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Dynamic Dewetting through Micropancake Growth James R. T. Seddon,*,† Olesya Bliznyuk,‡ E. Stefan Kooij,‡ Bene Poelsema,‡ Harold J. W. Zandvliet,§ and Detlef Lohse† †
Physics of Fluids, ‡Solid State Physics, and §Physical Aspects of Nanoelectronics, MESAþ Institute for Nanotechnology, and IMPACT, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands Received January 16, 2010. Revised Manuscript Received May 6, 2010 We experimentally investigate the dynamics of nanometer-high, micrometer-wide gassy layers at the interface between a hydrophobic solid and bulk water. These micropancakes grow laterally in time, on the timescale of an hour, leading to partial dewetting of the solid. The growth is directional, mediated by chemical roughness on the substrate, and transient, occurring within the first hour after liquid deposition. We use circularity to measure the roundness of a micropancake (circularity C = 2(πA)1/2/L, where A is the surface area and L is the perimeter). The growth is anisotropic, as demonstrated by a decrease in circularity with time. However, once a micropancake reaches size saturation, its bulk rearranges its shape in order to minimize the length of its three-phase line. We interpret this combination of growth followed by bulk rearrangement as dynamic dewetting.
Introduction Substrate wetting is a fundamental issue in both nature and science. Plants and flowers use hydrophobicity to repel water from their petals in order to remain clean and dry,1 and many insects employ hydrophobicity to survive.2-5 Wettability is also used in several industrial processes, such as with self-cleaning surfaces6 or inkjet printing control through hydrophilic/hydrophobic patterned surfaces,7 and medical applications include hydrophilic coatings of medication in intravenous drug delivery.8 Recently, microscopic gaseous domains were found at the solid-liquid interface.9-11 These domains have typical heights of 1 to 2 nm but extend laterally for several hundred nanometers or even micrometers. Thus, they are named micropancakes. The original researchers9 suggested that micropancakes are gaseous, conceivably made of either air or vapor, and confined to two dimensions by the interaction potentials of both the substrate and bulk liquid. However, it is important to note that other possible explanations also present themselves, such as multilayer adsorbates.
Micropancake bilayers have also been discovered, as have nanobubble-micropancake composites where nanobubbles (e.g., refs 12-21) sit on top of the micropancakes below.11 Regardless of their structure, micropancakes disappear upon degassing and are composed of molecules that would be gaseous if not confined. Thus, they are a new phenomenon connected to surface wetting properties. Indeed, it is important to note that micropancakes9-11 are distinct objects from surface nanobubbles.12-21 Both entities are constructed from gas dissolved in liquid, and both are trapped at the solid-liquid interface. However, whereas micropancakes are quasi-2D gaseous layers with a micrometer lateral extent, surface nanobubbles are spherical cap bubbles with heights and widths of ∼15 and ∼100 nm, respectively. In this article, we describe the results of an experimental investigation of micropancake dynamics on a hydrophobized silicon surface. Micropancakes at the solid-liquid interface are found to grow in time until size saturation is reached. The growth is directional, mediated by substrate pinning, and corresponds to a dynamic dewetting phenomenon.
Experimental System
*Corresponding author. E-mail:
[email protected].
(1) Barthlott, W.; Neinhuis, C. Planta 1997, 202, 1–8. (2) Hu, D. L.; Chan, B.; Bush, J. W. M. Nature 2003, 424, 663–666. (3) Gao, X.; Jiang, L. Nature 2004, 432, 36. (4) Zheng, Y.; Gao, X.; Jiang, L. Soft Mater. 2007, 3, 178–182. (5) Yan, F.; Gang, S.; TongQuing, W.; Qian, C.; LuQuan, R. Chin. Sci. Bull. 2007, 52, 711–716. (6) Watanabe, T.; Nakajima, A.; Wang, R.; Minabe, M.; Koizumi, S.; Fujishima, A.; Hashimoto, K. Thin Solid Films 1999, 351, 260–263. (7) Wang, J. Z.; Zheng, Z. H.; Li, H. W.; Huck, W. T. S.; Sirringhaus, H. Nat. Mater. 2004, 3, 171–176. (8) Gref, R.; Domb, A.; Quellec, P.; Blunk, T.; M€uller, R. H.; Verbavatz, J. M.; Langer, R. Adv. Drug Delivery Rev. 1995, 16, 215–233. (9) Zhang, X. H.; Zhang, X.; Sun, J.; Zhang, Z.; Li, G.; Fang, H.; Xiao, X.; Zeng, X.; Hu, J. Langmuir 2007, 23, 1778–1783. (10) Zhang, X. H.; Maeda, N.; Hu, J. J. Phys. Chem. B 2008, 112, 13671–13675. (11) Zhang, L.; Zhang, X.; Fan, C.; Zhang, Y.; Hu, J. Langmuir 2009, 25, 8860– 8864. (12) Parker, J. L.; Claesson, P. M.; Attard, P. J. Phys. Chem. 1994, 98, 8468– 8480. (13) Tyrrell, J. W. G.; Attard, P. Phys. Rev. Lett. 2001, 87, 176104. (14) Tyrrell, J. W. G.; Attard, P. Langmuir 2002, 18, 160–167. (15) Fan, T.-H.; Vinogradova, O. I. Phys. Rev. E 2005, 72, 066306. (16) Zhang, L.; Zhang, Y.; Zhang, X.; Li, Z.; Shen, G.; Ye, M.; Fan, C.; Fang, H.; Hu, J. Langmuir 2006, 22, 8109–8113. (17) Borkent, B. M.; Dammer, S. M.; Sch€onherr, H.; Vancso, G. J.; Lohse, D. Phys. Rev. Lett. 2007, 98, 204502.
