Langmuir 2007, 23, 9823-9830
9823
Decoupling of the Liquid Response of a Superhydrophobic Quartz Crystal Microbalance P. Roach, G. McHale,* C. R. Evans, N. J. Shirtcliffe, and M. I. Newton School of Biomedical and Natural Sciences, Nottingham Trent UniVersity, Clifton Lane, Nottingham, NG11 8NS, United Kingdom ReceiVed April 14, 2007. In Final Form: July 8, 2007 Recent reports using particle image velocimetry and cone-and-plate rheometers have suggested that a simple Newtonian liquid flowing across a superhydrophobic surface demonstrates a finite slip length. Slippage on a superhydrophobic surface indicates that the combination of topography and hydrophobicity may have consequences for the coupling at the solid-liquid interface observed using the high-frequency shear-mode oscillation of a quartz crystal microbalance (QCM). In this work, we report on the response of a 5 MHz QCM possessing a superhydrophobic surface to immersion in water-glycerol mixtures. QCM surfaces were prepared with a layer of SU-8 photoresist and lithographically patterned to produce square arrays of 5 µm diameter circular cross-section posts spaced 10 µm center-to-center and with heights of 5, 10, 15, and 18 µm. Non-patterned layers were also created for comparison, and both non-hydrophobized and chemically hydrophobized surfaces were investigated. Contact angle measurements confirmed that the hydrophobized post surfaces were superhydrophobic. QCM measurements in water before and after applying pressure to force a Cassie-Baxter (non-penetrating) to Wenzel (penetrating) conversion of state showed a larger frequency decrease and higher dissipation in the Wenzel state. QCM resonance spectra were fitted to a Butterworth-van Dyke model for the full range of water-glycerol mixtures from pure water to (nominally) pure glycerol, thus providing data on both energy storage and dissipation. The data obtained for the post surfaces show a variety of types of behavior, indicating the importance of the surface chemistry in determining the response of the quartz crystal resonance, particularly on topographically structured surfaces; data for hydrophobized post surfaces imply a decoupling of the surface oscillation from the mixtures. In the case of the 15 µm tall hydrophobized post surfaces, crystal resonance spectra become narrower as the viscosity-density product increases, which is contrary to the usual behavior. In the most extreme case of the 18 µm tall hydrophobized post surfaces, both the frequency decrease and bandwidth increase of the resonance spectra are significantly lower than that predicted by the Kanazawa and Gordon model, thus implying a decoupling of the oscillating surface from the liquid, which can be interpreted as interfacial slip.
Introduction High aspect ratio patterns or high levels of roughness of a hydrophobic surface enhance the water contact angle, leading to a superhydrophobic surface. In the Cassie-Baxter model of superhydrophobicity, water bridges between the peaks of surface features and is suspended across troughs in the surface, while, in the Wenzel model, water remains in contact with the entire surface area below it.1-4 The Cassie-Baxter state is often described as a slippy state in the sense that droplets of water move more easily on such a surface than on a smooth and flat surface of the same material possessing the same surface chemistry. In contrast, the Wenzel state tends to increase the difficulty with which droplets can be set into motion and is therefore described as a sticky state.5 Within this context, several authors have asked whether the flow of a simple Newtonian liquid over a Cassie-Baxter surface can be described by a noslip boundary condition or whether such a boundary condition needs to be relaxed and a slip length, b, introduced (Figure 1a,b).6-8 * Corresponding author. E-mail:
[email protected]: +44 (0)115 8483383. (1) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546-551. (2) Johnson, R. E.; Dettre, R. H. Contact Angle, Wettability and Adhesion; Advances in Chemistry Series; American Chemical Society: Washington, DC, 1964; pp 112-135. (3) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988-994. (4) Wenzel, R. N. J. Phys. Colloid Chem. 1949, 53, 1466-1467. (5) Que´re´, D.; Lafuma, A.; Bico, J. Nanotechnology 2003, 14, 1109-1112. (6) McHale, G.; Newton, M. I. J. Appl. Phys. 2004, 95, 373-380. (7) Joseph, P.; Cottin-Bizonne, C.; Benoit, J.-M.; Ybert, C.; Journet, C.; Tabeling, P.; Bocquet, L. Phys. ReV. Lett. 2006, 97, article 156104.
Figure 1. Possible boundary conditions: (a) no-slip boundary condition, (b) slip boundary condition, and (c) mixed flow across a superhydrophobic surface.
The solution of the Navier-Stokes equations for flow across a Cassie-Baxter-type surface with a parallel stripe topography predicts b ) Lf(φs)/2π, where f(φs) is a function of the solid area fraction φs, and L is the periodicity of the surface features.9-12 (8) Neto, C.; Evans, D. R.; Bonaccurso, E.; Butt, H. J.; Craig, V. S. J. Rep. Prog. Phys. 2005, 68, 2859-2897. (9) Philip, J. R. Z. Angew. Math. Phys. 1972, 23, 960-968, 353-372. (10) Lauga, E.; Stone, H. A. J. Fluid Mech. 2004, 489, 55-77. (11) Cottin-Bizonne, C.; Barrat, J. L.; Bocquet, L.; Charlaix, E. Nat. Mater. 2003, 2, 237-240.
10.1021/la701089a CCC: $37.00 © 2007 American Chemical Society Published on Web 08/18/2007
9824 Langmuir, Vol. 23, No. 19, 2007
Roach et al.
