Anal. Chem. 1993, 65,1546-1551
1546
Operation of an Ultrasensitive 30-MHz Quartz Crystal Microbalance in Liquids Zuxuan Lin, Christopher M. Yip, I. Scott Joseph, and Michael D. Ward* Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455
A new ultrasensitive quartz crystal microbalance (QCM), based on chemically milled 30-MHz ATcut shear mode crystals, for operations in gas and liquid phases, is described. In liquid media, changes in the liquid viscosity (TL) and density ( P C ) lead to changes in the resonant frequency (Af) of the QCM. A linear relationship between Afand ( t l ~ p ~was ) ~ observed, / ~ in agreement with theory. Impedance analyses also showed a linear dependence of equivalent resistance on (TUL)'/~. The capabilities of these resonators in electrochemical QCM (EQCM) applications are demonstrated by the electrodeposition of copper at the QCM surface. Simultaneous measurements of frequency and charge afforded sensitivity constants that were in exact agreement with theory, indicating that energy trapping of the fundamental mode is very efficient for the 30-MHz resonators. The high sensitivity of these devices portends their use in applications such as miniature viscometers, chemical and biological sensors, and for fundamental investigations of interfacial processes. These results also suggest that miniaturization and microfabrication of shear mode devices, which will require thinner quartz crystals operating at high frequency, can be accomplished with retention of performance.
INTRODUCTION The quartz crystal microbalance (QCM) and the electrochemical quartz crystal microbalance (EQCM) have played important roles in probing interfacial processes at surfaces and thin films.' The low cost and conceptual simplicity of this method portend its development in a diverse variety of commercial and research applications. The operation of the QCM relies on an alternating strain field induced by an electrical field applied across the quartz crystal with two metal electrodes on opposite sides of a thin wafer a t AT-cut quartz. This leads to the vibration of the quartz crystal via the converse piezoelectric effect. For an AT-cut quartz crystal thickness-shear mode, this vibrational motion results in the generation of a transverse acoustic wave that propagates across the thickness of the crystal. The resonant frequency of the QCM, established when a standing wave condition is fulfilled, decreases with increasing crystal thickness according to eq 1 .
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(1) ( 8 ) Nornura, T.; Minemura, A. Nippon Kagaku Kaishi 1980, 52, 1979. (hi Rruckenstein, S.; Swathirajan, S.Electrochim. Acta 1985,30, &SI. ( c ) Buttry, D. A. In Electroanalytical Chemistry; Bard, A. J., Ed.;
Marcel Dekker: New York, 1990; Vol. 17, p 1. (d) Ward, M. D.; Buttry, D. A. S c i ~ n c c1990,249.1000. (e) Buttry. D. A.; Ward, M. D. Chem. Re['. 1992. 92. I'iS,.
where v is the velocity of sound in the quartz crystal and t, is the thickness of the quartz resonator. The velocity is given by eq 2, where pq and p, are the density and shear modulus of the quartz crystal ( p q = 2.648 g ~ m -p,~ = , 2.947 X 10" g cm-l
s-2).2
The dependence of the resonant frequency on thickness enables determination of mass changes occurring in thin films at the QCM surface, according to the Sauerbrey relationship (eq 313 (3)
where Af is the measured frequency shift, fo is the resonant frequency, Am is the mass change, Apiezoisthe piezoelectrically active area, and Cf is an integral sensitivity. This relationship is valid if the mass changes are uniformly distributed and the thin films are very thin and rigid.* This mass sensing property has led to the wide use of QCMs as thickness monitors in metal evaporations and as sensors based on analyte adsorption into thin films on the resonator surfaces5 Recent advances in QCM methodology enable the examination of mass changes at the resonator surface while the QCM is immersed in liquid media. Applications in liquid media range from mass sensing in chemical and biological systems to measurement of electrochemically induced interfacial mass changes associated with electron transfer a t surfaces and in thin In liquid applications, however, the QCM frequency also depends on the viscosity and density of the liquid in contact with the resonator, according to eq 4;z8
