On the Role of the Three-Phase Contact Line in Surface Deformation

Feb 29, 2012 - In the first case we show that there is a surface deformation at the ... Carré et al. measured the height of the wetting ridge, h, to ...
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On the Role of the Three-Phase Contact Line in Surface Deformation Aisha Leh,† Hartmann E. N’guessan,† Jianguo Fan,‡,§ Prashant Bahadur,† Rafael Tadmor,*,† and Yiping Zhao‡ †

Dan F. Smith Department of Chemical Engineering, Lamar University, Beaumont, Texas 77710, United States Department of Physics and Astronomy, Nanoscale Science and Engineering Center, University of Georgia, Athens, Georgia 30602, United States § Center for Advanced Ultrastructural Research, University of Georgia, Athens, Georgia 30602, United States ‡

ABSTRACT: Viscoelastic braking theories developed by Shanahan and de Gennes and by others predict deformation of a solid surface at the solid−liquid−air contact line. This phenomenon has only been observed for soft smooth surfaces and results in a protrusion of the solid surface at the threephase contact line, in agreement with the theoretical predictions. Despite the large (enough to break chemical bonds) forces associated with it, this deformation was not confirmed experimentally for hard surfaces, especially for hydrophobic ones. In this study we use superhydrophobic surfaces composed of an array of silicon nanostructures whose Young modulus is 4 orders of magnitude higher than that of surfaces in earlier recorded viscoelastic braking experiments. We distinguish between two cases: when a water drop forms an adhesive contact, albeit small, with the apparent contact angle θ < 180° and when the drop− surface adhesion is such that the conditions for placing a resting drop on the surface cannot be reached (i.e., θ = 180°). In the first case we show that there is a surface deformation at the three-phase contact line which is associated with a reduction in the hydrophobicity of the surface. For the second case, however, there cannot be a three-phase contact line associated with a drop in contact with the surface, and indeed, if we force-place a drop on the surface by holding it with a needle, no deformation is detected, nor is there a reduction in the hydrophobic properties of the surface. Yet, if we create a long horizontal three-phase contact line by partially immersing the superhydrophobic substrate in a water bath, we see a localized reduction in the hydrophobic properties of the surface in the region where the three-phase contact line used to be. The SEM scan of that region shows a narrow horizontal stripe where the nanorods are no longer there, and instead there is only a shallow structure that is lower than the nanorods height and resembles fused or removed nanorods. Away from that region, either on the part of the surface which was exposed to bulk water or the part which was exposed to air, no change in the hydrophobic properties of the surface is observed, and the SEM scan confirms that the nanorods seem intact in both regions.

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(shear modulus of 0.63 MPa), which they termed “wetting ridge” (cf. Figure 1).

INTRODUCTION The dynamics of liquid drops on solid surfaces plays an important role in many applications, such as oil recovery,1 drug delivery,2 paints,3 textiles,4 and pesticides.5 A lot of attention is given to superhydrophobic surfaces which are designed to minimize drop adhesion to the surface. A classic way to reduce drop−surface adhesion is by generating an effective high surface area on a hydrophobic surface. One common example is the fabrication of surfaces with various protruding nanostructures, giving rise to an effective surface area much higher than the nominal one. A drop placed on such a hydrophobized surface spans between the tops of the nanostructures. Cassie and Baxter6 define an apparent contact angle, θCB, of a drop in this configuration in terms of the Young equilibrium contact angle, θ0, as cos θCB = ϕ cos θ0 + ϕ − 1, where ϕ is the fraction of the area of solid surface in contact with the liquid. Of particular interest here is the force required to slide drops on surfaces. This force has been linked to the three-phase contact line and especially to the deformation it induces on the solid surface.7−11 Carré et al.10 provided explicit experimental evidence of this deformation, on a soft elastomeric substrate © 2012 American Chemical Society

Figure 1. Schematic illustration of a liquid drop on a solid substrate, showing the deformation (not drawn to scale; the actual deformation is not visible on a macroscopic scale) formed at the three-phase contact line.

