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Sensor Response of Superhydrophobic Quartz Crystal Resonators

G. McHale, P. Roach, C. R. Evans, N. J. Shirtcliffe, S. J. Elliott and M. I. Newton School of Science and Technology

Nottingham Trent University Clifton Lane, Nottingham, NG11 8NS, UK

e-mail: glen.mchale@ntu.ac.uk

Abstract—Quartz crystal microbalances are used to sense mass deposition from the gas or liquid phase, to determine the viscosity-density product of a liquid and to extract the shear moduli of polymers. These situations are described by the Sauerbrey equation, the Kanazawa and Gordon equation and by viscoelastic modeling of the full impedance spectrum of a crystal. In all of these cases the fundamental assumption in the theories of the sensor response is that a no-slip boundary condition is valid. For a smooth surface, this may be the case, but recently surfaces have been constructed that use high aspect ratio surface features to amplify the effect of surface chemistry (superhydrophobic surfaces). On these surfaces, droplets are effectively suspended on the tips of the surface features and roll easily. Moreover, recent reports have suggested that the steady flow of a simple Newtonian liquid, such as a water-glycerol mixture, over such a surface effectively occurs over a layer of air and so with greatly reduced drag. In this report, we discuss the effect of superhydrophobic surfaces on quartz crystals and develop an acoustic reflection view of crystal resonance to describe how the acoustic response might be modified. We present data for three types of superhydrophobic surfaces: a) a micro-post based surface, b) a titanium dioxide based surface and c) two silicon dioxide based surfaces. The impedance spectra are analyzed for frequency and dissipation changes in response to immersion in water-glycerol solutions. We compare the results to i) a theory for a quartz crystal in contact with a Newtonian liquid assuming a slip boundary condition, and ii) to an acoustic reflection view of the sensor response. When the slip length is much less than the shear wave penetration depth, the slip boundary condition predicts the frequency response has a response equal to a Kanazawa and Gordon liquid term plus an additional Sauerbrey "rigid" liquid mass; to first order the dissipation is unchanged from the Kanazawa and Gordon value. The data for the surfaces with the shortest micro-posts and for the titanium dioxide based surfaces is consistent with these expectations. We interpret this as due to penetration of the liquid into the surface structure. For the surface with the tallest micro-posts and for one of the silicon dioxide surfaces both frequency decrease and dissipation increase are substantially less than predicted by the Kanazawa and Gordon equation. We interpret this within the acoustic reflection view as due to the presence of an air layer, due to the superhydrophobicity, and its effect on decoupling the response of the crystal.

I. INTRODUCTION Surface tension becomes dominant over gravity when the

relevant length scale becomes small enough. The force due to gravity depends on mass and so scales as gρR3, where g is the acceleration due to gravity, ρ is the density of the liquid and R is a typical length. The force due to surface tension, γLV, depends on length and so scales as γLVR. Comparing these two forces gives a characteristic (capillary) length, κ-1=(γLV/ρg)1/2, which for water is 2.73 mm. When a solid surface has protrusions that are hydrophobic and tall enough, and which are sufficiently close (i.e. much less than κ-1), water does not penetrate between them. In effect the water skates across the tips of the surface features and becomes suspended. If we now imagine that these protrusions are dilute (small in number) then a droplet will ball up on the surface under the action of surface tension. Moreover, because of the small number of points of contact with the solid, the droplet will become extremely mobile and roll easily across the surface. The surface is said to be “slippy” and is described by the Cassie-Baxter equation (Fig. 1a) [1]. An analogy is to a person lying on a bed of nails – unless sufficient pressure is applied the nails do not penetrate their skin. The skin of water can be penetrated if the surface protrusions are insufficiently hydrophobic or too widely spaced apart, or if sufficient pressure is applied. If this occurs, the water contacts the solid surface everywhere including the bottom of the surface structure and up the sides and across the tops of the surface features. A droplet may still ball up, but it becomes immobile and unable to roll. The surface is said to be “sticky” and is described by the Wenzel equation (Fig. 1b).

Figure 1. Droplet states on hydrophobic solids: a) Droplet is suspended upon the surface features, and b) droplet penetrates the surface features.

The financial support of the UK Engineering and Physical Sciences Research Council (EPSRC) and MOD/Dstl under grant EP/D500826/1 is gratefully acknowledged.