.(4) where p~ and p~ are viscosity and density of the liquid in contact with the QCM, respectively. If density changes are smaller than viscosity changes, the QCM can serve as a (2) The resonant frequency actually depends upon the combined thickness of the quartz plate and the metal electrodes. However, the thickness of the latter is generally much smaller than that of the quartz plate. If identical acoustic impedances are assumed for quartz and the metal electrodes, the combined thickness can be substituted for t,,, ( 3 ) Sauerbrey, G. Z. Phys. 1959, 155, 206. (4) Lu, C.; Lewis, 0. J. J. Appl. Phys. 1972, 43, 4385. ( 5 ) (a) Guilbault, G. G. lon-Sel.ElectrodeReo. 1980,2,3. (b) Guilbault, G. G.; Jordan, J. M. CRC Crit. Reu. Anal. Chem. 1988,19,1. (c) Lu, C., Ed. Applications of Piezoelectric Quartz Crystal Microbalances; Elsevier: New York, 1984; Vol. 7. (d) Ngeh-Ngwainbi, J.; Foley, P. H.: Kuan, S. S.; Guilbault, G. G. J . Am. Chem. SOC.1986, 108, 5444. (6) (a) Muramatsu, H.; Dicks, J. M.;Tamiya, E.;Karube,I. Anal. Chem. 1987,59,2760. (b) Ebersole, R. C.; Miller, J. A,; Moran, J. R.; Ward, M. 1). J . Am. Chem. SOC. 1990, 112, 3239. ( 7 ) (a) Nomura, T.; Watanabe, M.; West, T . S. Anal. Chim. Acta 1985, 175. 107. (b) Nomura, T.; Nagamune, T. Anal. Chim. Acta 1983, 155, 231. (c) Bruckenstein, S.; Shay, M. Electrochim. Acta 1985, 30, 1295. ( 8 ) (a) Kanazawa, K. K.; Gordon, J. G., I1 Anal. Chem. 1985,57,1771. (b) Kanazawa, K. K.; Gordon, J. G., I1 Anal. Chim. Acta 1985. 175, 99.
0003-2700/93/0365-1546$04.00/00 1993 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 65. NO. 11. JUNE 1, 1993
convenient and economical viscometer. While the QCM has been employed widely, the use of ATcut thickness-shear mode QCMs and EQCMs can he somewhat limited by the sensitivity at the operating frequencies typically used (5-11M H Z ) . Inspectionofeqs ~~ 3 and4reveals that the sensitivity of QCMs increases with increasing fundamental (operating) frequency. However, lower frequency crystals are commonly used because of the fragility ofthe thinner, higher frequency crystals (eq 1). For example, 5- and 30-MHz crystals have thicknesses of about 330 and 55 pm, respectively. This prompted us to examine chemically milled quartz resonators in which quartz plates are etched only in the center, forming a thin quartz membrane with a thick, mechanically stable outer ring. Fabrication of the excitation electrodes on the thinned region of the crystal provides high resonant operating frequencies, hut with improved mechanical stability and signal-to-noise characteristics that are claimedto he better than those of other high frequency acoustic wave devices.10 AT-cut quartz crystals with resonant frequencies up to 950 MHz for frequency control applications have been prepared successfully in this manner." However, the behavior of the higher frequency thicknessshear mode quartz resonators in liquids has not been examined. In addition to advancing the sensitivity limits of the QCM and EQCM, investigation of the behavior of higher frequency resonators in liquids is paramount if shear mode transducers are to be miniaturized and manufactured by conventional microfahrication technology, as smaller crystal and electrode diameters require thinner, higher frequency quartz plates.'2J" Herein we describe a n ultrasensitive QCM based on 30MHz AT-cut shear mode crystals prepared hy chemical milling." The operation and behavior of these resonators in air and liquids are described in term of the mass sensitivity, dependence on solution viscosity, and electrochemical applications. The results clearly indicate that high frequency AT-cut thickness-shear mode quartz resonators can be operated successfully in liquids, providing enhanced sensitivity for mass detection and viscosity measurements.
