Langmuir 2009, 25, 1893-1896
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Shape, Vibrations, and Effective Surface Tension of Water Marbles Edward Bormashenko,* Roman Pogreb, Gene Whyman, Albina Musin, and Yelena Bormashenko Ariel UniVersity Center of Samaria, The Research Institute, Ariel 40700, Israel
Zahava Barkay Wolfson Applied Materials Research Center, Tel AViV UniVersity, Ramat-AViV 69978, Israel ReceiVed August 31, 2008. ReVised Manuscript ReceiVed January 4, 2009 The surface of water “marbles” obtained with hydrophobic lycopodium and polyvinylidene fluoride particles was investigated first with environmental scanning electron microscopy. The shape of water marbles was studied both experimentally and theoretically. The mathematical model describing the deformation of marbles by gravity is proposed. The model allowed the calculation of the effective surface tension of marbles and gives 0.09 J/m2 for marbles coated with PVDF and 0.06 J/m2 for marbles coated with lycopodium. The effective surface tensions of marbles calculated independently by the horizontal vibration of marbles were in semiquantitative agreement with the above values (0.07 J/m2 for marbles coated with PVDF and 0.055 J/m2 for marbles coated with lycopodium).
1. Introduction Nonstick liquid/solid interfaces attracted significant attention from investigators because of their technological and scientific importance.1-18 There exist two main approaches for manufacturing nonstick surfaces. The first one is a biomimetic approach mimicking the hierarchical roughness of lotus leaves.1-12 Biomimetic artificial surfaces supply pronounced water repellency to solid surfaces. The second, more recent approach supplies liquid droplets with nonstick properties.1,13-18 This approach exploits the modification of the liquid interface with hydrophobic colloidal particles. These particles absorbed on the liquid/air interface lead to the formation of liquid “marbles” (i.e., liquid drops wrapped with micro- or nanoparticles of low surface energy).13-18 Plenty of work has already been devoted to understanding the water repellency of lotuslike nonstick surfaces, and much understanding has already been achieved in this field, * Corresponding author. E-mail:
[email protected]. (1) de Gennes, P. G.; Brochard-Wyart, F.; Que´re´, D. Capillarity and Wetting Phenomena; Springer: Berlin, 2003. (2) Erbil, H. Y. Surface Chemistry of Solid and Liquid Interfaces; Blackwell Publishing: Oxford, U.K., 2006. (3) Barthlott, W.; Neinhuis, C. Planta 1997, 202, 1–8. (4) Shibuichi, A.; Onda, T.; Satoh, N.; Tsujii, K. J. Phys. Chem. 1996, 100, 19512–19517. (5) Que´re´, D. Rep. Prog. Phys. 2005, 68, 2495–2532. (6) Que´re´, D.; Reyssat, M. Philos. Trans. R. Soc. London, Ser. A 2008, 366, 1539–1556. (7) Nosonovsky, M.; Bhushan, B. AdV. Funct. Mater. 2008, 18, 843–855. (8) Nosonovsky, M.; Bhushan, B. J. Phys.: Condens. Matter 2008, 20, 225009. (9) Roach, P.; Shirtcliffe, N. J.; Newton, M. I. Soft Matter 2008, 2, 224–240. (10) Bormashenko, E.; Stein, T.; Whyman, G.; Bormashenko, Y.; Pogreb, R. Langmuir 2006, 22, 9982–9985. (11) Bormashenko, E.; Bormashenko, Y.; Stein, T.; Whyman, G.; Bormashenko, E. J. Colloid Interface Sci. 2007, 311, 212–216. (12) Patankar, N. A. Langmuir 2004, 20, 7097–7102. (13) Aussillous, P.; Que´re´, D. Nature 2001, 411, 924–927. (14) Mahadevan, L. Nature 2001, 411, 895–896. (15) Bhosale, P. S.; Panchagnula, M. V.; Stretz, H. A. Appl. Phys. Lett. 2008, 93, 034109. (16) Larmour, I. A.; Saunders, G. C.; Bell, S. E. J. Angew. Chem., Int. Ed. 2008, 47, 5043–5045. (17) Aussillous, P.; Que´re´, D. Proc. R. Soc. London, Ser. A 2006, 462, 973– 999. (18) Amarouchene, Y.; Cristobal, G.; Kellay, H. Phys. ReV. Lett. 2001, 87, 206104.
whereas the physics and chemistry of liquid marbles are less understood. This motivated our research.