978-1-4244-1795-7/08/$25.00 ©2008 IEEE 698

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The two situations in fig. 1 show the importance of the interplay between surface chemistry and surface topography in determining the type of interface that occurs when a solid surface is immersed into a liquid. Superhydrophobic surfaces achieve the first of these two states with a high contact angle (characterizing the extent to which a droplet balls up) and low contact angle hysteresis (characterizing how “slippy” the surface is to droplets).

Liquid phase quartz crystal microbalances (QCMs) sense interactions within the shear wave penetration depth, δ=(η/πfρ)1/2, where f is the resonant frequency of the crystal and η is the viscosity of the liquid; for a 5 MHz crystal immersed in water δ∼250 nm. Intuitively, we would expect a very different QCM response to immersion in liquid depending upon whether its surface coating was superhydrophobic or not. Moreover, if the surface chemistry was to change from hydrophobic to less hydrophobic (or to hydrophilic), or if the properties of the liquid changed, a dramatic change in interfacial state can occur. For example, it has already been show that superhydrophobic surfaces can be designed so that they switch a liquid from skating across surface features to penetrating between surface features [2, 3]. Triggers for the switching can include temperature, surface tension changes (alcohol content, surfactant, etc) or applied voltage via an electrowetting effect. Another sensor mechanism could be to design a surface such that the attachment of a molecule causes a hydrophobicity change and triggers a switching of the wetting state [4]. Thus, molecules with masses too small to be sensed via their mass might be detectable by their effect on the balance of interfacial tensions between the solid and the liquid (and the vapor). However, to date there have been very few studies of QCMs with superhydrophobic surfaces and the basis of understanding that would enable sensors to be designed and constructed is therefore extremely limited.

Previously we reported preliminary results for QCM frequency changes for a surface consisting of regularly spaced hydrophobic posts immersed in water-polyethylene glycol (PEG) solutions [5] and, more recently, impedance spectra for a surface consisting of lithographically fabricated micro-posts immersed in water-glycerol solutions [6, 7]. Fujita et al. also reported on a superhydrophobic QCM surface consisting of a polystyrene layer containing PTFE particles [8] and Kwoun et al. reported on multi-resonance devices coated with a hydrophobized silica nanoparticle layer [9]. In this report, we first review the results of a model of QCM response under the assumption of a slip boundary condition. We then develop an acoustic reflection view potentially applicable to QCMs with superhydrophobic surfaces. Finally, we report new data for QCMs possessing i) a superhydrophobic titanium dioxide based sol-gel coating, and ii) an organo-silane treated silicon dioxide nanoparticle based superhydrophobic coating. Frequency shift and dissipation data for the titanium dioxide based coating is consistent with a penetrating form of wetting. Data for one size of the superhydrophobic silicon dioxide coating shows significantly reduced magnitude of frequency decrease and dissipation compared to the Kanazawa and Gordon model and is consistent with a decoupling of the QCM response due to a superhydrophobic state.

II. THEORETICAL CONCEPTS Modeling of the sensor response of a QCM can be

performed by setting up a wave equation for the substrate and either a wave equation for a solid contacting layer or the Navier-Stokes equations for a contacting fluid. These equations are solved for the substrate and layer/fluid displacements and then the solutions are matched at the various boundaries [10]. For a liquid the usual no-slip boundary condition is that the speeds of displacement of the substrate and the liquid at the solid-liquid interface match. A simple pictorial acoustics view for an unloaded QCM is that a strong reflection occurs at the substrate-air interface and the crystal substrate forms an acoustic cavity in which a standing wave is created (Fig. 2a). Depositing a solid layer does not alter the fact that there is a strong solid-air reflection and so a strong resonance persists with little additional dissipation, but within a slightly longer cavity (Fig. 2a). The additional length of the cavity results in a decrease in resonant frequency and using the density of the deposited layer this can be interpreted as due to a deposited mass per unit area, i.e. the Sauerbrey equation. When an unloaded crystal is brought into contact with a liquid a viscous entrainment of the liquid occurs (Fig. 2b). An effective reflection plane exists within the penetration depth and so the acoustic cavity is lengthened. In addition, the acoustic reflectivity at the substrate-liquid interface is less than the substrate-air interface and so some energy is lost into the liquid. Thus, contact with a liquid results in both increased magnitude of frequency decrease and increased dissipation as described by the Kanazawa and Gordon equation.

