Drop Impact on Soft Surfaces: Beyond the Static Contact Angles

Dec 7, 2009 - Superhydrophobicity and liquid repellency of solutions on polypropylene. R. Rioboo , B. Delattre , D. Duvivier , A. Vaillant , J. De Con...
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Drop Impact on Soft Surfaces: Beyond the Static Contact Angles Romain Rioboo,* Michel Voue, Helena Ad~ao, Josephine Conti, Alexandre Vaillant, David Seveno, and Jo€el De Coninck Laboratoire de Physique des Surfaces et des Interfaces, Universit e de Mons, Place du Parc, 20, 7000 Mons, Belgium Received September 30, 2009. Revised Manuscript Received November 18, 2009 The wettability of cross-linked poly(dimethylsiloxane) elastomer films and of octadecyltrichlorosilane self-assembled monolayers with water has been measured and compared using various methods. Contact angle hysteresis values were compared with values reported in the literature. A new method to characterize advancing, receding contact angles, and hysteresis using drop impact have been tested and compared with usual methods. It has been found that for the rigid surfaces the drop impact method is comparable with other methods but that for elastomer surfaces the hysteresis is function of the drop impact velocity which influences the extent of the deformation of the soft surface at the triple line.

Introduction The characterization of the wettability of a material almost inevitably requires the measurement of the contact angle (CA) that the liquid drop forms on top of the solid surface.1,2 We shall here differentiate static CA and dynamic CA by the fact that the three phrase contact line is moving (dynamic) or not (static) within the time span of the physical phenomena we are looking at. To validate the consistency of the measured angles, the first question that shall be answered concerns the physical and the chemical homogeneity of the surface. Provided that the surface is ideally homogeneous, the static CA is unique and reproducible. Beyond these static CA measurements, it is conventional to characterize the solid via γc, the critical surface tension of the surface. Methods have been proposed to calculate γc using a homologous series of liquids.3,4 The principle of those methods is simple, and they are helpful to determine the behavior of a liquid on a solid surface: if the surface tension of the liquid γ is higher than the critical surface tension of the solid surface γc, the liquid will form a drop on top of the solid surface. In the opposite case (γ < γc), the liquid will completely spread and will form a film on the solid. Most commonly, a homologous series of n-alkanes (with aliphatic chains from C6 to C16) is used. In practice, the interpretation of the results is not so simple because γc depends on the nature of the probe liquid and in particular on the polar and nonpolar components of the liquid surface tension.5 For nonideal surfaces, a hysteresis appears1,6-8 in the static CA. Johnson and Dettre6,9 proposed a method to determine this hysteresis: the sessile drop method. This method requires the advancing and the receding static CAs (θa and θr, respectively) to be measured. Practically, small amounts of liquid are injected *To whom correspondence should be addressed. [email protected]. (1) De Gennes, P. Rev. Mod. Phys. 1985, 57, 827–863. (2) Adamson, A. W. Physical chemistry of surfaces; John Wiley & Sons, Inc.: New York, 1990. (3) Good, R.; Girifalco, L. J. Phys. Chem. 1960, 64, 561–565. (4) Zisman, W. Adv. Chem. 1964, 43, 1–51. (5) Valignat, M.-P. Ph.D. Thesis, Universite de Paris XI Orsay, 1994. (6) Johnson, R. E.; Dettre, R. H. Adv. Chem. 1964, 43, 113–135. (7) Collet, P.; De Coninck, J.; Dunlop, F. Europhys. Lett. 1993, 22, 645–650. (8) Collet, P.; De Coninck, J.; Dunlop, F.; Regnard, A. Phys. Rev. Lett. 1997, 79, 3704–3707. (9) Johnson, R. E.; Dettre, R. H. In Wettability; Berg, J. C., Ed.; Marcel Dekker: New York, 1993; Chapter Wetting of Low-Energy Surfaces, pp 1-74.