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The substrate used was a silicon wafer that had been hydrophobized with perfluorodecyltrichlorosilane (PFDTS), following the guidelines in ref 22. Briefly, the procedure was as follows: (i) degas the chamber that contains the uncoated substrate to a pressure of ∼50 μbar (below the vapor pressure of the silane); (ii) open this chamber to a reservoir of degassed PFDTS for 5 min so that the silane molecules adsorb onto the substrate; and (iii) close the PFDTS reservoir and open the system to a reservoir of degassed pure water for 30 min to increase the pressure of the system to the vapor pressure of water and allow the reagents to react. The resulting rms roughness was 0.4 nm, and the contact angles were ∼110° (equilibrium), ∼116° (advancing), and ∼104° (receding). A topographical AFM image of the dry substrate is shown in Figure 1. (18) Yang, S.; Dammer, S. M.; Bremond, N.; Zandvliet, H. J. W.; Kooij, E. S.; Lohse, D. Langmuir 2007, 23, 7072–7077. (19) Zhang, X. H.; Quinn, A.; Ducker, W. A. Langmuir 2008, 24, 4756–4764. (20) Brenner, M. P.; Lohse, D. Phys. Rev. Lett. 2008, 101, 214505. (21) Borkent, B. M.; Sch€onherr, H.; Ca€er, G. L.; Dollet, B.; Lohse, D. Phys. Rev. E 2009, 80, 036315. (22) Rathgen, H. Ph.D. Thesis, University of Twente, 2008
Published on Web 05/14/2010
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Figure 1. Topographical image of the dry PFDTS-coated Si surface. The image scale is 1.4 μm 1.4 μm 1 nm. Such imaging was then repeated under water, which was prepared using a Simplicity 185 purification system (Millipore SAS, France). Topographical imaging was performed with an atomic force microscope (AFM) operated in tapping mode (on both Veeco Multimode V and Agilent 5100 systems) with a typical scan speed of 4 to 5 μm/s. The AFM cantilevers were hydrophilic, Auback-coated Si3N4 (radius of curvature, 30 nm; full tip cone angle, 35°) Veeco NPG probes. These cantilevers are very soft, with typical spring constants and resonance frequencies in air of 0.58 N/m and 60 kHz, respectively, and are ideal for tapping-mode operation in a liquid environment. In the current experiments, ωliq 0 was found to be 25-30 kHz and the AFM was operated at a frequency ∼0.2 kHz lower than this with a set point of 85%. It is useful to describe the experimental conditions during deposition of the liquid. The PFDTS-coated Si substrate and pure water were held at room temperature (295 ( 1 K) prior to deposition, and the liquid was deposited onto the substrate as a droplet using a glass and metal syringe. Then the substrate was immediately placed under the AFM, and scanning was initiated.
Figure 2. Typical image of a micropancake on PFDTS-coated Si. The micropancake was flat, with an average height of 1.2 nm. Strong substrate pinning was a common feature of all micropancakes, leading to their irregular shapes. This image represents an area of 1.4 μm 1.4 μm 5 nm.
