Electrowetting-Dominated Instability of Cassie Droplets on

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Electrowetting-Dominated Instability of Cassie Droplets on Superlyophobic Pillared Surfaces Yu-Chung Chen, Yuji Suzuki, and Kenichi Morimoto Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b02825 • Publication Date (Web): 15 Jan 2019 Downloaded from http://pubs.acs.org on January 16, 2019

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Electrowetting-Dominated Instability of Cassie Droplets on Superlyophobic Pillared Surfaces Yu-Chung Chen, Yuji Suzuki, and Kenichi Morimoto* Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan *[email protected]

Abstract The liquid-air interface of Cassie droplets on superhydrophobic/superlyophobic surfaces has been directly captured with a high-precision laser displacement meter. The measured profile of the interface shape and the critical voltage with which the Cassie-toWenzel transition occurs are compared against those from numerical simulations of the electric field coupled with the interface shape. Under the applied voltage, the collapsing behavior of water, glycerol and hexadecane droplets on SU-8, CYTOP, and overhanging Si/SiO2 pillars has been uniquely identified dependent on the liquid properties, the pillar geometry, and the pillar material. It is shown that, with increasing the voltage, the contact angle at the 3-phase contact line approaches the maximum advancing angle along pillar sidewalls, above which the depinning from the pillar edge leads to slide-down motion. The slide-down instability is dominant over the pull-in instability both on dielectric pillars and conductive overhanging pillars examined in the present study. It is indicated that the collapsing behavior on the present overhanging pillars is closely related to contact angle saturation in electrowetting and stick-slip motion of the contact line.

Keywords Superlyophobic surface, MEMS-based pillar, Measurement of 3-D interface shape, Electrowetting, Cassie-to-Wenzel transition, Critical voltage

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Introduction Recently, superhydrophobic/superlyophobic surfaces (1-3) presenting extremely large contact angle (CA) and small contact angle hysteresis (CAH) have been of much interest due to potential applications in various liquid-handling devices (4-10). Superhydrophobic/superlyophobic surfaces with low wettability and low friction would allow for faster liquid motion with less contamination/adsorption during droplet manipulation. Among various techniques, electrowetting on dielectric (EWOD) (4-6) and liquid dielectrophoresis (L-DEP) (7, 8) are often used in droplet manipulation. Whereas EWOD can be applied to only conductive liquids, L-DEP can be applied to both conductive and non-conductive liquids at the cost of high driving voltage. Recently, liquid dielectrophoresis on electret (L-DEPOE) (9, 10) in which only low driving voltage is required was also proposed. In L-DEPOE, electret with permanent trapped charges is used as a virtual voltage source. Since liquid droplets in L-DEPOE devices with flat electret surfaces suffer from large viscous resistance, superlyophobic surfaces (SLS) with extremely-small wettability even for low surface tension liquids (2, 3) are desired for high-speed droplet manipulation. In view of L-DEPOE application, we previously proposed superlyophobic structure for liquid-tolerant electret, based on charged overhanging pillars (10, 33). The scope of the present study lies in the electric fieldinduced Cassie-to-Wenzel transition on the SLS. Since the CA is significantly decreased when the Cassie state collapses to the Wenzel state, the accurate prediction of the transition is of utmost importance in order to establish design criteria under different external disturbances. The Cassie-to-Wenzel transition can be caused by various factors such as hydraulic pressure (11), evaporation (12-14), vibration (15), droplet impact (16), and surface reactions (17, 18). The electric fieldinduced instability (hereafter referred to as electric instability) of the liquid-air interface of the Cassie droplets has been also extensively studied in recent years (19-25). However, the scope of previous studies was limited to the superhydrophobic surfaces. Manukyan et al. (19) observed the liquid-air interface on SU-8 pillars by optical measurements, showing the instability mechanisms under the electric field. It was reported that, among the two competing modes of the electric instability: touch-down and electrowetting (EW)

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-dominated transitions, EW-dominated transition is mostly observed in their condition. Song et al. (23) investigated the electrostatic instability of liquid droplets on Si-based pillars with a constant solid fraction of 0.01. It was shown that a force-balance model incorporating the pinning force and the surface tension force can mimic the experimental data of the critical voltage for different pitches and different liquid properties. The critical voltage is defined as the minimum applied voltage with which the Cassie-to-Wenzel transition takes place. It was implied that the pull-in (touch down) of the liquid-air interface is the dominant mechanism of the instability for the range of the height-to-pitch ratio smaller than 0.5. In the present study, the touch down-dominated transition is referred to as the pull-in instability. The pull-in of the liquid-air interface occurs at the central interface region, where the deformation is maximized, surrounded by supporting pillars. The EWdominated transition, on the other hand, is more specifically named as the slide-down instability, which is triggered by the depinning of the 3-phase contact line from the pillar edge, as will be detailed in this work. Chamakos et al. (24) and Kavousanakis et al. (25) showed the effects of the thickness of the dielectric material upon the electrowetting on structured surfaces. Their theoretical approach is based on an augmented Young-Laplace equation with a disjoining pressure term (26), and no predefined criteria is required for detailed stability analyses. The solid geometry, the electric field, and the droplet interface shape are fully coupled to analyze the Cassie-to-Wenzel transition induced by electrowetting, but the numerical study is still limited to 2-D pillar configurations. Further studies are needed to fully understand the instability phenomena for different pillar materials and pillar geometries. For superhydrophobic surfaces based on dielectric pillars, the electric field between the liquid-air interface and the bottom substrate can be approximated as that for parallel surfaces (19, 20). On the other hand, for superlyophobic surface using conductive pillars with an insulation layer, the conductive core distorts the electric field, which makes it more complex to estimate the electrical force exerted on the interface. In the present study, the electric instability on superlyophobic overhanging structure has been investigated both from experimental and analytical approaches for the first time.

