Anal. Chem. 2008, 80, 5930–5936
Human Serum Albumin Adsorption Study on 62-MHz Miniaturized Quartz Gravimetric Sensors Ping Kao,† Ashish Patwardhan,† David Allara,*,‡,§,| and Srinivas Tadigadapa*,†,| Department of Electrical Engineering, Department of Chemistry, Materials Science & Engineering, and the Materials Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802 We have designed and fabricated 25-µm-thick quartz resonators operating at a fundamental resonance frequency of ∼62 MHz. The results show a substantial increase in the mass sensitivity compared to single monolithic commercial resonators operating at lower frequencies in the ∼5-10-MHz range. The overall performance of the micromachined resonators is demonstrated for the example of human serum albumin protein adsorption from aqueous buffer solutions onto gold electrodes functionalized with self-assembled monolayers. The results show a saturation adsorption frequency change of 6.8 kHz as opposed to 40 Hz for a commercial ∼5MHz sensor under identical loading conditions. From the analysis of the adsorption isotherm, the equilibrium adsorption constant of the adsorption of the protein layer was found to be K ) 8.03 × 10^6 M^-1, which is in agreement with the values reported in the literature. The high sensitivity of the miniaturized QCM devices can be a significant advantage in both vapor and solution adsorption analyses. Commercial quartz crystal microbalances (QCM) have been extensively used for the characterization and measurement of deposited and adsorbed thin films in both vacuum and liquid environments.1–4 The most commonly available commercial QCM consists of a ∼300-µm-thick and ∼25-mm-diameter disk made from an AT-cut quartz crystal with gold electrodes on each face, has a shear resonance frequency in the 5-MHz range, and exhibits a sensitivity of ∼17 ng cm-2Hz-1.5 Although quartz crystals with fundamental resonances in the 10-MHz range and a few with even higher frequencies are commercially available, the inherent fragility of large-area thinner resonators has precluded their extensive use in comparison to the 5-MHz resonators.6 Under the conditions that the adsorbed film material is rigid, sufficiently thin compared to the quartz crystal, and attached to the sensor surface * To whom correspondence should be addressed. E-mail: [email protected]
psu.edu; [email protected]
† Department of Electrical Engineering. ‡ Department of Chemistry. § Materials Science & Engineering. | Materials Research Institute. (1) Kanazawa, K. K.; Gordon, J. G. Anal. Chem. 1985, 57 (8), 1770–1771. (2) Janshoff, A.; Galla, H.-J.; Steinem, C. Angew. Chem., Int. Ed. 2000, 39, 4004–4032. (3) Granstaff, V. E.; Martin, S. J. J. Appl. Phys. 1994, 75 (3), 1319. (4) Schumacher, R. Angew. Chem., Int. Ed. Engl. 1990, 29 (4), 329–343. (5) O’Sullivan, C. K.; Guilbault, G. G. Biosens. Bioelectron. 1999, 14 (8-9), 663–670.