EXPERIMENTAL SECTION Materials. Chemicallymilled30-MHzcrystalswereohtained from Piezo Technology, Inc. (Orlando, FL). The 30-MHz ATcut resonators have thicknesses of approximately 55 pm in the center. The chemical milling process isaccomplished by NHl+Fetching of the quartz wafer, providing a thin region in the center and a thicker outer ring (Figure la).'OJ4 The quartz crystal is sandwiched between two gold electrodes (600 A thick with 60 A Cr underlayers) on both sides of the crystal and is mounted on a custom holder with two metallic pins contacting the gold electrodes on the crystal. This configuration allowed for facile connection to the impedance analyzer, oscillator circuit, and potentiostat. The quartz crystal diameter is 6.45 mm, and the excitation electrode diameter is 1.92 mm. Assuming that the piezoelectrically active area is confined to the region in which (9) Sham, 2. A.; Radtke, D. E.; Kelksr, U. R.; Josse, F. Anal. Chim. "^*" 300" " 1 1 "Ill
Symposium,1986: pp 292-306. ' (12) (a) Beehmann, R. J. Sei. Instrum. 1952,29,73. (b) Beehmann, R. Proe. Annu. Freq. Control Symp. 1958, 12, 437. (e) Beehmann, R. Proe. IRE 1961,49,523. (13) Tiersten, H. F. Proc. Anal. Fmq. Control Symp. 1914, 28, 44. (14) (a) Vig, J. R.; LeBus, J. W.; Filler, R. L. Chemically Polished Quartz. In Proceedings of the 32st Annual Frequency Control Symposium,1977;pp 131-143. (b) Vig, J. R.; Randmayr, R. J.; Filler, R. L. Etching Studies on Singly and Doubly Rotated Quartz Plates. In Proceedings of the 33rd Annual Frequency Control Symposium,1979, pp 351-358.
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Figure 1. Schematic representationsof the chemlcaliymilled 30-MHz crystal and QCMcell. (a) Ring-supported resonator. The dlameter of the crystal Is 6.45 mm and that of the gold electrode Is 1.92 mm. (bl Side view of the crystal mounted in the liquid cell.
theopposingelectrodesoverlap,AD;8zo = 0.029 cm2. Experiments in liquid media were performed with the upper electrode facing solutionand theother facingtheair. Theelectrochemicallyactive area was Ae~ac,,o = 0.063 cmz,as determined with chronoamperometry methods hy electrochemical oxidation of K4Fe(CN)G.'S The geometry and procedure for preparation of planwplano AT-cut 5-MHz crystals are identical to those described previo ~ s l y . 'The ~ upper electrode facing solution has a radius of 0.32 cm, and the lower electrode facing air has a radius of 0.24 cm. The piezoelectrically active area ADjemfor this 5-MHz QCM is 0.18 em2,based on the electrode overlap region. Aqueous solutions were prepared from 18 MR water purified with a Milli-Q purification system (Millipore Corp., Bedford, WA). Different weight percent (0-26 w t % ) glucose and sucrose solutions were prepared to obtain different viscosities. Experiments were performed at room temperature (20 "C), and the values for density and viscosity of these solutions were obtained from standard tables.17 Apparatus and Procedure. The resonant frequency response to mass changes and liquid properties, and the electromechanical properties of the quartz resonators, were measured using either a broadband RF amplifier with the crystal in a feedback loop or an impedance analyzer. In the feedback mode, a homemade oscillator in conjunction with a Hewlett Packard 6234Adual output power supply was designedto drive the crystal at its resonant frequency. The frequency of the QCM was monitored with a Hewlett Packard 5384A frequency counter, with a precision of 1 Hz at a gate time of 0.1 s at the 30-MHz operating frequency. Impedance analyses were performed with a Hewlett Packard 4194A impedanceigain-phase analyzer. Equivalent circuit values were determined with the internal algorithm of the HP 4194A analyzer. An RF isolation cage was not used as the system proved to he sufficiently stable to highfrequency noise. The cell configuration used for impedance analysis of 5-MHz QCMs was identical to that described in ref 16. The 30-MHz QCM liquid cell was designed and fabricated to minimize stress on the quartz crystaland to electrically isolate the two excitation (15) (a) Stackelberg, M. "on; Pilgram, M.; Toome. V. Z. Electroehem. 1953.57, 342. (b) Adams, R. N. Electrochemistry at Solid Electrodes; Marcel Dekker: New York, 1969. (16) Hillier, A. C.; Ward, M. D. Anal. Chem. 1992,64,2539. (17) CRCHondboook of ChernistryondPhysics.63rded.. Weast,Robert, C., Astle, Melvin, J., Ed.; CRC Press: B o a Raton, FL, 1982.