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The 3-D surface shape of the liquid-air interface is directly captured with a high-precision confocal laser displacement meter, and the droplet collapsing behavior on SU-8, CYTOP, and overhanging Si/SiO2 pillars is detected. The present pillar design covers a wide range of geometrical parameters that can support the electric voltage up to 200 V. The electric field coupled with the curvature change of the interface profile is analyzed through 3-D simulations. Through comparisons between experiments and numerical simulations, the effects of the electric field on the liquid-air interface behavior are examined. Also, the Cassie-state instability mechanism on the present superlyophobic overhanging pillars is discussed in relevance to electrowetting effects.

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Experimental and Simulation Procedures Present Pillared Surfaces Figure 1 shows the SEM images of the present pillared surfaces: (a) SU-8 pillars, (b) CYTOP pillars, and (c) Si/SiO2 pillars. The SU-8 and CYTOP pillars were prepared as non-conductive pillars with superhydrophobicity and fabricated based on the standard photolithography techniques (23). The Si/SiO2 pillars with overhanging structure on the pillar top, on the other hand, were prepared as superlyophobic pillars, and the fabrication technique is originally developed in the present study. The fabrication details are provided in Figure S1 in the Supporting Information. For SU-8 pillars, a glass wafer is sputtered with 200-nm-thick ITO, and 45-µm-thick SU-8 photoresist is spin-coated. After the patterning of SU-8 pillars with UV-exposure, the pillars are deposited with 1H,1H,2H,2H-Perfluoro-octyltrichlorosilane (PFOTS) hydrophobic monolayer. For CYTOP pillars, CYTOP CTL-M (Asahi Glass Co., Ltd.) (35, 36) with amidosilyl end groups is used for the pillar material. CYTOP is amorphous fluorinated polymer, and its hydrophobic nature was reported (36). First, a Si wafer is deposited with 15-µm-thick CYTOP and 350-nm-thick Cu layer. Cu mask patterns are formed with standard photolithography process. Then, CYTOP pillars are formed through magnetron plasma etching (TEP-Xd, Tateyama Machine Co., Ltd.). Finally, the pillars are annealed at 180 ºC for 10 min to promote the hydrophobicity. For Si/SiO2 pillars, a Si wafer with thermally oxidized 300-nm-thick SiO2 is spincoated with OEBR CAP-112 photoresist. The photoresist is patterned with E-beam lithography, followed by SiO2 etching using ICP-RIE (CE-300I, ULVAC, Co., Inc.) with CHF3 plasma. The DRIE Bosch process (MUC-21, SPP Technology Co., Ltd.) is applied to Si etching, where overhanging caps are formed dependent on the etching selectivity between Si and SiO2. The whole surface is then oxidized to form 670-nm-thick SiO2 and deposited with PFOTS monolayer. In the present study, a wide range of the geomterical parameters; the pich P, the depth D, and the height H, as listed in Table S1, is examined. For SU-8 and CYTOP pillars, the pillar height corresponds to the thickness of the coating layer. For Si/SiO2 pillars, the overhanging length is 2 µm − 3 µm, dependent on the side etching, while the

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solid fraction is kept constant at ~ 0.01 with the same pitch of P = 80 µm. Snapshot images of glycerol dropltes on a Si/SiO2 pillar are shown in Figure S2. In the present designs, the height-to-pitch ratio (t* = H/P) is mostly larger than our previous condition where the pull-in instability is predominant (23).

(a)

(c)

(b)

Figure 1. SEM images of the fabricated structures: (a) SU-8 pillars with (P, D, H) = (80 µm, 15.7 µm, 43.2 µm), (b) CYTOP pillars with (P, D, H) = (24 µm, 2.5 µm, 14.5 µm), and (c) Si/SiO2 pillars with (P, D, H) = (40 µm, 9.1 µm, 72.3 µm). White bars in the figure denote the scale for 10 µm.

Liquid-Air Interface Measurement Liquid droplets with a constant volume of ~ 5 µl are placed on the pillar surface. An ITO glass with a thickness of ~ 100 µm is attached on top of the droplet. The voltage is applied across the ITO glass and a Si substrate on the backside of the samples. The liquid-air interface is measured with a confocal laser displacement meter (LT-9500V, Keyence Corp.). Figure 2a shows the working principle of the present interface capturing approach. The semiconductor laser with a wavelength of 405 nm and a spot size of 0.9 µm is focused with a lens that is actuated by a tuning fork to adjust the focusing distance. The detector receives the confocal signal and determines the focusing distance that has local maximum intensity. The signal intensification by the focused laser indicates that the

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liquid-air interface is captured at each location. The resolution in the vertical (z-) direction is 0.01 µm with a sampling time period of 640 µs. Figure 2b shows the schematic of the identification of the liquid-air interface. The laser passes through the ITO glass and focuses on the liquid-air interface. The xy-position of the laser is controlled by an auto-stage (KY0725C-L, Suruga Seiki Co., Ltd.) with a spatial resolution of 0.5 µm. The motion of the stage and the recording of the laser focusing position are controlled by a PC. Under a fixed applied voltage, the focusing position is scanned over a square area of 100 µm × 100 µm with an interval of 2 µm, resulting in 51 × 51 data points in total. The present imaging window covers the liquid-air interface supported by four adjacent pillars as shown later in Figure 4. For the criticalvoltage measurements, the focusing position is fixed at the middle of the pillars, and the applied voltage is increased from zero until the liquid-air interface collapses.