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under a no-slip condition, the dependence of the frequency change (∆f) of a resonating quartz crystal to the mass loading (∆m) is given quite accurately by the Sauerbrey equation: ∆f ) - (f0 ⁄AxqFq)∆m ) - (2f02 ⁄ √µqFqA)∆m ) -Sf
where f0 is the fundamental resonant frequency with no attached mass, µq is the shear modulus of the quartz (2.947 × 1010 N m-2 for AT-cut quartz), Fq is the density of quartz (2.648 × 103 kg m-3), xq is the thickness of the crystal, and A is the area of the electrode on the quartz crystal. The negative sign indicates a reduction in the resonance frequency upon mass loading. A very important aspect of eq 1) is that the change in frequency (∆f ) for the same mass loading (∆m) increases as the thickness xq and the area A of the crystal are made smaller. This provides a possible way of making large enhancements in the performance of quartz crystal resonators if methods of fabrication can be developed to miniaturize them. The purpose of the work reported in this paper is to demonstrate that such improvements are possible. One of the important applications of QCM devices is to assay adsorption in liquid environments, often with significant viscosity, and these effects were of considerable interest in our development of miniature resonators. These conditions can both compromise the ultimate performance of the devices by damping of the resonance and change the form of the frequency-mass loading response. Examples include polymer adsorption, electrochemical deposition/stripping, protein adsorption, and cell attachment/detachment.7,8 It is important to assess these effects in the development of new types of QCMs. In such applications, the fundamental mode QCM frequency shift in eq (1) is modified to one that depends upon the square root of the viscosity-density product of the liquid, as given by
∆f ) -
where FL and ηL are the density and viscosity of the liquid, respectively.1 In liquid medium applications, the shear wave rapidly damps out as it travels through the thickness of the liquid, and consequently, the QCM typically samples a layer of thickness (6) The 9-10-MHz quartz resonators are commercially available from Maxtek Inc. (a division of Inficon), and 27-MHz resonators are commercially available from Initium Inc. (a division of Ulvac). (7) Kanazawa, K. K.; Melroy, O. R. IBM J. Res. Dev. 1993, 37 (2), 157. (8) Bruckenstein, S.; Shay, M. J. Electroanal. Chem. 1985, 188 (1-2), 131. 10.1021/ac8005395 CCC: $40.75 2008 American Chemical Society Published on Web 06/21/2008
equivalent to the decay length δ = (ηL/πFLf0)0.5. The change in the dissipation factor can be written as9
For a commercial 5-MHz QCM, the typical decay length in water is ∼250 nm, which is large in comparison to the thickness of molecular or even polymer and biomolecular (e.g., proteins) films, which often can reach thickness of 10-50 nm. As a result, a commercial QCM not only samples the adsorbed film but is also significantly affected by the viscous fluid layer above it. However, if the QCM thickness is decreased, its fundamental resonance frequency increases inversely as a function of the thickness of the quartz and thus the decay length in liquid also decreases consequently. For example, if the thickness of a quartz resonator is decreased from 330 (commercial 5-MHz resonator) to 25 µm (miniaturized 62-MHz resonator), the decay length in water is reduced to ∼68 nm. Motivated by the fact that the sensitivity to mass loading and the interfacial depth response can be significantly improved via miniaturization of quartz resonators, we have designed and fabricated 25-µm-thick devices operating at a fundamental resonance frequency of ∼62 MHz. In this paper, we present the performance of these resonators using the example of adsorption of human serum albumin (HSA) protein from buffered solution onto gold electrodes functionalized with self-assembled monolayers. While single resonator devices with fundamental resonance frequencies up to 94 MHz have been reported, the behavior of resonators with fundamental frequencies higher than 30 MHz, under liquid and viscoelastic loading conditions, has not been studied or reported thus far.10–13 Such a study is imperative for the development of miniaturized QCM-based sensor arrays for applications such as biochemical sensing. This study helps to fill this gap and demonstrates that much higher performance QCM devices than currently available are possible through appropriate fabrication and engineering. EXPERIMENTAL SECTION Miniaturized Resonator Design Considerations. The primary challenge is to be able to maintain a high Q-factor while simultaneously suppressing spurious resonance modes. A resonator with an electroded area of limited extent (radius rq) on a finite radius wafer that in turn is mounted on low Q supports can have a high Q-factor only if a very large fraction of its vibration energy is restricted to the electrode regions. Energy trapping in the case of such finite-sized electrode resonators is dominated by total internal reflection of vibrations at the edge of the electrodes. In cases for which the width of the electrodes is small compared to (9) Rodahl, M.; Kasemo, B. Sens. Actuators, B 1996, B37 (1-2), 111. (10) Abe, T.; Esashi, M. Sens. Actuators, A 2000, A82 (1-3), 139–143. (11) Abe, T.; et al. Energy dissipation in small-diameter quartz crystal microbalance experimentally studied for ultra-high sensitive gravimetry. In Micro Electro Mechanical Systems; MEMS-03 Kyoto, IEEE The Sixteenth Annual International Conference, 2003. (12) Buttgenbach, S. Proc. SPIE-Int. Soc. Opt. Eng. 2001, 4205, 207–217. (13) Rabe, J. B. S.; Schroder, J.; Hauptmann, P. Monolithic miniaturized quartz microbalance array and its application to chemical sensor systems for liquids. In Sensors 2002; Proc. IEEE, 2002.