Results and Discussion A typical image of a micropancake is shown in Figure 2. The micropancakes had heights of 1.1-1.3 nm corresponding to three to four atomic length scales, whereas they were found to extend laterally for several hundred nanometers. Time progressions for two different experimental runs are shown in Figure 3. These progressions are constructed from consecutive AFM images and represent real-time separations of approximately 8.5 min between frames. In the left-hand system, the pancake increased in size and rearranged in shape. The growth was not uniform in all directions, as can be seen most clearly in the top right of this micropancake, and the rearrangement led to the edges becoming smoother with time. This procedure of growth followed by rearrangement was common to all of the micropancakes that we investigated, and we stress that the growth was in-plane (within error, no variation in height was measured). The right-hand system in Figure 3 started with two micropancakes, separated from each other by approximately 85 nm at their position of closest approach. Both micropancakes grew in size and rearranged their shapes before merging and continuing the growth and rearrangement processes. These observations suggest that surface-coarsening phenomena such as Ostwald ripening through surface diffusion do not occur for micropancake systems because otherwise the expectation would be for micropancakes with a lower radius of curvature to shrink at the expense of larger ones growing. Therefore, the growth of both micropancakes was mediated by gas condensing out of the bulk liquid. Thus, it is likely that the bulk liquid was supersaturated with gas. Although we allowed the purified water to equilibrate at laboratory temperature prior to deposition, it is important to note that atomic Langmuir 2010, 26(12), 9640–9644
Figure 3. Two typical time progressions of micropancakes. (Left) A single micropancake grew, and (right) two micropancakes grew, merged, and rearranged in shape. Images are black-white thresholds representing 2.7 μm 2.7 μm. Consecutive images are separated by ∼8.5 min, and the order runs from top to bottom.
force microscopy is a dynamic measurement technique that will have pushed the system slightly out of equilibrium. Measurements of temperature variations in both AFM models used in the present study were 6 °C in 25 min for the Agilent system and 8 °C in 60 min for the Veeco system. Despite this difference in heating, data from both systems were quantitatively the same. We performed similar experiments in degassed water. We degassed the liquid by continuously evacuating it until the O2 level DOI: 10.1021/la101414x
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Figure 4. (a) Area growth and (b) circularity of a typical micropancake with time. The micropancake grew during the first ∼50 min (indicated by the dashed line) before saturating in size. The growth was anisotropic, with a decrease in circularity with time. Once size saturation was reached, the micropancake rearranged in shape to become more circular again. Time is measured with respect to initial deposition.
dropped to below 15 ppb and remained at this level for over an hour. (This should be compared to ∼10 ppm for gas-equilibrated water.) No micropancakes formed in this situation. Zhang et al. described the relative free energies of nanobubbles and micropancakes in a composite.10 In their experiments, they investigated the destruction of micropancakes and nanobubbles on HOPG in supersaturated water. Annihilation was caused through the subsequent addition of ethanol to the liquid after the formation of the gaseous domains. The ethanol acts as a gas sink because its solubility is much higher than that of water and so reduces the amount of available gas (i.e., lowers the amount of supersaturation). They note that all micropancakes were destroyed at ∼5 vol %, compared to ∼20 vol % for the nanobubbles.10 Thus, micropancakes require supersaturation to be stable and a much higher level of supersaturation than nanobubbles. Furthermore, Dammer and Lohse23 used molecular dynamics to investigate the motion of dissolved gas in the vicinity of a solid-liquid interface. They found that the gas density is much larger at the interface than in the bulk. However, Sendner et al.24 demonstrated that this is not dependent on supersaturation. (They examined systems close to saturation and far above saturation, with no noticeable differences between the two cases.) The effect is independent of gas type but dependent on the surface energy of the substrate (i.e., the hydrophobicity). Thus, although it is likely that our micropancakes formed because of supersaturation of the liquid with gas, we note that supersaturation may not be a formal requirement. To shed more light on the micropancake growth phenomenon, time-progression data in the form of area growth is plotted in Figure 4a for a typical micropancake. The micropancake grew for the first ∼50 min after deposition, whereupon growth stopped and the micropancake leveled off in size. In total, the micropancake grew approximately 65% larger than its initial size and remained at this new size for as long as we continued to measure it, (23) Dammer, S. M.; Lohse, D. Phys. Rev. Lett. 2006, 96, 206101. (24) Sendner, C.; Horinek, D.; Bocquet, L.; Netz, R. R. Langmuir 2009, 25, 10768–10781.