2. Experimental Section 2.1. Materials. To manufacture marbles, we used polyvinylidene fluoride (PVDF) nanobeads supplied by Aldrich with a molecular weight of Mw ) 534 000 and a density of 1.74 g/cm3; lycopodium was supplied by Fluka. The average diameter of PVDF particles was established as 130 nm with SEM imaging. Marbles manufactured with the use of superhydrophobic surfaces described below were deposited afterwards on extruded polyethylene (PE) and polypropylene (PP) substrates. 2.2. Manufacturing of Superhydrophobic Surfaces. Marbles were prepared with use of superhydrophobic surfaces produced in a way similar to that previously reported.10 Polytetrafluoroethylene (PTFE) 100-200 nm powder was spread on a polymethyl methacrylate (PMMA) substrate and pressed with a rifled stamp. The PMMA substrate had been softened by heating and trapped PTFE particles (which remained solid under the pressing temperature). Hot pressing has been carried out at t ) 95 °C. 2.3. Preparing Marbles. Drops of 5-200 µL were deposited with a precise microdosing syringe onto the superhydrophobic surface described in section 2.2 and covered with a layer of PVDF beads. A slight tilting of the superhydrophobic surface caused the drop to roll, and it was coated with PVDF beads or lycopodium. Afterwards, marbles were rolled onto PE and PP substrates (Figure 1). 2.4. Environmental Scanning Electron Microscope Study of the Marble Surface. An environmental scanning electron microscope (ESEM) study of marbles was carried out with Quanta 200 FEG (field emission gun) ESEM. Prior to the ESEM pump-down process, a liquid marble of 10 µL volume was carefully deposited on top of a PP film precooled on a Peltier stage to 2 °C. After the pump down, the pressure in the sample chamber was stabilized to just about the dew point. In addition, prior to the pump-down process, a few droplets of water were added to regions around the stage held at room temperature, which minimized the possibility of fluctuations and evaporation of the studied marble during the ESEM pump-down sequence. The marble surface was imaged with a GSED (gaseous secondary electron detector) in the ESEM wet mode under a pressure of 5.4 Torr and a temperature of 2 °C, which guaranteed stability during the experiment in the ESEM. While venting the chamber at the end of the ESEM experiment, in one case, the nonstick droplet rolled toward the edge of the stage, remaining there until full venting.
10.1021/la8028484 CCC: $40.75 2009 American Chemical Society Published on Web 01/16/2009
1894 Langmuir, Vol. 25, No. 4, 2009
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Figure 3. ESEM images of marble surfaces. (A) Marbles coated with lycopodium and (B) marbles coated with PVDF.
Figure 1. (Top) Water marble coated with PVDF at a volume of 10 µL. (Bottom) Water marble coated with PVDF at a volume of 50 µL.
Figure 2. Scheme for the calculation of geometrical characteristics of the truncated oblate spheroid.
2.5. Study of Marble Shape. The shape and contact angles of marbles were measured with a homemade goniometer and an imageprocessing technique. A horizontal laser beam illuminated the marble profile and produced its enlarged image on the screen using a system of lenses. Gravity deformed the marbles, and we supposed that the marble shape was close to that of an oblate spheroid (Figure 2). The contact diameter AB, the height CD, and the maximal width of the droplet image EF were measured, and from these parameters the lengths of the spheroid axes were calculated. 2.6. Vibration of Marbles. Marbles were vibrated with an experimental device similar to that reported in other papers.19-21 The superhydrophobic substrate (described in section 2.2) with the marble was bound up with the moving part of the vibration generator producing horizontal vibrations. The horizontal laser beam illuminated all of the marble profile and projected its enlarged image onto a screen using a system of lenses. The amplitude of vibration was 100-150 µm. The frequency of vibration was varied, and the lowest eigenfrequency of the volume modes was fixed.
