Attractive Encounter of a Nanodrop toward a Nanoprotrusion - The

‡Department of Chemical and Materials Engineering and §Department of Physics, National Central University, Jhongli, Taiwan 32001. J. Phys. Chem. C ...
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Attractive Encounter of a Nanodrop toward a Nanoprotrusion Yu-En Liang,† Yu-Hsuan Weng,† I-Fan Hsieh,† Heng-Kwong Tsao,*,‡,§ and Yu-Jane Sheng*,† †

Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617 Department of Chemical and Materials Engineering and §Department of Physics, National Central University, Jhongli, Taiwan 32001

‡

S Supporting Information *

ABSTRACT: The encounter of a nanodrop with a nanoprotrusion on a hysteresis-free surface is explored by many-body dissipative particle dynamics (MDPD) and surface evolver (SE). On a smooth surface, a nanodrop exhibits random motion but will be captured as it encounters a protrusion. For both lyophilic and lyophobic systems, there exists an attraction between the drop and the protrusion. The potential energy profiles associated with the detachment processes with and without crossing the protrusion are acquired by the determination of the displacement of the captured drop responding to the externally applied forces. It is found that the critical force and depth of the energy well of the lyophilic system are greater than those of the lyophobic system. Moreover, the drop straddling on the protrusion symmetrically is stable for the lyophilic system but becomes unstable for the lyophobic system. Our results can shed some light on the effect of surface roughness on droplet wetting.

1. INTRODUCTION The wetting phenomenon of liquid drops on a solid substrate is ubiquitous in nature and industrial applications such as printing and microfluidics. In terms of the contact angle (CA), the wettability of a surface by a liquid is determined by Young’s equation,1 cos θY = (γSG − γSL)/γLG. Here γij represents the interfacial tension between i and j phases. The subscripts S, L, and G depict solid, liquid, and gas, respectively. Although the intrinsic CA on a smooth (ideal) surface (θY) is dependent on the chemical composition only, the wetting behavior is also influenced by surface roughness which is always present on real surfaces.2−6 Two models are commonly used to describe the effect of surface roughness on CA. In the Wenzel model for the completely wetted rough surface, the apparent CA (θ) is related to θY, cos θ = r cos θY,7 where r depicts the area ratio of the wetted surface to the projected one (r ≥ 1). On the contrary, in the Cassie−Baxter model for the completely nonwetted rough surface, θ can be determined by cos θ = α cos θY − (1 − α), where α is the area fraction of the wetted surface (α < 1). A superhydrophobic surface can be constructed based on this model with air pockets.7 Although the aforementioned models imply a unique CA for a liquid on a surface, the real CA is often in a range bounded by θr ≤ θ ≤ θa, where θa and θr are the advancing and receding © 2017 American Chemical Society

CAs, respectively. The difference between them is defined as the extent of contact angle hysteresis (CAH), Δθ = θa − θr. CAH is generally associated with the pinning of the contact line on the solid surface. Three mechanisms are frequently invoked for the origin of CAH: pinning by chemical defects,3,8,9 adhesion hysteresis,9−12 and surface roughness.6,13−15 In the third mechanism, surface grooves can result in a series of apparent CAs associated with stable drop shapes.6,14 Periodic surfaces have been used to show these metastable states corresponding to local minimums in the energy landscape.14 For random surfaces with small roughness, the third mechanism is shown to be equivalent to the first mechanism.3,16 On a hysteresis-free surface, a nanodrop exhibits a 2-D random motion due to thermal fluctuations. When the drop encounters a blemish which is more lyophilic than the rest of the surface it will be attracted to the chemical defect readily. However, as a free drop encounters a trench with the same wettability as the smooth surface, it will be repelled by the trench. The invasion of the contact line will be halted by the Received: January 16, 2017 Revised: March 22, 2017 Published: March 22, 2017 7923

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2.2. Surface Evolver (SE). SE is a public domain software developed by Brakke, and its algorithm is based on the finite element method35 and has been used to explore the complicated system such as a drop between a cone and a plane.36 In SE, the phase interface (modeled by unions of triangles with vertices) evolves toward the minimum of the system free energy subject to some constraints. For a drop on a substrate subject to the external force f along the x direction, the total free energy F is expressed as