This basic scaling law can be deduced for a superhydrophobic surface consisting of a square lattice of hydrophobic posts by considering regions that either have no-slip (Poiseuille flow above the posts) or complete slip (plug flow between the posts) (Figure 1c). Experimental studies of whether flow of water past a superhydrophobic surface can be described by a slip length have started to appear in the literature. One of the most complete studies to date used a carbon nanotube forest superhydrophobic surface described by a solid surface fraction, φs ) a2/L2, with L ) 1-7 µm, and the resulting microparticle image velocimetry flow profiles gave slip lengths scaling as b ) 0.28L, i.e., up to 1.5 µm in these experiments7 (see Figure 1c). A macroscopic approach has been adopted by Choi et al. who used a coneand-plate rheometer and reported significant drag reduction for flow across a superhydrophobic nanograte surface13 and a sharptip nanostructured surface,14 while Gogte and co-workers15 reported that the application of a surface texture and hydrophobic coating to a hydrofoil in a water tunnel results in drag reduction on the order of 10% or higher. While much of the focus has been on the slippy state, it is known that applying pressure causes a conversion to a Wenzel state, with full water penetration into the surface structure. In this situation, the effective drag is increased compared to a smooth and flat surface.7 A common method of investigating solid-liquid interfacial coupling used in many sensor applications is to use an immersed surface undergoing shear motion, such as a quartz crystal microbalance (QCM).16-18 Models of the response of the QCM account for attachment of mass and for changes in viscosity and density of the liquid, but tend not to take into account accompanying changes in hydrophobicity19 or how such a change may couple to the surface topography.6 In a Newtonian liquid, the shear mode of oscillation of a QCM surface creates a damped shear-mode oscillation in the liquid, which decays within a characteristic penetration depth of the interface δ ) (η/πfsF)1/2, where F and η are the density and viscosity of the liquid, respectively, and fs is the resonant frequency. When immersed in a Newtonian liquid, both a frequency decrease, ∆f, and a bandwidth increase, ∆B, occur in proportion to the square root of the viscosity-density product:
( )
1 fsηF ∆f )fs Zq π
1/2
and
( )
∆B 2 fsηF ) fs Zq π
1/2
(1)
where the specific acoustic impedance of quartz is Zq ) (µqFq)1/2 ) 8.8 × 106 kg m-2 s-1; similar relations exist for overtone frequencies. Often the effect of the loading caused by immersing a QCM is represented by a complex load impedance, ZL, which, for a Newtonian liquid, is
ZKG L ) (1 + j)xπfsηF
(2)
where j ) (-1)1/2. In this formalism, the complex frequency shift is (12) Cottin-Bizonne, C.; Barentin, C.; Charlaix, E.; Bocquet, L.; Barrat, J. L. Eur. Phys. J. 2004, 15, 427-438. (13) Choi, C. H.; Ulmanella, U.; Kim, J.; Ho, C. M.; Kim, C. J. Phys. Fluids 2006, 18, article 087105. (14) Choi, C. H.; Kim, C. J. Phys. ReV. Lett. 2006, 96, article 066001. (15) Gogte, S.; Vorobieff, P.; Truesdell, R.; Mammoli, A.; van Swol, F.; Shah, P.; Brinker, C. J. Phys. Fluids 2005, 17, article 051701. (16) Sauerbrey, G. Z. Phys. 1959, 155, 206-222. (17) Bruckenstein, S.; Shay, M. Electrochim. Acta 1985, 30, 1295-1300. (18) Kanazawa, K. K.; Gordon, J. G. Anal. Chim. Acta 1985, 175, 99-105. (19) Ellis, J. S.; McHale, G.; Hayward, G. L.; Thompson, M. J. Appl. Phys. 2003, 94, 6201-6207.
()
∆fs + j∆B/2 j ZL ) fs π Zq
(3)
which emphasizes that a Newtonian response can be deduced from a dependence of both the frequency shift and the change in bandwidth on the square root of the viscosity-density product and by verifying that their changes are correlated, such that ∆f ) -∆B/2. Bandwidth is a measure of the loss of energy and of the damping of the shear-mode oscillation of the liquid close to the solid-liquid interface, and so some authors prefer to define a dissipation as D ) B/fs (also equal to Q-1). In an earlier report we considered theoretically how a textured hydrophobic surface consisting of regularly spaced posts might introduce a slip-length dependence into the response of a QCM.6 We subsequently reported preliminary results for QCM frequency changes for such a surface using regularly spaced hydrophobic posts and water-poly(ethylene glycol) (PEG) solutions;20 in that work the height of posts was limited, dissipation was not measured, and the water-PEG mixtures did not provide a Newtonian liquid at the highest concentrations. Complementary experimental results have also been reported by Fujita et al.,21 who studied slip conditions using a 9 MHz QCM coated with a 1-2 µm thick polystyrene layer containing poly(tetrafluoroethylene) particles to achieve a superhydrophobic surface. They showed that the transition from a Cassie-Baxter to a Wenzel wetting state could be discriminated and that a Cassie-Baxtertype state reduced energy loss while a Wenzel one increased energy loss. Kwoun et al. have also reported frequency shifts in water for multi-resonance thickness shear-mode devices coated with a hydrophobized 0.6 µm thick silica nanoparticle layer.22 They observed a reduced frequency shift, which they interpreted as effective slip. In this report we provide an extensive experimental study of whether a decoupling of a high-frequency oscillating surface immersed in a Newtonian liquid occurs when that surface supports the liquid in a superhydrophobic (Cassie-Baxter) state. Our focus is on the types of responses of a QCM possessing a superhydrophobic surface rather than the possible use of a QCM as a tool to provide a measurement of a slip length. The system reported is a QCM possessing a surface of lithographically fabricated posts in SU-8 photoresist, both untreated and treated with a hydrophobizing fluorochemical, and subsequently immersed in water/glycerol mixtures. The QCM data are based on a full Butterworth-van Dyke (BVD) model fitting approach to impedance spectra to extract changes in both frequency and dissipation; these data are complemented by contact angle measurements on droplets of the liquids. We first show that a Cassie-Baxter superhydrophobic state exists for the fluorochemical-treated post surfaces for the full range of water-glycerol mixtures deposited as droplets. We then show that this state is retained when the crystal is immersed in the mixtures and that conversion of these liquids on these superhydrophobic surfaces from the Cassie-Baxter state to the Wenzel state by application of pressure increases the magnitude of the QCM response. Subsequently, we demonstrate that a Newtonian response, defined as a linear relationship between frequency-bandwidth changes, occurs for water-glycerol mixtures on three of our four types of untreated post surfaces. Finally, we report a rich variety of responses of QCMs having superhydrophobic post surfaces, all (20) Evans, C. R.; McHale, G.; Shirtcliffe, N. J.; Newton, M. I. Sens. Actuators, A 2005, 123-124, 73-76. (21) Fujita, M.; Muramatsu, H.; Fujihira, M. Japn. J. Appl. Phys. 2005, 44, 6726-6730. (22) Kwoun, S. J.; Lec, R. M.; Cairncross, R. A.; Shah, P.; Brinker, C. J. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2006, 53, 1400-1403.
Liquid Response of a Superhydrophobic QCM
Figure 2. Electron micrographs of 5 µm diameter circular posts fabricated in SU-8 photoresist in square lattice array patterns with 10 µm center-to-center spacing on a QCM. Post heights are (a) 5 µm, (b) 10 µm, (c) 15 µm, and (d) 18 µm.
of which are consistent with a partial decoupling of the motion of the crystal surface from the liquid, and which, for the tallest posts, can be interpreted as interfacial slip. Experimental Patterned surfaces were prepared directly onto the gold electrode of a QCM by photolithographic patterning of SU-8 photoresist (Figure 2). Layers of SU-8 were spun on to achieve the required thickness and irradiated with UV through a mask using a MJB3 SU ¨ SS mask aligner. A square array of circular posts of diameter d ) 5 µm with center-center spacing of L ) 10 µm was used, with post heights in the range of h ) 0-18 µm. Fabricating tall SU-8 posts on the highly reflective QCM electrodes proved to be technically difficult compared to previous surfaces onto which we have fabricated these types of structures.23 To partially overcome the reflectivity problems and to reduce undercutting of the post features, an antireflective layer, XHRiC (Brewster Scientific), was pre-coated onto the gold electrode surface; patterned surfaces were hydrophobized as previously described.20 Briefly, samples were immersed in a dilute fluorocarbon containing solution (Grangers Wash-In), rinsed in deionized water, and heated 20 min at 100°. Liquid contact angles were measured on a Kru¨ss DSA 10 system using 5 µL droplets, with droplet images being taken immediately to minimize evaporation effects. The reported contact angles are the average of at least four measurements taken on each surface for each concentration of mixture. The purpose of the contact angle data is to determine whether droplets of solutions are in the Cassie-Baxter or Wenzel states rather than to determine the contact angle hysteresis; we have previously reported and discussed advancing and receding contact angles for equivalently prepared surfaces.23 Quartz crystals having a fundamental frequency of 5 MHz and diameter of 25 mm were used (Testbourne, Ltd.), with frequency spectra being monitored using an Agilent Technologies E5061A network analyzer over the range of 4.8-5.4 MHz. Resonance spectra were recorded for crystals in air and in liquid at 25 °C and fitted to a BVD model using LabView 6.1. In the BVD model, the quartz crystal and its load is regarded as a series LCR resonant circuit with capacitance Cs, inductance Ls (23) Shirtcliffe, N. J.; Aqil, S.; Evans, C.; McHale, G.; Newton, M. I.; Perry, C. C.; Roach, P. J. Micromech. Microeng. 2004, 14, 1384-1389.
Langmuir, Vol. 23, No. 19, 2007 9825 ) L1 + L2, and resistance Rs ) R1 + R2, where L1 and R1 are the values for the unloaded resonator and L2 and R2 are the additional resistance and inductance upon loading the resonator. The formulas for the fitting of the model also allows for a parallel capacitance Cp and a series impedance, assumed here to be the output resistance, Ro, of the network analyzer. Fitting the resonance curve as a function of angular frequency (ω) allows a load impedance to be extracted as a series combination of a resistance and an inductance, i.e., ZL ) R2 + jωL2; the bandwidth is given by B ) Rs/2πLs, and the series resonant frequency is given by fs ) 1/(2π(LsCs)1/2). Distilled water and glycerol (99+% Fisher) were mixed to cover a wide viscosity-density product range for a Newtonian liquid; ethanol (Haymans) was also used as a complete wetting test liquid, although detailed results for this liquid are not presented in this report. Water-glycerol mixture concentrations, densities, viscosities, and shear wave penetration depths are given in Table 1 for concentrations below 80%. Data for 89.4%, 94.7%, and 100% glycerol were also recorded, but it should be noted that glycerol is hygroscopic and so absorbs water from the atmosphere. Since experiments were conducted in an open lab with a typical relative humidity between 45% and 50%, calculations of viscosity-density product using the nominal percent weight concentration of glycerol for viscosity and density will not be accurate for concentrations above 80%. Resonance spectra of liquids in Cassie-Baxter and Wenzel wetting states on crystals possessing posts were investigated. In these investigations, air pressure was applied above the liquid using a syringe to force liquid to penetrate between the posts and so force a conversion from the superhydrophobic Cassie-Baxter state. Spectra were recorded before pressure was applied and were monitored for several minutes after returning to normal conditions.