3. Results and Discussion 3.1. ESEM Study of the Surfaces of Marbles. An ESEM study of the marble surfaces supplied valuable information (19) Celestini, F.; Kofman, R. Phys. ReV. E 2006, 73, 041602. (20) Bormashenko, E.; Pogreb, R.; Whyman, G.; Erlich, M. Langmuir 2007, 23, 6501–6503. (21) Bormashenko, E.; Pogreb, R.; Whyman, G.; Erlich, M. Langmuir 2007, 23, 12217–12221.
concerning the makeup of marbles. Figure 3A,B demonstrates that particles of lycopodium and aggregates of PVDF particles are separated by water clearings. The ESEM study validates the results already obtained by Aussillous and Que´re´ with optical microscopy.17 It could be recognized that on the microscopic scale the surface of the marble is complicated and comprises solid particles and water clearings. We propose to characterize the surface tension of marbles on the macroscopic level with an effective surface tension constituting macroscopic properties of marbles such as shape and eigenfrequencies of vibrations. (See also the paper by Aussillous and Que´re´.17) 3.2. Shape and Effective Surface Tension of Marbles. As could be recognized from Figure 1, with the increase in volume V the marble takes a more oblate form that may be characterized by the axis ratio ε, contact radius r, and so forth. For marbles with a volume of V < 20 µL, the axis ratio ε is relatively close to unity, ε ≈ 0.9; however, marbles with volume V ) 50 µL are already deformed strongly by gravity as depicted in Figure 1 (bottom). The measured geometrical characteristics are presented in Figure 4 and compared there to the values calculated with the elaborated oblate spheroid model for the droplet form. In the mentioned model, an upper droplet surface is approximated by a truncated oblate spheroid surface Sside formed by rotation of the ellipse
(y - RR)2 + R3x2 ) R2R2
(1)
around the y axis (Figure 2). Here, R/R and RR are the ellipse hemiaxes, and R < 1 is a dimensionless parameter. The oblate spheroid is truncated at the height Rb. It can readily be verified that this body has the same volume V as the spherical cap of radius R truncated at the height b from below. The total energy of the droplet connected with its deposition onto a substrate comprises three parts: two surface energies and the gravitational energy
E ) γSside + (γcont - γSA)Scont + FVgH
(2)
where γ is the surface tension (the average energy per unit surface) on the liquid-air interface, γSA is the surface tension coefficient on the solid-air interface, F is the density of a liquid, H is the center mass height, and g is the acceleration due to gravity. In our case, when marbles and not drops are treated we have no true solid/liquid surface.17 Thus, we introduce γcont defined as the mean energy of the unit contact area of the interface between the solid substrate and the marble. The contact area is much larger
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Langmuir, Vol. 25, No. 4, 2009 1895
volume V, which should be constant, is independent of R and is expressed explicitly through β as
R)
[
3V π(2 - β)2(1 + β)
]
1⁄3
(6)
Therefore, the energy can be minimized by the variation of these two free, independent parameters. The values R0 and β0 providing the energy minimum, found with Mathematica software, may be used for the calculation of the contact angle θ* of the droplet, the contact radius, the axis ratio, or other geometrical characteristics:
cos θ * )
β0 - 1 , r ) R0√β0(2 - β0)/R0, ε ) R3/2 (7) h(R0, β0)
Note that the energy expression contains two physical parameters connected with interfaces; these are γ and γcont γSA. These are related to each other by the Young equation
cos θ˜ )
Figure 4. (A) Variational parameters R0 and β0, axis ratio ε, and contact radius r calculated in the framework of the mathematical model and corresponding to the energy minimum for marbles coated with PVDF. Continuous curves show the results of calculation, and symbols correspond to measured values. The calculation corresponds to γ ) 0.09 J/m2 and θ˜ ) 137°. (B) Variational parameters R0 and β0, axis ratio ε, and contact radius r calculated in the framework of the mathematical model and corresponding to the energy minimum for marbles coated with lycopodium. Continuous curves show the results of calculation, and symbols correspond to measured values. The calculation corresponds to γ ) 0.06 J/m2 and θ˜ ) 138°.