(a)

Semiconductor laser Light receiver CCD

Actuation

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(b)

Tuning fork Sensor Sample Blue laser SiO2/ITO Liquid h

z

V

Air x

Substrate Figure 2. Schematic of the present scanning of the liquid-air interface: (a) confocal laser displacement meter, and (b) identification of the liquid-air interface. 7


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Simulation of the Electric Field and the Interface Shape In order to examine the effect of the electric field on the macroscopic behavior of liquid-air interface, 3-D simulations of the electric field coupled with the change of the interface profile have been performed. The present simulation follows the similar procedure provided in previous studies (20, 32). The shape of liquid-air interface is determined from the Young-Laplace equation: ⎛1 1⎞ γ lv ⎜⎜ + ⎟⎟ = Δp , ⎝ R1 R2 ⎠

(1)

where γlv, R1, 2 and Δp are the surface tension, the principal radii of curvature, and the Laplace pressure, respectively. The Laplace pressure is decomposed into: 1 2 Δp = Δp0 + ε En , 2

(2)

where ε and En denote the air permittivity and the normal component of the electric field at the interface. In eq 2, the first term is the reference pressure difference across the interface, and the second term is the electrical pressure due to the jump in the Maxwell stress across the interface. The constant pressure Δp0 is obtained by curve fitting with the initial deformation in scanned liquid-air interface without applied voltage. The electric field En is calculated from the gradient of the electrostatic potential V: En = n ⋅ ∇V ,

(3)

where the potential is governed by the Laplace equation from Gauss’s law: ∇ 2V = 0 .

(4)

The curvature is calculated as:

1 h ′′ = , R1 (1+ h ′ 2 )3 2

(5)

where h denotes the height position of liquid-air interface. h ′ and h ′′ denote the first and second order derivatives with respect to the principal axes. Figure 3 shows the schematic of the present simulation. The resistivity of liquid is assumed to be zero, while that of insulation layer and the dielectric solid is infinitely high. Considering the symmetry along the center of the pillar cylinder and the middle between

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adjacent pillars, the rectangular box depicted by bold gray lines is chosen as the computational domain. On the liquid-air and liquid-solid interfaces, the electrostatic potential is given as V = 0. On the boundary of the conductive solid, the potential is given as the applied voltage. For dielectric pillar, the conductive solid is only on the bottom substrate. The electrostatic potential inside the dielectric pillar is obtained from eq 4. For conductive pillar, on the other hand, the conductive solid is also embedded inside the pillar with the applied voltage conducted. A finite difference method is employed to solve the governing equations in Cartesian coordinate system. For the potential field V and the height distribution h in eqs 4 and 5, the second-order central difference scheme is applied. For the electric field at the liquidair interface, the second-order backward differencing is applied on the electric potential in the air. The electric field En is dependent on the distribution of the electrostatic potential V, and the height distribution of the liquid-air interface h is solved in an iterative way. The iteration is repeated until the solved h no longer changes the potential distribution. Further numerical details including grid-number information and the convergence criteria are provided in Figure S3. In the present simulation, the change of the liquid-air interface is obtained as a function of the applied voltage until the pull-in voltage with which the interface touches down to the substrate due to the electrostatic instability (23). In the present study, it is assumed that the slide-down motion is triggered when the CA at the pillar edge exceeds the maximum advancing CA that is obtained from separate measurements on flat surface with the same material. Thus, the critical voltage from the present simulation corresponds to either the pull-in or the slide-down voltage as explained in Figure S4. It is noted that, if the simulated CA does not reach the advancing CA before the pull-in limit, the slidedown voltage cannot be determined and the critical voltage corresponds to the pull-in voltage. As such, the critical voltage with which the Cassie-to-Wenzel transition occurs is determined dependent on the simulated profile of the liquid-air interface and the maximum advancing CA from the measurements. Briefly, the simulation represents the process of liquid-air interface deformation, under the condition with which the surface tension balances with the Laplace pressure for deformed interface. The increased deformation with the voltage finally meet the

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condition of (i) advancing CA at the pillar edge, or (ii) touch down of the interface to the bottom surface, which corresponds to (i) slide-down or (ii) pull-in instability.

(a)

D

(b)

θ0

H P

P/2

Conductive liquid, V = 0

Conductive solid, V = given value

Dielectric solid, V to be solved

Air, V to be solved

Symmetric condition

Figure 3. Schematic of the present simulation for the electric field of the liquid-air interface: (a) dielectric pillar, and (b) conductive pillar with an insulation layer. The electric potential in liquid is set as V = 0. The boundary condition on conductive solid is given by a constant value of the applied voltage. The bottom substrate is assumed to be conductive in both cases. For conductive pillar, the conductive solid extends to the pillar core.