Carré et al. measured the height of the wetting ridge, h, to be in agreement with the theoretical prediction of Shanahan and de Gennes,11 which provided a general prediction relating to surfaces of any stiffness.12 Various reports have been presented Received: May 27, 2011 Revised: February 28, 2012 Published: February 29, 2012 5795

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to describe the wetting ridge theoretically,13,14 numerically15,16 and experimentally,17,18 generally attributing the deformation to the unbalanced normal component of the liquid surface tension in the vectorial description of the Young equation. Shanahan and de Gennes described11 the wetting ridge height by eq 1: h(x) ≈

γ sin θ0 ⎛ d ⎞ ln⎜ ⎟ ⎝x⎠ 2πG

surfaces.29−32 In this study, we were able to describe the deformation of superhydrophobic nanostructured surfaces induced by the water−air−substrate three-phase contact line. We used surfaces composed of rigid nanorods, which, owing to the spacing between them, give rise to a lower effective modulus33 (which we quantify later on). The deformation was observed, not in the form of a protrusion, but in the form of breakage of the nanorods, which are limited in their ability to be pulled up or bent due to their high rigidity. This process is characterized by stronger retention forces for drops placed on the surface.

(1)

where γ sin θ0 is the unbalanced normal component of the surface tension force in Young equation:19,20 γ is the liquid surface tension, G is the shear modulus of the solid, x is the distance perpendicular to the three-phase contact line and parallel to the solid surface, and d is the distance at which no displacement occurs within the solid. As White already noted,21 Shanahan’s model11,22,23 uses the theory of linear elasticity, which diverges at the three-phase contact line. To overcome this difficulty, Shanahan postulated a length scale, ε, around the line inside which the material is plastically deformed. This length scale lacks a value or a way to calculate it, thereby obscuring the exact quantification of the ridge height. White’s study overcomes this problem by considering also the disjoining and Laplace pressures, ΠSLV and ΔP, respectively, which results in eq 2. h(x) = −

∫0

x0

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x′K (x , x′)[ΠSLV (y(x′) − h(x′)) + ΔP] dx′ (2)

where y is the liquid height at x', and x0 is the drop's radius K (x , x′) =

1 − σ2 2π πE 0

∫

dθ (x 2 + x′2 − 2xx′ cos θ ) (3)

and E is Young’s modulus and σ is Poisson’s ratio. The deformation of the solid surface also gives rise to the drop retention force, F||, i.e., the force required to move a drop of liquid on the solid surface.7,24−26 F =

4γ 2 sin θ (cos θA − cos θ R ) Γ

EXPERIMENTAL SECTION

The preparation of the superhydrophobic nanorod surfaces was reported earlier.34 Briefly, silicon nanorods were deposited onto a silicon wafer in an electron beam deposition system (Torr International, NY), with an oblique vapor incident angle of 88°, a nominal deposition rate of 0.3−0.4 nm/s, and a substrate azimuthal rotation speed of 0.15 rev/s. We obtained three sets of samples by varying the deposition times. The morphologies of the samples were characterized by scanning electron microscopes (Zeiss EP1450 variable pressure SEM and FEI Inspect field emission SEM) at high vacuum mode. The nanorod height (H), nanorod diameter (at top) (D), and rod−rod separation (L) are as follows: For the first sample, H = 270 ± 30 nm, D = 140 ± 20 nm, and L = 280 ± 90 nm. We denote this sample as S(270/140/280 nm). For the second sample, denoted as S(460/130/ 400 nm), H = 460 ± 90 nm, D = 130 ± 20 nm, and L = 400 ± 80 nm. For the third sample, H = 160 ± 60 nm, D = 70 ± 10 nm, and L = 110 ± 30 nm. We denote this sample as S(160/70/110 nm). The nanorod substrate was then oxidized in piranha solution (sulfuric acid mixed with hydrogen peroxide at v/v 4:1), rinsed with deionized water, and dried with N2 gas. Finally, the surface was coated with a fluorocarbon layer by vacuum evaporation of (heptadecafluoro-1,1,2,2tetrahydrodecyl)trichlorosilane (CF3(CF2)7CH2CH2SiCl3: HFTS) (Gelest Inc.). Water drops of volume 9 μL (distilled water, Barnstead Nanopure Purification system which provides specific resistivity of 18.2 MΩ·cm at 25 °C) were observed on superhydrophobic substrates using an AVT Pike CCD camera (210 fps). The substrate was placed on a leveled horizontal stage inside a centrifugal adhesion balance (CAB). The CAB was described elsewhere.7 Figure 2 shows how it allows an independent manipulation of normal and lateral forces by combining centrifugal and gravitational forces. In this study, the CAB was used only at a constant normal acceleration of 1g (horizontal CAB chamber) while the lateral force, F||, was varied as the lateral rotation of the CAB arm was varied according to eq 5 until the drop began to slide.