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 11, JUNE 1, 1993
electrodes by only allowing the upper side to contact the liquid (Figure lb). The lower face of the quartz crystal was isolated by encapsulating the region below the crystal in an epoxy (Conap Inc., Olean, NY), taking care that the epoxy did not contact the inner region of the crystal. In order to ensure electrical isolation, the metal contacts at the QCM electrodes were encapsulated with a minute amount of 5-min epoxy. The liquid cell was completedby sliding a polyethylenetube (9.4mm outer diameter; 6.5 mm inner diameter) over the assembly. The tube was compressed against the outside of the holder with a nylon wire tie, which provided a liquid tight seal. This proved to be an effective and reliable way to fabricate a QCM cell, allowingfacile disassembly and cleaning of the cell. The 30-MHz QCM was connected directly to the test fixture of the impedance analyzer for admittance measurements. In air, the quality factor and resonator stability decreased only slightly after the crystal was mounted. The height of solution in the cell was always kept constant in order to maintain constant hydrostatic pressure.18 Electrochemical experiments were performed with the upper electrode facingthe solution and acting as the working electrode. An EG&G Princeton Applied Research 273 potentiostat (Princeton Applied Research, Princeton, NJ) was used with this working electrode at hard ground (through the oscillator hard ground). Current was measured from the voltage drop across a 1000-Qresistor in series with the counter electrode connection by a Keithley Microvolt DMM 177 (Keithley Instruments, Inc., Cleveland, OH), similar to the method described previo~sly.'~ The time, current, and frequency were collected during both the electrodeposition and the removal cycles by a microcomputer; electrochemical charge was calculated from integration of the current.
RESULTS AND DISCUSSIONS Impedance Analysis. In order to characterize the electromechanical properties of the 30-MHz resonators and their behavior in liquids, impedance (or admittance) analyses were performed for both 30- and 5-MHz QCMs in air and water for comparison purposes. These experiments involve the measurement of electrical current through the quartz resonator at a known applied voltage over a specified range of frequencies. The oscillation of quartz crystals can be represented by the commonly accepted Butterworth-van Dyke equivalent circuit, which allows analysis of the mechanical properties from readily measured electricalparameters. 1e,20,21 The electrical parameters represent the mechanical properties of the resonator, with CO attributed to the static quartz capacitance, C1 the compliance of the quartz resonator, L1 the inertial mass, and R1 the damping associated with dissipation of the acoustic energy. In Newtonian liquids, if no mass loading at the QCM is considered, the influence of the liquid is to add resistance R2 and inductance Lz in series with the motional branch of the equivalent circuit (Figure 2). The values for each parameter are given by eqs 5-10 21 (5) L , = 1/w,2c1
(7)
(18) Heusler, K. E.; Grzegorzewski,A,; Jackel, L.; Pietrucha, J. Ber. Bensenges Phys. Chem. 1988, 92, 1218. (19) Ward, M. D. J. Chem. Phys. 1988, 92, 2049. (20) Bottom, V.E.Introduction t o Quartz Crystal Unit Design; Van Nostrand Reinhold: New York, 1982. (21) Martin, S.J.; Granstaff, V. E.; Frye, G. C. Anal. Chem. 1991,63, 2272.
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where €22 is the quartz permittivity (a4.34 where EO is the permittivity of free space), A is the area of electrode overlap, Ko2 is the electromechanical coupling constant, w, is the resonant (angular) frequency, and w is the angular excitation frequency. The effective quartz viscosity, vq, is determined empirically from experimenkx22 Impedance analysis indicated that the conductance peak width and maximum conductance, G, are nearly identical for the 30-MHz QCM before and after mounting the QCM cell (Figure 3). The small shift in f ~ ,is likely due to the small stress associated with the mounting. However, a dramatic increase in the width of the conductance peak as well as a decrease in,G accompanies immersion of the upper side of the 30-MHz resonator in water. The decrease of fG, is attributed to the loading of the viscous liquid (eq 4).23 Impedance measurements are especially critical for the 30MHz oscillators because of their smallthickness values, which can result in a large increase in CO. The increase in COleads to a shift in the admittance locus upwards on the admittance plane (by the amount equal to COCO), increasing the likelihood that the admittance locus will not cross the real axis. Under this condition, operation at the resonant frequency using a feedback-mode oscillator can be difficult because this mode requires operation a t zero phase angle. Fortunately, the (22) Reed, C. E.;Kanazawa, K. K.; Kaufman, J. H. J. Appl. Phys. 1990.68. 1993. (23) Under our conditions, in which the resonatorspossess high quality factors, fa, = fo.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 11, JUNE 1, 1993