sharp edge of the groove, resulting in the (advancing) contact line pinning and the increment of the front CA.17−19 This phenomenon is referred to as the edge effect and is originated from the boundary minimum of the free energy. Consequently, one must apply a large enough force to the drop so that the resistance of the edge can be overcome and the trench becomes impregnated. Once the nanodrop sits on the trench, its motion is confined (1-D random motion). To escape from the groove, work must be done to overcome the energy barrier. In fact, the trench is considered as a lyophobic blemish for impregnation but acts like a lyophilic blemish for detachment.19 The interaction of a drop with surface roughness is critical in determining the droplet wetting behavior including imbibition and CAH. The encounter of the local contact line with a concave or convex roughness may exhibit different outcomes.3 The effect of surface roughness can be exaggerated by considering a nanodrop on a nanorough surface in which the nanodrop size is comparable to surface roughness. Previous studies have demonstrated the resisting and pinning of a nanodrop by a trench (concave roughness) on a hysteresis-free surface.19−26 In this work, the encounter of a free nanodrop with a protrusion (convex roughness) on a smooth surface is explored by many-body dissipative particle dynamics (MDPD) and surface evolver (SE). The protrusion possesses the same wettability as the smooth surface, and both lyophilic and lyophobic systems are considered. Different from the trench, the nanodrop is attracted to the protrusion. The potential energy profiles (critical forces and depth of the energy well) for the detachment processes with and without crossing the protrusion are acquired to demonstrate the interaction between nanodrop and protrusion.

F = gLGALG − gLGASL cos θ + k

∫ ∫ ∫ V x dV

(2)

The first term on the right-hand side of eq 2 denotes the liquid−gas interfacial energy. γLG and ALG represent the tension and area between liquid and gas phases. The second term arises from the combination of the solid−gas and solid−liquid interfacial energies with the Young equation, and ASL is the solid−liquid contact area. The third term is the energy due to a body force acting throughout the drop volume V in the x direction, and k = f/V is the force density. During iterations, the contact line lies on the solid surface and the drop volume is conserved. In this study, SE are primarily performed to examine the outcomes of MDPD simulations and used to construct the potential profiles for both lyophilic and lyophobic systems. Input conditions/parameters (e.g., the drop volume, protrusion structure, Young’s CA, external force) are the same as those obtained from MDPD.

3. RESULTS AND DISCUSSION Consider a drop on a planar surface with a rectangular protrusion, as illustrated in Figure 1. The width and height of

2. SIMULATION METHODS 2.1. Many-Body Disspipative Particle Dynamics (MDPD). MDPD is modified from classical dissipative particle dynamics (DPD) and is capable of simulating a solid/liquid/ vapor system.19,27−34 In MDPD, the conservative force contains attractive and repulsive potentials FijC = aijωc(rij)eij + bij(ρi + ρj )ωd(rij)eij

Figure 1. Snapshot of a nanodrop undergoing random motion on a smooth surface before encountering a long protrusion, which possesses the length L, width W, and height H.

(1)

where the parameters aij < 0 and bij > 0 are associated with the attraction and repulsion between beads i and j, respectively. rij represents the interparticle distance, and eij depicts the unit vector, rij/rij. The weight functions are chosen as ωc(rij) = 1 − rij/rc and ωd(rij) = 1 − rij/rd. They depend on rij and decrease to 0 as rij≥ rc for ωc(rij) and as rij≥ rd for ωd(rij). Here one sets rc = 1.0 and rd = 0.75. The local density ρi is introduced for repulsion. In general, aij and bij are set as −40 and 25, respectively, for the interaction between the same kind of beads. In this work, the behavior of a nanodrop encountering a protrusion is investigated for both lyophilic and lyophobic systems. For a lyophilic system, aij between solid and liquid bead (aSL) is set as −35 to obtain θY = 60°. For a lyophobic system, one has aSL = −20 to acquire θY = 125°. In MDPD simulations, the number densities of liquid (nanodrop) and solid (substrate and protrusion) phases are 6 and 8, respectively. The surface tension is determined as γLG = 7.5.34 All units are nondimensionalized by the bead mass m, cutoff radius rc, and thermal energy kBT. The body force f is applied to the nanodrop to observe its wetting behavior on the protrusion. The unit of the force is kBT/rc. For each simulation, at least 105 steps are run for equilibration.

the protrusion are W and H, respectively. The length is denoted by L, which is large compared to the droplet size. The planar surface and the protrusion are made of the same material, and therefore, the wettabilities of the drop on the plane and protrusion can be represented by the same contact angle θY. 3.1. Drop Captured by a Lyophilic Protrusion. 3.1.1. Attraction between Drop and Protrusion. Since CAH on a smooth surface is negligible, a nanodrop exhibits a 2dimensional random walk on a planar surface due to thermal fluctuations.19 When the nanodrop encounters a groove (long trench), it will be repelled by this defect and circumvent it regardless of wettability. For the capture of the freely moving drop by the trench, a large enough external force must be applied to result in impregnation.19 However, when the nanodrop encounters a long protrusion, the outcome is totally different. As demonstrated in Figure 2 for a drop of V = 8300 and θY = 60°, the lyophilic drop undergoes random motion initially. When the drop is in contact with a long protrusion with W = 6.0 and H = 1.5 it will wet the protrusion spontaneously and be trapped by this defect eventually. The 7924

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Figure 2. Capture process for a nanodrop encountering a protrusion. Variation of the drop shape is shown by (a) side view and (b) top view.