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(or withdrawn) into (from) the sessile drop as slowly as possible to estimate these while the contact line is not moving. The experiment is therefore not carried out anymore at constant drop volume. The difference between θa and θr defines the static contact angle hysteresis (CAH). Each value of the CA between the advancing and the receding static CA is the consequence of a metastable state of the drop9 related to its experimental conditions. Repeated experiments on different locations of the solid surface provide a reliable measure of the wettability of the macroscopically apparently homogeneous surface. Alternative methods are available to determine the static CAH: for example, the Wilhelmy plate method,9 the flattening of a drop in between two plates,10 the tilting plate method,11,12 or the capillary bridge technique.13 Nevertheless, the latter requires transparent films to be coated on a transparent spherical surface, typically a watch glass. In parallel with these classical wettability methods, a new trend in wettability concerns the impact of drops on solid surfaces and recent studies14-17 showed the importance of the surface energy on drop impact phenomenon. It appears to be rather complex,18,19 and many parameters beside the liquid characteristics (density, surface tension, and viscosity) influence its outcomes. In the case of an impact on flat, macroscopically homogeneous solid dry surfaces, the results are strongly dependent on solid-related parameters. As a function of the wettability of the material, deposition or impact over its surface will result in different outcomes and break-up processes.20-22 Nonwettable materials show the (10) De Jonghe, V. Ph.D. Thesis, Institut National Polytechnique de Grenoble, France, 1993. (11) Extrand, C. W.; Kumagai, Y. J. Colloid Interface Sci. 1996, 184, 191–200. (12) Extrand, C. W.; Kumagai, Y. J. Colloid Interface Sci. 1997, 191, 378–383. (13) Restagno, F.; Poulard, C.; Cohen, C.; Vagharchakian, L.; Leger, L. Langmuir 2009, 25, 11188–11196. (14) Fukai, J.; Shiiba, Y.; Yamamoto, T.; Miyatake, O.; Poulikakos, D.; Megaridis, C. M.; Zhao, Z. Phys. Fluids 1995, 7, 236–247. (15) Mao, T.; Kuhn, D. C. S.; Tran, H. AIChE J. 1997, 43, 2169–2179. (16) Richard, D.; Quere, D. Europhys. Lett. 2000, 50, 769–775. (17) Rioboo, R. Ph.D. Thesis, Universite Pierre et Marie Curie (Paris VI), France, 2001. (18) Rein, M. Fluid Dyn. Res. 1993, 12, 61–93. (19) Yarin, A. L. Annu. Rev. Fluid Mech. 2006, 38, 159–192. (20) Rioboo, R.; Tropea, C.; Marengo, M. Atomization Sprays 2001, 11, 155– 165. (21) Mock, U.; Michel, T.; Tropea, C.; Roisman, I.; Ruhe, J. J. Phys.: Condens. Matter 2005, 17, S595–S605. (22) Rioboo, R.; Adao, M. H.; Voue, M.; De Coninck, J. J. Mater. Sci. 2006, 41, 5068–5080.