A derivation of the QCM sensor response under the assumption of a slip boundary condition has previously been performed [11-13]. In this case, the slip length, b, is an effective parameter arising from the extrapolation of the fluid speed from the bulk to allow matching of the solid-fluid boundary. A slip boundary condition has also sometimes been suggested to explain possible molecular slip at the solid-liquid interface of a quartz crystal [14]; this has been modeled for acoustic wave sensors using the Blake-Tolstoi theory for molecular and hydrodynamic slip [15]. However, slip can also be regarded as modeling an effective average solid-fluid interface; a negative b moves the effective interface to the fluid side of the substrate-fluid boundary [13]. The slip model in reference [11] shows that the acoustic impedance, ZL

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Figure 2. Acoustic reflection generating crystal resonances with a) solid

layer, and b) immersion in liquid. In both cases the cavity length for the standing shear wave increases and so the frequency decreases. In the liquid case, energy loss also occurs increasing the damping.

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When the slip length, b, is small compared to the shear wave penetration depth, δ, the model predicts a fractional frequency shift equal to that expected from the Kanazawa and Gordon equation multiplied by (1-2b/δ), but there is no additional dissipation. Defining a liquid mass per unit area as Δmf=bρf, allows the result to be stated as a response on immersion in a fluid that equals a Kanazawa and Gordon contribution plus an additional frequency shift due to a Sauerbrey-like “trapped” liquid mass [13]; an effect previously suggested by Martin et al. [16, 17]. The slip-boundary condition view assumes all locations across a surface are equivalent. This assumption fails for a superhydrophobic surface because the surface structure varies with location across the surface. However, the concepts of effective reflection planes and changes in acoustic reflectivity of boundaries provide an understanding of how superhydrophobic QCM surfaces may behave.

Fig. 3 shows a QCM with a hydrophobic surface structure immersed in a liquid. The surface protrusions are well-separated and a small fraction of the planar projection of the surface area (i.e. dilute). In the superhydrophobic case, the crystal appears to be separated from the liquid by a layer of air and the micro-posts appear not to exist as far as the acoustic reflection is concerned (Fig. 3a). In such an extreme situation, the resonance will be dominated by the acoustic cavity defined by the crystal thickness. In addition, the reflection at the substrate-air interface will remain strong. Despite the crystal being immersed in the liquid it is effectively decoupled from the liquid. Consequently, the decrease in resonant frequency and increase in dissipation can be expected to be far less than predicted by the Kanazawa and Gordon equation. This is also consistent with a slip model using a large slip length (in the extreme case b→∞) to decouple the QCM motion from the liquid. If the liquid penetrates into the surface structure and the surface protrusions are narrow and widely separated, the acoustic cavity will be defined by the crystal thickness and the entrainment of the liquid (Fig. 3b). We would expect this to result in a Kanazawa and Gordon response with both a frequency decrease, due to the effective reflection occurring within the penetration depth above the lower surface of the surface structure, and an increase in dissipation. If the spacing of surface features compared to the shear wave penetration depth is small, the average entrainment may be induced at the upper surface of the surface protrusions (not shown in fig. 3) and contribute an effective Sauerbrey-like “trapped” liquid mass in addition to the Kanazawa and Gordon contribution.

Figure 3. Acoustic reflections occurring for a crystal with a dilute surface structure immersed in a liquid: a) the superhydrophobic case results in a layer of air separating the substrate from the liquid, and b) the penetrating case results in liquid entrainment at the upper crystal surface.