Figure 3. Escape process (type I) of a nanodrop from a protrusion by applying the external force f scaled by kBT/rc. Variation of the drop shape with f is shown by side and top views. Drop is on the left side of the protrusion initially.

trapping dynamics can be followed from the side and top views. When the front contact line of the drop just touches the protrusion, the displacement of the center of mass of the drop as depicted in Figure 2b is accompanied by the shape deformation corresponding to the increase of the sideward width. Last, the drop sticks to the protrusion and wets the left and top sides of the protrusion without applying any external force. The top of the protrusion is partially wetted, and the rightmost contact line of the drop does not reach the right edge of the protrusion, as illustrated in Figure 2a and 2b. This process corresponds to the spontaneous transition from free to trapped state and is shown in Videos S1a (top view) and S1b (side view) of the Supporting Information. 3.1.2. Detachment from the Protrusion by External Force. In the absence of external force ( f = 0), the nanodrop is attracted to the protrusion and the rightmost contact line stands on top of the protrusion (state a of Figure 3). When the external force (f) is applied and increased, both the rear and the front contact lines of the drop move rightward gradually. As f = 4, the front contact line is in contact with the right edge of the protrusion (state b of Figure 3). When f is further increased, however, the front contact line is still halted by the right edge but the portion of the contact line at the right edge grows, as illustrated in states c−e of Figure 3. Note that the front CA with respect to the top plane of the protrusion exceeds θY and grows with f due to the edge effect.19 As f exceeds a critical value (f cr), the repelling force exerted by the protrusion on the drop is overcome and the drop starts to cross the protrusion (state f of Figure 3). Once the front contact line moves across the protrusion, the drop keeps moving and detaches from the defect eventually, as long as the external force persists ( f > f cr). The detachment process of the drop at f = 200 is shown in Videos S2a (top view) and S2b (side view) of the Supporting Information. At f > f cr, the drop can move across the protrusion. If the external force is suddenly turned off during the process, the nanodrop will stop its motion and adjust its position spontaneously so that the protrusion is eventually in the center

of the drop, as shown in state a′ of Figure 4. When a very small external force f is reapplied, the rear contact line of the drop

Figure 4. Escape process (type II) of a nanodrop from a protrusion by applying the external force f. Variation of the drop shape with f is shown by side and top views. Drop straddles on the protrusion initially.

moves rightward but is captured by the protrusion, as can be seen in state a″ of Figure 6. The top of the protrusion is partially wetted, and the leftmost contact line is away from the left edge of the protrusion. This shape is very similar to that shown in state a of Figure 3 with f = 0, but the drop is in the 7925

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The Journal of Physical Chemistry C opposite side of the protrusion. When a small external force ( f = 10) is applied, both the rear and the front contact lines move further, as depicted in state b′ of Figure 4. As the external force is increased to f = 37.5, both the rear and the front contact lines move forward and the rear contact line is in contact with the right edge of the protrusion (state c′ of Figure 4). When f is further increased, the rear contact line is still halted by the right edge of the protrusion but the portion of the contact line at the right edge of the protrusion decreases, as shown in state d′ of Figure 4. Note that the rear CA with respect to the plane of the right side of the protrusion exceeds θY but decays with f due to the edge effect.19 The base length of the drop is prolonged by the force, and the height of the drop is decreased so that the constant volume condition is satisfied. As f exceeds a critical value ( f cp), the attractive force acted on the drop by the protrusion is overcome and the drop starts to detach from the protrusion (state e′ of Figure 4). The detachment process of the drop at f = 55.0 is shown in Videos S3a and S3b of the Supporting Information. Note that for both detachment processes demonstrated in Figures 3 and 4 a small amount of liquid is left at the two sides of the protrusion for the former case, while almost no liquid remained at the protrusion in the latter case. The amount of residual water on the lyophilic protrusion is reproducible in multiple runs. 3.1.3. Potential Energy for the Interaction between Nanodrop and Protrusion. The aforementioned results of MDPD simulations can be quantitatively explained by the potential energy surface constructed from the SE simulations. For a specified force (f), the equilibrium center of mass of the drop (xc) and the surface free energy (ΔE) are determined by SE simulations. The center of the protrusion is defined as xc = 0. The reference state is defined as the surface energy associated with a free sessile drop. It is found that under the same condition, the equilibrium shapes obtained from SE simulations are consistent with those acquired from MDPD simulations. Dependent on the initial position of the drop, two types of potential energy profiles are considered. Figure 5 shows the