Figure 1. Schematic illustration of the micromachined quartz crystal microbalance.
the wafer thickness, leakage of acoustic energy through the volume of the wafer increases considerably and vibrational energy reflection at the electrode edges becomes increasingly small. As a consequence, poor Q-factors are observed. On the other hand, for the effective suppression of the spurious modes, the rule of thumb thickness of quartz to electrode radius ratio is given by14
∆fpb < f0
2.337 xq N2 rq
where f0 is the resonance frequency of the quartz crystal of thickness xq after the mass loading due to the electrodes, and ∆fpb is the plate back frequency i.e., the frequency difference between the resonance frequency of the bare crystal and after deposition of top and bottom electrodes of radius rq. This implies that as the quartz resonator thickness is reduced the electrode diameter also must be reduced in order to effectively suppress spurious modes. Excessive decrease in the electrode diameter, however, will result in acoustic energy leakage and poor confinement of energy resulting in small Q-factors. These opposing requirements entail a design compromise. Our results show that, for 50-70-MHz resonators with 100 nm of gold electrodes on both faces, the optimal electrode diameter (2rq) to resonator thickness (xq) ratio is ∼10-20. Large deviations from this value either way result in resonators with poor characteristics. One important consideration to note is that, once etched, a 25µm-thick quartz crystal is extremely fragile to handle and readily shatters. Thus, the thinned resonator regions need to be essentially carved into a thicker quartz plate. This coupled with the requirement to allow for biochemical (liquid) experiments to be performed on the resonator surface results in an inverted mesa design, shown in Figure 1, in which the thin resonator regions are etched out of a thicker quartz plate. The thicker regions allow for easy handling of the device, and these regions are essentially glued onto a package to allow for the liquid testing. To allow for easy contact to the electrode on the etched side, the etched regions of the pixels were extended to the edge of the chip as shown in Figure 1. The unetched surface was designed to be the reaction surface and had the “front-side” electrode. This config(14) Lucklum, R.; Eichelbaum, F. Interface circuits for QCM sensors. In Piezoelectric Sensors; Steinem, C., Janshoff, A., Eds.; Springer Verlag: New York, 2007; pp 3-47.
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Figure 2. (a-e) Schematic illustration of the fabrication process used. See text for detailed description of the individual steps. (f) Optical photo of a fabricated QCM (g) Packaged sensor in a modified dual-in line ceramic package with a plastic reactor attached using silicone adhesive.
uration allowed the top (reaction)-side electrode to be at low potential while the resonator was excited via the “back-side” electrode. Fabrication of the Quartz Crystal Microbalance. An inductively coupled plasma (ICP) etch process was used for quartz etching.15 The process uses a mixture of SF6 and Ar as the etching gases. Mirror finish with average surface roughness less than 2 nm was achieved even after an etch depth of 75 µm by etching at a very low base pressure of 1 mTorr. Electroplated nickel on a Au/Cr seed layer was used as the etching mask. The fabrication process of the quartz crystal microbalance is illustrated schematically in Figure 2. A patterned nickel hard mask layer was deposited by electroplating (Figure 2b). The quartz crystal was thereafter etched in a high-density ICP RIE etcher using SF6 + Ar gases (Figure 2c). High selectivity (∼10) for the Ni mask and high etch rates (∼0.5 µm/min) using an ICP etcher have been already reported by our and other groups.15,16 The hard nickel mask was then stripped and lithographic patterning and etching performed on the bottom side Cr/Au electrodes (Figure 2d). Finally the top-side electrodes were aligned and patterned using liftoff to complete the QCM device (Figure 2e). Figure 2f shows an optical picture of the fabricated QCM. A 5 × 5 mm2 square hole was machined in a 24-pin, dual in-line ceramic package (DIP). The plane (unetched) side of the resonator having the front-side electrode where the mass sensing experiments are to be performed was placed facing the machined hole in the package and attached using room-temperature vulcanized silicone elastomer adhesive. The front-side electrode was electrically connected to the gold layer on the DIP package using silver epoxy and wire bonded to one of the pads while the back-side electrode of the resonator was directly wire bonded to any other available pad in the package. An Agilent 4294A impedance analyzer was used for all the reported characterization of the resonance (15) Goyal, A.; Hood, V.; Tadigadapa, S. J. Non-Cryst. Solids 2006, 352 (6-7), 657. (16) Abe, T.; Esashi, M. Sens. Actuators, A 2000, 82, 139–143.