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which was approximately 2 h. Therefore, we refer to the micropancake as having reached size saturation. It was possible that the growth may have occurred because of the proximity of the continuously scanning AFM cantilever. To examine this possibility, we performed scans twice on another micropancake in a different region of the substrate, separated in time by ∼4 h. This micropancake also grew in time by approximately 40%, thus it is likely that the growth is not a feature that is (solely) due to the measurement technique. There was strong evidence of substrate pinning in all of the micropancakes investigated, which led to the highly irregular micropancake shapes in Figures 2 and 3. A useful measure for describing the roundness of a micropancake is its circularity. We define this as C = 2(πA)1/2/L, where A and L are the area and perimeter of the micropancake, respectively. Circularity falls within the limits of 0 E C E 1, where C=1 corresponds to a circular pancake and C moves progressively closer to 0 as the pancake becomes less circular. (As examples, a square would correspond to C ≈ 0.89, whereas C = 0 corresponds to a stripe of infinitesimally small width.) The circularity of the micropancake from Figure 4a is plotted as a function of time in Figure 4b. During the growth stage (t j 50 min, indicated in Figure 4 by the vertical dashed line), the circularity decreased from ∼0.24 to ∼0.16 (i.e., the micropancake became less circular with time). Note that circularity would be time-independent for isotropic growth, thus this time dependence indicates that the micropancake grew anisotropically, probably because of the distribution of pinning sites. However, once the micropancake reached size saturation and stopped growing, its circularity increased from ∼0.16 to ∼0.32 in the remaining 2 h of measurement (i.e., the micropancakes rearranged in shape to minimize the length of their interfacial lines). Thus, the micropancakes exhibited a very strong correlation between their directional growth and their shape rearrangement. The rearrangement was done through systematic detachment from individual pinning sites before the contact line snapped to form new rounded edges. Circularity did not saturate within this 2 h period. However, once a micropancake was large enough that the network of pinning sites on the substrate appeared to be finegrained, we would expect that the rearrangement to full circularity would require only a sufficient amount of time for statistical fluctuations to allow all pinning sites to be overcome. Also, we expect the rate of the rearrangement process to decrease rapidly with time because for systems with larger radii of curvature further jumps will lead to relatively small energy gains. However, a linear extrapolation from Figure 4b leads to Cf 1 in time t J15 h. It is important to note that the substrate pinning sites were not topographical defects. Scanning the dry substrate showed no correlation in the radial distribution function. Instead, the pinning was due to local density changes in the PFDTS coating and so should be considered to be point-source chemical inhomogeneity. During the chemical coating of an amorphous substrate, it is usual that domains of limited size are created, with chemical inhomogeneities at their borders. Thus, possible explanations for the local density changes in PFDTS include (i) the local density of PFDTS fluctuating during substrate coating or (ii) some PFDTS being damaged such that the functional chemical group was altered. To understand the roughness in more detail, the nearestneighbor separations of pinning sites are plotted in Figure 5. These were measured from the AFM images, where the location of a pinning site is defined as when the local curvature of the edge of a micropancake changes sign. The primary peak is at 75 ( 5 nm, corresponding to the nearest-neighbor separation, and a secondary peak exists at 150 ( 5 nm, corresponding to a pancake segment bridging across a pinning site. Thus, the secondary peak represents Langmuir 2010, 26(12), 9640–9644
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growth, the pinning force must fall within the range of 0 j fp j 2τ. Once the force from the two interfacial lines exceeds this pinning force (i.e., as R f 0), we expect the system to depin. Depinning after Size Saturation. The local fluctuation in the number of gas molecules within a micropancake, N, is (N)1/2 = ((phA/kT)1/2, where p is the internal pressure, h is the micropancake height, k is Boltzmann’s constant, and T is the temperature. Each one of the gas molecules has an energy of kT, so we can calculate how large a micropancake must be for statistical fluctuations in thermal energy to be able to depin a pinning site locally. From the ideal gas law, this system has a size of Figure 5. Nearest-neighbor pinning site separations on the PFDTS-
coated Si substrate. The peak at 75 ( 5 nm corresponds to the nearest-neighbor separation, whereas the secondary peak at 150 ( 5 nm corresponds to the next-nearest-neighbor separation.