Results and Discussion Contact Angle Data. The contact angle, θ, of glycerol solutions on flat and patterned surfaces before and after hydrophobization are summarized in Table 1 together with key physical and acoustic parameters. As an example, for 0% glycerol, the measured contact angles on flat surfaces are (75 ( 2)° and (115 ( 3)° for the non-hydrophobized and hydrophobized cases. The corresponding experimental data for the non-hydrophobized patterned surfaces with post heights of 5, 10, 15, and 18 µm are (106 ( 1)°, (118 ( 3)°, (119 ( 1)°, and (123 ( 2)°, respectively. For the hydrophobized post surfaces, the contact angles are (155 ( 2)°, (151 ( 1)°, (143 ( 3)°, and (138 ( 2)°, respectively. The corresponding Cassie-Baxter predictions for the non-hydrophobized and hydrophobized post surfaces based on the measured contact angles on the flat surfaces for this concentration are independent of height and are (138.9 ( 0.5)° and (152.5 ( 1)°, respectively. The Wenzel predictions depend on post height, and, because of the error range in the flat surface contact angle, this can give a range of values for any one height of post; for example, in the case of the 15 µm tall posts, the nonhydrophobized flat surface value of (75 ( 2)° predicts a Wenzel contact angle ranging from 11° to 50°. The predictions of the Kanazawa and Gordon equation for the effect of a 0% glycerol solution on the frequency shift and bandwidth shift of a QCM are given in the table as (-672 ( 3) Hz and (1344 ( 6) Hz, respectively. We have not included data for nominal concentrations above 80% because, in this range, the experimental concentrations could be much lower than nominal values due to the hygroscopic nature of glycerol. The first observation from the contact angle data is that any solution deposited on a patterned surface has a significantly larger contact angle than on the chemically equivalent flat surface (i.e., a non-hydrophobized post surface compared to a non-hydrophobized flat surface and a hydrophobized post surface compared to a hydrophobized flat surface). For the non-hydrophobized patterned surfaces with posts of height 5, 10, 15, and 18 µm,
9826 Langmuir, Vol. 23, No. 19, 2007
Roach et al.
Table 1. Solution Concentrations, Properties, and Measured Contact Angles on Flat and Patterned Surfaces with and without Hydrophobic Coatingsa θs/ degrees
θHs / degrees
θp/ degrees
θHp / degrees
θCB/ degrees
θHCB/ degrees
θW/ degrees
θHW/ degrees
δ/ µm
∆fKG/ Hz
∆BKG/ Hz
0.942
75 ( 2
115 ( 3
152.5 ( 1.1
1344 ( 6
113 ( 1
137.2 ( 0.5
151.7 ( 0.5
0.43
-1330 ( 15
2660 ( 30
5.29 ( 0.33
1128 ( 4
2.44 ( 8
73 ( 3
105 ( 5
138.3 ( 0.8
148.7 ( 0.8
0.55
-1745 ( 60
3490 ( 120
7.54 ( 0.41
1147 ( 4
2.94 ( 9
66 ( 2
109 ( 2
136.4 ( 0.5
150.2 ( 0.7
0.65
-2095 ( 60
4190 ( 120
136.9 ( 0.8
146.9 ( 1.8
0.92
-3065 ( 135
6130 ( 270
136.2 ( 0.6
150.9 ( 0.8
139 ( 8 164-180 180 180 134 ( 3 164-180 180 180 118 ( 10 132(19 126-180 136-180 126 ( 4 147 ( 10 169-180 180 108 ( 9 117 ( 14 126 ( 23 110-170 130 ( 4 147-180 180 180
-672 ( 3
69 ( 2
63 ( 3 48 ( 7 11-50 0-30 50 ( 4 0-33 0 0 58 ( 6 41(11 0-36 0-22 43 ( 5 0-16 0 0 48 ( 7 0-33 0 0 41 ( 5 0 0 0
0.24
1.86 ( 3
155 ( 2 151 ( 1 143 ( 3 138 ( 2 150 ( 1 148 ( 1 149 ( 1 149 ( 3 152 ( 3 147 ( 1 143 ( 2 138 ( 2 149 ( 2 148 ( 1 147 ( 1 148 ( 1 152 ( 1 151 ( 1 144 ( 2 137 ( 2 151 ( 1 149 ( 1 148 ( 1 150 ( 2
138.9 ( 0.5
1099 ( 3
106 ( 1 118 ( 3 119 ( 1 123 ( 2 101 ( 2 121 ( 1 127 ( 1 117 ( 1 95 ( 2 109 ( 1 117 ( 1 113 ( 4 96 ( 3 111 ( 2 95 ( 5 120 ( 2 88 ( 1 103 ( 1 115 ( 2 106 ( 2 86 ( 3 99 ( 8 118 ( 1 116 ( 2
1.38
-4680 ( 265
9360 ( 530
η/m Pa‚s
F/kg m-3
0.0
0.89 ( 0.01
997 ( 3
40.0
3.16 ( 0.07
51.3
58.2
wt %
(Fη)1/2/ kg m-2 s-1/2
69.2
15.7 ( 1.3
1175 ( 5
4.3 ( 0.2
68 ( 3
100 ( 5
78.2
35.9 ( 3.9
1199 ( 5
6.6 ( 0.3
65 ( 2
111 ( 2
For each concentration, data is given for surfaces with posts of heights 5, 10, 15, and 18 µm corresponding to a Cassie-Baxter fraction φs ) 0.196 and roughness factors rg ) 1.79, 2.57, 3.36, and 3.83, respectively. For completeness, the theoretical values of the Cassie-Baxter contact angle, θCB, the Wenzel contact angle, θW, the penetration depth, δ, and the predicted frequency shift, ∆fKG, and bandwidth, ∆BKG, for the Kanazawa and Gordon model have been included. a