(4)

where θA and θR are the drop advancing and receding contact angles, respectively. F|| is a pinning retention force, and Γ is a time-dependent yield stress characteristic of the molecular deformation of the substrate surface associated with this protrusion.27 For very rigid surfaces the three-phase line does not cause any significant protrusion. Yet the forces originating from surface tension phenomena are strong enough to break chemical bonds,28 and at the three-phase contact line they induce a molecular reorientation of the solid surface molecules that results in an increase of the drop−surface intermolecular attraction, i.e., drop pinning.7,24 Therefore, Γ is the yield stress associated with this molecular reorientation. The discussion above relates to a wide spectrum of surfaces including elastic and viscoelastic, soft and hard. Yet, nanostructured materials, especially aligned nanorod thin films or nanoporous layers, which are composites of rigid nanorods and air, result in a brittle nature. This property gives a different physics, for which the discussion above can serve only as a qualitative background. To the best of our knowledge, this is the first account (experimental or theoretical) for such systems. Moreover, experimental analysis of the viscoelastic breaking was limited to softer viscoelestic (Young modulus up to 400 kPa)

F = ρVω2R

(5)

where ρ is the density of the liquid drop, V is its volume, R is the distance from the axis of rotation to the drop, and ω is the angular velocity at which the drop begins to slide. The three-phase contact line experiments were carried out at room temperature in a dust-free laminar flow hood from Terra Universal (ULPA filters). This type of hood filters particles larger than 30 nm.

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RESULTS AND DISCUSSION

We used surfaces made of silicon nanorods, which, together with the spaces (air) between them, can be viewed as composite surfaces.33 Such nanocomposite surfaces give rise to effective moduli that are between those of silicon and those of air. Calculations of the effective bulk (K*) and shear (G*) 5796

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Figure 3. A water drop placed on a superhydrophobic nanostructured surface S(270/140/280 nm). The deformation of the drop is caused by gravity. Drop volume = 9 μL; θ = 160°.

varying resting time periods for a particular position on the surface. In this study we use “accumulative resting time”, taccum, which is defined as the accrued amount of resting times of drops placed at the same position on the surface. Thus, for a particular position, accumulative resting time is described by eq 8:

Figure 2. The CAB: a rotating arm has a closed chamber at one end and a counterbalance at the other. The sample is placed in the chamber were it is recorded by a camera (not shown) which is powered by the control box. The camera image is transfers wirelessly to a computer placed nearby outside the rotating assembly. The angular velocity is measured using the encoder. By independent manipulation of the angular velocity and the tilt angle of the chamber, any combination of normal and lateral forces can be achieved.

n

taccum, n =

moduli of the nanocomposite surface were obtained from eqs 6 and 7:33 (1 − f )K sts + fKata K∗ = (1 − f )ts + fta

(6)

(1 − f )Gsvs + fGata (1 − f )vs + fva

(7)

G∗ =

∑ trest, i i=1

(8)

where trest,i is the resting time of the ith drop. Plots of retention force, F|| (force required to set a drop in motion), versus the accumulative resting time, taccum, are shown in Figure 4, where

where Ks and Gs are the bulk (100 GPa) and shear (80 GPa) moduli, respectively of silicon, Ka and Ga are the bulk (1.01 × 10−4 GPa) and shear (0 GPa) moduli, respectively, of air; vs, ts, va, and ta represent scalar strain factors of the silicon and the air;35 and f is the fractional volume of the air (0.92). We found the effective bulk and shear moduli to be K* = 4.5 GPa and G* = 3.4 GPa, respectively. Compared to the moduli of PTFE (Teflon) (K ∼ 1.5−2.8 GPa; G ∼ 0.1−0.6 GPa)36,37 and silicon (K ∼ 90−100 GPa; G ∼ 50−80 GPa),38−40 we can consider these composite substrates to be effectively “soft” while the nanorods themselves, being of silicon, are highly rigid.41 Typically, surfaces on which sessile drops obtain an apparent contact angle,42 θ, higher than 150° are considered to be “superhydrophobic”.43−45 All surfaces used in this study were such; however, we distinguish between two surface types: those on which the drops form an adhesive contact, albeit small, with the surface, and those on which drop−surface contact is such that the conditions for placing the drop at rest on the surface cannot be reached. The latter refers to a case of a horizontally leveled surface on which the drop is unable to rest as we explain later on. Creation of a Circular Three-Phase Line. We started with a surface on which θ is 160° (see Figure 3). In this case, we placed a drop on the leveled horizontal surface and allowed it to rest for some prescribed resting time, trest (the time taken from when a drop is first placed on a surface46 to when it (the whole three-phase line) moves from its position of placement). The retention force was measured by rotating the CAB arm until the drop rolled off. This procedure was repeated for