the bottom of the energy well is stable. If the drop tends to cross the protrusion, there exists an energy barrier, as shown in states a−e of Figure 5. Applying an external force will move xc forward, but the drop is still confined in the energy well (states a−e of Figure 3). As f exceeds the critical force f cr, which is the maximum slope of the profile, the effective energy barrier vanishes37 and the process takes place spontaneously. Since the detachment process is transient (state f of Figure 3), ΔE(xc) cannot be obtained from SE simulations. If the drop sits on the protrusion initially (type II, Figure 4), there exists a local minimum at xc = 0 as illustrated in the inset of Figure 6. Therefore, the drop tends to straddle on the

Figure 6. Energy landscape (type II, corresponding to Figure 4) for the nanodrop on the surface of θY = 60°. Drop straddles on the protrusion initially. Enlargement of the landscape around state a′ is shown in the inset.

protrusion symmetrically (see state a′ of Figure 4). The detachment process involves the application of an external force. However, a small value of f leads to the change from the local minimum (a′ state) to the global minimum (a″ state), as depicted in Figure 6. The global minimum corresponds to the state of spontaneous capture. Similar to Figure 5, further increase of the external force results in the rightward movement of xc. Again, as f > f cp, the energy barrier is overcome and the drop escapes from the protrusion. For type I, the free energy associated with the critical force f cr corresponding to the maximum slope is greater than the free energy of the freely moving state (see state e of Figure 5). For type II, the free energy of the drop staying on the protrusion symmetrically (see state a′ of Figure 6) is higher than that of the drop captured by the protrusion (see state a″ of Figure 6). Since both states are significantly lower than the free energy of the freely moving state, they can be considered as being in the stable state. For both type I and type II processes, the work can be estimated from the f−Δxc plot in Figure 7. The free energy landscape associated with multiple stable states can be acquired by calculating the reversible work required for the displacement of the center of mass (xc), as shown in Figures 5 and 6. The variation of f with Δxc for type I is more rapid than that for type II. Obviously, the critical force for type I ( f cr) is greater than that for type II (f cp), but the maximum displacement (from f = 0 to fc) for the former is less than that for the latter. In type II, the nanodrop is elongated by the protrusion before it detaches from the protrusion. The total work required for detachment is more for type I (a−e) than type II (a″−d′).

Figure 5. Energy landscape (type I, corresponding to Figure 3) for the nanodrop on the surface of θY = 60°. Drop is on the left side of the protrusion initially. Energy ΔE is scaled by kBT while the position xc by rc.

variation of the free energy with the center of the mass of the drop for the encounter of a freely moving drop with the protrusion (type I, Figures 2 and 3). The behavior of spontaneous capture and partial wetting on the protrusion can be clearly elucidated by the energy drop associated with the spontaneous change of xc. Evidently, this state corresponding to 7926

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Figure 7. External force is plotted against the displacement for both type I (states a−e) and type II (states a″−d′) processes for the lyophilic system (θY = 60°). Enlargement of the f around state b is shown in the inset.

3.2. Drop Trapped by a Lyophobic Protrusion. 3.2.1. Attraction between Drop and Protrusion. It is not surprising that a nanodrop is attracted to a lyophilic protrusion upon their encounter. However, what will happen when a nanodrop comes across a lyophobic protrusion? Consider a lyophobic system which is the same as the lyophilic system. The only difference is θY = 125° instead of 60°. It is observed that the nanodrop also wets the lyophobic protrusion spontaneously, though it is subject to random motion initially. The trapping dynamics can be seen from the top and side views, as demonstrated in Videos S4a (top view) and S4b (side view) of the Supporting Information. Again, the drop on the left side of the protrusion is captured by the protrusion, and the left and top sides of the protrusion are wetted. The drop deformation in the lyophobic system is significantly less than that in the lyophilic system. 3.2.2. Detachment from the Protrusion by External Force. In the absence of external force ( f = 0), the nanodrop stays partly on the lyophobic protrusion (state a of Figure 8). As the external force (f) is applied, the contact line of the drop move rightward and the front contact line contacts the right edge of the protrusion at f = 20 (state b of Figure 8). The front contact is always impeded by the right edge until f exceeds the critical value ( f cr = 47.5). The front CA at the edge exceeds θY but rises with f owing to the edge effect.19 As illustrated in state d of Figure 8 for f = 50, the resistant force is overcome, the drop moves across the protrusion, and it leaves the defect eventually. The detachment process is shown in Video S5 of the Supporting Information. Note that the critical force f cr in the lyophobic system is much less than that in the lyophilic system. In the lyophilic system, if the drop is placed atop the protrusion, the drop will straddle on it symmetrically, corresponding to the local minimum in the potential energy profile. However, for the same situation in the lyophobic system, the drop is unable to stand on the top of the protrusion and tends to slip toward either side of the protrusion to stay, as shown in Video S6 of the Supporting Information. If the rear end of the drop is initially on the right side of the protrusion, the detachment process subject to an external force shown in Figure 9 is different from the case that the front end of the drop is initially in the left side of the protrusion (Figure 8). The initial state of the drop with f = 0 (state a′ of Figure 9) is the same as that in state a of Figure 8 but on the opposite