Table I. Impedance Analysis Parameters for 5- and 30-MHz QCMs 30 MHz, air 30 MHz, water paramebra expt calc exvt calc
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smaller area of electrode overlap for the 30-MHz resonators diminishes this effect. The 30-MHz resonators also should have smaller values of the equivalent resistance and inductance, R1 and L1,owing to the smaller thickness of these crystals compared to the 5-MHz crystals. Indeed, impedance analysis of the resonators in air indicated smaller R1 and L1 values for 30-MHz resonators. Immersion of the upper face of crystals in water resulted in a substantial increase in R for both frequencies, although the relative increase was larger for 30-MHz resonators (Table I). Successful operation of the 30-MHz resonator, therefore, will depend upon the contribution of these factors, particularly the effect on R of liquid damping. Because R1 (resistance in the air) is normally much smaller than Rz, we can assume R = R2. According to eq 9, for a 30-MHz crystal, LzILl < lo-' and, therefore, L = L1.The calculated values for CO (A = 0.029 cm2 for the 30-MHz crystals,and A = 0.18 cm2for the 5-MHz crystals) were smaller than those from experiments. The extra static capacitance was believed coming from other sources, such as the holder and the test fixture. It was found that COof 5-MHz quartz crystals was very sensitive to the cell configuration and the connection between the crystal and the test fixture. For example, a cell configuration in which the crystal is mounted between two O-rings, as described previously,lg gave significantly larger COvalues. We have also found that COdepends strongly on the length and diameter of cables connecting the crystal to the analyzer. The values in Table I for the 5-MHz QCM were acquired with electrical leads with a length of 6 cm and diameter of 0.024 cm. Using eq 6, the motional capacitance C1 (unperturbed) is 1.341 X 10-14 F for the 30MHz crystal and 1.344 X F for the 5-MHz crystal (for lossless quartz, KoZ = 0.008 20). The close agreement of these values with the experimentallyobtained values indicated that parasitic capacitancesdid not influencethe motional elements. These values are affected, however, by the actual vibrating area of the quartz crystal, which can extend beyond the electrode edges in liquids (field fringing).16.24 In liquids, an increase of the effective area of electric field can increase CO and C1, resulting in a decrease of the motional inductance L1 (eq 7). A small contribution from this effect is consistent with impedance analysis results, which indicate larger Coand C1values and larger L values in water than in air. Quantitative calculation of this fringing effect is difficult, although we will show later that the fringing is negligible in terms of mass measurements. The calculated values for Rz, using L combined with R1 (resistance in the air) for both 5- and 30-MHz crystals in the water (eq lo), were less than those measured experimentally. This difference may be due to hydrostatic pressure, surface stress, and other losses associated with the acoustic coupling of the liquid layer to the quartz crystal. The admittance data reveal trends that are indicated by the data above (Figure 4). Immersion of the upper surface of the crystal results in a decrease in the diameter of the admittance locus, consistent with damping in liquid media. It is also clear that under identical operation conditions, the diameter of the 30-MHz locus is larger than that of the 5-MHz (24) Martin, B. A.; Hager, H. E. J. Appl. Phys. 1989, 65,2630.
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locus, reflectingthe smallerR value for the 30-MHz resonators. A slight upwards shift of the locus is also observed for the 30-MHz resonator compared to the 5-MHz resonator. The admittance data for both the 5- and 30-MHz crystals crossed the real axis (conductance, G)in air and water. These results clearly indicate that the higher frequency QCMs can be operated successfullyin liquids using conventional oscillator circuits. We also note that the conductancevalue at the series resonant frequency, fs, where the admittance locus crosses the real axis, is larger for the 30-MHz crystals than for the 5-MHz crystals. Because QCM experiments using the feedback mode operate a t fs, this suggeststhat the 30-MHz crystals can be operated with lower loss in liquid media than the more commonly used 5-MHz crystals. In addition, the observed sensitivityof the 5-MHz crystalsto cell configuration suggests that the performance of the 30-MHz crystals could be further improved by the optimization of the cell design. Viscosity Measurements. There is growing interest in using acoustic wave devices as liquid microsensors. The behavior of QCM in Newtonian liquids and the underlying physical principles have been described by Kanazawae and examined at QCM resonant frequencies up to 11 MHz.7-9 In order to examine the dependence of the 30-MHz QCM on viscosity, frequency measurement and impedance analysis were performed in liquids, in which the viscosity was systematically varied by the addition of either glucose o r sucrose. Both feedback mode and impedance analyzer gave similar frequency responses. Feedback mode operation indicated a linear relationship between frequency decrease and ( v ~ p ~ ) ' /(Figure ' 5a), with