Figure 4. Force, F||, required to move a water drop on a superhydrophobic surface S(270/140/280 nm), before (■) and after (other symbols) submerging the surface halfway into a water bath for 90 min, as a function of the accumulative resting time, taccum. The water drops were placed on the part of the substrate that was exposed to air (●), at the region of the horizontal three-phase line (▲), and immersed in water (◆). The solid lines are guides to the eye.

each of the plots corresponds to a different position on the same substrate (note that taccum is only relevant for drops placed on the same position). Figure 4 shows that the force, F||, required to set a drop in motion on the surface increases with the accumulative resting time and approaches a plateau as the accumulative time approaches infinity. Unlike previous time-effect studies where the increase in force is associated with resting time7,25,47 and not accumulative resting time, i.e., similar force is required to slide the first drop and the nth drop (n being any serial number), here the increase in the force is associated with the 5797

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accumulative resting time, suggesting plastic changes of the solid surface. Yet, in agreement with earlier time effect studies,7,25,47 we also believe that the increase in force is associated with an increase in the intermolecular interactions between solid and liquid molecules, which results from the deformation of the solid surface molecules.24 The time scale associated with this observed phenomenon is also within the range associated with similar phenomena reported in previous studies.7,25 The increase in retention force with time also represents a gradual transition from a Cassie state to a Wenzel state, which is known to occur as water drops rest or evaporate on nano- or micro-structured surfaces.48−51 The origin of such a transition is therefore a result of the molecular reorientation of the solid surface molecules induced primarily by the Shanahan−de Gennes type three-phase line substrate deformation which results in a stronger solid−liquid intermolecular interaction, and hence Wenzel state. One interesting feature in Figure 4 is the fact that the force required to slide a drop on the region where the three-phase contact line used to be (the historic three-phase line) is higher than the force required to slide a drop at other regions (we consider the two lower curves to be of similar force magnitude). It should be noted that drops placed near the historic three-phase line were drawn toward it, suggesting a potential gradient with a minimum at the historic three-phase line (i.e., the historic three-phase line is the least hydrophobic location). We return to this issue later on. The above section addresses surfaces with θ larger than 150° (θ = 150° is one of the well-known conditions to define a superhydrophobic surface) on which the drops form a weak adhesive contact.52 We also created surfaces on which drop− surface contact is such that the conditions for placing the drop on a surface cannot be reached, i.e., a water drop placed on such a surface rolls off even if the surface is horizontal,53 manifesting an apparent contact angle of 180°. Prolonged contact between a water drop and such a solid surface was achieved by holding a captive drop54 on an unwettable superhydrophobic surface such that it hangs from a syringe needle and is forced to touch the surface as shown in Figure 5. Once the drop was released from the needle, it always rolled away, escaping from the surface and requiring no additional force to set it into motion (Figure 6). It should be noted that in this captive drop configuration, the drop was almost never perfectly at rest in one position over time.

Figure 6. Force, F||, required to move a water drop as a function of the accumulative resting time for a completely superhydrophobic surface S(460/130/400 nm); θ0 = 180°. Captive drops were used on such surfaces. The solid line is a guide to the eye.

The survival of a perfectly nonwettable surface despite rather long contact times between the captive drop and the surface suggests no surface damage. Note, however, that unlike the system described in Figure 4, which did exhibit surface damage, the system described in Figures 5 and 6 cannot form a threephase contact line as the equilibrium contact angle the drop creates with the surface is θ0 = 180°, in which case there can only be a three-phase contact point.55 Creation of a Generally Horizontal Three-Phase Contact Line. The substrates for which the conditions for placing a drop on it cannot be reached were partially immersed in distilled water for a period of time and then withdrawn.56 During the time the surface was still and partially in the water, a long three-phase line was created (Figure 7).57

Figure 7. Schematic of a surface partially immersed in distilled water to create a horizontal solid−liquid−air interfacial line on an otherwise unwettable surface.

Upon withdrawal from water, changes in the hydrophobicity of the substrate surface were observed at the historic threephase contact line as shown in Figure 8. The historic threephase contact line was characterized by an increased retention force for drops placed on it. While prior to the substrate immersion a drop placed on the surface would either bounce repeatedly or roll off, exhibiting zero retention force (as in Figure 6); now, adhesion between the drop and the substrate was observed at the historic three-phase line (last two frames of Figure 8). The sequence of frames in Figure 8 describes a drop bouncing on the surface following its release from a syringe

Figure 5. A captive drop held on a superhydrophobic surface S(460/ 130/400 nm). The drop appeared to be unstable; i.e., it cannot remain in one place over time despite being held by the syringe needle. 5798

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Figure 8. Water drop bounces on the part of the surface S(460/130/400 nm) that was above the historic three-phase line and stops on it.