Figure 8. Escape process (type I) of the lyophobic system. Variation of the drop shape with f is shown. Drop is on the left side of the protrusion initially.

Figure 9. Escape process (type II) of the lyophobic system. Variation of the drop shape with f is shown. Drop is on the right side of the protrusion initially.

side. When a small external force (f = 17.5) is applied, the rear contact line of the drop moves rightward to the right edge, as depicted in state b′ of Figure 9. As f is further increased, the rear contact line is still stopped at the right edge of the protrusion but the portion of the contact line at the right edge is reduced. The rear CA at the edge is greater than θY but declines with increasing f. Once f is greater than the critical value (f cp = 22.5), the resistance by the protrusion is overcome and the detachment takes place (state d′ of Figure 9). Video S7 of 7927

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The Journal of Physical Chemistry C the Supporting Information demonstrates the detachment process at f = 25.0. The critical force f cp in the lyophobic system is also much less than that in the lyophilic system. For both detachment processes illustrated in Figures 8 and 9, essentially no liquid is left at the lyophobic protrusion, while a small amount of residues is found at the protrusion for the lyophilic case in Figure 3. 3.2.3. Potential Energy for the Lyophobic System. Just like the lyophilic system, two types of potential energy profiles depending on the initial position can be obtained. Figure 10

Figure 11. External force is plotted against the displacement for both type I (states a−c) and type II (states a′−c′) processes for the lyophobic system (θY = 125°).

the free energy in Figure 10. The plot of f−Δxc in the lyophobic system is distinct from that in the lyophilic system. For a given force ( f), the drop displacement of type I is greater than that of the type II in the lyophobic system, while Δxc of type II is larger in the lyophilic system. Nonetheless, in both systems, the critical force for type I ( f cr) is always greater than that for type II ( f cp) and the total work required for detachment is more for type I (a−c) than type II (a′−c′). A careful examination of each curve in both systems reveals the presence of a turning point, for example, the state b (type I) in the inset of Figure 7 as well as the state b (type I) and state b′ (type II) in Figure 11. This transition indicates the change of the interaction between the contact line and the right edge of the protrusion. For type I, the turning point corresponds to the beginning of the contact between the front contact line and the right edge of the protrusion. For type II, the turning point shows the occurrence of the contact between the rear contact line and the right edge. In other words, no liquid is left on the top surface of the protrusion. From ΔE−xc and f−Δxc, the work of both types required for a drop crossing over a protrusion is higher for lyophilic systems. This result is consistent with our intuition that it is more difficult to detach a drop trapped by a lyophilic protrusion. However, the work is still required to detach a drop captured by a protrusion in a lyophobic system. The protrusion is found to attract a nanodrop, which is very different from the trench repulsing a nanodrop. This finding may be used in microfluidics systems to collect microdrops or guide the movement of microdrops. In our simulations, the protrusion and the surface are made of the same material and have the same contact angle with the drop. In experiments, such a nanosized protrusion can be fabricated by semiconductor photolithography. By coating both the smooth surface and the protrusion made of silicon oxide with fluorosilane, the case of high contact angle can be acquired with water drops while the case of low contact angle can be achieved by hexadecane drops.38,39

Figure 10. Energy landscape (type I, corresponding to Figure 8) of the lyophobic system (θY = 125°). Type II (corresponding to Figure 9) process is shown in the inset.