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Results and Discussion Profiles of the Liquid-Air Interface Figure 4 shows the scanned liquid-air interface of glycerol droplets on SU-8 pillars with/without the electrical voltage. Without voltage, the liquid-air interface is slightly deformed by only about 1.9 µm from the pinning edge. It is seen that the symmetric interface profiles are captured in the present measurement and the voltage-dependent deformation is observed. The deformation in the vertical (z-) direction is maximum at the center (x, y) = (40 µm, 40 µm), and increases to about 3.2 µm and 6.6 µm under the applied voltage of 140 V and 240 V, respectively. The counterparts for the present simulations are presented in Figure S4 in the Supporting Information.

(a)

(b)

(c)

Figure 4. Scanned liquid-air interface of glycerol droplets on SU-8 pillar with (P, D, H) = (80 µm, 15.7 µm, 43.2 µm) under the applied voltage of: (a) 0 V, (b) 140 V, and (c) 240 V.

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Z-position [µm]

2

Z-position [µm]

(a)

Under no voltage

0 -2 Scanned Data Fitted curve with scanned data Simulation

-4 -6 -8 2

(b)

Under V = 140 V

(c)

Under V = 240 V

0 -2 -4 -6 -8 2

Z-potision [µm]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0 -2 -4 -6 -8 0

10

20

30

40

X-position [µm]

Figure 5. Profiles of the liquid-air interface of glycerol droplets on SU-8 pillar with (P, D, H) = (80 µm, 15.7 µm, 43.2 µm) from scanned data (circle symbol representing the raw data and dotted line representing the fitted curve) and the simulations (solid line) under: (a) 0 V, (b) 140 V, and (c) 240 V.

Figure 5 shows the profiles of the liquid-air interface of glycerol droplets on SU-8 pillars. The z-position is shifted to make the top of the pillar z = 0 for all the plots. The circle symbol and the dotted line represent the scanned data points of the liquid-air 12


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interface and the fitted curve, respectively. The solid line represents the data from the present simulations. By curve fitting with the scanned data, the constant pressure Δp0 is estimated to 100 Pa, which is assumed in the simulation. The data for the central-point deformation H − hC and the CA from the measurement and the simulation are summarized in Table S2. It is seen from Figure 5 that, at both 140 V and 240 V, the simulation shows smaller deformation with larger CA in comparison to the measurement. Without voltage, the scanned data show the interface shape in good agreement with the simulation. On the other hand, with increasing the voltage, the scanned data shows a more cone-like interface shape with larger deformation but smaller CA on the pillar sidewall. The conelike parabolic profile has been also reported in Oh et al. (20) and our previous work (23). Since the charge uniformity is assumed in the present simulation, the deviation from the scanned data is considered to be due to the non-uniform distribution of the electrical charge.

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2

Z-position [µm]

(a) Water under V = 0

(b) Water under V = 160 V

0 -2 Scanned Data Fitted curve with scanned data Simulation

-4 -6 -8 2

(c) Glycerol under V = 0

(d) Glycerol under V = 140 V

(e) Hexadecane under V = 0

(f) Hexadecane under V = 85 V

0 -2 -4 -6 -8 2

Z-position [µm]

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0 -2 -4 -6 -8 0

10

20

30

40 0

10

X-position [µm]

20

30

40

X-position [µm]

Figure 6. Profiles of the liquid-air interface on overhanging Si/SiO2 pillar with (P, D, H) = (80 µm, 9.2 µm, 42.8 µm) from the scanned data and the simulation for: (a, b) water, (c, d) glycerol, and (e, f) hexadecane. The applied voltage is 0 for (a, c, e), and close to the critical voltage for (b, d, f).

Figure 6 shows the profiles of the liquid-air interface for water, glycerol, and hexadecane droplets on overhanging Si/SiO2 pillars without voltage and under the voltage near the critical voltage of the Cassie-to-Wenzel transition. The data for the central-point deformation and the CA are summarized in Table S3. In the present measurement, the

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collapsing of the Cassie droplet is observed at 163 V, 146 V, and 89 V for water, glycerol, and hexadecane, respectively. It is confirmed that, with decreasing the surface tension of the liquid, the initial deformation increases and the critical voltage decreases. The present deformation without voltage is equivalent to the Laplace pressure of 20 Pa − 70 Pa, and the measured profiles are in good agreement with the simulations. Although the Laplace pressure is usually small and often neglected in previous studies (19-23), the critical voltage becomes 1.25 times larger for the present geometrical condition. Thus, the Laplace pressure due to the initial deformation is taken into account in the present simulation. As shown in Figure 6, the deformation under the applied voltage for the present overhanging pillars increases by 2.7 µm − 4.4 µm, and the CA increases by 6º − 10º until the collapsing. In the present simulation for the conductive overhanging pillars, the liquid-air interface is deformed toward the pillar sidewall due to the electric potential in the pillar core, showing hyperbolic shapes. Nevertheless, the qualitative tendency of the maximum deformation and the interface shape remains the same as observed in Figure 5: the interface profile from the scanned data is closer to the parabolic shape, rather than the hyperbolic shape obtained in the simulation. Thus, the voltage with which the CA reaches the advancing CA becomes smaller by 30 V − 40 V in the simulation. Therefore, the accurate prediction of the CA is the key to the better estimation of the critical voltage. The conductive core inside the pillar might affect the charge distribution and make the electrowetting effects near the sidewall more complicated. The present instability mechanism will be further examined later.