Figure 9. SEM image taken of a substrate surface (a) that was not partially immersed in water (no three-phase line was created) showing undamaged nanorods (scale bar 2 μm); (b) after immersion in water; scanned around the three-phase contact line region so that the lower side is directed toward the part that was immersed in water. The damaged portion was, within our error, the location of the three-phase line (scale bar 3 μm).

deformation; however, being a composite substrate made of highly rigid silicon41 nanorods, the high forces associated with the substrate deformation are more likely to tilt and bend nanorods and eventually break them, rather than to create a wetting ridge of the solid surface (as is the case for softer homogeneous surfaces). A possible description of the surface deformation is shown in Figure 10: At the three-phase contact line the capillary forces and the weight of the drop act in a nonsymmetric way on the nanorods, i.e., the nanorods in the middle of the drop experience isotropic pressure; however, nanorods that are just on the three-phase contact line will experience the drop pressure on one side and atmospheric pressure on the other, causing them to bend and deform, which later leads to them breaking away from the surface.

about 1 cm above the surface. As the drop was bouncing, it also migrated slowly toward the place where the three-phase contact line used to be, and when it finally reached this location, it adhered to the surface. The retention force remained zero outside the three-phase contact line region, as demonstrated in the first six frames of Figure 8. To demonstrate the topographical aspect of these changes, SEM scans of a surface before (a) and after (b) partial immersion in water are presented in Figure 9. Figure 9a shows individual nanorods of a surface that was not immersed in water while Figure 9b shows that at the region where the three-phase contact line used to be, there is a band about 2 μm wide within which the nanorod structures are no longer present. There are flattened textures in this narrow region instead of nanorods. The flattened area is lower than the nanorods in height and consists of smooth patches which resemble fused or removed nanorods. This ∼2 μm thickness is in agreement with the observation of Bomashenko et al.,58 who reported an ESEM study of the structure of the three-phase line of water drops on rough polymer substrates. They observed a “film of 1−5 μm width formed in the nearest vicinity of the drop”. Away from the three-phase region (above and below), the nanorods seem to be intact, similar to those shown in Figure 9a. But directly above and below the three-phase region, there are thinner regions of nanorods which seem to be in transition between the two states described above. We attribute the damage at the three-phase line to a viscoelastic braking type surface deformation, which is associated with the unbalanced normal component of the surface tension.7,10,11,25 Because of the low effective surface rigidity (of the order of that of Teflonsee the beginning of the Results and Discussion section), we can obtain a notable

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CONCLUSION We demonstrated the accumulative destruction effect of resting water drops on silicon nanostructured superhydrophobic surfaces. For surfaces on which water drops form an adhesive contact, we showed that the presence of the drops on the surface results in an increasing drop retention force at the position on which the drop was placed. This renders the surface less and less hydrophobic with the accumulative time the drops rested on it. We associate this hydrophilication process with an increase in the intermolecular interactions between solid and liquid molecules, which is induced by the Shanahan−de Gennes type three-phase line solid surface molecular deformation.24 We also relate the increase in retention force to a Cassie to Wenzel wetting transition, known to occur as water drops rest on, or evaporate from, a nanostructured surface.48−51 This transition is thus primarily related to the reorientation of the surface molecules, induced by the Shanahan−de Gennes type surface deformation. 5799

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.G.F. and Y.P.Z. were supported by National Science Foundation under Contract CMMI-0824728. P.B., H.E.N., A.L., and R.T. acknowledge support from National Science Foundation Grants DMR-0619458 and CBET-0960229.