than the size of hydrophobic particles coating the marble; this scaling argument justifies the use of the notion γcont. Substitution of the derived expression for Sside, the contact area surface Scont and the center mass height H gives
{(
E ) πR2
γ 1 + (1 - β)h(R, β) + R R3
(
(1 - β)√1 - R3 + h(R, β)
))
+ 1 - √1 - R3 (γcont - γSA)β R (2 - β) + FgR2(2 - β)(4 - β2) R 12
√1 - R3
(
ln
)}
(3)
Here one more dimensionless parameter β determined by the truncation height
β)
b R
(4)
and designation
h(R, β) ) √1 - (1 - R3)β(2 - β)
(5)
are used. It should be emphasized that the dimensionless parameters R and β are completely free (0 < R < 1, 0 < β < 2) because the
γSA - γcont γ
(8)
for the contact angle θ˜ of the marble (θ˜ , of course, is not a well-known Young angle in the case of marbles because of the fact that we have no true solid/liquid interface; actually, it is a kind of apparent contact angle). Therefore, some useful physical information can be extracted from the best-fit requirement for measured and calculated geometrical characteristics of the drop form. Constants γ and θ˜ obtained in this way are γ ) 0.09 J/m2 and θ˜ ) 137° for marbles obtained with PVDF and γ ) 0.06 J/m2 and θ˜ ) 138° for marbles coated with lycopodium. The degree of agreement between measured and calculated quantities for marbles obtained with lycopodium and PVDF is seen in Figure 4A,B. 3.3. Vibration of Water Marbles. The vibration of water droplets and gaseous bubbles was used by several groups to establish the surface tension of liquids, equilibrium contact angles, and contact angle hysteresis.19-30 We applied the vibration method to the measurement of the effective surface tension of marbles. The analysis of drop vibration is a complicated task.27 However, the eigenfrequencies of bulk vibrations could be calculated easily if the spherical form in the equilibrium state and pinning of the marble to the substrate are presumed.19 It should be mentioned that the vibration experiment turned out to be impossible when marbles were deposited on PE and PP substrates as a result of the rolling of vibrated marbles (the contact area was not pinned). At the same time, the rough superhydrophobic surface described in section 2.2 promoted pinning of the contact area, which is necessary for measurement. This observation supports the suggestion by Que´re´ that marbles actually rest on hydrophobic particles (lycopodium or PVDF).17 In a somewhat paradoxical way, the rough relief of superhydrophobic surface puts obstacles in the way of the marble and promotes the pinning of the contact area. (22) Matsumoto, T.; Nakano, T.; Fujii, H.; Kamai, M.; Nogi, K. Phys. ReV. E 2002, 65, 031201. (23) Fujii, H.; Matsumoto, T.; Izutani, S.; Kiguchi, S.; Nogi, K. Acta Mater. 2006, 54, 1221–1225. (24) Vicente, C.; Yao, W.; Maris, H. J.; Seidel, G. M. Phys. ReV. B 2002, 66, 214504. (25) Chang, C.-H.; Franses, E. I. J. Colloid Interface Sci. 1994, 164, 107–113. (26) Chang, C.-H.; Coltharp, K. A.; Parkm, S. Y.; Franses, E. I. Colloids Surf., A 1996, 114, 185–197. (27) Wilkes, E. D.; Basaran, O. A. Phys. Fluids 1997, 9, 1512–1528. (28) Della Volpe, C.; Maniglio, D.; Morra, M.; Siboni, S. Colloids Surf., A 2002, 206, 47–67. (29) Daniel, S.; Chaudhury, M. K. Langmuir 2002, 18, 3404–3407. (30) Meiron, T. S.; Marmur, A.; Saguy, I. S. J. Colloid Interface Sci. 2004, 274, 637–644.
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Figure 5. Scheme illustrating the horizontal vibration of the droplet.
Figure 6. Resonance frequency dependence on droplet volume for marbles coated with PVDF (() and lycopodium (2). The continuous curves show the results of calculation, and symbols relate to measured values. The best fit corresponds to γ ) 0.07 ( 0.004 J/m2 for PVDF and γ ) 0.055 ( 0.003 J/m2 for lycopodium. The apparent contact angles θ are 140° for PVDF and 138° for lycopodium.