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frequency and dissipation. All measurements reported in this work are based on single pixel measurements (details on parallel measurements will be reported elsewhere). Tested resonators were ∼25 µm thick, electrode diameter of 500 µm, with a fundamental resonance frequency of ∼62 MHz. Experimental Procedure and Setup. Materials. HSA (Sigma Aldrich) and glycerol (JT Baker) were used directly. The phosphate buffer solution (PBS) was made by dissolving phosphatebuffered saline powder (Sigma Aldrich) into 18 MΩ · cm DI water (Millipore Milli-Q system; Barnstead International). Different HSA concentration solutions were made by diluting a 10 mg/mL stock solution. Water-glycerol mixtures, ranging from pure water to 80% glycerol, were made in increments of 10%. Surface Functionalization. The micromachined QCM was cleaned by three cycles of exposure to UV ozone, each 30 min long, followed by thorough rinsing with ethanol and immersion in ethanol for 1 h. Finally, the electrodes were exposed to 1 mM hexadecanethiol solution for 48 h. This procedure has been demonstrated in our laboratory to result in the formation of a hexadecanethiolate selfassembled monolayer (HD-SAM), which is well organized and highly hydrophobic (as verified by advancing contact angles of ∼115 and 46° for water and hexadecane, respectively). Instrument Setup. An Agilent 4294A impedance analyzer was used to characterize the micro-QCM device. Ceramic dual in-line packages similar to the ones used for the packaging of the QCM device were modified to provide open and short circuit compensation fixtures for accurate calibration of the QCM. A 100 Ω resistor was used to simulate the load for compensation at 62-MHz frequency range. The impedance analyzer was set up to simultaneously measure the impedance magnitude and phase angle as a function of frequency. The calibrated impedance and phase angle data were recorded using Labview data acquisition setup. A nonlinear regression was used to fit the phase angle data to a Lorentzian function. All measurements were carried out inside a 2 in. × 3 in. × 5 in. aluminum die-cast box to prevent rf interference from the surroundings. The packaged QCM device was suspended from two BNC connectors fixed on the box using soldered wires. Finally, the custom-made die-cast box was placed inside a large, temperature-controlled chamber with the temperature set at 23(±0.1) °C. Protein Adsorption. Prior to performing protein adsorption experiments, the gold electrode surfaces were functionalized with the HD-SAM. A ∼15-µL drop of PBS solution was delivered to the electrode surface, and the QCM was allowed to stabilize for 1 h to a constant frequency. This was followed by the sequential injection of increasing concentration protein solutions. Prior to changing to each new concentration solution, the QCM surface was rinsed twice with PBS solution, rinsed thoroughly, and gently dried under a filtered N2 stream. RESULTS Under the temperature-controlled conditions of 23 ± 0.1 °C, the as-fabricated resonators exhibited a fundamental resonance frequency of ∼62 MHz with frequency stability (drift) of around 30 Hz over a period of 10 h and a frequency fluctuation noise of ∼13 Hz in air. The Q-factor of the resonators was found to be ∼6758 with a phase rotation of ∼10°. For the same resonator (bare, i.e., without SAM layer) in PBS solution, the Q-factor decreased to 3396 with a frequency noise of ∼25 Hz measured over a period of 30 min. Coating the resonator with the SAM layer
Figure 3. Decrease in the resonance frequency and the increase in the dissipation factor as function of weight percent concentration of glycerol in DI water.