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slope A f / ( q ~ p ~ ) = ' / 1.1057 ~ X lo5g1 cm2 s-1/2. This compared favorably with the value of 1.101 X lo5g1cm2 expected from eq 4, where fo = 30.97 MHz. Therefore, the frequency dependenceon ( q ~ p ~ can ) l /be ~ expressed as eq 11. The higher
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operating frequency of the 30-MHz resonators results in enhanced sensitivity to viscosity changes compared to previously reported QCMs. Whereas a 275-Hz frequency de-
crease was observed when a 5-MHz QCM was transferred from water to a 15 w t % glucose sblution,8 and a 650-Hz decrease for a 11-MHz crystal: a 3395-Hz frequency decrease was observed for the 30-MHz QCM. The density of glucose or sucrose solutions remains essentially constant acrossthe 0-26 w t % composition range, while the viscosity changes substantially. Accordingly, if a stability of kt10 Hz is assumed for this 30-MHz QCM (which is conservative), a minimum relative viscosity change of A&qwabr = 2 X 1 W can be detected (PL = P H ~ O= 1 g ~ m - ~ ) . Impedance analysis clearly indicates the effect of viscosity on energy damping, as evident from plots of conductance versus frequency for different viscosities (Figure 5b). The maxima of conductance decreased with increasing viscosity. Furthermore, the conductance peaks were broadened due to greater damping, indicative of decreasing quality factor. The resistance increased linearly with ( q ~ p ~ ) '(Figure /* 5c), in qualitativeagreement with results reported by Muramatau.25 Because of a lack of reliable data on the quartz crystal electrode area, and the use of an 'effective electromechanicalconstant" used in their experiments, quantitative comparison with the model of Muramatau is not possible. However, the data agree well with that expected from eq (R/(qLPL)1/2)calc= 2736 and ( R / ( q o ~ ) ' / ~ )=~2794.7 ~ ~ t n g' cm2s1/2. They-intercept value where ( q ~ p ~ )vanishes l/~ is 49 fl. This is slightly larger than the R value in air, but it may reflect small energy dissipation contributions from the electrode edge moving against the liquid or stresses induced by the hydrostatic pressure. The quality factor Q also exhibited a linear dependence on ( ~ L P L ) - ~as I ~ ,expected from the inverse dependence of Q on R. The 30-MHz chemically milled QCMs therefore can be operated successfully in liquid media, and the frequency dependence on the liquid properties was in good agreement with ideal behavior. Copper Deposition. Because the QCM is sensitiveto mass changes at electrode surfaces and in films on the excitation electrodes, it is often used in conjunctionwith electrochemical measurements for in situ experiments. When the QCM is used in this way, it is often referred to as electrochemical QCM (EQCM). For an electrochemical process at the electrode interface, the charge consumed in the electrodes is related to the mass change according to eq 12 Am = AQ(MW)/nF (12) where MW is the molar mass associated with the changing mass, n is the number of electrons involved in the reaction, and F is the Faraday constant. The capabilities of the 30-MHz EQCM were demonstrated by electrodeposition of copper in 0.1 M CuS04 solution. Electrodeposition was measured by decreasing the applied potential at a rate of 5 or 10 mV/s from 0.5 V to -0.1 V (VB Ag/AgCl). After deposition, the potential scan was reversed and held at 0.5 V for 15 s between cycles to ensure complete removal of electrodeposited Cu. Linear dependence of frequency on the charge consumed was found in both Cu deposition and depletion (Figure 6). The slight curvature in the plot of Af versus Q may reflect changes in the surface morphology, as previously observed for 5-MHz resonator operating at the third harmonic (15 MH~).26-~7 The slope (Af/Q) was obtained based on the average of five experiments. For Cu electrodeposition, slope = (1.135 f 0.036) X lo7 Hz C-l and for Cu removal, slope = (1.064 f 0.043) X 107 Hz C-l. These values can be compared with that expected from (25) Muramatau, H.; Tamiya, E.; Karube, I. Anal. Chem. 1988, 60, 2142. (26) Schumacher,R.; Borges, G.; Kanazawa, K. K. Surf.Sci. 1985,163, L621. (27) Schumacher,R.; Gordon, J. G.; Melroy, 0.J.Electroanal. Chem. 1987, 216, 127.