shows the variation of the free energy with the drop position for a drop encountering the protrusion (type I). The features of spontaneous capture and partial wetting on the protrusion is manifested by the small energy drop corresponding to the spontaneous change of xc from −15.0 to −13.5. The energy well corresponding to the stable state (state a of Figure 10) is much smaller than that in the lyophilic system. There exists an energy barrier preventing the drop from crossing the protrusion. Applying small forces will displace the drop slightly forward, but it is still confined in the energy well. As f exceeds the critical force f cr corresponding to the maximum slope of the profile (state c of Figure 10), the detachment occurs spontaneously. The drop crosses the protrusion and continues sliding. If the drop stays on the right side of the protrusion initially (type II), the free energy is minimum (state a′ of the inset of Figure 10) corresponding to the state of spontaneous capture. Note that the free energy at xc = 0 is relatively high so that a drop sitting on the center of a protrusion is unstable, unlike the lyophilic system. Applying the force results in the rightward displacement of xc. Again, as f > f cp (maximum slope), the energy barrier is overcome and the drop escapes from the protrusion. For type I, the surface energy at f cr in the lyophobic system is significantly greater than that in the lyophilic system, indicating that more shape deformation compared to the state of a free sessile drop is required for the escape in the lyophobic system. For type II, the surface energy at f cp in the lyophobic system is slightly larger than that of a free drop but the surface energy at f cp in the lyophilic system is significantly smaller than that of a free drop. This is because the drop straddling on the protrusion evenly is unstable for the former but stable for the latter. Figure 11 shows the variation of the force with the displacement of xc for both types of the lyophobic system, whose integration yields

4. CONCLUSIONS The interaction between a nanodrop and a rectangular protrusion on a smooth surface is investigated by MDPD and SE simulations. The protrusion possesses the same contact angle as that of the smooth surface. Both lyophilic and lyophobic cases are considered. The drop undergoes random motion on a smooth surface but becomes trapped as it is in 7928

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The Journal of Physical Chemistry C contact with the protrusion, that is, there exists an attraction between the drop and the protrusion. This scenario is distinctly different from the encounter of a drop with a trench. In the latter case, the drop is repelled by the trench. By applying an external force to the drop, the displacement of the captured drop is determined, and the potential energy profile (ΔE−xc) associated with the detachment process is acquired. For the lyophilic system, there are two energy wells. The deep well corresponds to the scenario that the drop stands side by side with the protrusion, a portion of the contact line being on the top surface of the protrusion. The shallow well represents that the drop straddles on the protrusion symmetrically. To detach from the protrusion completely, the force applied to the drop must exceed a critical value. Dependent on whether the drop is required to cross the protrusion or not, there are two critical forces. The critical force associated with crossing the protrusion is significantly greater than that without crossing. For the lyophobic system, the drop straddling the protrusion is unstable and the free energy is maximum. The energy well corresponding to the trapped state for the lyophobic system is much shallower than that in the lyophilic system. Obviously, it is more difficult to detach a drop trapped by a lyophilic protrusion than a lyophobic one. Nonetheless, the work is always required to separate a drop from a protrusion even in a lyophobic system.

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Detachment process of the drop on the right side of the protrusion (θY = 125°) at f = 25.0 by MDPD simulation (side view) (AVI)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Heng-Kwong Tsao: 0000-0001-6415-8657 Yu-Jane Sheng: 0000-0002-3031-8920 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Y.-J.S and H.-K.T. thank the Ministry of Science and Technology of Taiwan for financial support.