had little effect on the frequency noise or drift, which increased by ∼1% of the values for the bare resonator. Calibration Experiments. Two separate experiments were carried out to measure the mass loading-frequency sensitivity of the devices in order to compare with the predictions from eqs (1) and (2). In the first measurement, a QCM device with a fundamental frequency of 62.319 367 MHz, was placed inside a vacuum deposition chamber with the sample connected to the frequency measurement via an electrical feedthrough. Deposition of a 3.0-nm-thick, highly uniform gold film resulted in ∆f ) -10.524 ± 0.025 kHz, or –3.51 kHz · nm-1. In contrast, eq (1) predicts ∆f ) -51.684 kHz, or –17.2 kHz · nm-1. Thus, the sensitivity of the fabricated micromachined QCM was found to be 0.203 (∼1/5) of the theoretical value as computed using eq 1. The second calibration was done to check the dependence of ∆f on medium viscosity as determined from water-glycerol mixtures. As seen in Figure 3, except at very high concentrations of 50% glycerol and above, a plot ofFLηL versus ∆f and dissipation (∆D) change shows a near-linear dependence, as expected according to eqs 2 and 3, respectively. Once again, however, the predicted ∆f by eq 2 is found to be ∼6 times larger than the measured ∆f. Dividing eq 2 by eq 3 we obtain -2
∆f )f ∆D 0
Note the experimental ratio of ∆f/∆D ∼ -f0/2, as predicted by eq 5. These calibration experiments show that the frequency sensitivity of the fabricated QCM is ∼0.17-0.2 of the theoretically expected value. It is important to note that the change in dissipation factor also reduces by a proportional amount, establishing a self-consistency in the resonance frequency value. Although the reduced, sensitivity behavior is not clearly understood at this time, it is important to emphasize that the absolute magnitude of the frequency change, as well as the signal-to-noise ratio, for these miniaturized resonators is superior to commercially available 5-MHz QCMs. Table 1 summarizes the performance of the miniaturized QCM under various glycerol loading conditions. Protein Adsorption Experiment. General Adsorption Isotherm Shape and Dissipation Characteristics of the HSA Layer. A plot of the resonance frequency shifts versus HSA solution concentration
for adsorption on HD-SAM-coated gold electrodes is shown in Figure 4. A similar shaped curve was obtained in an earlier study using a nominal 5-MHz QCM.17 Both sets of data show very close fits with high (>0.99) R2 values to a sigmoidal function. The curves differ, however, in that the full span of the frequency shift over similar HSA concentration ranges was ∼40 Hz for the 5-MHz QCM in contrast to the ∼6.8-kHz span for our 62-MHz QCM (Figure 4). For saturation coverage, this implies a signal-to-noise ratio of 523 in air and 272 in PBS with an insignificantly small decrease for the SAM-coated device. These values are ∼20 times higher than the signal-to-noise ratio of a 5-MHz resonator. In Figure 5, the observed change in the dissipation factor ∆D is plotted against the change in frequency ∆f for the various concentrations of HSA. The slope reveals the rigidity of the adsorbed layer. A low value of ∆D/∆f indicates a highly rigid, low-dissipation layer, and conversely, a high ∆D/∆f value indicates a soft, dissipative film. From Figure 5, the adsorption of HSA on the HD-SAM surface shows ∆D/∆f of ∼7.28 × 10-9 s, a low value consistent with a rigid adsorbed film.18 Previous work17 has shown that the HSA protein forms a monolayer near saturation coverages, and given the relatively small size of HSA (66.3 kDa) in comparison to other proteins, the observed high rigidity of the adsorbed HSA film is not surprising. Langmuir Isotherm Model Behavior. Assuming a limiting coverage of a single, uniform layer, the HSA adsorption behavior can be tested for a fit to a Langmuir isotherm. The basic Langmuir equilibrium is represented as K