III. EXPERIMENTAL The first type of surface was a model surface consisting of

a square array of micro-posts. Photolithographic patterning on smooth polished 5 MHz quartz crystals of diameter 25 mm with gold electrodes was used to prepare square arrays of circular cross-section SU-8 photoresist micro-posts [6, 7]. Posts were of diameter d=5 μm, separation L=10 μm and heights of h=5, 10, 15 and 18 μm. Patterned crystals were hydrophobized by immersion in a dilute fluorocarbon containing solution (Granger’s Extreme Wash-In), rinsing in deionized water and then heating for 20 minutes at 100o C; patterns that had not been hydrophobized were also investigated. The second type of surface was hydrophobized titanium dioxide based sol-gels. The sol-gels were produced by the rapid hydrolysis of titanium isopropoxide, and these were spun onto the quartz crystals and then treated with the Granger’s solution. Electron micrographs showed a surface structure consisting of micron scale aggregated clusters of particles separated by gaps of microns to tens of microns, which revealed the Granger’s treated gold surface of the quartz crystal. The third type of surface consisted of fumed silica nanoparticles, reacted with an organo-silane to provide a hydrophobic surface chemistry, dust-coated onto a 1.7 μm thick spin-coated layer of S1813 photoresist; the photoresist layer acts as a glue to fix the particles on the crystal surface. Two sizes of silicon dioxide particles were used with sample a1 having 5 nm particles and sample b1 having 3 nm particles.

Contact angles for droplets of water-glycerol mixtures were measured using a Krüss DSA 10 system. Quartz crystal spectra were recorded in air and liquid using an Agilent Technologies E5061A Network Analyzer and fitted to a Butterworth van Dyke (BVD) model to determine the bandwidth, B, and series resonance frequency, f. Measurements were also performed on the polished crystals, polished crystals treated with the Granger’s solution and photoresist layers with and without treatment with the Granger’s solution. To investigate Newtonian liquids, mixtures of distilled water and glycerol (99+% Fisher) were used and the concentration used to calculate the viscosity-density product. Experiments were conducted in an open lab. Since glycerol is hygroscopic, the viscosity-density product calculated using the nominal percentage weight concentration of glycerol is only accurate up to concentrations ∼ 80%.

Full data sets for the micro-post systems have recently been reported in reference [6]. A selection of this data is included here for comparison to the TiO2 and SiO2 surfaces. On the hydrophobized micro-post surfaces contact angles in the range 143o-152o were observed with little dependence on concentration of glycerol. Visually, droplets appeared to be in the suspended (“slippy”) Cassie-Baxter superhydrophobic state on these surfaces, although previous work has indicated a relatively large contact angle hysteresis for this type of surface [18]. The expected change in QCM impedance spectra of a frequency decrease and broadening of resonance on applying pressure to a droplet to force it into the pattern was confirmed on the micro-posts. Contact angles were measured for droplets on the TiO2 and SiO2 surfaces and a simple visual assessment of droplet mobility was noted. On the TiO2 surface the contact angle reduced from 154o before the QCM experiments to 138o

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after the experiments. Moreover, droplets did not roll even when the surface was tilted vertically, thus indicating that liquid had either partially or fully penetrated into the surface structure (i.e. the “sticky” Wenzel state). The two SiO2 based surfaces behaved differently to each other. In the case of sample a1 the contact angle decreased to 140o after the QCM experiments and droplets were immobile in a similar manner to the TiO2 surface; it appears that the initial surface may have been unstable and its final state involved penetration by the liquid. In the case of sample b1 the contact angle was 154o following the QCM experiments and the droplet rolled freely on the surface, thus indicating a suspended (“slippy”) Cassie-Baxter superhydrophobic state. Measurements repeated at a later date showed this surface remained superhydrophobic.

IV. QUARTZ CRYSTAL DATA AND DISCUSSION For smooth flat quartz crystal surfaces immersed in

water-glycerol mixtures a Newtonian response described by the Kanazawa and Gordon equation was observed. The magnitude of the decrease in frequency was half of the increase in the bandwidth as predicted. By verifying that frequency and bandwidth changes are correlated it is possible to confirm that any deviation from linear in these two parameters when plotted against (ηρ)1/2 is not simply a consequence of errors in estimating the viscosity arising from the hygroscopic nature of glycerol. The data for the micro-posts surfaces are shown in fig. 4 and fig. 5 with the straight lines indicating a Newtonian response. The data for 5 μm ( ), 10 μm ( ), 15 μm (∆∆∆) and 18 μm ( ) tall micro-post surfaces with no hydrophobic treatment are shown as open-symbols. The corresponding data for the hydrophobized micro-post surfaces is shown using solid symbols. Fig. 4 shows that the majority of the data for the four heights of non-hydrophobized micro-post surfaces lie parallel to, and above, the Kanazawa and Gordon line. The data points for the 5 μm ( ) and 10 μm ( ) surfaces, which in fig. 4 are enclosed in dotted curves, correspond to mixtures with greater than 80% glycerol.

