Spreading Kinetics of Water Drops on Self-Assembled Monolayers of

Jul 16, 2005 - The authors acknowledge Charles and Caroll McArthur for the MSE Fellowship awarded to D.C. The droplet spreading events were recorded ...
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Langmuir 2005, 21, 7733-7738

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Spreading Kinetics of Water Drops on Self-Assembled Monolayers of Thiols: Significance of Inertial Effects Jaroslaw Drelich* and Dorota Chibowska Department of Materials Science and Engineering, Michigan Technological University, Houghton, Michigan 49931 Received February 12, 2005. In Final Form: May 4, 2005 Spreading of 5-15 µL water drops on self-assembled monolayers of 1-hexadecanethiol and 11-mercapto1-undecanol, both homogeneous and mixed compositions, formed on gold-coated silicon wafers or glass slides was recorded with a high-speed video camera. The time (t) evolution of the drop base diameter (D) during spreading was analyzed by a power law-correlation: D ∼ tn. The n value was found to increase from n ) 0.3-0.5 for water drops on hydrophobic surfaces characterized by the advancing water contact angle of θA ) 94-104° to n ) 0.5-0.8 on less hydrophobic surfaces (θA ) 45-66°). These experimental values were found to be of similar magnitude as the literature values reported for small drops and bubbles, which spread over a variety of different substrates including water and water-ethanol drops on self-assembled monolayers of alkylsilanes, air bubbles in water on glass, molten metals on solid metals and ceramics, hydrocarbon drops on water, and others. Inertial effects, which are often not accounted for in the analysis of spreading results, appear to have an impact on the spreading kinetics of small drops in at least the first few milliseconds of the spreading phenomenon.

Introduction Two theoretical models most commonly used to describe the kinetics of a liquid droplet spreading over a solid surface are hydrodynamic1 and molecular-kinetic2 models. Both models were derived for a complete wetting condition. The hydrodynamic model was derived based on the assumption that wetting dynamics is governed by a competition between capillary and viscous forces. In the molecular-kinetic approach, the motion of the three-phase contact line is determined by a competition between capillary force and molecular displacement within the three-phase contact zone. The hydrodynamic model predicts that the droplet base diameter (D) increases as a function of time according to the formula D ∼ t1/10, whereas the dynamic contact angle (θd) decays according to θd ∼ t-3/10.3,4 On the other hand, the molecular-kinetic model predicts that changes in D and θd should scale approximately as D ∼ t1/7 and θd ∼ t-3/7.3,4 Both theories describe the experimental results fairly well for viscous liquids at low and moderate velocities of the three-phase contact line. The hydrodynamic model appears to be also more suitable in describing a final stage of spreading phenomenon, whereas the molecular-kinetic theory describes better the spreading at stages that are far from the equilibrium state.3 Because of a limited number of experimental data, suitability of the hydrodynamic and molecular-kinetic theoretical models to high velocity spreading conditions observed for low viscosity liquids remains under-explored. Sporadic literature reports indicate differences, often of significant magnitude, between experimental data and theoretical predictions of both hydrodynamic and molecular-kinetic models.4-6 Importantly, recently presented data on the spreading of droplets * Corresponding author. E-mail: [email protected]; fax: (906) 487-2934; phone: (906) 487-2932. (1) Cox, R. G. J. Fluid Mech. 1986, 168, 169-94. (2) Blake, T. D.; Haynes, J. M. J. Colloid Interface Sci. 1969, 30, 421-3. (3) de Ruijter, M. J.; Charlot, M.; Voue, M.; de Coninck, J. Langmuir 2000, 16, 2363-8. (4) von Bahr, M.; Triberg, F.; Yaminsky, V. Colloids Surf., A 2001, 193, 85-96.