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possibility of a receding phase,14,15 with and without rebounds.16,20 The dynamics of the receding have already been studied either experimentally,17,23,24 theoretically,25 or numerically using molecular dynamics26 or computational fluid dynamics.14 It appeared to be of primary importance to the rebound process. In most drop impact studies, the importance of the characterization of the wettability of the system liquid/solid/gas14 and of the solid surface roughness27 is generally well admitted. In this Article, we combine drop impact phenomena with CAH determination to show that the CAH of, at least, low wettability materials can also be measured using the dynamics of impinging drops. The results of this new method are compared with those of the sessile drop and the Wilhelmy plate methods. To that purpose, we considered two types of hydrophobic model surfaces: octadecyltrichlorosilane (OTS) self-assembled monolayers and cured poly(dimethylsiloxane) (PDMS) surfaces. Their wettability was probed against water. As described hereafter, the comparison puts in evidence differences between the methods for the deformable material only. The wettability of these surfaces has been intensively studied, and numerous studies report values for advancing and receding static CAs as well as for CA hysteresis. OTS-grafted silicon wafers show low hysteresis: the advancing static CA of water drops is in the range 110°-114°, and the receding static CA is between 100° and 112°.28-32 Reported values of the CAH are between 2° and 10°. Cured PDMS is a material widely used for its deformability and its electrical insulation and hydrophobicity properties. Various studies have quantified the deformability of PDMS measuring its Young’s modulus. Fuard and co-workers showed that the Young’s modulus is a function of the amount of cross-linker used in the mixture resin/cross-linker.33 Several publications have shown that the Young’s modulus of PDMS is a function of the thickness of the film used.34,35 In all cases, the Young’s modulus of PDMS presented in the literature varies between 0.012 and 7.7 MPa, proof of the high deformability of this material. Many studies also report its wettability with water either with the sessile drop method or with the Wilhelmy plate method. Using the Wilhelmy plate method, Uilk and co-workers36 showed the complexity of the wetting behavior of this material: the static CAs are different when the interaction of water with the polymer network induces conformational changes of the polymer chains at (23) Rioboo, R.; Marengo, M.; Tropea, C. Exp. Fluids 2002, 33, 112–124. (24) Sikalo, S.; Wilhelm, H. D.; Roisman, I. V.; Jakirlic, S.; Tropea, C. Phys. Fluids 2005, 17, 062103. (25) Roisman, I. V.; Rioboo, R.; Tropea, C. Proc. R. Soc. London, Ser. A 2002, 458, 1411–1430. (26) Gentner, F.; Rioboo, R.; Baland, J. P.; De Coninck, J. Langmuir 2004, 20, 4748–4755. (27) Stow, C. D.; Hadfield, M. G. Proc. R. Soc. London, Ser. A 1981, 373, 419– 441. (28) Wasserman, S. R.; Tao, Y. T.; Whitesides, G. M. Langmuir 1989, 5, 1074– 1087. (29) Tidswell, I. M.; Rebedeau, T. A.; Pershan, P. S.; Kosowsky, S. D.; Folkers, J. P.; Whitesides, G. M. J. Chem. Phys. 1991, 95, 2854–2861. (30) Parikh, A. N.; Allara, D. L.; Azouz, I. B.; Rondelez, F. J. Phys. Chem. 1994, 98, 7577–7590. (31) Peters, R. D.; Nealey, P. F.; Crain, J. N.; Himpsel, F. J. Langmuir 2002, 18, 1250–1256. (32) Voue, M.; Rioboo, R.; Bauthier, C.; Conti, J.; Charlot, M.; De Coninck, J. J. Eur. Ceram. Soc. 2003, 23, 2769–2775. (33) Fuard, D.; Tzvetkova-Chevolleau, T.; Decossas, S.; Tracqui, P.; Schiavone, P. Microelectron. Eng. 2008, 85, 1289–1293. (34) Liu, M.; Sun, J.; Sun, Y.; Bock, C.; Chen, Q. J. Micromech. Microeng. 2009, 19, 035028. (35) Thangawng, A.; Ruoff, R.; Swartz, M.; Glucksberg, M. Biomed. Microdevices 2007, 9, 587–595. (36) Uilk, J. M.; Mera, A. E.; Fox, R. B.; Wynne, K. J. Macromolecules 2003, 36, 3689–3694. (37) She, H.; Chaudury, M. K.; Owen, M. J. In Silicones and Silicone-Modified Materials; Clarson, S. J., Fitzgerald, J. J., Owen, M. J., Smith, S. D., Eds.; American Chemical Society: Washington, DC, 2000; Vol. 729.

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the interface or not.37 Advancing static CAs of 118° for the first cycle and 108° for the following ones were measured. In the same way, receding static CAs were 83° or 87°. Using the sessile drop method, various authors have reported advancing CAs values in the range 105°-118° and receding ones between 75° and 111°.32,37-41 The hysteresis associated with these measurements is between 2° and 38°. Moreover, the dynamic wetting properties of such elastomer surfaces are also made more complex by the deformation of the solid material in the region of the contact line.32,42,43 On soft substrates, the normal component of the liquid surface tension deforms the substrate near the triple line. As the contact line moves, the deformation also moves, thus dissipating energy. For a given driving force, contact line displacement occurs at a speed lower than the one measured on a nondeformable surface of similar surface free energy and roughness. This phenomenon is known as the “viscoelastic braking”. It has been evidenced by Carre and Shanahan,44 and it affects the spontaneous spreading as well as the forced wetting.45 Viscoelastic braking is also a supplementary source of hysteresis.46 The elasticity of the solid surface not only influences the spreading of the drop42 but also significantly influences the outcome of the impact phenomenon as shown by our recent study.47