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Charge (Coulombs)
1551
film behaved like a rigid film and the energy trapping of the fundamental mode within the electrode overlap region is very efficient for the 30-MHz resonators, contraryto behavior observed for 5-MHz plano-plan0 resonators.16 The integral sensitivity for this 30-MHz QCM determined from copper electrodeposition is 2.17 Hz cm2 n g l , in exact agreement with ideal case (2.16 Hz cm2 ng-l). The sensitivity of the 30-MHz QCM deviceis dramatically greater than that of other lower frequency QCMs (0.057 Hz cm2n g l and 0.274 Hz cm2 n g l for 5- and 11-MHzEQCM, respectively). The enhanced sensitivity and improved energy trapping properties of the 30-MHz resonator suggest their usefulness in quantitative analysis of surface and submonolayer phenomena. In summary, these data clearly show that these 30-MHz resonators can be used effectively in EQCM applications.
CONCLUSIONS
-loo00
I
r '
-0.001
0
0.001 0.002
0.003
0.004
0.005
Charge (Coulombs) Flgure 6. Frequency dependence on the charge consumed at the electrode during electrodeposition and removal of copper in 0.1 M CuSO, solution. (a) Electrodeposition of copper, slope = 1.135 f 0.036 X lo7 Hz C-I. (b) Electrochemical removal of copper, slope = 1.064 f 0.043 X lo7 Hz C-'. The applled potential was scanned at rate of 5 or 10 mV/s from 0.5 V to -0.1 V (vs Ag/AgCI) for electrodeposition of copper and was reversed for electrochemical removal of copper. The potentlalwas held at 0.5 V for 15 s between cycles to ensure complete removal of electrodeposited Cu.
eq 3; however, the difference between the electrochemically active area, Aelectro, and the piezoelectrically active area, Apiezo, must be taken into account. Because the charge is consumed over the entire area of working electrode, Aeiectro, the charge associated with Apiezo(AQpiezo) can be determined by eq 13.
This allows determination of the mass change occurring on Apiezoonly. Therefore, the Sauerbrey equation (eq 3) can be rewritten as eq 14 (14) where for copper deposition and removal, the MW of Cu is 63.55 g/mol and n = 2. Calculation of the constants reduces eq 14 to eq 15 Af = -1.114 X lO'AQ (15) which indicates quantitative agreement with our experimental results. The agreement between the measured Af/AQ values and that predicted from eq 3 using the geometric area of the electrode overlap region indicates that the deposited copper
The results described above clearly show that high frequency AT-cut quartz thickness-shear mode resonators can be operated successfully in liquids. Although the vibrating portion of the quartz crystal is thin and fragile, the overall mechanical stability provided by the thick outer ring allows the resonators to be handled conveniently. The greater sensitivity of these resonators compared to their lower frequency relatives can significantly expand the utility of QCMs and EQCMs in fundamental investigations of interfacial phenomena as well as in sensing applications. Indeed, extension of these studies to even higher frequency resonators will make the sensitivity of QCMs comparable to surface acoustic wave, shear-horizontalplate mode, and flexure mode devices. It is especially important to note the impact of these results on the fabrication of miniature QCMs, which is highly desirablefor sensor applications. The Bechmann numbers'ZJ3 dictate that for a crystal diameter that is 50 times the crystal thickness, the electrode diameter must be 18times the crystal thickness in order to avoid interference from other acoustic modes. Accordingly, a reduction in crystal and electrode diameter must be accompanied by a corresponding reduction in the crystal thickness in order to maintain frequency stability. The successful operation of the thin 30-MHz resonators in liquids, therefore, should encourage attempts to fabricate miniature QCMs using conventional microfabrication technology. The highly efficient energy trapping suggested by our studies also should facilitate design of miniature QCMs as deleterious effects due to crystal mounting should be negligible. These characteristics portend the development of highly sensitive, mechanically robust, economical sensors that can be readily modified for chemical and biological sensor applications.
ACKNOWLEDGMENT The authors acknowledge the generous donation of 30MHz chemically milled AT-cut crystals from Mr. Robert Smythe a t Piezo Technology, Inc. This work was supported by a grant from the National Science Foundation (NSF/CTS9111OOO). Z.L.acknowledges the support from the NSF Center for Interfacial Engineering (NSF Engineering Research Center Program CDR 8721551). RECEIVED for review January 7, 1993. Accepted March 2, 1993.