there is a trend that higher glycerol concentrations lead to slightly lower contact angles. The range of contact angles on each of these surfaces is 86-106°, 99-121°, 95-127°, and 106-123°, respectively. The contact angles for the solutions on the hydrophobized post surfaces did not have any dependence on the glycerol concentration. On these surfaces, the contact angles were (152 ( 3)°, (149 ( 2)°, (146 ( 3)°, and (143 ( 6)° for the 5, 10, 15, and 18 µm tall posts, respectively. For the design of post pattern we used, the Cassie-Baxter surface area fraction is φs ) πd2/4L2 ) 0.196, and, using cos θCB ) φs cos θs - (1 - φs), this predicts that contact angles on smooth surfaces of θs ) 100-115° should be increased to the range θCB ) 147-153° on post surfaces. This is consistent with the contact angle data for the hydrophobic patterned surfaces with post heights of 5, 10, and 15 µm. We therefore conclude that water-glycerol mixtures for concentrations up to 80% are in the suspended Cassie-Baxter state when deposited on these three hydrophobic post patterned surfaces. The agreement of data for the fourth hydrophobic patterned surface with post heights of 18 µm is slightly less, but the analysis still supports the conclusion that liquid is in the suspended Cassie-Baxter state. Since the fabrication process resulted in posts with slightly nonparallel sides, the post tops are larger than designed; the CassieBaxter fraction is therefore slightly higher and so results in lower contact angles. This is consistent both with the SEM images (Figure 2) and with the systematic decrease in the measured contact angles from (152 ( 3)° down to (143 ( 6)° as the post height was increased from 5 to 18 µm. To achieve the contact angles observed on the 18 µm tall posts, a 21% increase in diameter of the top of the posts gives φs ) 0.288 and so implies θCB ) (143° ( 3.5°). In the case of non-hydrophobized flat surfaces, the contact angles were in the range θs ) 65-75°, and, on non-hydrophobized patterned surfaces, the contact angles were increased to 86106°, 99-121°, 95-127°, and 106-123° for the 5, 10, 15, and 18 µm tall post surfaces, respectively. The Cassie-Baxter prediction for these surfaces is θCB ) 136-139°, and so we conclude that the solutions are not fully suspended by these
surfaces. In the Wenzel case, the contact angle is deduced from cos θ ) rs cos θs, where the roughness, rs ) 1 + πdh/L2, is 1.79, 2.57, 3.36, and 3.83, respectively, for the 5, 10, 15, and 18 µm tall posts. Since the contact angles for the non-hydrophobized flat surfaces are all less than 90°, a Wenzel state with complete penetration of the liquid into the non-hydrophobized patterned surfaces would be expected to reduce the observed contact angle, and this is inconsistent with the data. A further qualitative indicator is that incomplete penetration produces a visual appearance of contrast different from that of a liquid with air beneath it. We therefore conclude that a partial penetration of the solutions into the non-hydrophobized patterned surfaces occurs. QCM Impedance Spectra Procedures and Accuracy. To verify the ability of our fitting procedure based on the reflected power data, we used a polished 5 MHz crystal and water-glycerol solutions. We then considered the response to water-glycerol solutions of quartz crystals with spin-coated layers of SU-8 of thickness 5, 10, 15, and 18 µm. In each case (polished crystal and SU-8 layers), we repeated experiments after hydrophobizing the surfaces. We considered using four-parameter fits for each separate resonance curve at each mixture concentration and compared this to determining the values Cs and fp ) 1/(2π(LsCp)1/2) in an initial four-parameter fit in air and then retaining these values and using two-parameter fits for all subsequent experiments in the sequence using the various mixtures. We also considered using a four-parameter fit to determine the values in water and then retaining these values for subsequent twoparameter fits for all water-glycerol mixtures in a given experimental sequence. Our conclusion was that a higher level of scatter in the data for fs and B occurred when allowing all four parameters to be varied for each resonant curve and that, for consistency across any given data set, the same values of Cs and fp should be retained on the basis of a crystal in its holder with its O-ring seal and in position immersed in water. All frequencies and bandwidths reported for crystals immersed in glycerolwater mixtures refer to two-parameter fits of the resonance curves using the values of Cs and fp from an initial four-parameter fit for the crystal immersed in water. For crystals with post surfaces,
Liquid Response of a Superhydrophobic QCM
Figure 3. Frequency shift, ∆f, and bandwidth shift, ∆B, from air values for quartz crystals with flat SU-8 photoresist layers upon immersion in water-glycerol mixtures. The non-hydrophobized surfaces are shown by open symbols (SU-8 thicknesses: 5 µm ) 0 0 0, 10 µm ) ] ] ], 15 µm ) ∆ ∆ ∆, and 18 µm ) O O O), and the equivalent thicknesses of hydrophobized surfaces are shown by the solid symbols. The fits to the data for polished crystals (+++) and polished crystals with hydrophobized surfaces (***) are shown by solid and dashed lines.