of liquid metals on solid metals and ceramics were viewed as having unusually high kinetics as compared to the spreading of organic liquids.7 On the contrary, results from our own research, along with several research results presented in the literature (to be briefly reviewed in the Results and Discussion), indicate that the time evolution of the base diameter for millimeter-sized liquid-metal drops presented by Saiz and Tomsia7 is not much different than for low-viscosity organic liquids or water. In this paper, we provide additional experimental evidence to support this statement and show that the rate of droplet spreading does not necessarily scale with t1/10 or t1/7 for drops released from a needle and made of a low viscosity liquid. New results presented in this paper are for water droplets placed on self-assembled monolayers of thiols of either CH3- or HO- or CH3-/HO-mixed functionalities. Monolayers were prepared on glass and silicon wafer slides coated with a thin film of gold, possessing a nanoscale roughness. Experimental Procedures Samples and Their Characterization. Pieces of silicone wafer and glass slides were cleaned with the Micro-90 surfactant solution and then water in an ultrasonic cleanser for approximately 3 min each. After substrates were removed from the ultrasonic cleanser, they were rinsed several times with deionized water, methanol, and acetone. Drying of substrates took place in a clean oven at 100 °C for about 5 min. Any residual organic contaminants remaining on the surfaces of the silicon wafer and glass were removed with an ultraviolet radiation applied by a Bioforce Labs cleaner for 40 min. A thin gold film (approximately 20 nm thick) was deposited on cleaned glass and silicon substrates using the Hummer 6.2 sputtering system under conditions of a 15 mA current and a vacuum of 0.07 Torr. Gold-coated samples were immersed into ∼10 mM solutions of 1-hexadecanethiol (92%, Aldrich) or 11-mercapto-1-undecanol (97%, Aldrich) or a mixture of both, in a volumetric ratio varying from 1:1 to 1:10, in (5) Phan, C. M.; Nguyen, A. V.; Evans, G. M. Langmuir 2003, 19, 6796-801. (6) Alteraifi, A. M.; Sherif, D.; Moet, A. J. Colloid Interface Sci. 2003, 264, 221-7. (7) Saiz, E.; Tomsia, A. P. Nat. Mater. 2004, 3, 903-9.

10.1021/la0503956 CCC: $30.25 © 2005 American Chemical Society Published on Web 07/16/2005

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histological methanol (Fisher Scientific). The substrates were left in the solutions for at least 16 h at a room temperature (20-22 °C). The substrates with formed self-assembled monolayers of thiols were rinsed with methanol and acetone and placed for 5 min in an oven to dry at a temperature of 100 °C. Topographical images were recorded for two selected glass and silicon wafer substrates coated with a thin film of gold using the intermittent contact mode operation on a Digital Instruments Dimension 3000 AFM (Santa Barbara, CA). The 2 µm × 2 µm and 1 µm × 1 µm images with 256 × 256 resolution were captured for each surface, using a scan rate of 0.75-1 Hz. RMS and Rq roughness parameters were determined using the instrument software. Also, cross-sections of images were analyzed to determine the size of asperities. All asperities were assumed to be spherical caps, and the base diameter of an asperity (d) and its height (h) were measured from each image for 20 asperities (see ref 8 for details). Measurements of advancing (static) contact angles for water drops on dried samples were carried out using the Kruss G10 Instrument with the Drop Shape Analysis software using a procedure similar to that described in a previous paper.9 The glass syringe with a 0.5 mm stainless steel needle was used to form the droplets with a 5-10 mm base diameter, and the measurements of the contact angles were taken 15-20 s after drop size enlargement. High-Speed Video Study. The spreading of 5-15 µL drops of deionized water was recorded using a High-Speed Star video system with the software provided by LaVision. Before taking pictures, the camera was focused and calibrated. The droplets were released from a glass syringe equipped with a 0.5 diameter stainless steel needle. The droplet spreading event was repeated two to eight times at each sample. Sixteen frames were taken in each experiment. The interval between frames was set to 0.5 ms (1 ms in selected experiments). The diameter at the droplet base was measured from each frame using LaVision software. Before each experiment, the sample was rinsed with methanol and placed into an oven to dry. The attachment of the droplet to the substrate surface rarely coincided with the capture of the first frame; therefore, less than 16 experimental points were collected in each experiment. The droplet remained attached to the needle during its contact with the substrate surface, but it usually detached from the needle in a final stage of the spreading event. This way the impact effects associated with drops falling on the solid substrate, such as drop flattening and drop oscillation that affected drop base diameter and the value of contact angle, were minimized. Also, due to the small dimensions of water drops used in this study, gravity forces can be assumed as negligibly small as compared to capillary forces. The water drops were still large enough to ignore the effect of curvature on the kinetics of spreading.