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REFERENCES

(1) Tan, C. S.; Gee, M. L.; Stevens, G. W. Optically profiling a draining aqueous film confined between an oil droplet and a solid surface: Effect of nonionic surfactant. Langmuir 2003, 19, 7911−7918. (2) Chow, K. T.; Chan, L. W.; Heng, P. W. S. Characterization of spreadability of nonaqueous ethylcellulose gel matrices using dynamic contact angle. J. Pharm. Sci. 2008, 97, 3467−3482. (3) Garbero, M.; Vanni, M.; Baldi, G. CFD modelling of a spray deposition process of paint. Macromol. Symp. 2002, 187, 719−729. (4) Gao, Q.; Zhu, Q.; Guo, Y.; Yang, C. Q. Formation of Highly Hydrophobic Surfaces on Cotton and Polyester Fabrics Using Silica Sol Nanoparticles and Nonfluorinated Alkylsilane. Ind. Eng. Chem. Res. 2009, 48, 9797−9803. (5) Tominack, R. L. Herbicide formulations. J. Toxicol., Clin. Toxicol. 2000, 38, 129−135. (6) Cassie, A. B. D.; Baxter, S. Wettability of porous surfaces. Trans. Faraday Soc. 1944, 40, 546−551. (7) Tadmor, R.; Bahadur, P.; Leh, A.; N’Guessan, H. E.; Jaini, R.; Dang, L. Measurement of Lateral Adhesion Forces at the Interface between a Liquid Drop and a Substrate. Phys. Rev. Lett. 2009, 103, 266101. (8) Lester, G. R. Contact angles of liquids at deformable solid surfaces. J. Colloid Sci. 1961, 16, 315−326. (9) Rusanov, A. I. Theory of the Wetting of Elastically Deformed Bodies. Colloid J. USSR 1975, 37, 614−622. (10) Carré, A.; Gastel, J. C.; Shanahan, M. E. R. Viscoelastic effects in the spreading of liquids. Nature 1996, 379, 432−434. (11) Shanahan, M. E. R.; de Gennes, P. G. Physique des Surfaces et des Interfaces. C. R. Acad. Sci., Sér. II 1986, 302, 517−521. (12) Calculations in ref 11 include hard surfaces like mica and soft surfaces like rubber. (13) Fredrickson, G. H.; Ajdari, A.; Leibler, L.; Carton, J. P. Surface modes and deformation energy of a molten polymer brush. Macromolecules 1992, 25, 2882−2889. (14) Long, D.; Ajdari, A.; Leibler, L. Static and Dynamic Wetting Properties of Thin Rubber Films. Langmuir 1996, 12, 5221−5230. (15) Madasu, S.; Cairncross, R. A. Static wetting on flexible substrates: a finite element formulation. Int. J. Numer. Methods Fluids 2004, 45, 301−319. (16) Yu, Y.-S.; Zhao, Y.-P. Elastic deformation of soft membrane with finite thickness induced by a sessile liquid droplet. J. Colloid Interface Sci. 2009, 339, 489−494. (17) Pu, G.; Severtson, S. J. Characterization of Dynamic Stick-andBreak Wetting Behavior for Various Liquids on the Surface of a Highly Viscoelastic Polymer. Langmuir 2008, 24, 4685−4692. (18) Voué, M.; Rioboo, R.; Bauthier, C.; Conti, J.; Charlot, M.; De Coninck, J. Dissipation and moving contact lines on non-rigid substrates. J. Eur. Ceram. Soc. 2003, 23, 2769−2775. (19) Adamson, A. W.; Gast, A. P.Physical Chemistry of Surfaces; John Wiley & Sons: New York, 1997. (20) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: New York, 2007. (21) White, L. R. The contact angle on an elastic substrate. 1. The role of disjoining pressure in the surface mechanics. J. Colloid Interface Sci. 2003, 258, 82−96.

Figure 10. A possible description of the nanorods distortion before they break from the surface.

Surfaces too hydrophobic for water drops to rest on were not affected by forced-placed drops for an extended period of time. The reason for this is that the drops cannot form a three-phase contact line (but only a point). If, however, a contact line was created on such a surface by partial immersion of the surface vertically in a water bath, we showed that the surface maintains its superhydrophobic characteristics in the regions either above or below the contact line. In the vicinity of the three-phase contact line, however, the retention force increased and the local hydrophobicity decreased. We attribute this change to a plastic surface deformation occurring at the three-phase line such as those described theoretically by White,21 Shanahan and de Gennes,11 and Yu and Zhao.16 Note that in those theories the solid surface deforms as an outward continuous protrusion (elastic and plastic). In our system, a combined effect of gravity and unbalanced surface force resulted in breaking of the nanorods. The broken nanorods were located around the threephase contact line. SEM scans of this area showed a ∼2 μm wide band of smooth shallow patches that resemble fused or removed nanorods. This study completes a spectrum of studies dealing with the effect of the three-phase contact line on the substrate: This contact line was shown to induce elastic and plastic deformations in continuous smooth substrates, which was measured for soft surfaces;10 then it was attributed for molecular reorientation associated with hard surfaces, which induced a time-dependent increase in the drop retention force;7 and here we demonstrate its effect on silicon nanostructured surfaces in which it is responsible for breaking of the nanorods. Thus, we see three types of effects induced by the three-phase contact line: topographical viscoelastic changes, chemical changes, and here nanomechanical fracture and yield changes. 5800