Figure 4. Changes in resonant frequency, Δf, and bandwidth, ΔB, QCM’s with hydrophoized (open-symbols) and non-hydrophobized (solid symbols) QCMs with lithographic micro-posts immersed in glycerol-water solutions (0-100%). Post heights are 5μm ( ), 10μm = ( ), 15μm (∆∆∆) and 18μm ( ). The dotted line shows the Kanazawa and Gordon theory.

Figure 5. Data for QCMs with hydrophoized (open-symbols) and non-hydrophobized (solid symbols) lithographic micro-posts immersed in glycerol-water solutions (0-100%); symbols are the same as in fig. 4.

For these high levels of glycerol concentration the penetration depth increases rapidly from 2 μm to 7 μm. This complicates the interpretation because it introduces a length scale that could match that of the micro-post pattern and cause resonances leading to, e.g., compressional waves.

In fig. 4 the data for the hydrophobized 5 μm surface ( ) lies parallel to the Kanazawa and Gordon line, but each data point is closer to the origin. The data for the hydrophobized 10 μm surface ( ) shows frequency decreases well below the Kanazawa and Gordon prediction for glycerol concentration below 80%, but positive frequency shifts for higher concentrations of glycerol. The data for the hydrophobized 15 μm surface (▲▲▲) describes an anti-clockwise arc and appears anomalous with decreasing rather than increasing bandwidth. The data for the hydrophobized 18 μm surface ( ) also describes an anticlockwise arc, but with small bandwidth increases and frequency decreases. Fig. 5 show the same data plotted against (ηρ)1/2. At each concentration of glycerol the magnitude of changes in frequency shift and bandwidth for the hydrophobized surfaces are smaller than for the equivalent height non-hydrophobized micro-post surface. Thus it appears some decoupling of the surfaces results from the combination of the hydrophobic

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surface chemistry with the topography. However, only the surface with 18 μm tall hydrophobized micro-posts ( ) shows systematic reductions in the magnitudes of frequency decrease and bandwidth increase below the values predicted by the Kanazawa and Gordon equation. The unusual positive bandwidth change in the data for the surface with 15 μm tall hydrophobized micro-posts (▲▲▲) may indicate that some length scale is being matched and, e.g., compressional waves generated.

Fig. 6 shows the correlation between frequency and bandwidth changes for the hydrophobic TiO2 sol-gel surface. The data lies above the Kanazawa and Gordon prediction on a straight line with -Δf=0.608ΔB+0.247 where Δf and ΔB are in KHz. For comparison, fig. 6 also shows data for a smooth polished crystal (∆∆∆) and for a hydrophobized smooth polished crystal (▲▲▲). In both of these cases, the data is well-described by the Kanazawa and Gordon equation with a gradient of 0.5 and intercept of zero. Fig. 7 shows the same data plotted against (ηρ)1/2. The hydrophobic TiO2 sol-gel shows an enhanced frequency decrease described by -Δf=0.820(ηρ)1/2+0.435 where Δf is in kHz and (ηρ)1/2 is in kg m-2 s-1/2. However, there is no significant change from the bandwidth shift predicted by the Kanazawa and Gordon equation. Taken together, these data are suggestive of a partial or complete penetration by the liquid and are consistent with the expected results from the small slip length model interpreted as a Sauerbrey-like “trapped” liquid mass, Δmf=bρf. This interpretation is consistent with the high contact angle, but immobile droplet, arising from a Wenzel state on a hydrophobic surface with liquid penetrating partially or fully into the surface structure. Such a Wenzel state would be expected from the electron microscope images, which show a low height structure (order of magnitude ∼ 1 μm) of titanium dioxide particle clusters compared to the gaps between the clusters (order of magnitude ∼ <1 μm to ∼ 30 μm).

Figure 6. Changes in resonant frequency, Δf, and bandwidth, ΔB, for QCMs with a hydrophoized TiO2 sol-gel coating ( ) at 25 oC. Data for a polished crystal with no coating (∆∆∆) and for a polished crystal with the hydropobic treatment (▲▲▲) is shown for comparison; the dotted line shows the Kanazawa and Gordon theory.