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Figure 1. Spreading of a water droplet on the surface of HOterminated self-assembled monolayer (θA) 45 ( 2°). The diameter of the needle is 0.5 mm.

Results and Discussion Spreading Kinetics. Examples of the image frames acquired by the high-speed video system at different stages of water droplet spreading are shown in Figures 1 and 2. The diameter of the droplet base was measured with an accuracy of ∼0.05 mm from the frames such as shown in Figures 1 and 2 and correlated with recorded times (Figures 3 and 4). Similar results were obtained for selfassembled monolayers with OH/CH3 mixed functionalities. By reducing the ratio of 1-hexadecanethiol (CH3-terminated thiol) to 11-mercapto-1-undecanol (HO-terminated thiol) in the assembled monolayers of mixed functionality, the hydrophobicity of the substrate was reduced. The hydrophobicity of self-assembled monolayers was quantified by the value of the measured advancing (static) contact angle. The advancing water contact angle varied from about 45° for the self-assembled monolayer of 11-mercapto1-undecanol to 104° for surfaces made of 11-hexadecanol. (8) Tormoen, G. W.; Drelich, J.; Beach, E. R. J. Adhesion Sci. Technol. 2004, 18, 1-17. (9) Drelich, J.; Miller, J. D.; Good, R. J. J. Colloid Interface Sci. 1996, 179, 37-50.

Figure 2. Spreading of a water droplet on the surface of predominantly CH3-terminated self-assembled monolayer (θA ) 98 ( 3°). The diameter of the needle is 0.5 mm.

Self-assembled monolayers of mixed OH/CH3 functionalities demonstrated advancing water contact angles larger than 45 but smaller than 104°.

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Figure 5. Dependence of the parameter n in D ) ktn on wetting characteristic of self-assembled monolayers expressed in terms of measured advancing (static) water contact angle.

Figure 3. Time evolution of the drop base diameter (a) and dynamic contact angle (b) for water drop spreading over the OH-terminated self-assembled monolayer of thiol prepared on a gold-coated silicon wafer.

Figure 4. Time evolution of the drop base diameter (a) and dynamic contact angle (b) for water drop spreading over the CH3-terminated self-assembled monolayer of thiol prepared on a gold-coated silicon wafer.

As shown in Figures 3 and 4, the experimental results of the drop base diameter versus time are scattered; nevertheless, relatively reproducible trends were recorded. The scatter of the data, we believe, is from imperfections of the experimental setup adopted in this study and technical difficulties associated with recording spontaneous spreading phenomenon. The results of the drop base diameter (D) versus time (t) were correlated by a simple power law: D ) ktn, where k and n are constants. A correlation coefficient (R2) for a fit of the experimental data to the power law was better than 0.88, with R2 ) 0.94-0.99 for most of the results. The value of k was found

to vary from about 1.2 to 1.7, but no clear correlation between solid surface characteristics and k value was found. The variation in the k value most likely reflects the variation in the drop volume during experimentation.10 The calculated n values are shown in Figure 5 for selfassembled monolayers of varying wetting characteristics expressed in the term of measured advancing (static) contact angles. We recognize that the static contact angle might not be an appropriate parameter to which the value n is correlated for different systems. If literature results are compared to our n values, many of them will not fit with the curve shown in Figure 5. In this contribution, however, the θA versus n correlation is a convenient way to compare the spreading kinetics of water drops on selfassembled monolayers of different wetting characteristics. The values of n increased from n ) 0.30-0.45 ((0.03) for hydrophobic surfaces (θA > 90°) to n ) 0.55-0.76 ((0.10) for predominantly HO-terminated surfaces (θA < 70°). These results suggest enhanced spreading of water droplets over solid surfaces that exhibit stronger interactions with water. Intermolecular or surface forces at the triple line could, therefore, be an important factor in spreading kinetics of water drops on self-assembled monolayers of thiols. The effect of solid-liquid interactions on the kinetics of liquid drop spreading was also observed previously. For example, Lelah and Marmur10 reported an increase in the spreading of aqueous droplets on a glass with increasing pH of the liquid. Alkaline aqueous solutions wet glass better than acidic solutions, mainly because of the cleaning power of alkaline solutions and the increased negative surface potential of glass with increasing pH. Increasing negative potential enhances the repulsive interactions between glass surface and water surface (also negatively charged) near the three-phase contact line. Further, Lopez et al.11 analyzed theoretically the effect of intermolecular forces on the spreading of liquid drops. A model they derived predicts that the drop radius scales with t0.5. The value n ) 0.5 is remarkably close to our experimental values, although it must be recognized that the theoretical model derived by Lopez et al.11 applies to a complete spreading situation (positive spreading coefficient), as compared to partial wetting conditions examined experimentally in this study. Although the solid surface imperfections could contribute to the scatter of the data, they cannot, in our opinion, explain 3-5 times larger n values obtained for partial wetting systems studied here than hydrodynamic and molecular-kinetic theories predict for complete wetting (10) Lelah, M. D.; Marmur, A. J. Colloid Interface Sci. 1981, 82, 518-25. (11) Lopez, J.; Miller, C. A.; Ruckenstein, E. J. Colloid Interface Sci. 1976, 56, 460-8.