Materials and Methods Chemicals. Unless otherwise stated, all chemicals and solvents are of analytical grade and were used as purchased, without further purification. Water used for the wettability and drop impact experiments was 18.2 MΩ resistivity Milli-Q water. Substrate Preparation. Elastomer Substrates and Films. The elastomer substrates and films were prepared from SL 6600 silicon resin (General Electrics), which contains PDMS mixed with platinum (80 ppm) as catalyst, according to the manufacturer specifications. The PDMS is vinyl-terminated at both ends, and the following physical characteristics are provided by the manufacturer: viscosity η = 225 mPa s at 25 °C, surface tension γ = 22 mN/m, and density d = 0.97. The elastomer was prepared by mixing the resin and a cross-linker (SI 4330C, 2.5% w/w). The cross-linking process occurs by hydrosilylation reaction in the presence of hexane. To obtain the samples referred to as the “bulk elastomer”, no extra solvent was added. The mixture was poured in a Petri dish to obtain a 3 mm thick layer and baked in the oven for 5 min at 120 °C in view of obtaining a 100% crosslinked elastomer. To obtain substrate-supported elastomer films, either standard glass microscope slides (75 mm  25 mm) or glass cover slides (60 mm  24 mm), cleaned in piranha solution,48,49 were coated with a solution of resin/cross-linker containing from 0% to 99% hexane. The coating experiments were carried out using a WS 400A-6NPP/Lite spin-coater (Laurell Tech. Corp.). The thickness of the films was determined by spectroscopic ellipsometry in the visible or infrared range, after curing of the samples. OTS Surfaces. The OTS self-assembled monolayers on glass were prepared by cleaning microscope slides in piranha solution (38) Chaudhury, M. K.; Whitesides, G. M. Langmuir 1991, 7, 1013–1025. (39) Perutz, S.; Kramer, E. J.; Baney, J.; Hui, C. Y. Macromolecules 1997, 30, 7964–7969. (40) Hillborg, H.; Sandelin, M.; Gedde, U. W. Polymer 2001, 42, 7349–7362. (41) Olander, B.; Wirsen, A.; Albertsson, A. C. Biomacromolecules 2002, 3, 505– 510. (42) Carre, A.; Gastel, J. C.; Shanahan, M. E. R. Nature 1996, 379, 432–434. (43) Shanahan, M. E. R.; Carre, A. Colloids Surf., A 2002, 206, 115–123. (44) Carre, A.; Shanahan, M. C. R. Acad. Sci. Paris 1993, 317(2), 1153–1158. (45) Shanahan, M. E. R.; Carre, A. C. R. Acad. Sci. Paris 2000, 1(4), 263–268. (46) Shanahan, M. E. R. C. R. Acad. Sci. Paris 1988, 306(2), 113–116. (47) Voue, M.; Rioboo, R.; Adao, M. H.; Conti, J.; Bondar, A. I.; Ivanov, D. A.; Blake, T. D.; De Coninck, J. Langmuir 2007, 23, 4695–4699. (48) Voue, M.; Semal, S.; De Coninck, J. Langmuir 1999, 15, 7855–7862. (49) Semal, S.; Voue, M.; de Ruijter, M. J.; Dehuit, J.; De Coninck, J. J. Phys. Chem. B 1999, 103, 4854–4861.

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Figure 1. Different stages of drop impact (see text for description). during 8 min before immersing them during 12 h in an OTS solution (0.08%) in a CCl4/C16H34 mixture (7:3 v/v ratio) at 6 °C (relative humidity < 8%). Grafted surfaces were rinsed in CCl4 and kept in that solvent for further use. Spectroscopic Ellipsometry. Spectroscopic ellipsometry was performed to determine film thicknesses. Experimental Setup. The ellipsometric experiments were carried out with a Sopra GESP5 rotating polarizer instrument operating in the visible and near-infrared spectral ranges. The ellipsometric angles Ψ and Δ were measured in the range 350-850 nm, eventually 550-1650 nm for the thickest samples, with a spectral resolution of 10 nm. The polarizer was rotated at 9 Hz. Measurements were carried out at 70° of incidence in a parallel beam configuration (lateral resolution: 4 mm). Very thick samples (>20 μm) were measured in the mid-infrared spectral domain using a GES-FTIR ellipsometer (SOPRA, France). In this case, the wavenumber range covered by the instrument was 600-6000 cm-1 and the spectral resolution was 2 cm-1.50 Optical Modeling. The optical properties and thickness of the elastomer layers were determined by fitting simultaneously the thickness of the polymer layer and the parameters of a Cauchytype dispersion law for the real and imaginary parts of the refraction index n and k.51 Due to the possible thickness inhomogeneity of the spin-coated polymer film, a roughness layer could be included in the optical model using a Bruggeman effective media approximation.52

Contact Angle Measurements.