A + * 98 A*
where A is the solution species, * represents an adsorbate-free region of the surface, A* is an adsorbate species, and K is the associated equilibrium constant. The Langmuir isotherm model assumes (i) a reversible adsorption process, (ii) no lateral interactions between adsorbates, and (iii) a single uniform adsorbate layer at saturation coverage. At equilibrium, the coverage is independent of time and can be given by Γeq KC ) Γmax 1 + KC
where Γeq and Γmax are the number of adsorbates per unit area at the equilibrium point for solution concentration C and at the saturation coverage (asymptotically approached as C f ∞). In the actual HSA adsorption experiment, Γeq and Γmax are represented by the masses per unit area (∆m and ∆mmax) of adsorbed HSA at each particular HSA concentration (C) and at the maximum limit, respectively. In turn, ∆m and ∆mmax are determined directly from the observed frequency shifts (∆f and ∆fmax). Equation (7) can now be rewritten as C C 1 ) + ∆m ∆mmax (K∆mmax)
From the plot of C/∆f versus C in (17) Krishnan, A.; Liu, Y.-H.; Cha, P.; Allara, D. L.; Vogler, E. A. J. R. Soc. Interface 2006, 3 (7), 283. (18) Hook, F.; Rodahl, M.; Brzezinski, P.; Kasemo, B. Langmuir 1998, 14 (4), 729–734.
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Table 1. Glycerol Loading Performance of the Micro-QCM at the Fundamental Resonance Modea wt % 10 20 30 40 50 60 70 80
fmeas (MHz) 62.672 279 62.365747 6 62.365 163 6 62.363 583 7 62.361 594 7 62.358 225 6 62.350 222 7 62.343 263 2
f ) -2∆fmeas/∆Dmeas (MHz)
36792.9 43254.6 52060.9 64534.1 82969.8 113028.0 165459.7 275127.9
5381 6861 7445 9025 11014 14383 22386 29345
3.6721 4.1581 4.4673 5.0177 5.8126 6.9679 10.015 12.548
1.90 2.38 2.69 3.24 4.04 5.19 8.24 10.8
56.72 57.58 55.30 55.66 54.55 55.39 54.33 54.48
0.91 0.92 0.89 0.89 0.87 0.89 0.87 0.87
a The change in frequency ∆(fcalc) has been calculated using eq (2). f0(air) ) 62.372 608 6 MHz and D0(air)) 1.7748 × 10-4 have been used to calculate the ∆fmeas and ∆Dmeas.
Figure 4. Shift of the QCM resonance frequency as a function of the natural logarithm of the concentration of HSA in solution for adsorption on a HD-SAM gold electrode.
Figure 5. Change in the dissipation factor (∆D) plotted against the change in the resonance frequency (∆f) for different concentrations of HSA protein solutions. The slope of the linear fit yields a value of 7.8 × 10-9 s.
Calculation of the Langmuir equilibrium constant over the full range of values yields a value of K ) 8.03 × 106 M-1. As a further test of the validity of the Langmuir model, the data can be fit at the low-concentration end where the adsorbate molecules are statistically isolated from one another, minimizing adsorbateadsorbate interaction effects and mass transport limited adsorption-desorption kinetic deviations from true equilibrium. Fitting a straight line to the first five data points at low concentrations (Figure 6) yields K ∼3.5 × 108 M-1, a value ∼43 times larger than the full concentration range value above. It must be noted that in the low-concentration region there can be considerable 5934
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Figure 6. Langmuir model plot of adsorbed HSA mass, represented by ∆f, versus HSA concentration in the high concentration range. The solid line is a linear fit to the data, consistent with a Langmuir behavior. The inset shows the slope.