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REFERENCES

(1) Zhang, J.; Han, Y. A Topography/chemical Composition Gradient Polystyrene Surface: Toward the Investigation of the Relationship between Surface Wettability and Surface Structure and Chemical Composition. Langmuir 2008, 24, 796−801. (2) Ö ner, D.; McCarthy, T. J. Ultrahydrophobic Surfaces. Effects of Topography Length Scales on Wettability. Langmuir 2000, 16, 7777− 7782. (3) de Gennes, P. G.; Brochard-Wyart, F.; Quéré, D. Capillarity and Wetting Phenomena, Drops, Bubbles, Pearls, Waves; Springer: New York, 2004. (4) Feng, L.; Zhang, Y.; Cao, Y.; Ye, X.; Jiang, L. The Effect of Surface Microstructures and Surface Compositions on the Wettabilities of Flower Petals. Soft Matter 2011, 7, 2977−2980. (5) Ito, Y.; Heydari, M.; Hashimoto, A.; Konno, T.; Hirasawa, A.; Hori, S.; Kurita, K.; Nakajima, A. The Movement of a Water Droplet on a Gradient Surface Prepared by Photodegradation. Langmuir 2007, 23, 1845. (6) Johnson, R. E.; Dettre, R. H. Contact Angle Hysteresis I. Study of an Idealized Rough Surface. Adv. Chem. Ser. 1964, 43, 112−135. (7) Marmur, A. Wetting on Hydrophobic Rough Surfaces: To be Heterogeneous or not to be? Langmuir 2003, 19, 8343−8348. (8) Extrand, C. W. Contact Angles and Hysteresis on Surfaces with Chemically Heterogeneous Islands. Langmuir 2003, 19, 3793−3796. (9) Hong, S. J.; Chang, C. C.; Chou, T. H.; Sheng, Y. J.; Tsao, H. K. A Drop Pinned by a Designed Patch on a Tilted Superhydrophobic Surface: Mimicking Desert Beetle. J. Phys. Chem. C 2012, 116, 26487− 26495. (10) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: New York, 1985. (11) Chou, T. H.; Hong, S. J.; Sheng, Y. J.; Tsao, H. K. Drops Sitting on a Tilted Plate: Receding and Advancing Pinning. Langmuir 2012, 28, 5158−5166. (12) Hong, S. J.; Chang, F. M.; Chou, T. H.; Chan, S. H.; Sheng, Y. J.; Tsao, H. K. Anomalous Contact Angle Hysteresis of a Captive Bubble: Advancing Contact Line Pinning. Langmuir 2011, 27, 6890− 6896. (13) Chamakos, N. T.; Kavousanakis, M. E.; Papathanasiou, A. G. Enabling Efficient Energy Barrier Computations of Wetting Transitions on Geometrically Patterned Surfaces. Soft Matter 2013, 9, 9624−9632. (14) Promraksa, A.; Chen, L. J. Modeling Contact Angle Hysteresis of a Liquid Droplet Sitting on a Cosine Wave-like Pattern Surface. J. Colloid Interface Sci. 2012, 384, 172−181. (15) Chang, C. C.; Wu, C. J.; Sheng, Y. J.; Tsao, H. K. Air Pocket Stability and the Imbibition Pathway in Droplet Wetting. Soft Matter 2015, 11, 7308−7315.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b00428. Process of the spontaneous transition of the lyophilic drop (θY = 60°) from the free to the trapped state by MDPD simulation (top view) (AVI) Process of the spontaneous transition of the lyophilic drop (θY = 60°) from the free to the trapped state by MDPD simulation (side view) (AVI) Detachment process of the drop on the left side of the protrusion (θY = 60°) at f = 200 by MDPD simulation (top view) (AVI) Detachment process of the drop on the left side of the protrusion (θY = 60°) at f = 200 by MDPD simulation (side view) (AVI) Detachment process of the drop on the right side of the protrusion (θY = 60°) at f = 55.0 by MDPD simulation (top view) (AVI) Detachment process of the drop on the right side of the protrusion (θY = 60°) at f = 55.0 by MDPD simulation (side view) (AVI) Process of the spontaneous transition of the lyophobic drop (θY = 125°) from the free to the trapped state by MDPD simulation (top view) (AVI) Process of the spontaneous transition of the lyophobic drop (θY = 125°) from the free to the trapped state by MDPD simulation (side view) (AVI) Detachment process of the drop on the left side of the protrusion (θY = 125°) at f = 50 by MDPD simulation (side view) (AVI) Dynamic process of a drop on the protrusion initially and slipping toward either side of the protrusion for the lyophobic system (θY = 125°) (side view) (AVI) 7929