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systems (n ) 0.10-0.143). According to the AFM analysis, both types of substrates used, gold-coated glass and goldcoated silicon wafer, had a similar nano-roughness characteristic with a root-mean-square roughness RMS ) 4.7-6.3 nm and geometrical roughness Rq ) 3.84.4 nm. Nano-asperities of the substrates had a base diameter of d ) 66.4 ( 23.2 nm and a height of h ) 17.0 ( 5.6 nm. Heterogeneity of the self-assembled monolayers due to molecular defects and phase separation in systems of the mixed functionality cannot be ruled out as well. Both surface roughness and heterogeneity could affect the rate of drop base expansion at different levels of spreading phenomenon. For example, grooves in the rough hydrophilic surface, such as HO-terminated self-assembled monolayers in this study, can accelerate the spreading of liquid due to a capillarity effect. It is, however, unlikely that the value n could increase above 0.5, which is a typical value both predicted and measured in a penetration of capillaries. The surfaces used in this study were not completely wetted by water, the condition that validates the assumption of the hydrodynamic and molecular-kinetic models. However, we expect that the spreading of a liquid at partially wetting surfaces can only proceed at a slower rate than at completely wetting surfaces, due to a smaller driving capillary force. The n values recorded in this study are very close to the values (n ) 0.4-0.5) recorded for hydrocarbon (pentane, heptane, dodecane, and hexadecane) drops, which spread over the water surface;12 neither substrate surface roughness nor heterogeneity could affect the experiments in the liquid/ liquid/air system to any great extent. Importantly, the drop spreading velocity observed in this study is also close to the reported values for a number of other systems involving solid surfaces. Lavi and Marmur13 reported n values from n ) 0.31 to 0.39 for a number of liquid drops placed on dodecyltrichlorosilane-modified silicon wafers. von Bahr et al.4 showed that the spreading of water or aqueous solutions of ethanol on self-assembled monolayers of dimethyloctylchlorosilanes exhibits a ∼tn power law with n ) 0.39-0.47 (approximated to 0.5 in ref 4). Even the experimental data on the air bubble base diameter expansion at the glass surface in water presented by Phan et al.5 indicate a value of n close to 0.4. We also calculated a similar value of n from the results on the spreading of metal drops on the surfaces of metals and ceramics at high temperatures, reported recently by Saiz and Tomsia.7 Additional examples of similar, as well as different, n values are further reviewed in ref 13. It is clear from the above brief review of reported experimental data that an enhanced velocity of droplet base expansion is not only a feature of molten metals, as recently suggested by Saiz and Tomsia,7 but of a number of different low-viscosity liquids. As the reported literature results show, a variation in the n value can be significant, and small drops spread at a rate that is larger than hydrodynamic and molecular-kinetic theoretical models predict. Additionally, no simple correlation between the n value and either the viscosity or the surface tension or the vapor pressure for used liquids could be concluded from the reported data (not shown). Dynamic Contact Angles. The driving force for the liquid to spread over a surface is a capillary force, usually expressed as a difference between cosine of dynamic and equilibrium contact angles and multiplied by the liquid (12) Drelich, J.; Miller, J. D. Ann. Univ. Mariae CuriesSklodowska 1999/2000, 54/55, 105-113. (13) Lavi, B.; Marmur, A. Colloids Surf., A 2004, 250, 409-14.