Figure 7. Data for changes in resonant frequency, Δf, and bandwidth, ΔB, of QCMs with a hydrophoized TiO2 sol-gel coating ( ) at 25 oC plotted against (ηρ)1/2; symbols are the same as in fig. 6.

Fig. 8 shows the data for the two hydrophobic SiO2 based surfaces; data for 45%, 55% and 65% glycerol concentrations corresponding to (ηρ)1/2= 2.3, 3.02 and 4.2 kg m-2 s-1/2 were measured out of sequence in a later experiment. The data for the a1 surface ( ) appears to follow a straight line with a slightly smaller gradient than the Kanazawa and Gordon equation. Fig. 9 shows the same data for changes in frequency and bandwidth plotted against (ηρ)1/2. The majority of data for the a1 surface lies below the Kanazawa and Gordon lines, but the three points corresponding to the 45%, 55% and 65% glycerol concentrations taken in a later experiment lie close to the Kanazawa and Gordon lines. A high contact angle and immobile droplet was observed for this surface after the QCM experiments. It therefore appears the a1 surface was initially superhydrophobic with a decoupling of the QCM liquid response, but that this state was unstable and liquid eventually penetrated into the surface structure. If this did occur, then given the small (nanometer) size of the SiO2 particles we would expect little change of the frequency decrease and bandwidth increase from the Kanazawa and Gordon values; this is consistent with data for the 45%, 55% and 65% glycerol concentration taken at the later time.

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Figure 8. Changes in resonant frequency, Δf, and bandwidth, ΔB, for QCMs with hydrophobic SiO2 particles dusted onto a layer of S1813 photoresist (a1 surface and b1 surface ) at 20 oC. Data for a polished crystal with no coating (∆∆∆) and for a polished crystal with the hydropobic treatment (▲▲▲) is shown for comparison; the dotted line shows the Kanazawa and Gordon theory.

The data in fig. 8 for the b1 surface ( ) does not follow a curve similar to Kanazawa and Gordon, but clusters close to the origin of the graph. Fig. 9 shows that nine from twelve data points for this surface have large reductions in the magnitude of both the frequency shift and bandwidth for any given value of (ηρ)1/2, compared to the Kanazawa and Gordon equation. For glycerol concentrations from 30% to 80% the data appears to be a scatter around an average frequency decrease ∼ 0.5 KHz and an average bandwidth increase ∼ 0.9 kHz. There is no obvious increase in the magnitude of frequency decrease and bandwidth increase with increasing concentration of glycerol. For the two lowest concentrations (0% and 10%) a frequency decrease larger than the Kanazawa and Gordon value was observed. It is unclear whether this might have been due to some loose SiO2 particles on the initial surface, which were then cleared early in the experimental sequence, or whether it might be an effect from the lower value of shear wave penetration depth for dilute glycerol solutions; these experiments are currently being repeated.

The decoupling of the QCM response from the liquid for the majority of data for the b1 surface is consistent with the observed high contact angle and complete mobility of droplets on the surface after the QCM experiments. This behavior is expected from the acoustic reflection interpretation, or equivalently an infinite slip length, for the immersion of a QCM with a superhydrophobic coating into a liquid. When the liquid is suspended on the tips of the hydrophobic surface structure and does not penetrate into the structure, there is effectively a layer of air separating the QCM surface from the liquid. This would be expected to decouple the QCM oscillation from the liquid and cause a significant reduction in magnitude of both the frequency decrease and bandwidth increase compared to the Kanazawa and Gordon equation. Once that occurs, changes in liquid density and viscosity will have little influence on the QCM response unless they are accompanied by changes in interfacial tensions causing liquid to penetrate into the surface structure.

Figure 9. Data for changes in resonant frequency, Δf, and bandwidth, ΔB, of QCMs with hydrophobic SiO2 particles dusted onto a layer of S1813 photoresist (a1 surface and b1 surface ) at 20 oC plotted against (ηρ)1/2; symbols are the same as in fig. 8.