difference between the initial and equilibrium concentrations of HSA since a sizable proportion of it can be adsorbed out of the solution phase on to the QCM surface. Since we did not independently confirm the equilibrium concentration of HSA in the supernatant liquid, we use the initial concentration values in the generation of this plot. This can explain some of the difference observed between the K-values obtained in the high- and lowconcentration regimes. These values of K span the intermediate value of K ) 2.12 × 107 M-1 reported for HSA adsorption on silica particles.19 Furthermore, the differences at both ends can be attributed to differences in the experimental conditions and the chemical natures of the surfaces in the two studies. Whereas in our work the protein solution is essentially allowed to equilibrate under “static” conditions, in the earlier report the interaction between the silica particles and protein was enhanced by active flow conditions. With regard to chemical differences, our studies involve a highly hydrophobic surface (HD-SAM) in contrast to the hydrophilic SiO2 surface in the earlier report. Viscoelastic Characteristics of the Adsorbed HSA Layer. For analysis of viscoelastic effects, the adsorbed protein layer adjacent to the solution medium can be considered schematically as shown in Figure 7. Given the thin (∼2 nm), chemically attached, dense nature of the HD-SAM layer, it can be accurately considered as a rigid extension of the electrode. The adsorbed HSA layer on the other hand is only attached to the HD-SAM surface via van der Waal’s forces with each molecule surrounded by water and in (19) Docoslis, A.; Wu, W.; Giese, R. F.; van Oss, C. J. Colloids Surf., B: Biointerfaces 1999, 13 (2), 83.
Figure 7. Schematic representation of the various layers present on the quartz resonator during the HSA adsorption experiment and the approximations used to model their effect on the quartz resonator frequency response.
contact with the PBS.17 In this situation, the HSA layer is considered to have some degree of viscoelastic character with the surrounding PBS solution, containing only a very low volume fraction of protein molecules, represented as a Newtonian fluid. According to Krishnan and co-workers, an adsorbed HSA layer at saturation coverage on a hydrophobic surface can be modeled as having a hexagonal type of close packing, a coverage of 750 ng · cm-2 and an ∼7-10-nm thickness.20 In comparison, the decay length (δ; see earlier) of the acoustic wave in the fluid (PBS) for a 62-MHz resonator is ∼67 nm. Since this value is roughly 1 order of magnitude larger than the protein film thickness, the QCM surface load from HSA can be treated as a finite viscoelastic layer in a fluid ambient. Bandey and co-workers provided the full onedimensional model of responses of a thickness-shear mode resonator under these loading conditions, and the surface mechanical impedance Zs is represented by.21
Zs ) Z film s
Z fluid Cosh(γhf) + Z film Sinh(γhf) s s Z film Cosh(γhf) + Z fluid Sinh(γhf) s s
where Zsfluid is the characteristic mechanical impedance of a Newtonian fluid given by
Z fluid ) s
(1 + j)
where Ff and hf are the film density and thickness, respectively and γ is the complex wave propagation constant given by γ ) jω(Ff ⁄ Gf)1⁄2
√Cm(Lm + Lm′ )
where L′m is the motional inductance contributed due to adsorption of the protein layer. The values of the static and motional capacitances, C0 and Cm, and the motional inductance before and after adsorption of the thiol layer were determined experimentally using the Agilent 4294A impedance analyzer. Using the values of C0 ) 4.577 pF, Cm ) 7.437 aF, Lm ) 876.74 mH, and f0 ) 62.325 MHz and approximating the density and viscosity of the PBS/HSA solution with those of water yields a ∆f value of 50.725 kHz. This value is based on an ideal resonator behaving according to eq 1. If we correct for the ratio of the observed and ideal sensitivities, (∆f/ ∆m)obs/(∆f/∆m)ideal ∼0.2 (see Calibration Experiments), we obtain a frequency shift of 10.145 kHz, closely comparable to the experimentally measured frequency shift of 11.136 kHz with respect to air. Furthermore, the frequency shift was not found to be a very sensitive function of the storage and loss modulii of the protein layer. For example, changing the value of G′ by a factor of 100 from the reported value for mussel protein22 only results in a 6% change in the resonance frequency in our calculations.