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surface tension (F ) γL(cos θd - cos θ0)) in many theoretical models. Therefore, an attempt was made to measure the dynamic contact angles for each droplet during the entire recorded spreading sequence. Examples of contact angle results for HO- and CH3-terminated self-assembled monolayers are shown in Figures 3 and 4, respectively. As shown in Figures 3 and 4, the experimental contact angles were poorly reproducible from experiment to experiment. The contact angle values seem not only to decrease, as should be expected, but also to oscillate from larger to smaller and back to larger values. Such oscillation in the contact angle value is not an unusual phenomenon as a similar variation of dynamic contact angles can be concluded from recently reported results for molten gold droplets during their spreading over a nickel substrate.7 Unfortunately, most of the literature reports on similar experimentation lack any discussion on this phenomenon, which appears to be very important in interpretating the results on the spreading of small droplets, particularly when they are transferred from needles or other holding bodies. Fluctuation in the contact angle value is expected to be caused by inertial effects, influencing the shape and oscillation of the spreading drop. Inertial Effects. As shown in Figures 1 and 2, the shape of the drop during the drop release from the needle and its spreading over the solid surface deviated significantly from sphericity in many experiments. Simple theoretical models do not account for the distortion of the drop shape. The force driving the droplet to spread over the substrate surface can be influenced by evolution of the liquid-gas surface area and inertial effects associated with such changes. For example, interestingly, it was noticed in several instances that the enlargement of the drop base continued, although the contact angle, which we measured (apparent contact angle), remained unchanged, at least at the resolution of our measurements (Figure 4). As mentioned previously, the spreading of water droplets observed in this study could be affected by a departure of the liquid drop from a spherical shape, an effect that is usually unaccounted for by researchers who analyze the spreading phenomena based solely on measured dynamic (but macroscopic) contact angles. Indeed, our conclusion on the importance of geometrical effects in the spreading of small droplets is supported by recent results of lattice Boltzmann modeling presented by Dupuis and Yeomans.14 They found that the base radius of small droplets during the spreading on homogeneous surfaces expanded at t0.28, and this relation was found to hold for a range of liquid viscosities and surface tensions. The value n ) 0.28 is close to some of the values that were recorded for water drops on hydrophobic surfaces in this study and, importantly, is much larger than the hydrodynamic and molecular-kinetic models predict. It must be recognized, however, that geometries of a liquid drop at each stage of the spreading phenomenon analyzed by Dupuis and Yeomans14 do not overlap perfectly with geometries of spreading drops recorded in our studies (Figure 1). Therefore, further theoretical simulation is necessary to better understand the impact of drop geometry and its shape transformations on the spreading of small water drops in our systems. Experimental work done in the past indicates that a departure of the drop from sphericity does not need to be reinforced by a needle or any other object from which the drop is released. Here, we would like to refer to the previous (14) Dupuis, A.; Yeomans, J. M. Future Gener. Comput. Syst. 2004, 20, 993-1001.

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Figure 6. Spreading event for the dodecane droplet on the water surface that was captured with a high-speed video camera during research conducted by J. Drelich at the University of Utah; numerical results of the droplet base diameter vs time were presented in ref 12. The first (upper row on the far left) and last (lower row on the far right) pictures illustrate a ∼3 mm dodecane drop floating on the water surface before spreading and a formed dodecane lens after spreading was completed. The pictures between these two frames show the droplet spreading at different stages: ∼0, 2, 4, and 6 ms.