High-Speed Imaging.

For drop impact experiments, high-speed imaging was performed using a high-speed high-resolution C-MOS motion camera (HCC-1000, Vossk€ uhler GmbH, Germany). A high-speed stroboscope and electronic delayer helped to provide sharp images at 923 images per second (resolution: 1024  512 pixels, depth: 8 bits). A syringe pump and Hamilton needles of various diameters were used to deliver drops on demand. The drop impact velocity and the size of the drop were modified by changing the height of the fall of the drop and the diameter of the needles used. To improve reproducibility in drop size, the tips of the needles were waxed. The image sequences recorded at high speed were analyzed to (50) Pickering, C.; Leong, W. Y.; Glasper, J. L.; Boher, P.; Piel, J.-P. Mater. Sci. Eng., B 2002, B89, 146–150. (51) Tompkins, H. G.; McGahan, W. A. Spectroscopic Ellipsometry and Reflectometry; John Wiley & Sons, Inc.: New York, 1999. (52) Aspnes, D.; Theeten, J. Phys. Rev. B 1979, 20, 3292–3302. (53) Vega, M. J.; Seveno, D.; Lemaur, G.; Adao, M. H.; De Coninck, J. Langmuir 2005, 21, 9584–9590.

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obtain the profile of the drop, the static and dynamic CAs, and the spreading diameter.53 Contact Angle Hysteresis. Hysteresis measurements using the sessile drop method9 were performed with a Kr€ uss DSA100 system (frame rate: 25 images/s) with a typical liquid injection rate of 15 μL/min. The drop volume was varied from 5 to 15 μL. Wilhelmy Plate Technique. Advancing and receding dynamic CAs of water were determined tensiometrically with a claimed precision of 0.1°, using a KSV-3000 balance. The glass samples were dipped and withdrawn through the air-water interface at various speeds (from 0.1 to 40 mm/min). The contact angle θ was calculated from the force F acting on the solid substrate according to F = W þ γp cos θ - FA, where W is the weight of the sample in air, γ is the liquid surface tension, p is the perimeter of the sample, and FA is the buoyancy force. One complete cycle (dipping and withdrawal of the sample) allowed a hysteresis loop to be determined and static CAs to be extrapolated.54

Results and Discussion Two types of hydrophobic surfaces are studied in the present paper: OTS-grafted glass surfaces which can be considered as rigid surfaces and several cross-linked PDMS-coated glass slides which are elastomer or “soft” surfaces. The thickness of PDMS layers was varied from sub-micrometer thickness (50 nm) to millimeter thickness (3 mm). The critical surface tension γc of those solid surfaces was determined according to the Zisman method,4 using a series of alkanes. For the OTS surface, the critical surface tension was 20.0 ( 1.2 mN/m, attesting to the compact CH3 nature of the surface functional groups. The critical surface tension of the elastomer surfaces determined by the same method was slightly higher: 21.8 ( 0.2 mN/m.32 The rms roughness of the PDMScoated surfaces measured by optical profilometry was of 5.1 ( 3.5 nm (image size: 450 μm  600 μm). Typically, OTS-grafted on glass surfaces present even lower roughness. Such a low value of the roughness indicates that the origin of the hysteresis of the static CA is not coming from the physical heterogeneity of the surface.1 Water drop impact experiments were performed over the OTS and the cured PDMS samples. Let us consider impact conditions (54) Semal, S.; Blake, T.; Geskin, V.; de Ruijter, M.; Castelein, G.; De Coninck, J. Langmuir 1999, 15, 8765–8770.