In eq 10, Fl and ηl are the liquid density and shear viscosity, respectively. The viscoelastic HSA film is characterized by its complex shear modulus according to Gf ) G′ + jG″, where G’ and G′′ are the storage and loss modulii, respectively. The surface mechanical impedance Zsfilm can be written as Z sfilm ) (GfFf)1⁄2 tanh(γhf)
In order to analyze for the viscoelastic response behavior the values of Ff and hf were estimated to be ∼1040 kg · m-3 and ∼ 7 nm, based as on the reported HSA aeral density of ∼750 ng · cm-2 at saturation coverage with the thickness set at the lower limit of the range 7-10 nm.20 The storage and loss modulii (G′, G′′) were assumed to be 6.6 × 104 and 7.1 × 105 N · m-2, respectively, based on values taken from published work on mussel adhesive protein onanonpolarsubstrate.22 AssumingthevalidityoftheButterworth-Van Dyke model for the quartz resonator, we used eq 9 to calculate the complex mechanical impedance as seen by the quartz resonator. Since the motional capacitance Cm of the quartz resonator remains unchanged during the experiment, the imaginary part of the mechanical impedance implies a change in the motional inductance. Therefore, the quartz series resonance frequency as a function of the protein surface coverage and can be explicitly written as
(20) Krishnan, A.; Siedlecki, C. A.; Vogler, E. A. Langmuir 2003, 19 (24), 10342– 10352. (21) Bandey, H. L.; Martin, S. J.; Cernosek, R. W.; Hillman, A. R. Anal. Chem. 1999, 71 (11), 2205–2214.
CONCLUSIONS We have reported the design, fabrication and performance of ∼25-µm-thick (62.23 MHz), 500-µm-diameter miniaturized quartz resonators as gravimetric sensors. In comparison to a commercial 5-MHz QCM, the miniaturized 62-MHz QCM, in spite of a reduced (1/5) mass sensitivity from the ideal value, shows ∼170 times larger frequency change and ∼20 times higher signal-to-noise ratio for saturation HSA adsorption on a hydrophobic thiol SAMs surface. In the high-concentration limit, the equilibrium adsorption rate constant for the HSA protein was determined to be K ) 8.03 × 106 M-1, which is in reasonable agreement with the values reported in the literature. Furthermore, due to the reduced penetration depth of the acoustic wave in the sampling fluid, the complete multilayered viscoelastic model has to be used to explain the observed frequency shift rather than a simple mass loading (Sauerbrey) model. This should prove to be a very useful tool for (22) Hook, F.; Kasemo, B.; Nylander, T.; Fant, C.; Scott, K.; Elwing, H. Anal. Chem. 2001, 73 (24), 5796–5804.
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probing the viscoelastic properties of nanometer scale adsorbed biomaterials. One major issue that currently remains unresolved is the observation of reduced mass sensitivity by a factor of ∼5 and the low phase rotation in the sensor resonance characteristics. We believe that the main cause of this is related to the built-in stress in the resonators from the packaging processes. Further experiments are currently underway to determine the cause for the reduced sensitivity.
Science (MRSEC DMR-0080019) and the use of facilities at the PSU Site of the NSF NNIN under Agreement 0335765. Experimental assistance from Yi-Hsiu Liu and Dr. Abhijat Goyal in the initial setup of the measurements and experimental protocol is also acknowledged. S.T. acknowledges the support of research fellowship from the Alexander von Humboldt Foundation and Walton Fellowship from the Science Foundation of Ireland.
ACKNOWLEDGMENT The authors acknowledge partial financial support from the NSF funded Pennsylvania State University Center for Nanoscale
Received for review March 14, 2008. Accepted May 14, 2008.
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