the values of these two parameters in water differed from that in air, but the results for the frequency and bandwidth shifts, ∆f ) (fs - fair) and ∆B ) (B - Bair), from the air reference values upon immersion in the solution did not differ significantly according to which values of Cs and fp were used to obtain fs and B. In general, the agreement for ∆f was within 1%, while the agreement for ∆B was within 12%, except for the 15 and 18 µm tall hydrophobized posts. In these last two cases, the agreement for ∆B was only 15-25% for the first lowest concentrations of glycerol; it should be noted that these also corresponded to the lowest absolute changes in bandwidth. QCM Data for Flat Surfaces. Figure 3 shows a test on polished (+++) and hydrophobized polished crystal (***) of the Kanazawa and Gordon relationship, ∆f ) -∆B/2; solution concentrations range from 100% water to (nominally) 100% glycerol. The fits to the data are shown by the solid and dashed lines and have slopes of 0.494 and 0.506 and intercepts of -72 Hz and -51 Hz, respectively, which is consistent with the Kanazawa and Gordon model. The initial values in air were fair ) 5.000947 MHz and Bair ) 800 Hz, and fair ) 5.004269 MHz and Bair ) 388 Hz, respectively, for the polished and hydrophobic polished crystals. Data for spin-coated SU-8 layers are also shown Figure 3, with open symbols representing nonhydrophobic surfaces and solid symbols representing the same thickness layer, but with a hydrophobic treatment; the square, diamond, triangle, and circle symbols correspond to 5, 10, 15, and 18 µm thick layers, respectively. In each case, the frequency and bandwidth shifts are the differences from the air reference values for the spin-coated system. The data for these flat SU-8 layers have a larger scatter than that for the polished crystals, which probably indicates some roughness. However, the curves demonstrate that SU-8 prepared as flat layers of these thicknesses does not show viscoelastic behavior. In general, the Kanazawa and Gordon model is a reasonable representation of the data for crystal possessing an SU-8 layer over a wide range of solution concentrations, whether the layer has been hydrophobized or not. In Figure 4, we show data for the frequency shift dependence on the square root of the viscosity-density product; the straight line shows the prediction from the Kanazawa and Gordon model. In this case, only the data for the concentration range up to 78% glycerol is shown because of the inaccuracy in the viscosity-
Langmuir, Vol. 23, No. 19, 2007 9827
Figure 4. Dependence of frequency shift, ∆f, on the square root of the viscosity-density product, (ηF)1/2, for the data in Figure 3 (the symbols are the same); the dotted line is the Kanazawa and Gordon prediction.
density product for concentrations above this value arising from the hygroscopic nature of glycerol; this inaccuracy is not a problem for Figure 3, since, in that case, concentration parametrizes the curve and, provided the data obeys the Kanazawa and Gordon equation, any inaccuracy in concentration simply scales the data up and down the straight line. The data for both the polished and hydrophobized polished crystal is in good agreement with the Kanazawa and Gordon model; fitting the data gives slopes of 598 and 696 kg-1 m2 s-1/2 and intercepts of 305 and 54.5 Hz, respectively, compared to the expected values of 713 kg-1 m2 s-1/2 and 0 Hz. Restricting the fits to concentrations below 70%, to ensure that hygroscopic effects are not influencing the fits, gives fits with slopes of 696 and 719 kg-1 m2 s-1/2 and intercepts of 55 and 8 Hz, respectively, which is consistent with theory and suggests that our experimental procedures are accurate for the polished crystal. For the QCMs with flat SU-8 layers, the data tends to show a larger frequency shift for a given solution than the polished crystal. This is not due to Sauerbrey mass loading from the SU8 layer, as the shift is calculated from the air value for the quartz crystal with the layer. We believe it likely arises from a slight roughness of the spin-coated SU-8. While this reduces the absolute accuracy and increases the scatter of the results for SU-8 layers, it does not alter the overall type of response demonstrated in Figure 3 for the coupled frequency-bandwidth behavior. Figure 5 shows the equivalent data for the increase in bandwidth in solution. The data for both the polished (+++) and hydrophobized polished crystal (***) is in good agreement with the Kanazawa and Gordon model; fitting the data for the polished and hydrophobic polished crystal gives slopes of 1143 and 1287 kg-1 m2 s-1/2 and intercepts of 690 and 476 Hz, respectively, compared to the expected values of 1427 kg-1 m2 s-1/2 and 0 Hz. Again, improved agreement with the Kanazawa and Gordon model could be obtained by restricting the fits to the range of concentrations less than 70% glycerol to ensure hygroscopic effects are not important. Similarly to the frequency shift, the data for QCMs with flat SU-8 layers have a slightly larger bandwidth increase upon immersion in a given solution than the polished crystal, which we again attribute to a slight roughness of the spin-coated SU-8 layer. We therefore conclude that our experimental procedures are capable of determining a Newtonian response in water-glycerol solutions from the coupled frequencybandwidth response (e.g., Figure 3), that the Kanazawa and Gordon model is a reasonable description of the response of our SU-8-coated crystals, which do not show a viscoelastic response,
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Figure 5. Dependence of bandwidth shift, ∆B, on the square root of the viscosity-density product, (ηF)1/2, for the data in Figure 3 (the symbols are the same); the dotted line is the Kanazawa and Gordon prediction.