Critical Voltage of the Cassie-to-Wenzel Transition The change of the CA would play a key role in the Cassie-to-Wenzel transition under the electric field (19, 20). If we assume the parabolic profile of the liquid-air interface (19, 23), the contact angle θ0, as shown in Figure 3, can be simply expressed as a function of the central-point deformation and the geometrical parameters as:

π ⎞ ∂h H − hC ⎛ . tan ⎜ θ 0 − ⎟ = = 4⋅ ⎝ 2 ⎠ ∂x x=(P−D )/2 P−D

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(6)

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As shown in Tables S2 and S3 in the Supporting Information, the CA estimated from eq. 6 is in good agreement with the value directly obtained from the scanned data. This corresponds to the fact that the liquid-air interface under the electric field presents the parabolic profile for the present pillar structures. Figure 7 shows the schematic of the CA at the pillar edge for dielectric and conductive (overhanging) pillars. For the dielectric pillar, the CA along the pillar sidewall is defined considering the fact that the present structure is slightly tilted from the vertical direction. For the overhanging pillar, the contact line is pinned at different locations dependent on the surface tension: the high-surface-tension liquid (water, glycerol) is pinned at the top edge with the CA of θ1, and the low-surface-tension liquid (hexadecane) is pinned at the bottom edge of the overhang with the CA of θ2.

(a)

θ1

(b)

θ1 θ2

Figure 7. Schematic of the contact angle at the pillar edge: (a) angle θ1 along the sidewall on dielectric pillar, and (b) angle θ1 on the top edge and θ2 on the bottom edge on overhanging pillar.

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hµ

(a)

º

25

(b) P: 12 D: 2.7

20

hC [µm]

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15 10 5 0 0

P: 20 D: 9

P: 40 D: 9 50

100

150

200

250

300

Applied Voltage [-V]

Figure 8. Liquid-air interface motions on dielectric pillars: (a) on SU-8 pillar with (P, D, H) = (80 µm, 15.7 µm, 43.2 µm). The circle symbol and the broken line represent the measured hC and the measured CA, respectively. (b) on CYTOP pillars with a constant H of 15 µm and different P and D as indicated in the unit of µm. The symbols and the dashed lines represent the data from measurements and simulations, respectively.

Figure 8 shows the liquid-air interface motions on dielectric pillars. The measured height of the liquid-air interface and the measured CA are plotted for the SU-8 pillar in Figure 8a. At the critical voltage of 283 V, the CA along the sidewall becomes close to the advancing CA of 108º, which results in the sliding of the contact line to the collapsing of the Cassie state. The measurement and simulation results for glycerol on the CYTOP pillar are shown in Figure 8b. The critical voltage ranges from 95 V to 270 V, depending on the pitch and the diameter. Smaller pitch and larger diameter lead to larger resistance from surface tension to the electric field-induced deformation, so that the slide-down voltage is increased. When the data for (P, D) = (40 µm, 9 µm) and (12 µm, 2.7 µm), of which the solid fraction is kept the same, are compared, the critical voltage is much 17


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increased with the smaller pitch. It is noted that noticeable disturbances are observed in the measured profiles for the CYTOP pillar because of the internal reflection from the solid-air interface. In all of the simulation results here, the critical voltage corresponds to the slide-down voltage. Since the difference of the critical voltage between the measurement and the simulation is as small as 10 V, showing good agreement in each condition, the present measurement results are considered to be dominated by the slidedown instability. In our precious work (23) for Si-based pillars with the dielectric coating with C4F8 films, the surface deformation of the liquid-air interface by the electrostatic field overwhelms the CA reduction effect by the electrowetting on the pillars with the heightto-pitch ratio (t*) smaller than 0.5. Thus, the pull-in of the liquid-air interface is the dominant mechanism of the instability for small t* range. In the present study, on the other hand, the electrowetting effect is more pronounced with increased pillar height, which leads to the switching of the dominant instability mechanism.

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Critical Voltage [V]

400

(a)

Water 300 200

Measurement Sim. Pull-in Sim. Slide-down

100


0 400

(b)

Glycerol 300 200 100


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(c)

Hexadecane 300


200 100 0 20

30

40

50

60

70

80

Pillar Height [µm]

Figure 9. The critical voltage versus the pillar height for overhanging Si/SiO2 pillars with (P, D, H) = (80 µm, 9.2 µm, 25 µm − 72 µm): (a) water, (b) glycerol, and (c) hexadecane. The solid and empty markers represent the data from measurements and simulations, respectively. The pull-in and the slide-down conditions are considered in the simulation.

Figure 9 shows the critical voltage versus the pillar height on the overhanging Si/SiO2 pillars with the pillar pitch and the pillar diameter kept constant for varied heights. Here, both the measurement and simulation results are plotted for comparison. The data from the simulation is based on either the pull-in or the slide-down conditions. In the