V. CONCLUSION The effect of a rough surface structure on the response of a

quartz crystal has a strong dependence on the surface chemistry. In the case of a hydrophobized titanium dioxide based sol-gel with a low aspect ratio for the surface structure, liquid penetrating into the structure causes an additional frequency decrease beyond that expected from the Kanazawa and Gordon equation, but no significant change in the dissipation (bandwidth). This effect can be interpreted as due to a small negative slip length or, equivalently, as due to an additional Sauerbrey-like “trapped” liquid mass. In the case of a hydrophobic silicon dioxide surface, on which droplets display a high contact angle and are completely mobile indicating a non-penetrating superhydrophobic state, the QCM frequency decrease and increased dissipation on immersion in the liquid are greatly reduced compared to the values expected from the Kanazawa and Gordon equation. This effect can be interpreted using an acoustic reflection view as due to the crystal resonance remaining defined by the strong reflection from the upper crystal surface, which remains mainly in contact with air despite the immersion of the crystal in the liquid. Equivalently, the effect of the air layer between the

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crystal and the liquid can be interpreted as introducing an infinite slip length. The very different QCM responses observed for the penetrating and non-penetrating liquid states create the opportunity for new sensors based on hydrophobic effects. For example, surfaces could be designed to switch from the non-penetrating superhydrophobic state to a penetrating liquid state under a physical stimulus (binding event, temperature change, liquid property change) and such a change would provide large measurable changes in QCM resonant frequency and bandwidth.

REFERENCES [1] D. Quéré, A. Lafuma and J. Bico, “Slippy and sticky microtextured

solids,” Nanotechnology, vol 14, pp. 1109-1112, 2003. [2] N. J. Shirtcliffe, G. McHale, M. I. Newton, C. C. Perry and P. Roach,

“Porous materials show superhydrophobic to superhydrophilic switching,” Chem. Comm., issue 25, pp. 3135-3137, 2005.

[3] N. J. Shirtcliffe, G. McHale, M. I. Newton, C. C. Perry and P. Roach, “Superhydrophobic to superhydrophilic transitions of sol-gel films for temperature, alcohol or surfactant measurement,” Maters. Chem. Phys., vol 103, pp 112-117, 2007.

[4] M. Thompson, G. McHale and M. I. Newton, “Acoustic biosensor for detecting surface interactions, such as surface binding events, comprises super-nonwetting or super-wetting surface,” Canadian patent application CA2451413 published 28 May 2005.

[5] C. R. Evans, G. McHale, N. J. Shirtcliffe and M. I. Newton, “The effect of SU-8 patterned surfaces on the response of the quartz crystal microbalance,” Sens. Act., vol A123-24, pp. 73-76, 2005.

[6] P. Roach, G. McHale, C. R. Evans, N. J. Shirtcliffe and M. I. Newton, “Decoupling of the liquid response of a superhydrophobic quartz crystal microbalance,” Langmuir, vol 23, pp. 9823-9830, 2007.

[7] P. Roach, C. R. Evans, N. J. Shirtcliffe, G. McHale and M. I. Newton, “Response of quartz crystal resonators possessing a superhydrophobic surface,” Proc. IEEE IFCS., vols 1-4, pp. 587-590, 2007.

[8] M. Fujita, H. Muramatsu and M. Fujihira, “Energy dissipation at ultrasonically oscillating superhydrophobic surface in various liquids,” Jap. J. Appl. Phys., vol 44, pp. 6726-6730, 2005.

[9] S. J. Kwoun, R. M. Lec, R. A. Cairncross, P. Shah and C. J. Brinker, “Characterization of superhydrophobic materials using multiresonance acoustic shear wave sensors,” IEEE Trans. Ultrason. Ferroel. Freq. Control., vol 53, pp. 1400-1403, 2006.

[10] D. S. Ballantine, et al., Acoustic Wave Sensors, London: Academic Press, 1996.

[11] G. McHale, R. Lücklum, M. I. Newton and J. A. Cowen, “Influence of viscoelasticity and interfacial slip on acoustic wave sensors,” vol. 88, pp. 7304-7312, 2000.

[12] J. S. Ellis, G. McHale, G. L. Hayward and M. Thompson, “Contact angle-based predictive model for slip at the solid-liquid interface of a transverse-shear mode acoustic wave device,” J. Appl. Phys., vol 94, pp. 6201-6207, 2003.

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