Figure 6. Example change in impedance spectra as water ingress is induced between the 18 µm tall posts of a hydrophobic patterned surface. The solid curve is the data before pressure is applied, and the dotted curve is the data after pressure has been applied.
and that this remains true for these layers whether or not they have been hydrophobized. Cassie-Baxter to Wenzel Transition. The contact angle data for droplets indicate that a Cassie-Baxter state with liquid suspended across hydrophobized posts should occur unless sufficient pressure is applied to cause penetration of the liquid between the posts and so convert the state to a Wenzel form. To verify that the liquids remain in the suspended Cassie-Baxter state on an immersed crystal and to investigate the QCM response to these two different wetting states, water was added over each of the hydrophobized patterned surfaces, and pressure was applied to force the water between the posts. Visually, from the contrast of light below the liquid, we believe the Cassie-Baxter state was maintained for the immersed crystal. Frequency spectra were taken before and after applied pressure, showing that, as the water entered the surface texture, both a decrease in frequency and an increase in bandwidth occurred. Figure 6 gives an example of the spectra for a crystal with 18 µm tall posts. These effects are consistent with increased coupling between the surface and the water. Using the BVD model with the initially immersed hydrophobized patterned crystals as the reference state (i.e., for the selection of the capacitance values in the BVD model), the orders of magnitude of frequency decreases in the transition from Cassie-Baxter to Wenzel states were 1.8, 2.4, 3.2, and 3.1 kHz, for 5, 10, 15, and 18 µm tall post surfaces, respectively. Similarly, the orders of magnitude of the bandwidth increases were 1.6, 1.2, 0.4, and 0.8 kHz, respectively. For water, the
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Figure 7. Frequency shift, ∆f, and bandwidth shift, ∆B, from air values for quartz crystals with 5 µm diameter circular SU-8 photoresist posts arranged in a square lattice of period 10 µm upon immersion in water-glycerol mixtures. The non-hydrophobized surfaces are shown by open symbols (post heights: 5 µm ) 0 0 0, 10 µm ) ] ] ], 15 µm ) ∆ ∆ ∆, and 18 µm ) O O O), and the equivalent heights of the hydrophobized post surfaces are shown by the solid symbols. The dotted line is the Kanazawa and Gordon prediction for a flat surface.
Kanazawa and Gordon model predicts that water coming into contact with a smooth surface would give a 0.67 kHz decrease in resonant frequency and a 1.34 kHz increase in bandwidth, and scaling these by the surface fraction 1 - φs ) 1 - 0.196 ) 0.804 gives 0.54 kHz and 1.08 kHz. This illustrates that a simple contact area scaling does not account for the change. An in-depth explanation of the QCM response to the Wenzel state is beyond the scope of this report, which focuses on the types of response observable from a QCM with a Newtonian liquid in the CassieBaxter suspended state. QCM Data for Patterned Surfaces. The open symbols in Figure 7 show the test of the Kanazawa and Gordon relationship, ∆f ) -∆B/2 for non-hydrophobized post surfaces using solution concentrations ranging from pure water to (nominally) 100% glycerol. The data for the 15 and 18 µm tall post surfaces (open triangles and open circles, respectively) fall on a straight-line with a slope similar to that predicted by the Kanazawa and Gordon model, but with an additional offset. This would be consistent with a Newtonian liquid response, but with the pattern causing an additional Sauerbrey mass-like contribution to the frequency shift. This interpretation would be consistent with the contact angle data, which imply a partial penetration of the liquid into the non-hydrophobized patterned surfaces. Similarly, the data for 5 µm tall post surfaces (open squares) can be interpreted in the same manner, providing that the data points corresponding to concentrations above 80% glycerol are neglected. The data for the 10 µm tall post surfaces (open diamonds) describe a clockwise arc, which is different from the other data and does not fit such an interpretation; for the highest concentrations of glycerol, the resonant frequency is greater than that in air, while damping of the crystal oscillation is strong. However, we know that, as the concentration of glycerol increases from 85% to 100%, the shear wave penetration depth will increase from 2 to 7 µm. It is possible that this triggers a nonlinear response for surfaces with post heights on a similar length scale, such as the 10 µm tall post surface. Arcs in these types of plots are also characteristic of a load material with a viscoelastic response, but since neither the flat layer nor taller post surfaces show such a response, material viscoelasticity is unlikely to be the origin of the response. Whether microposts could couple nonlinearly, and so imitate a viscoelastic response, is an open question. QCM
Liquid Response of a Superhydrophobic QCM
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Figure 8. Dependence of frequency shift, ∆f, on the square root of the viscosity-density product, (ηF)1/2, for the data in Figure 7 (the symbols are the same).