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slide-down condition, the CA at the pillar edge is assumed to θ1 for water and glycerol, and θ2 for hexadecane, respectively. In the present measurements, with increasing the height from 25 µm to 72 µm, the critical voltage increases from 125 V to 200 V for water, 70 V to 226 V for glycerol, and 42 V to 152 V for hexadecane, respectively. Whereas the simulated profile of the liquid-air interface deviates from the scanned data as previously shown in Figure 6, the qualitative tendency of the measured critical voltage is wellpredicted in the present simulation. For water and glycerol, it is seen that the present simulations assuming the slidedown instability are mostly in good agreement with the measurements. If the Cassie-state collapsing occurs at the CA of θ2 due to the pull-in instability as in previous studies (20, 23), the pull-in voltage should be much larger as shown in Figures 9a and 9b. Thus, the collapsing for water and glycerol is considered to occur at the CA of θ1. Exceptionally, for water with H = 25 µm, the pull-in is considered to be dominant in accordance with the previous condition (23). For hexadecane, on the other hand, it is predicted that the pull-in instability is dominant for H = 25 µm while the slide-down instability is dominant for H = 42 µm and 72 µm. For H = 34 µm, the slide-down and pull-in voltages are comparable. For hexadecane, the contact line is pinned at the CA of θ2 even without voltage, and the instability modes differ dependent on the pillar height. It is noted that the critical voltage from the present measurement does not fully agree with the simulation; one possible source of the difference between the present measurement and simulation is the instability of the advancing CA, which will be discussed in more detail below.

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Observed Collapsing 150

Contact Angle [º]

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Water

100

Glycerol Hexadecane

50

0 0

50

100

150

200

250

300

Applied Voltage [-V]

Figure 10. Measured advancing CA (symbols with error bars) on a flat SiO2 surface with PFOTS and the measured CA (dashed line) on overhanging Si/SiO2 pillar with (P, D, H) = (80 µm, 9.2 µm, 42.5 µm). The CA corresponds to θ1 for water and glycerol, and θ2 for hexadecane, respectively.

Figure 10 shows the measured advancing CA on a flat SiO2 surface with PFOTS modification and the measured CA for the Si/SiO2 pillar with (P, D, H) = (80 µm, 9.2 µm, 42.5 µm). When the transition takes place at 163 V, 146 V, and 89 V for water, glycerol, and hexadecane, respectively, the CA of θ1 approaches the advancing CA measured on the flat surface. If the contact line slides from the top of the overhanging edge to the bottom side, the CA of θ2 will become much smaller than the advancing CA and the further sliding is not likely to occur. When compared to the scanned data, the CA in the present simulation is much larger for the applied voltage close to the critical voltage as shown in Figure 6. The change of the CA in the simulation is about 3 times larger than that in the scanned data. Based on the Young-Lippmann equation, the CA on a flat surface is predicted to decrease with increasing the voltage. The measured CA, however, becomes saturated as shown in Figure 10: the CA is kept at almost constant level even for the increased voltage. It is considered that the overestimation of the CA in the present simulation is mainly due to the CA saturation, which is often observed in electrowetting. The saturation effect might be caused by the charge accumulation in the liquid and the dielectric layer, the finite

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electrical resistance, the current flow in the materials, and the instability of the contact line (27-30). The accurate prediction of the saturation itself still remains an open issue, and further study is needed. Figure 11 shows the CA instability of the water droplet on a flat Si/SiO2 surface with PFOTS. Here the instability refers to the CA fluctuation caused by the step-wise change of the applied voltage. When the applied voltage increases from 190 V to 200 V, the CA suddenly drops down and then gradually returns to its original level. The decrease of the CA might trigger the slide-down event at a smaller voltage in spite of the larger advancing CA. Since the dip in the CA is associated with the electrical conductivity (σ) of the liquid, the larger fluctuation of the CA during the electrowetting process is expected for low- σ hexadecane. As shown in Figure 10, the standard deviation (SD) of the measured advancing CA for hexadecane is as large as 10º − 15º in the voltage range from 50 V to 130 V.

º

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 11. Contact angle instability of water on a flat Si/SiO2 surface with PFOTS in response to the step-wise change of the applied voltage.

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Dielectric versus Conductive Pillar With the voltage inside the conductive core, the critical voltage for the conductive pillar becomes smaller than that for the dielectric pillar under the same geometrical condition. For the design of pillar structure assuming the Cassie state that might be valid for high-voltage environments, the dielectric pillar is favorable over the conductive type. The critical voltage with which a given advancing CA is attained is estimated to be 1.3 times larger on the dielectric pillar than on the conductive pillar. For applications that utilize the electric field acting on the droplet, the conductive pillar has the benefit of the power reduction since the required CA and thus the electrical force can be obtained at the smaller voltage. On the conductive pillar, it is also important to consider that the electric field from liquid-solid interface still induces additional capacitance and thus affects the performance of the devices such as L-DEP. For example, in the pillar with P = 80 µm, D = 9 µm, and H = 40 µm, the capacitance value on the conductive pillar is about 9 times larger than that on the dielectric pillar, which might increase the apparent critical voltage.

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(a)

Liquid

Air

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θslp

θadv

θstk

Solid (b)

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θ = θadv

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θ < θadv (c)

Liquid

θ = θadv

θ > θ adv ′

Pillar

θ >θ adv ′

θ >θ adv ′

Figure 12. Schematic of the slide-down mechanisms: (a) stick-slip motion, (b) slide down without stick-slip motion, and (c) slide down with stick-slip motion.

