are driven along the well-designed track with hierarchically-structured surfaces without any surface modification at almost no inclination of the substrate (video S1 and video S2). Moreover, the water droplet moves with the velocity of 11.7 cm/s along the S-shaped track with a curvature of smaller radius of 4.3 cm as shown in Figure 6c and video S3. The S-shaped track has a length of 155.7 mm at an inclination angle of about 4.7°. It should be noted that we installed walls with a height of about 0.5 mm at both sides of the track in Figure 6c because fast moving droplets can run off the track with a curvature of small radius due to their inertia. The results indicate the potency of our proposed method to easily fabricate the functional substrates, enabling the directional controlling of droplets, for their wide applications to the systems that need liquid-repellent properties or nearly self-driven movement of droplets like microfluidic channels. In summary, we demonstrate the facile method to fabricate functional polymer surfaces to propel droplets directionally using molding process. The molding template consists of ratchet-

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like micro-structures, nano-spheres, and ultra-thin protecting layer. The hierarchical structures are well implemented to a variety of polymers as the ratchet-like micro-structures with nanodimples with high fidelity and repeatability, which can be a big cost-saving factor for industrial applications. The surface wettabilities, such as hydrophobic, superhydrophobic, and omniphobic properties, of the molded polymer depend on the intrinsic properties of polymers. Further surface modification can render the molded omniphobic substrates superomniphobic. The hierarchicallystructured polymer surfaces can directionally drive a variety of droplets, including water, glycerol, ethylene glycol, and soybean oil, at the substrate inclination of less than 10°. Such onedimensional movement of droplets can be extended to two-dimensional controlling of droplet movement by constructing the tracks with well-designed, hierarchically-structured surfaces. The proposed method can be further developed to large-area hot pressing or injection molding process for integrating functional surfaces to practical applications. The successful demonstration of two-dimensional controlling of droplet movement at almost no inclination of the substrates opens up the applications of functional surfaces to the fluidic devices which can benefit from the nearly self-driven movement of droplets due to highly liquid-repellent properties.

Acknowledgement This work was supported by the Intelligent Synthetic Biology Center of Global Frontier Project of the National Research Foundation of Korea (NRF-2012M3A6A8054889), funded by the Ministry of Science, ICT, and Future Planning. This research was also supported by the Commercializations Promotion Agency for R&D Outcomes (COMPA) funded by the Ministry of Science, ICT and Future Planning (MISP, 2016K000128).

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Supporting Information Supporting information is available free of charge on the ACS Publications website. SEM images of hierarchically-structured template before and after repeated molding processes, dynamic droplet behaviors of soybean oil on omniphobic and superomniphobic PTFE surfaces and control planar surfaces, comparison of droplet movement along and against force-generating direction of the ratchet-like micro-structures on omniphobic and superomniphobic PTFE surface, fabrication of superhydrophobic substrate with random structures, growth of water droplet on superhydrophobic surfaces under slow injection of water through a needle, and videos of directional movement of droplets along curved tracks.

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25. Mishchenko, L.; Hatton, B.; Bahadur, V.; Taylor, J. A.; Krupenkin, T.; Aizenberg, J., Design of Ice-free Nanostructured Surfaces Based on Repulsion of Impacting Water Droplets. ACS Nano 2010, 4, 7699-7707. 26. Pan, S.; Kota, A. K.; Mabry, J. M.; Tuteja, A., Superomniphobic Surfaces for Effective Chemical Shielding. J. Am. Chem. Soc. 2012, 135, 578-581. 27. Segur, J. B.; Obestar, H. E., Viscosity of Glycerol and Its Aqueous Solutions. Ind. Eng. Chem. 1951, 43, 2117-2120. 28. Elson T. In Concepts of Chemical Engineering for Chemists.; RSC: Cambridge, U.K., 2007; Chapter 3, pp 58. 29. Lang, W.; Sokhansanj, S.; Sosulski, F. W., Modelling the Temperature Dependence of Kinematic Viscosity for Refined Canola Oil. J. Am. Oil Chem. Soc. 1992, 69, 1054-1055.

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Figure Caption Figure

1. Schematic of one-step molding process to fabricate the polymer functional

surfaces to enable the unidirectional droplet movement. Fabrication of the polymer functional surfaces is based on the simple molding process using a variety of polymers with the hierarchically-structured template which consists of ratchet-like micro-structures, nano-spheres, and an ultra-thin protective layer.