Figure 9. Dependence of bandwidth shift, ∆B, on the square root of the viscosity-density product, (ηF)1/2, for the data in Figure 7 (the symbols are the same).
responses with a positive frequency shift accompanied by strong damping have previously been observed as a result of the generation of compressional waves.24,25 In such cases, a resonant matching of some size (e.g., liquid depth or droplet height) within the system occurs. Quartz crystals with structured surfaces clearly provide opportunities for resonances because of their introduction of characteristic length scales via the height, diameter, and spacing of the microposts. The solid symbols in Figure 7 show the equivalent data for the post surfaces after they have been hydrophobized and so have been converted into Cassie-Baxter-type superhydrophobic surfaces. Again, the data for the 5 µm tall hydrophobized post surfaces (filled square symbols) fall on a straight-line parallel to the Kanazawa and Gordon curve, thus implying a Newtonian liquid response, but with an additional contribution to the frequency shift and the data lying closer to the origin; data for the highest concentrations of glycerol are not shown because the resonances were too broad to fit. The data for the 10 µm tall hydrophobic post surfaces (filled diamond symbols) continue to describe an arc in a similar manner to the data for the 10 µm tall non-hydrophobized surfaces, but with a reduced radius for the arc; two data points for 85% and 89% glycerol concentration are missing because the curves could not be fitted, although the data for 95% and 100% glycerol are present. This may suggest the (24) Schneider, T. W.; Martin, S. J. Anal. Chem. 1995, 67, 3324-3335. (25) McKenna, L.; Newton, M. I.; McHale, G.; Lu¨cklum, R.; Schroeder, J. J. Appl. Phys. 2001, 89, 676-680.
Figure 10. Evolution of quartz crystal spectra for (a) hydrophobized 15 µm tall posts and (b) hydrophobized 18 µm tall posts, immersed in water-glycerol mixtures. The arrows show the effect of increasing glycerol concentration (Example data shown is for air ) b b b, water ) ***, and nominal glycerol concentrations of 51% ) 0 0 0, 78% ) O O O, 89.4% ) ∆ ∆ ∆, and 100% ) ] ] ]).
generation of compressional waves, but with a reduced efficiency. Particularly interesting is the change in the data for the 15 and 18 µm tall hydrophobized post surfaces (filled triangle and filled circle symbols, respectively). The data now describe anticlockwise arcs rather than straight lines with positive gradients. Both of the curves remain closer to the origin than the data for the equivalent non-hydrophobized surfaces. This is consistent with the trend from the other hydrophobized patterned surfaces and indicates a reduction in the acoustic coupling of the crystal to the liquid. Figures 8 and 9 show the data as a function of the square root of the viscosity-density product for mixture concentrations of up to 80% glycerol. Comparing the open symbols to the filled symbols in Figure 8, we note that, in all cases, the effect of hydrophobizing a patterned surface and so converting it to a Cassie-Baxter-type superhydrophobic surface is to reduce the magnitude of frequency shift for any given concentration of mixture. A similar reduction in shift in bandwidth can be seen in Figure 9, although it is most pronounced for the 15 and 18 µm tall post surfaces (triangle and circle symbols). Focusing on the data for the 15 µm tall hydrophobized post surface, we see the unusual behavior that, as glycerol concentration is increased, the resonant frequency decreases, but the resonance also becomes sharper. Surprisingly, for this surface, the resonance can be of better quality than that for the same surface in air, as shown by the spectra in Figure 10a; for clarity of presentation, the figure only includes selected data from the data set obtained for the full
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range of glycerol concentration up to the (nominally) pure glycerol. For this particular micropost surface, the resonance in air begins relatively broad, implying higher dissipative energy loss due to the surface structure, and progressively narrows as the solution concentration is increased. The data for the 18 µm tall hydrophobized post surface shows small increases in the magnitude of both frequency shift and the bandwidth with increasing glycerol concentration, but it is significantly less than would be predicted according to the Kanazawa and Gordon equation. For the 78% glycerol solution, the values are around 50% of those predicted, and, for higher concentrations, the values only increase slowly, if at all. Figure 10b shows examples of the corresponding impedance spectra.
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a separation of 10 µm, and heights up to 18 µm have been created on QCMs. Water-glycerol solutions were found to partially penetrate into the surface textures, but after a fluorochemical treatment to hydrophobize the surface, the liquids no longer penetrated between posts, and a superhydrophobic surface was observed. The effect of this change of liquid repellency on the crystal impedance spectra was strong, with changes in the type of response being observed in coupled frequency-shiftbandwidth-shift curves. For all of the post surfaces, hydrophobizing the surfaces reduced the acoustic coupling of the surfaces to the liquids. In the case of the tallest posts, the frequency decrease and bandwidth increase of the crystal resonance upon immersion was substantially lower than that for a flat surface, consistent with a slip interpretation.
Conclusion In this work, the combined effect of topography and hydrophobicity on the resonance response of a high-frequency oscillating surface immersed in a Newtonian liquid has been considered. Lithographically defined microtextured surfaces consisting of regularly spaced circular posts of diameter 5 µm,
Acknowledgment. The financial support of the U.K. Engineering and Physical Sciences Research Council (EPSRC) and MOD/Dstl under Grant EP/D500826/1 is gratefully acknowledged. LA701089A