Slide-Down on Conductive Overhanging Pillars The critical voltage for the slide-down event is determined by the condition where the CA reaches the advancing CA along the pillar sidewall. For the overhanging pillar, water and glycerol droplets slide down when the CA reaches the advancing CA on the top edge of the overhanging cap, and then the contact line moves to the bottom edge. Figure 12 shows the schematic of the possible slide-down scenarios for overhanging structure. Without stick-slip motion (31), which is schematically depicted in Figure 12a, the advancing front should stop at the bottom edge as shown in Figure 12b. The CA at the bottom edge is much smaller than the advancing CA. Without further slide-down motion, the collapsing is possible when the pull-in instability takes place. With stick-slip motion (31), on the other hand, further slide down occurs at the bottom edge as shown in Figure 12c. Here, θadv is the advancing CA with which the

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contact line moves forward. θslp is the slipping angle immediately after the advancing is triggered; the CA is drastically reduced during the following 30-40 ms. θ adv′ is the lowered advancing CA during the slipping with θslp ≥ θ adv′ . θstk is the sticking angle at which the slipping stops and the contact line sticks to the contact point. Once the CA reaches the advancing CA on the top edge, the contact line begins to slide down. The following advancing motion is governed by the slipping advancing angle. When the contact line reaches the bottom edge of the overhang, the CA along the lower surface remains larger than the slipping advancing angle ( θ adv′ ). Thus, the contact line passes through the bottom edge of the overhang and continues to slip along the pillar surface. For the overhanging pillar, two different mechanisms for the slide-down motion appear dependent on the liquid surface tension: For hexadecane, as shown in Figure 12b, the slide down will occur when the advancing CA becomes sufficiently small under electrowetting effect. For water and glycerol, on the other hand, the slide down will occur possibly due to the stick-slip motion as shown in Figure 12c.

120

Contact angle [º]

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θadv

100 80 60 40 20

θstk 0.0

0.5

1.0

1.5

Time [s]

Figure 13. Time history of the contact angle during the stick-slip motion of glycerol on a flat Si/SiO2 surface with PFOTS. The applied voltage is constant at 100 V.

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Figure 13 shows the stick-slip motion of glycerol droplets measured on a flat Si/SiO2 surface with PFOTS. The time history of the CA under a fixed voltage of 100 V is shown here. When the CA reaches the advancing CA of around 110º, the contact line starts to slip and then stops at a distant point with the CA of θstk ~ 36º. In the present measurement, the slipping distance is about 0.5 mm in 30 ms. One slip motion observed on the present flat surface covers the present dimension of the overhanging pillar (74 μm in the total length of the sidewall). Although the effect of the roughness of the pillar sidewalls on the slip motion needs further investigation, it is indicated from the observed collapsing due to the slide-down motion that the roughness effect is not obvious for the present pillars. The stick-slip motion is observed more significantly when the applied voltage becomes larger than 40 V. Therefore, it is postulated that the slide down due to the contact-line depinning is the dominant factor for the electric instability for high-surface-tension liquids on the present overhanging pillars.

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Summary and Conclusions In the present study, the Cassie-to-Wenzel transition under the electric field on superhydrophobic/superlyophobic surfaces has been investigated both from experimental and analytical approaches. The 3-D surface shapes of the liquid-air interface of Cassie droplets are directly measured with a high-precision confocal laser displacement meter. Under the applied voltage, the collapsing behavior of water, glycerol and hexadecane droplets on SU-8, CYTOP, and overhanging Si/SiO2 pillars has been uniquely identified dependent on the liquid properties, the pillar geometry, and the pillar material. The electric field coupled with the curvature change of the interface profile has been analyzed through 3-D simulations. It is found through comparisons between the present experiments and numerical simulations that the contact angle under the electric field plays a key role in the instability phenomena. For overhanging Si/SiO2 pillars, the effect of the conductive core inside the overhanging pillar is actually weaker than expected possibly due to the non-uniform distribution of the electrical charge. Although the liquidair interface is excessively attracted toward the pillar core in the present simulation, the critical voltage assuming the slide-down condition is shown to provide reasonable estimates in most cases. The Cassie-state instability mechanisms on the present pillar structures were discussed in relevance to the electrowetting effects. With increasing the voltage, the contact angle at the 3-phase contact line approaches the maximum advancing angle along the pillar sidewall, above which the depinning from the pillar edge leads to the slidedown motion. It is considered that the slide-down instability is dominant over the pull-in instability both on dielectric pillars and conductive overhanging pillars. On SU-8 and CYTOP pillars, the critical voltage is dominated by the slide down in the large pillarheight conditions examined. On the overhanging Si/SiO2 pillars, two different mechanisms for the slide-down motion appear dependent on the liquid surface tension: For hexadecane, the slide down will occur when the advancing angle becomes sufficiently small under the electrowetting effect. For water and glycerol, on the other hand, the slide down will occur possibly due to the stick-slip motion. It is inferred from the present results that the behavior of the Cassie-to-Wenzel transition under the electric

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field is closely related to electrowetting saturation, contact angle instability, and also the stick-slip motion.

Associated Content Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: *******/acs.langmuir.********. Details of fabrication of the present pillars, details of numerical simulations, and data from measurements/simulations (PDF)

Author Information Corresponding Author *E-mail: [email protected]. ORCID Kenichi Morimoto: 0000-0002-5763-603X Notes The authors declare no competing financial interest.

Acknowledgments The lithography was made using the University of Tokyo VLSI Design and Education Center (VDEC)’s 8-inch EB writer F5112+VD01 donated by ADVANTEST Corporation.