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(22) Shanahan, M. E. R. The influence of solid micro-deformation on contact angle equilibrium. J. Phys. D: Appl. Phys. 1987, 20, 945. (23) Shanahan, M. E. R. The spreading dynamics of a liquid drop on a viscoelastic solid. J. Phys. D: Appl. Phys. 1988, 21, 981. (24) Tadmor, R. Line energy, line tension and drop size. Surf. Sci. 2008, 602, L108−L111. (25) Tadmor, R.; Chaurasia, K.; Yadav, P. S.; Leh, A.; Bahadur, P.; Dang, L.; Hoffer, W. R. Drop retention force as a function of resting time. Langmuir 2008, 24, 9370−9374. (26) Yadav, P. S.; Bahadur, P.; Tadmor, R.; Chaurasia, K.; Leh, A. Drop retention force as a function of drop size. Langmuir 2008, 24, 3181−3184. (27) Note that the stress we refer to is not the macroscopic stress which is often found in tables, but rather, a molecular stress of the type described, for example, in reference 47 and in: Yu et al. (PRL 1997) Vol 79, Article Number 905; and in Spirin et al. (PRL 2011) Vol 106, Article Number 168301. (28) Sheiko, S. S.; Sun, F. C.; Randall, A.; Shirvanyants, D.; Rubinstein, M.; Lee, H.; Matyjaszewski, K. Adsorption-induced scission of carbon-carbon bonds. Nature 2006, 440, 191−194. (29) Jerison, E. R.; Xu, Y.; Wilen, L. A.; Dufresne, E. R. Deformation of an Elastic Substrate by a Three-Phase Contact Line. Phys. Rev. Lett. 2011, 106, 186103. (30) Pericet-Cámara, R.; Auernhammer, G. K.; Koynov, K.; Lorenzoni, S.; Raiteri, R.; Bonaccurso, E. Solid-supported thin elastomer films deformed by microdrops. Soft Matter 2009, 5, 3611−3617. (31) Pericet-Cámara, R.; Best, A.; Butt, H.-J.; Bonaccurso, E. Effect of Capillary Pressure and Surface Tension on the Deformation of Elastic Surfaces by Sessile Liquid Microdrops: An Experimental Investigation. Langmuir 2008, 24, 10565−10568. (32) Pu, G.; Guo, J.; Gwin, L. E.; Severtson, S. J. Mechanical Pinning of Liquids through Inelastic Wetting Ridge Formation on Thermally Stripped Acrylic Polymers. Langmuir 2007, 23, 12142−12146. (33) Steinhardt, P. J. Effective Medium Theory for the Elastic Properties of Composites and Acoustics Applications McLean, VA, The MITRE Corporation, JASON Program Office, 1992. (34) Fan, J. G.; Zhao, Y. P. Nanocarpet Effect Induced Superhydrophobicity. Langmuir 2010, 26, 8245−8250. (35) The specific values obtained were vs = ts = 1, in accordance with ref 33 (cf. p 9 there), while va = 2 and ta = 1.96 were calculated from eq 2-14 in ref 33. When calculating these values, we chose the shape of the inclusions based on the aspect ratio that was closest to our system, i.e., 1.3. The eventual values of K* and G* have the same order of magnitude regardless of these choices. (36) Kaye, G. W. C.; Laby, T. H. Tables of Physical and Chemical Constants; Longman Sci & Tech: Harlow, 1995. (37) Rae, P. J.; Dattelbaum, D. M. The properties of poly (tetrafluoroethylene) (PTFE) in compression. Polymer 2004, 45, 7615−7625. (38) Hopcroft, M. A.; Nix, W. D.; Kenny, T. W. What is the Young’s Modulus of Silicon? J. Microelectromech. Syst. 2010, 19, 229−238. (39) Wang, Y.; Zhang, J.; Wu, J.; Coffer, J. L.; Lin, Z.; Sinogeikin, S. V.; Yang, W.; Zhao, Y. Phase Transition and Compressibility in Silicon Nanowires. Nano Lett. 2008, 8, 2891−2895. (40) Wortman, J. J.; Evans, R. A. Young’s Modulus, Shear Modulus, and Poisson’s Ratio in Silicon and Germanium. J. Appl. Phys. 1965, 36, 153−156. (41) Zhang, G. G.; Zhao, Y. P. Mechanical characteristics of nanoscale springs. J. Appl. Phys. 2004, 95, 267−271. (42) Marmur, A. A guide to the equilibrium contact angles maze. In Contact Angle, Wettability and Adhesion; Mittal, K. L., Ed.; VSP: Boston, 2009; Vol. 6, pp 3−18. (43) Drelich, J.; Chibowski, E. Superhydrophilic and Superwetting Surfaces: Definition and Mechanisms of Control. Langmuir 2010, 26, 18621−18623. (44) McHale, G.; Herbertson, D. L.; Elliott, S. J.; Shirtcliffe, N. J.; Newton, M. I. Electrowetting of Nonwetting Liquids and Liquid Marbles. Langmuir 2006, 23, 918−924.