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Figure 2. Spreading diameter (left axis, plain line) and contact angle θ (right axis, dashed line) as a function of time (single headed arrow: time at which the contact line is not moving anymore; double headed arrow: CA hysteresis).

such that no splash (either prompt or corona splashes or receding breakup20) occurs. The evolution of the morphology of the drop during its impact is illustrated by an example of sequence of snapshots presented in Figure 1. Figure 2 illustrates this example of dynamic contact angle and spreading diameter versus time after the impact of a water drop on an OTS surface (D = 3.08 mm; V = 0.74 ( 0.02 m/s). The classical different stages of the drop impact on a hydrophobic surface15,23 appear in this sequence and are labeled (a) to (h). In this sequence, inertia is high enough to produce a partial rebound but low enough to prevent other kinds of splashes or breaking. Let us consider them one after each other: (i) A lamella is formed, and the initial spreading is dominated by the inertia of the drop (Figure 1a, t ≈ 2 ( 1 ms); (ii) At the maximum spreading radius, the drop has a discotic shape with a rim at its border (Figure 1b, t ≈ 6 ( 1 ms);23,25 (iii) After the receding stage (Figure 1c, t ≈ 11 ( 1 ms), the drop presents a partial rebound20 due to the relatively high inertia in the receding motion (Figure 1d, t ≈ 34 ( 1 ms). (iv) Following this partial rebound and the ejection of a secondary drop, the latter merges with the primary one (Figure 1e, t ≈ 52 ( 1 ms); (v) In Figure 1f (t ≈ 77 ( 1 ms) and g (t ≈ 115 ( 1 ms), the drop exhibits oscillations due to inertia while the contact line is still moving; (vi) Finally, the drop still oscillates, but its contact line is pinned within the limit of the optical resolution of the system, typically 10-15 μm/pixel (Figure 1h, t = 191 ( 1 ms). Generally, depending on the initial inertia of the drop and the wettability characteristics (advancing and receding static contact angles) of the surface, the diameter of the spreading liquid is oscillating between two asymptotic so-called “equilibrium” diameters associated with the advancing and receding static CAs.20,23 As the contact line moves backward and forward, the dynamic CAs are also changing. Because water was used as a probe liquid, the period of the oscillations was short due to low viscosity (μ = 0.001 Pa s), as illustrated in Figure 2. The period is =15 ms, a value consistent with the typical free oscillation time scale of a drop, considering its apex height instead of the free drop diameter.55 (55) Schiaffino, S.; Sonin, A. A. Phys. Fluids 1997, 9, 3172–3187.

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Figure 3. Advancing (red) and receding (green) static contact angles using various analysis methods ((A) OTS-grafted glass surfaces, (B) PDMS surfaces). Data ranges from literature are represented by the black bars at the right of the graph ((a) advancing static CA, (b) receding static CA). For OTS, they concern OTS-grafted silicon wafers. Abscissas values are velocities relative either to the plunging velocity (Wilhelmy plate method, in mm/min) or to the impact velocity of the water drop (impact method, in m/s, drop diameter: 3.08 ( 0.03 mm).

It is clearly seen that the oscillations affecting both the spreading diameter and the dynamic CA are damped. The oscillations’ amplitude of the spreading diameter reaches a null value earlier than the ones affecting the dynamic CA. It is important to notice that, at this moment, the liquid inside the drop is not at rest and that the drop is still oscillating by its CAs which are oscillating around a final value, θfin. The range of values taken by the oscillating static CAs (because the contact line is at rest) is a lower bound for the static CAH. In this typical example of Figure 2, the time at which the contact line is not moving anymore is =160 ms ( 1 ms. From this time on, we determined the maximum and the minimum angles reached by the system for all cases studied. According to this experimental scheme, the advancing (respectively, the receding) static CA during the drop impact experiment is conceptually a priori comparable to other methods that measure static CAs. The difference between the maximum and minimum CAs reached while the contact line is at rest is conceptually equivalent to the static CAH. We will investigate the effect of the impact velocity on such quantitative parameters for both the elastomer surfaces and the reference OTS surfaces. Drop impact experiments were carried out on OTS surfaces at different impact velocities. Relatively low CAH ( 0.3 m/s, the linear regression (using both errors in V and in CAH as weighting factors56) shows a slope significantly different from zero. The coefficients of the straight line CAH = a þ bV are a = 10.7 ( 8.5 and b = 13.3 ( 6.2 (χ2 = 0.437 and reduced χ2 = 0.146). Only impacting the drop instead of depositing it to the surface will allow the triggering of the vibrational modes of the (56) Press, W.; Teutlosky, S.; Vetterling, W.; Flannery, B. Numerical Recipes in FORTRAN. The Art of Scientific Computing, 2nd ed.; Cambridge University Press: Cambridge, 1992.