Figure 2. Surface morphologies of the template and the molded polymers. (a) Scanning electron microscopy (SEM) images of the template with the hierarchically-structured surfaces. The silica nano-spheres covered with the ultra-thin silica layer appears on the ratchet-like microstructures. SEM images of hierarchically-structured (b) ethylene vinyl acetate (EVA), (c) polypropylene (PP), (d) polytetrafluoroethylene (PTFE) after molding process. The surface morphology of the molded polymer has the clear hierarchical structures of the ratchet-like microstructures with the nano-dimples.

Figure 3. Wettabilities of the molded polymer surfaces with the hierarchical structures. Static contact angle and sliding angle measurement of (a) hydrophobic EVA, (b) superhydrophobic PP, (c) omniphobic PTFE, and (d) superomniphobic PTFE modified with perfluorodecyltrichlorosilane (PFDTS) substrates. The surface tensions of water, glycerol, ethylene glycol, and soybean oil are 72.1, 64.0, 47.3, and 27.6 mN/m, respectively. (e) the wettabilities of the molded polymers in terms of the repeated molding process using the same template. Twenty repeated molding processes per each material generate the hierarchicallystructured polymer surfaces with a similar level of wettabilities for the identical polymer.

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Figure 4. Comparison of dynamic droplet behaviors between the molded polymer surfaces with hierarchical structures and the control planar surfaces. (a) Superhydrophobic PP surface with hierarchical structures exhibits superior behaviors of dynamic droplets (i.e., 3 times and 1.5 times higher rebounding height of water and ethylene glycerol droplets, respectively) to the planar PP surface. (b) Water droplet rebounds from the omniphobic PTFE surface 1.6 times higher than from the planar PTFE surface both for water and ethylene glycerol. (c) PFDTSmodified superomniphobic PTFE surface repels the water droplet for 1.5 times larger and the ethylene glycol droplet for 1.3 times larger than the control PTFDTS-modified planar PTFE.

Figure 5. Unidirectional movement of various droplets on the hierarchically-structured PTFE surfaces. The hierarchical structures are designed to move the droplet from left to right. (a) Water droplet (blue) moves directionally on the the hierarchically-structured PTFE surfaces with the velocity of 1.9 cm/s at the substrate inclination of 1.5°. (b) Glycerol droplet (green) with the lower surface tension than the water droplet requires the more inclination of the substrate (about 6.2°) for the directional movement of the droplet, and the velocity of the glycerol droplet (~ 1.5 cm/s) is lower than that of the water droplet. (c) Ethylene glycol droplet (red) with the surface tension lower than the glycerol necessitates the further inclination of the substrate to about 9.2° for the directional movement. The ethylene glycol droplet moves at the velocity of 4.8 cm/s. (d) Soybean oil droplet (yellow) with the lowest surface tension among the tested liquids moves with the velocity of 0.8 cm/s at the substrate inclination of 9.8°. The surface of hierarchically-structured PTFE in (d) is modified with PFDTS for realizing superomniphobic properties.

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Figure 6. Controllable movement of water droplets on the S-shaped and U-shaped PTFE tracks. One-dimensional movement of water droplets on the hierarchically-structured polymer surfaces can be extended to two-dimensional movement, when the track is well-designed with the hierarchically-structured polymer surfaces. The water droplet (blue) itself moves along the tracks with the hierarchically-structured PTFE surfaces with no surface modification, no additional external force like vibration, and no guiding wall in both (a) S-shaped and (b) Ushaped track cases. The levelers in the pictures indicate the substrates are placed almost flat (less than 3°). (c) Water droplet moves along the S-shaped track with a curvature of smaller radius which consists of the hierarchically-structured PTFE surfaces. In the case (c), the walls with a height of 0.5 mm are installed at both sides of the track which has an inclination angle less than 5°. In the optical image (c), the droplet motion is successively captured with an interval of 150 ms.

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Table 1. Rebounding Heights of Various Liquid Droplets. Rebounding Height (mm) Type of Substrate Water

Ethylene Glycol

Soybean Oil

Planar PP

1.92 ± 0.08

1.49 ± 0.05

-

Superhydrophobic PP

5.95 ± 0.10

2.24 ± 0.10

-

Planar PTFE

4.22 ± 0.05

1.95 ± 0.06

0.81 ± 0.03

Omniphobic PTFE

6.60 ± 0.10

3.14 ± 0.05

0.94 ± 0.05

PFDTS-modified Planar PTFE

4.45 ± 0.06

2.43 ± 0.04

1.02 ± 0.03

Superomniphobic PTFE

6.69 ± 0.08

3.18 ± 0.05

1.08 ± 0.07

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