(45) Roach, P.; Shirtcliffe, N. J.; Newton, M. I. Progess in superhydrophobic surface development. Soft Matter 2008, 4, 224−240. (46) A drop which contacts a surface experiences spreading and vibration. Since our time scale is minutes, and the spreading and vibration takes fractions of a second, the latter time scale is negligible. (47) Tadmor, R.; Janik, J.; Klein, J.; Fetters, L. J. Sliding Friction with Polymer Brushes. Phys. Rev. Lett. 2003, 91, 115503. (48) Bormashenko, E.; Stein, T.; Whyman, G.; Bormashenko, Y.; Pogreb, R. Wetting Properties of the Multiscaled Nanostructured Polymer and Metallic Superhydrophobic Surfaces. Langmuir 2006, 22, 9982−9985. (49) Jung, Y. C.; Bhushan, B. Wetting transition of water droplets on superhydrophobic patterned surfaces. Scr. Mater. 2007, 57, 1057− 1060. See also: Hejazi, V.; Nosonovsky, M. Wetting Transitions in Two-, Three-, and Four-Phase Systems. Langmuir 2012, 28, 2173− 2180. (50) McHale, G.; Aqil, S.; Shirtcliffe, N. J.; Newton, M. I.; Erbil, H. Y. Analysis of Droplet Evaporation on a Superhydrophobic Surface. Langmuir 2005, 21, 11053−11060. (51) Reyssat, M.; Yeomans, J. M.; Quéré, D. Impalement of fakir drops. Europhys. Lett. 2008, 81, 26006. (52) By weak adhesive contact, we compare the values in Figure 4 (3.6−38 mN/m) with those of other water systems (typically 5−45.5 mN/m). For calculation of solid surface energy, see Mazzola, L.; Bemporad, E.; Carassiti, F. An easy way to measure surface free energy by drop shape analysis. Measurement 2012, 45, 317−324. And also, Chibowski, E.; Terpilowski, K. Surface free energy of sulfur−Revisited I. Yellow and orange samples solidified against glass surface. J. Colloid Interface Sci. 2008, 319, 505−513. And: Terpilowski, K.; Holysz, L.; Chibowski, E. Surface free energy of sulfur−Revisited II. Samples solidified against different solid surfaces. J. Colloid Interface Sci. 2008, 319, 514−519. (53) The horizontality or lack of tilt of the surface is estimated to be within ± 0.01°. (54) Drelich, J.; Miller, J. D.; Good, R. J. The effect of drop (bubble) size on advancing and receding contact angles for heterogeneous and rough solid surfaces as observed with sessile-drop and captive-bubble techniques. J. Colloid Interface Sci. 1996, 179, 37−50. (55) An equilibrium contact angle of 180° corresponds to a smaller as-placed contact angle [ Tadmor, R.; Yadav, P. S. J. Colloid Interface Sci. 2008, 317, 241 ]. We show here that a three-phase contact line is associated with measurable adhesive contact even if the conditions for placing the drop on a surface cannot be reached (i.e., force-creating a line by submerging the surface). This suggests that when the conditions for placing the drop on a surface cannot be reached, the equilibrium contact angle may be 180°, in which case there is only a three-phase contact point rather than a line. Thus, the value of 180° is consistent with the situation of inability to reach the conditions for placing the drop on a surface. (56) Immersion and emersion were done at a constant rate of 1.11 mm/s. (57) One can ask, how can a three-phase contact line be created if the surface cannot be wetted? To answer this, note that although there would be no wetting of the solid surface by a drop placed on it, a contact can occur, as it would between any two surfaces that are brought close enough to each other. This contact is however not as adhesive. During immersion, the surface is in contact with the water. Such a contact can exist also with drops, but in that case it is instantaneous, whereas with immersion, it is continuous. With drops, this temporary contact results in a three-phase contact point or a region of contact which is close to a point. Conversely, upon immersion, the contact is over a wide area and for a long time, resulting in a three-phase contact line at its border. (58) Bormashenko, E.; Bormashenko, Y.; Stein, T.; Whyman, G.; Pogreb, R.; Barkay, Z. Environmental Scanning Electron Microscopy Study of the Fine Structure of the Triple Line and Cassie-Wenzel Wetting Transition for Sessile Drops Deposited on Rough Polymer Substrates. Langmuir 2007, 23, 4378−4382.

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dx.doi.org/10.1021/la3000153 | Langmuir 2012, 28, 5795−5801