experiments on the spreading of hydrocarbon drops on the water surface.12 Figure 6 shows a hydrocarbon drop that spreads freely over the water surface without interference from the needle. As can be seen, even in this situation, where the drop lost contact with the needle, the drop shape was far from being spherical during spreading. In other words, the deformation of the drop such as in Figure 6 is caused by the spreading phenomenon. Spreading of the hydrocarbon drop shown in Figure 6 was so spontaneous that there seems to be a significant delay in the supply of liquid from the upper section of the drop to the interface (water-hydrocarbon interface in this case) to compensate a demand in oil at the drop base. In other words, the base of the drop expands much faster than the spherical (equilibrium) shape of the lens can be established (Figure 6). The importance of the inertial effects has been recognized during the capillary penetration by low-viscosity liquids and used to explain the enhanced kinetics of liquid into a capillary tube at an early stage of the liquid rise as well as to explain the oscillation of the liquid column around an equilibrium position.15 According to Quere,15 it is possible that the viscous boundary layer is not wellestablished in the early stages of fast kinetic spreading processes for low-viscosity liquids. The validity of this hypothesis in our systems needs to be proved experimentally. However, if correct, it means that the viscous dissipation work is negligibly small in at least the early phase of the liquid drop spreading. Therefore, if the gravitational potential energy is ignored in our systems due to the small dimensions of the drops, the inertia and capillary forces seem to be the only forces operating during the first few milliseconds of spreading of low-viscosity liquid drops. If these two forces are balanced (F ) δ(mv)/ δt, where m is the mass of the drop and v is the velocity of the spreading), the drop base diameter expansion should change linearly with time: D ∼ kt (k is the constant that depends on the magnitude of capillary force, drop volume, and liquid density). For a complete wetting case, de Gennes also concludes that the velocity of the drop spreading in the inertial regime should be constant and dependent on the surface tension of liquid, density of liquid, and drop (15) Quere, D. Europhys. Lett. 1997, 39, 533-8.

volume.16 Indeed, many of the D ) f(t) results from the early stage of spreading, in both this (i.e., Figure 3a) and previous12 studies, can fit with such a linear correlation. Also, the results presented by Phan et al.5 on the spreading of a gas bubble on a glass slide in water clearly show such a linear correlation between the radius of the expanding bubble base and the time in the first 5-6 ms of the recorded spreading phenomenon. However, a small number of experimental data obtained specifically in each of our experiments raises serious doubts as to if the D versus t linear correlation is valid. A larger number of accurate measurements for drop spreading, with a larger number of frames than recorded in this study, is needed to confirm the role of inertial effects in the spreading of low-viscosity and low-volume liquids and the existence of a linear regime in the D versus t correlation. Conclusion The spreading of small water drops (5-15 µL) on selfassembled monolayers of 1-hexadecanethiol and 11mercapto-1-undecanol, both homogeneous and mixed compositions, formed on gold-coated silicon wafers and glass slides was recorded with a high-speed video camera. The linear velocities of the drop base diameter expansion reached values as high as 0.5-1 m/s. The time (t) evolution of the drop base diameter (D) during spreading was analyzed by a power law-correlation: D ∼ tn. The n value was found to increase from n ) 0.3-0.5 for water drops on hydrophobic surfaces (characterized by an advancing water contact angle of θA ) 94-104°) to n ) 0.5-0.8 on less hydrophobic surfaces (θA ) 45-66°). The experimental n values were found to be of similar magnitude as the reported literature values for small drops and bubbles, which spread over a number of different solid and liquid substrates including water and water-ethanol drops on self-assembled monolayers of alkylsilanes, air bubbles in water on glass, molten metals on solid metals and ceramics, hydrocarbon drops on water, and others. This research, along with the literature data briefly reviewed in this paper, clearly demonstrates that the spreading kinetics recorded for small drops made of low-viscosity (16) de Gennes, P. G. Rev. Modern Phys. 1985, 57, 827-63.

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liquids can exceed values that hydrodynamic and molecular kinetics models predict. Therefore, the spreading of low-viscosity liquids seems to be significantly influenced by inertia. Such an event needs theoretical treatment different than what is offered for viscous liquids. Acknowledgment. The authors acknowledge Charles and Caroll McArthur for the MSE Fellowship awarded to D.C. The droplet spreading events were recorded with

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the high-speed video instrumentation purchased with the funds received from the U.S. National Science Foundation (MRI-0321003). The authors thank Dr. Jeffrey Allen for reading the manuscript and making valuable comments. D.C. is a summer scholar from the University of Warsaw (Poland). LA0503956