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(13) Moulinet, S.; Bartolo, D. Life and death of a fakir droplet: Impalement transitions on superhydrophobic surfaces. Eur. Phys. J. E 2007, 24 (3), 251–260. (14) Papadopoulos, P.; Mammen, L.; Deng, X.; Vollmer, D.; Butt, H.-J. How superhydrophobicity breaks down. Proc. Natl. Acad. Sci. 2013, 110 (9), 3254–3258. (15) Lei, W.; Jia, Z.-H.; He, J.-C.; Cai, T.-M.; Wang, G. Vibration-induced WenzelCassie wetting transition on microstructured hydrophobic surfaces. Appl. Phys. Lett. 2014, 104 (18), 2014. (16) Lee, C.; Nam, Y.; Lastakowski, H.; Hur, J. I.; Shin, S.; Biance, A.-L.; Pirat, C.; Ybert, C. Two types of Cassie-to-Wenzel wetting transitions on superhydrophobic surfaces during drop impact. Soft Matter 2015, 11 (23), 4592–4599. (17) Khan, M. R.; Eaker, C. B.; Bowden, E. F.; Dickey, M. D. Giant and switchable surface activity of liquid metal via surface oxidation. Proc. Natl. Acad. Sci. 2014, 111 (39), 14047–14051. (18) Yan, B.; Tao. J.; Pang, C.; Zheng, Z.; Shen, Z.; Huan, C. H. A.; Yu, T. Reversible UV-light-induced ultrahydrophobic-to-ultrahydrophilic transition in an α-Fe2O3 nanoflakes film, Langmuir 2008, 24 (19), 10569–10571. (19) Manukyan, G.; Oh, J. M.; van den Ende, D.; Lammertink, R. G.; Mugele, F. Electrical switching of wetting states on superhydrophobic surfaces: a route towards reversible Cassie-to-Wenzel transitions. Phys. Rev. Lett. 2011, 106 (1), 14501. (20) Oh, J. M.; Manukyan, G.; van den Ende, D.; Mugele, F. Electric-field-driven instabilities on superhydrophobic surfaces. Europhys. Lett. 2011, 93 (5), 2011. (21) Bahadur, V.; Garimella, S. V. Electrowetting-based control of static droplet states on rough surfaces. Langmuir 2007, 23 (9), 4918–4924. (22) Bahadur, V.; Garimella, S. V. Electrowetting-based control of droplet transition and morphology on artificially microstructured surfaces, Langmuir 2008, 24 (15), 8338– 8345. (23) Song, K.-Y.; Morimoto, K.; Chen, Y.-C.; Suzuki, Y. Electrostatic instability of liquid droplets on MEMS-based pillared surfaces. Sens. Actuators B 2016, 225, 492–497. (24) Chamakos, N. T.; Kavousanakis, M. E.; Papathanasiou, A. G. Neither Lippmann nor Young: Enabling electrowetting modeling on structured dielectric surfaces. Langmuir 2014, 30 (16), 4662–4670.

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(25) Kavousanakis, M. E.; Chamakos, N. T.; Ellinas, K.; Tserepi, A.; Gogolides, E.; Papathanasiou, A. G. How to achieve reversible electrowetting on superhydrophobic surfaces. Langmuir 2018, 34 (14), 4173–4179. (26) Snoeijer, J. H.; Andreotti, B. A microscopic view on contact angle selection. Phys. Fluids 2008, 20 (5), 057101. (27) Mugele, F.; Baret, J.-C. Electrowetting: from basics to applications. J. Phys. Condens. Matter 2005, 17 (28), R705. (28) Liu, J.; Wang, M.; Chen, S.; Robbins, M. O. Uncovering molecular mechanisms of electrowetting and saturation with simulations. Phys. Rev. Lett. 2012, 108 (21), 216101. (29) Ali, H. A. A.; Mohamed, H. A.; Abdelgawad, M. Repulsion-based model for contact angle saturation in electrowetting. Biomicrofluidics 2015, 9 (1), 014115. (30) Chevalliot, S.; Kuiper, S.; Heikenfeld, J. Experimental validation of the invariance of electrowetting contact angle saturation. J. Adhes. Sci. Technol. 2012, 26 (12–17), 1909–1930. (31) Nelson, W. C.; Sen, P.; C.-J. Kim. Dynamic contact angles and hysteresis under electrowetting-on-dielectric. Langmuir 2011, 27 (16), 10319–10326. (32) Bateni, A.; Susnar, S. S.; Amirfazli, A.; Neumann, A. W. Development of a new methodology to study drop shape and surface tension in electric fields. Langmuir 2004, 20 (18), 7589–7597. (33) Chen, Y.-C.; Song, K.-Y.; Morimoto, K.; Suzuki, Y. Liquid-tolerant electret using super-lyophobic pillar surface. Proc. 28th IEEE Int. Conf. on Micro Electro Mechanical Systems (MEMS’15), 2015, 1086–1089. (34) Chen, Y.-C.; Morimoto, K.; Suzuki, Y. Electric instability of Cassie droplets on super-lyophobic pillar surface: Pull-in versus electrowetting. Proc. 29th IEEE Int. Conf. on Micro Electro Mechanical Systems (MEMS’16), 2016, 137–140. (35) Sakane, Y.; Suzuki, Y.; Kasagi, N. The development of a high-performance perfluorinated polymer electret and its application to micro power generation. J. Micromech. Microeng. 2008 18 (10), 104011. (36) Berry, S.; Kedzierski, J.; Abedian, B. Irreversible electrowetting on thin fluoropolymer films. Langmuir 2007, 23 (24), 12429–12435.

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(b)

(c)

Interface Position [µm]

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Hexadecane Droplets on Overhanging Pillars

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Electrowetting-Dominated Instability of Cassie Droplets on

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