The bulk vibrations are allowed by the phenomenon of contact angle hysteresis.1,19 The contact angle is varied in the range of θ - δθ < θ < θ + δθ (Figure 5). We have shown in the previous paragraph that marbles maintain a spherical form when their volume is relatively small (V < 20 µL). Hence, we performed our vibration experiments with marbles of 5-20 µL volume. When a drop in the equilibrium state has the form of a truncated sphere, the frequencies of its bulk modes are given by the equation obtained by Celestini and Kofman19 ω)
R F(1 - cos6γh(θ) θ)(2 + cos θ)
-3 ⁄ 2
(9)
where h(θ) is the geometrical factor calculated by Celestini and Kofman19 and θ is the apparent contact angle as established experimentally. Usually, the measured quantity is a volume, so it is worthwhile to express the sphere radius R through the volume of the spherical segment V R)
[
3V π(1 - cos θ)2(2 + cos θ)
]
1⁄3
and eq 9 is transformed to a somewhat simpler expression ω)
2πγh(θ)(1FV- cos θ)
(10)
To test (calibrate) eq 10, we established surface tension for bidistilled water drops with a volume of 10 µL deposited on superhydrophobic surfaces as described in section 2.2. The experimentally established resonance frequency was 19 Hz; this value corresponds to γ ) 0.06 J/m2 for water. It could be concluded that eq 10, when used for the dynamic measurement of surface tension, underestimates its value. This reasoning is important for our future analysis. It is also noteworthy that other dynamic methods used for the measurement of a surface tension usually underestimated its value.22 The resonance frequencies calculated according to eq 10 were plotted versus measured ones (Figure 6). For marbles coated with PVDF, the observed contact angle value was 140°, h(140°)
) 0.16, and the surface tension γ ) 0.07 ( 0.004 J/m2 on the upper marble interface was chosen to give the best fit between calculated and measured values. For marbles coated with lycopodium, the observed contact angle value was 138°, h(138°) ) 0.18, and the surface tension was γ ) 0.055 ( 0.003 J/m2. It should be mentioned that the above values are in semiquantitative agreement with γ ) 0.09 J/m2 (PVDF-coated marbles) and γ ) 0.06 J/m2 (lycopodium-coated marbles) found with an independent method of geometric measurements (see the preceding section). As already mentioned, eq 10 used for the dynamic measurement of the effective surface tensions underestimates their values, which is why it supplied lower values of γ compared to those established with shape analysis. The values of effective surface tension are worth discussing; the surface tension of colloidal suspensions is a widely debated topic.31 Aussillous and Que´re´ have applied the analysis of marble shape to the calculation of the effective surface tension.17 The calculation carried out with a numerical solution of the equation describing the shape of the marble gave a value of γ ) 0.072 J/m2 for marbles coated with lycopodium, which coincided with a well-known value for pure water.17 Hence, it was concluded that the effective surface tension does not depend on the kind of hydrophobic particles coating a marble. Our results obviously contradict this conclusion. (See also ref 32.) To assure ourselves that our experimental results are not artifacts, we put water marbles coated with lycopodium and PVDF and also water drops of the same volume on the same strongly hydrophobic surface described in section 2.2 and in our earlier paper10 and subjected them to horizontal vibrations. Marbles coated with lycopodium and water drops demonstrated very similar resonance frequencies (this observation supports the results reported by Aussillous and Que´re´17), whereas marbles coated with PVDF had resonance frequencies that were 17% greater than those inherent for pure water and lycopodium. Hence, if it is supposed that the resonance frequency is stipulated by the surface tension for a given radius and contact angle of the marble, then it can be concluded that the effective surface tension of marbles coated with PVDF is larger than that of pure water. It could be assumed that the values of surface tension established for PVDF-coated marbles with shape analysis, which were significantly larger than 0.07 J/m2 for the pure water-air interface, reflect a possible strong association of PVDF colloidal particles suspended in water.31
4. Conclusions The procedure of manufacturing water marbles based on the use of superhydrophobic surfaces for coating droplets with PVDF powder and lycopodium is presented. An ESEM study of marble surfaces is reported. The proposed geometrical model based on the oblate spheroid approximation to the droplet form gives values of 0.09 J/m2 for the surface energy at the air-marble interface for measurements on PVDF-coated marbles and 0.06 J/m2 for lycopodium-coated marbles. The second method, which is based on the vibration of marbles, demonstrates only semiquantitative agreement with the results of the first method. We conclude that the effective surface tension of marbles is sensitive to the kind of hydrophobic particles coating the marble. Acknowledgment. We are thankful to Professor D. Que´re´ for inspiring discussions of the physical properties of liquid marbles. This work was supported by the Israel Ministry of Absorption. We are grateful to Professor M. Zinigrad for his generous support of our experimental activity. LA8028484 (31) Larsen, A. E.; Grier, D. G. Nature 1997, 385, 230–233. (32) McHale, G.; Elliott, S. J.; Newton, M. I.; Herbertson, D. L.; Esmer, K. Langmuir 2009, 25, 529–533.