Figure 6. Dependence of micropancake area on the perimeter for several pancakes on PFDTS-coated Si. The relationship is linear for A j 0.35 μm2, with a slope of 68 ( 3 nm. This length scale is in good agreement with the nearest-neighbor separations depicted in Figure 5. Micropancakes larger than this area rearranged in shape to become more circular.
the next-nearest-neighbor separation along a line and is equal to twice the nearest-neighbor separation. The overall dynamics of the micropancakes can be summarized by plotting the area versus perimeter for several pancakes, as shown in Figure 6. The relationship is linear for small micropancakes. Therefore, the directional growth found in Figure 4a,b was 1D rather than fractal. (The curve for uniform growth would be squared, with a prefactor of 1/4π.) The slope of the curve in Figure 6 represents a length scale and should reflect a key length scale within the system. The slope of the best-fit line to the linear portion of the data is R = 68 ( 3 nm, in good agreement with the nearest-neighbor separations of the chemical inhomogeneities. This supports our previous observation that micropancake growth was strongly mediated by the local network of pinning sites. Data for larger micropancakes detached from the linear curve and moved in the direction of the squared dependency that corresponds to isotropic growth. We expect complete migration to take at least 15 h or much longer if the rearrangement slows with increasing circularity. We can understand the two regimes of micropancake dynamics by examining the forces on a pinning site as well as the energy of a micropancake. Consider a quasi-2D micropancake of area A and perimeter L. The edge of the pancake may become attached to a pinning site on the substrate, but once a pinning site has been completely surrounded by the micropancake it is considered to have depinned. Depinning during Growth. The force on each pinning site is fp = 2τ cos(R/2), where R is the (liquid-side) angle between two interfacial lines leading from a pinning site. Growth corresponds to the value of R moving closer to zero. For depinning during Langmuir 2010, 26(12), 9640–9644
Atherm
φ2 phkT
ð1Þ
Setting Atherm =0.3 μm2 (taken from Figure 6), p=1 atm (micropancakes are flat), and and h = 1.2 nm (measured using AFM), the pinning potential of a pinning site would be φ ≈ 2.4 eV. Comparing this to the average thermal energy per molecule (∼25 meV), depinning due to thermal fluctuations can occur only when the micropancake contains at least (2.4/0.025)2 ≈ 10 000 molecules. Estimating the Line Tension. We can now use this value for the pinning energy to find an estimate of the line tension. The pinning force is related to the pinning energy as fpd=φ, where d is the typical dimension of a pinning site, so the line tension is given by τ ≈ fp/2 cos(R/2) = φ/2d cos(R/2). Taking the lower limit of R = 0 with d ≈ 1 nm leads to a value for the line tension of τ ≈ 0.3 nN. In the literature, the line tension is usually between 10-10 and 10-8 N;25 our value falls within this range and is a reasonable estimate.
Conclusions We have demonstrated that the growth of micropancakes on an immersed hydrophobic substrate is directional, with preferential 1D growth for small micropancakes on an isotropically rough substrate. Growth occurs because of gas leaving the supersaturated bulk liquid and is mediated by the network of pinning sites on the substrate. Furthermore, the growth is transient, occurring only within the first hour after deposition while the system equilibrates. After the initial growth, the micropancakes undergo size saturation. Then thermal fluctuations become the cause of the depinning. We would expect all of the micropancakes to become circular on a time scale of several hours. Whether micropancakes are gaseous or adsorbates remains an open question and is the topic of our current research. However, regardless of the solution that presents itself, the micropancakes are composed of molecules that would be gaseous if they were not confined (i.e., oxygen and/or nitrogen molecules in the current experiments; supersaturation of the liquid was a requirement for micropancake formation; no micropancakes existed when we used degassed liquid). This means that the substrate immediately underneath a micropancake is dewetted, so subsequent micropancake growth corresponds to a dynamic dewetting process. Once the composition of the micropancakes is fully understood, control of their growth is the obvious next step. Currently, we have no reason to believe that this phenomenon is restricted to the PFDTS-coated silicon used here or the HOPgraphite used in ref 9. In fact, preliminary experiments in our laboratory with OTS-coated silicon have also proved successful for micropancake formation. Hence, dynamic dewetting through micropancake growth may be a phenomenon inherent to all hydrophobic systems, thus posing new challenges in fluid dynamics and surface science. (25) Amirfazli, A.; Neumann, A. W. Adv. Colloid Interface Sci. 2004, 110, 121–141.
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The relationship between surface nanobubbles and micropancakes largely remains unknown. Zhang et al.11 demonstrated that nanobubbles could grow from micropancakes, mediated by the AFM cantilever tip and resulting in micropancake decay. However, preliminary results in our laboratory demonstrate distinct regions of existence in phase space for both nanobubbles and micropancakes, and this shall be the subject of an upcoming paper.
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Acknowledgment. The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement number 235873 and from the Foundation for Fundamental Research on Matter (FOM), which is sponsored by The Netherlands Organization for Scientific Research (NWO). Furthermore, J.R.T.S. acknowledges Patrick Markus from Veeco Instruments for the loan of a Multimode V system.
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