DOI: 10.1021/acs.jpcc.7b00428 J. Phys. Chem. C 2017, 121, 7923−7930

Article

The Journal of Physical Chemistry C (16) Joanny, J. F.; de Gennes, P. G. A Model for Contact Angle Hysteresis. J. Chem. Phys. 1984, 81, 552−562. (17) Chang, F. M.; Hong, S. J.; Sheng, Y. J.; Tsao, H. K. Wetting Invasion and Retreat across a Corner Boundary. J. Phys. Chem. C 2010, 114, 1615−1621. (18) Chen, X.; Ma, R.; Zhou, H.; Zhou, X.; Che, L.; Yao, S.; Wang, Z. Activating the Microscale Edge Effect in a Hierarchical Surface for Frosting Suppression and Defrosting Promotion. Sci. Rep. 2013, 3, 02515. (19) Chang, C. C.; Wu, C. J.; Sheng, Y. J.; Tsao, H. K. Resisting and Pinning of a Nanodrop by Trenches on a Hysteresis-free Surface. J. Chem. Phys. 2016, 145, 164702. (20) Wong, T. S.; Kang, S. H.; Tang, S. K. Y.; Smythe, E. J.; Hatton, B. D.; Grinthal, A.; Aizenberg, J. Bioinspired Self-repairing Slippery Surfaces with Pressure-stable Omniphobicity. Nature 2011, 477, 443− 447. (21) Epstein, A. K.; Wong, T. S.; Belisle, R. A.; Boggs, E. M.; Aizenberg, J. Liquid-infused Structured Surfaces with Exceptional Antibiofouling Performance. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 13182−13187. (22) Kim, P.; Wong, T. S.; Alvarenga, J.; Kreder, M. J.; AdornoMartinez, W. E.; Aizenberg, J. Liquid-Infused Nanostructured Surfaces with Extreme Anti-Ice and Anti-Frost Performance. ACS Nano 2012, 6, 6569−6577. (23) Anand, S.; Paxson, A. T.; Dhiman, R.; Smith, J. D.; Varanasi, K. K. Enhanced Condensation on Lubricant-Impregnated Nanotextured Surfaces. ACS Nano 2012, 6, 10122−10129. (24) Daniel, D.; Mankin, M. N.; Belisle, R. A.; Wong, T. S.; Aizenberg, J. Lubricant-infused Micro/nano-structured Surfaces with Tunable Dynamic Omniphobicity at High Temperatures. Appl. Phys. Lett. 2013, 102, 231603. (25) Wilson, P. W.; Lu, W.; Xu, H.; Kim, P.; Kreder, M. J.; Alvarenga, J.; Aizenberg, J. Inhibition of Ice Nucleation by Slippery Liquid-infused Porous Surfaces (SLIPS). Phys. Chem. Chem. Phys. 2013, 15, 581−585. (26) Kim, P.; Kreder, M. J.; Alvarenga, J.; Aizenberg, J. Hierarchical or Not? Effect of the Length Scale and Hierarchy of the Surface Roughness on Omniphobicity of Lubricant-Infused Substrates. Nano Lett. 2013, 13, 1793−1799. (27) Warren, P. B. Vapor-liquid Coexistence in Many-body Dissipative Particle Dynamics. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2003, 68, 066702. (28) Chen, C.; Zhuang, L.; Li, X.; Dong, J.; Lu, J. A Many-Body Dissipative Particle Dynamics Study of ForcedWater Oil Displacement in Capillary. Langmuir 2012, 28, 1330−1336. (29) Ghoufi, A.; Emile, J.; Malfreyt, P. Recent Advances in Many Body Dissipative Particles Dynamics Simulations of Liquid-vapor Interfaces. Eur. Phys. J. E: Soft Matter Biol. Phys. 2013, 36, 10. (30) Ghoufi, A.; Malfreyt, P. Calculation of the Surface Tension from Multibody Dissipative Particle Dynamics and Monte Carlo Methods. Phys. Rev. E 2010, 82, 016706. (31) Jakobsen, A. F. Constant-pressure and Constant-surface Tension Simulations in Dissipative Particle Dynamics. J. Chem. Phys. 2005, 122, 124901. (32) Liu, M.; Meakin, P.; Huang, H. Dissipative Particle Dynamics Simulation of Fluid Motion through an Unsaturated Fracture and Fracture Junction. J. Comput. Phys. 2007, 222, 110−130. (33) Arienti, M.; Pan, W.; Li, X.; Karniadakis, G. Many-body Dissipative Particle Dynamics Simulation of Liquid/vapor and Liquid/ solid Interactions. J. Chem. Phys. 2011, 134, 204114. (34) Chang, C. C.; Sheng, Y. J.; Tsao, H. K. Wetting Hysteresis of Nanodrops on Nanorough Surfaces. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2016, 94, 042807. (35) Brakke, K. The Surface Evolver. Exp. Math. 1992, 1, 141−165. (36) Liang, Y. E.; Weng, Y. H.; Tsao, H. K.; Sheng, Y. J. Meniscus Shape and Wetting Competition of a Drop between a Cone and a Plane. Langmuir 2016, 32, 8543−8549. (37) Lin, H. J.; Chen, H. Y.; Sheng, Y. J.; Tsao, H. K. Bell’s Expression and the Generalized Garg Form for Forced Dissociation of a Biomolecular Complex. Phys. Rev. Lett. 2007, 98, 088304.

(38) Dufour, R.; Perry, G.; Harnois, M.; Coffinier, Y.; Thomy, V.; Senez, V.; Boukherroub, R. From Micro to Nano Reentrant Structures: Hysteresis on Superomniphobic Surfaces. Colloid Polym. Sci. 2013, 291, 409−415. (39) Chang, C. C.; Wu, C. J.; Sheng, Y. J.; Tsao, H. K. Air Pocket Stability and the Imbibition Pathway in Droplet Wetting. Soft Matter 2015, 11, 7308−7315.

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DOI: 10.1021/acs.jpcc.7b00428 J. Phys. Chem. C 2017, 121, 7923−7930