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Figure 6. Influence of the immersion cycle on the Wilhelmy plate experiment results for a PDMS surface (immersion speed: 10 mm/min, cycle 1: plain line, cycles 4 and 5: dashed lines).

Figure 7. Contact angles and hysteresis taken from drop impact experiments on cross-linked PDMS surfaces: influence of impact velocity (filled circles: advancing CA, open circles: receding CA, open triangles: CA hysteresis). Dashed line: linear weighted fit of the hysteresis data for impact velocity > 0.3 m/s (see text for explanation).

drop. Biance et al.57 help us to determine which is the minimum velocity necessary to take into account the impact pressure effects against capillary effects that are encountered in the oscillation of the drop. They estimated by dimensional analysis arguments the maximum impact velocity where surface energy is transformed in kinetic energy without domination of impact pressure effects. Calculating this velocity for our case finds a value of 0.21 m/s. This allows us to not take into account the deposition cases in Figure 7 with too low impact velocities (below 0.3 m/s). A possible description of the event is the following. As the drop impacts at t = 0, the impact pressure deforms in flattening the drop and presumably triggers all the modes of vibration of the drop. The time at which the contact line is not moving anymore is obviously a function of the impact velocity. For both cases, OTS and elastomer surfaces, it grows linearly from approximately 40 ms for the 0.3 m/s impact velocity cases up to 90 ms for the 2 m/s impact velocity cases. We can assume that the static CAH taken from drop impact is function of the exact shape of the drop while oscillating. Various authors have reported on oscillations of free55 or sessile drops.58,59 While these works present studies on forced oscillations by acoustic generators, free oscillations equations are provided and tested on our data. Figure 8 compares observed experimental oscillations periods texp for various impact speeds on OTS and PDMS surfaces while the contact line is pinned with theoretical oscillations periods ttheor obtained from (57) Biance, A.-L.; Clanet, C.; Quere, D. Phys. Rev. E 2004, 69, 016301. (58) Noblin, X.; Buguin, A.; Brochard-Wyart, F. Eur. Phys. J. E 2004, 14, 395– 404. (59) McHale, G.; Elliott, S. J.; Newton, M. I.; Herbertson, D. L.; Esmer, K. Langmuir 2009, 25, 529–533.

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Figure 8. Theoretical oscillation times versus experimental ones for impact of drops on OTS-grafted and PDMS-coated surfaces at various impact velocities from 0.31 to 2.03 m/s (filled symbols: OTS surfaces; open symbols: PDMS surfaces). Theoretical times calculated according to the theories of Schiaffino and Sonin55 (squares), of Noblin et al.58 (triangles), and of McHale et al.59 (circles). Dashed lines: (10% error band on the theoretical value.

the three models proposed by Schiaffino and Sonin,55 Noblin et al.,58 and more recently by McHale et al.59 The model of Schiaffino and Sonin55 concerns the free oscillation time of a drop, and it is based on dimensional analysis considering inertia and surface tension effects. We adapted eq 3 in ref 55 in such a way that the characteristic geometrical dimension is not the spherical diameter D of the free oscillating drop anymore but its apex h while standing over a surface in a sessile position:

ttheor;SS

sffiffiffiffiffiffiffi Fh3 ¼ γ

ð1Þ

where γ is the surface tension of the liquid and F is its density. Both models of Noblin et al.58 and of McHale et al.59 consider acoustically excited vibrating drops. From those two models, we only retained the fundamental mode of oscillation, as suggested from our experimental observation: rapidly, the oscillations are leaving only two nodes observed. The period of this mode is given by simple algebraic modifications of eq 34 in ref 58 (ttheor,N) and of eq 46 in ref 59 (ttheor,MH): " ttheor;N ¼

# -1=2  γ 3 gq þ q tanhðqhÞ F

ð2Þ

where q = (3/2)(π/p) and p is the length of the air-liquid interface in the apex plane. "

ttheor;MH

4p3 F ¼ 27πγ

#1=2 ð3Þ

In these equations, γ and F have their usual meaning. In Figure 8, three lines are presented to guide the eye: the perfect match between the experimental and the theoretical values (plain line) and the dashed lines corresponding to an overestimation and to an underestimation of the theoretical values by 10%. The experimental values show little influence of impact velocity but a clear influence of the deformability of the solid material as elastomer surfaces present significantly lower periods of oscillation than OTS surfaces. All three models are relatively well fitting PDMS data, but they are systematically underestimating the oscillations periods for OTS surfaces. This unexpected result Langmuir 2010, 26(7), 4873–4879

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Figure 9. Possible mechanism of influence of the impact velocity on the static CAH during drop impact on elastomer surfaces. Oscillations around a final angle θfin from minimum receding angle (top), θr, to maximum advancing angle (bottom), θa, are occurring after the final diameter is reach for two different velocities (high velocity: left; low velocity: right).

shows that none of these models are adapted to an impact situation. Moreover, it is also important to notice that they are not aimed at and cannot predict the exact shape of the drop or the static CAH of an impacting drop. Shanahan46 predicted that viscoelastic braking was a supplementary source of static CAH, but no quantification was provided. Simple arguments based on minimization of the Helmholtz free energy of the system could explain the discrepancy between OTS-grafted surfaces and PDMS-coated surfaces. The Helmholtz free energy of the system F = Σi(-PV) þ Σi(nμ) þ Σj(γΩ) tends to reach a minimum in a situation of constant temperature and volume.6 The subscripts i and j, respectively, run over all the phases and the interphases. However, in the case of PDMS, the material is elastic around the contact line. A deformation term taking into account the stress and strain tensors (1/2Vsdσijεij) has to be added to the mechanical terms.60 In this additional term, Vsd defines the volume of the deformed solid elastomer and σij and εij are, respectively, the stress and strain tensor elements summed over the deformed zone. From the results presented in Figure 5, we can assume that the thickness of the deformed zone shall not be above 50 nm. The stress tensor is derived from the pressure (60) Landau, L. D.; Lifshitz, E. M. Theory of Elasticity; Butterworth Heinemann: Boston, 1986.

Langmuir 2010, 26(7), 4873–4879

Article

fluctuations induced by the moving liquid inside the drop and the vertical component of the surface tension at the contact line over the solid. These are difficult to determine, and this goal is beyond the scope of the present article, but it shows us that the volume of the deformed solid might influence the extent of the hysteresis. In order to provide a possible physical explanation of what is happening during drop impact over elastomer surfaces, let us summarize the last results: Figure 7 shows that for any given impact velocity the static CAH is higher for deformable surfaces than hard surfaces; Figure 8 shows that, independently of the impact velocity, drops with a pinned contact line oscillate faster on deformable surfaces than on hard ones; the Helmholtz free energy for elastomer surfaces present an additional source of minimization as a function of the solid deformability; and increasing the volume of the deformed part of the elastomer decreases the possibility of movement of the contact line over it, that is, enhances pinning. Figure 9 presents a possible mechanism to induce an influence of the impact velocity over the static CAH during a drop impact. It suggests that the volume and/or the deformation of the elastomer near the contact line region are larger for higher drop impact velocities. This can be explained by the fact that with high impact velocities the shear induced by the impact pressure during the spreading deforms the elastomer soft material. From the present results, it is expectable that the intensity of the deformation is increasing with the impact velocity. Further investigation, theoretical and experimental, is needed to understand in detail this effect and quantify it.

Conclusions Experimental investigation over two types of hydrophobic surfaces presenting a priori similar wettability characteristics has shown that differences could be highlighted using drop impact experiments. Moreover, it has been demonstrated that this technique could be used to measure in a single experiment the advancing and receding static contact angles and provide a reliable measure of the hysteresis and, more generally, of the wettability of a solid surface. This method allowed us to determine that the static contact angle hysteresis on soft or deformable surfaces was a function of the impact velocity: above a threshold value, the higher the impact velocity the higher the hysteresis. A possible mechanism for this phenomenon was provided. Acknowledgment. This work is partially funded by the Ministere de la Region Wallonne, the European Community, and the Fonds National de la Recherche Scientifique (FNRS) of Belgium.

DOI: 10.1021/la9036953

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