Anal. Chem. 1994,66, 3569-3574
Effect of the Generation of Compressional Waves on the Response of the Thickness-Shear Mode Acoustic Wave Sensor in Liquids Lok Tessler,' Fr6d6ric Patat, Nathalle Schmltt, and Guy Feulllard GIP Ultrasons, Laboratoire de Biophysique M&icale, Facult6 de Maecine, 2 Bis Boulevard Tonnellh, B.P. 3223, 37032 Tours Caex, France Michael Thompson Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 7A 7, Canada
The operation of a thickness-shear mode quartz oscillating with a liquid on one of its faces has been analyzed in terms of the complex acoustic impedance of the liquid load. Precise measurements put clearly in evidence that two additional impedanceshave to be added to the simple viscous loading: (1) a pure imaginary term corresponding to the nonviscous coupling caused by surface roughness effects; (2) a complex term that shows periodic changes with temperature and is interpreted as an effect of the generation of a standing compressional wave inside the cell cavity. Quartz resonators (AT-cut) operating in the thicknessshear mode (TSM) have been used extensively to monitor the rate of growth as well as the mass of deposited thin solid films. These devices, capable of measuring mass changes on the order of picograms, enjoy widespread use in mass and chemical meas~rements.l-~The great majority of work using AT-cut quartz resonators concerns mass detection in the gas phase; however, much recent attention has been focused on liquidphase applications. Indeed, this sensor is emerging as a major tool for measuring liquid hydrodynamic properties,& in addition to the study of the solid-liquid i n t e r f a ~ e .The ~ ~ latter ~ area includes applications in electrochemical analysis?JO in monitoring of electrodeposition,'l~2in analysis of proteinsurface i n t e r a c t i ~ n s , l ~and - ~ ~ as chemical or biological sensors.1619
* E-mail address: patatauniv-tours.fr. (1) Lu, C.; Czanderna, A. W. Applicafions of Piezoelecrric Quartz Crysfal Microbalances; Elsevier: New York, 1983; Chapter 2. (2) Benes, E. J. Appl. Phys. 1984, 56, 608. (3) Wajid, A. Rev. Sci. Instrum. 1991, 62, 2026. (4) Eggers, F.; Funck, Th. J. Phys. E: Sci. Instrum. 1987, 20, 523. (5) Tozaki, K.; Jimura, M.; Komatsu, N.; Itou, S.Jpn. J . Appl. Phys. 1992, 31, 2592.
(6) Reed, C.; Kanazawa, K. K.; Kaufman, J. H. J. Appl. Phys. 1990,68, 1993. ( 7 ) Schumacher, R. Angew. Chem., Int. Ed. Engl. 1990, 29, 329. (8) Yang, M.; Thompson, M.; Duncan-Hewitt, W.-C. Langmuir 1993, 9, 802. (9) Schumacher, R.; Borges, G.; Kanazawa, K. K. SurJ Sci. 1985, 163, L621. (10) Bruckenstein, S.;Shay, M. J. Electroanal. Chem. 1985, 188, 131. (11) Nomura, T.: Tsuge, K. Anal. Chim. Acta 1985, 169, 257. (12) Deakin, M. R.; Byrd, H. Anal. Chem. 1989, 61, 290. (13) Yang, M.; Thompson, M. Anal. Chem. 1993, 65, 1158. (14) Lacour. F.; Torresi, R.; Gabrielli, C.; Caprani, A. J . Electrochem. SOC.1992, 139, 1619. (15) Muratsugu, M.; Oha, F.; Miya, Y.; Hosokawa, T.; Kurosawa, S.;Kamo, N.; Ikeda, H. Anal. Chem. 1993,65, 2933. (16) Thompson, M.; Kipling, A. Duncan-Hewitt, W.-C.; Rajakovic, Lj. V.; CavicVlasak, B. A. Analyst 1991, 116, 881. (17) Davis, K. A,; Leary, T. R. Anal Chem. 1989.61, 1227. (18) Guilbault, G. G.; Hock, B.; Schmid, R. Eiosens. Eioelectron. 1992, 7, 411.
0003-2700/94/0366-3569$04.50/0 0 1994 American Chemical Soclety
A TSM sensor oscillating in a viscous liquid generates a strongly damped shear wave governed by hydrodynamical mechanisms. The coupling of the viscous liquid to the resonator causes a decrease of the resonant frequency,f,, as well as a lowering of its quality factor, Q, which is the ratio of the power stored in the resonator to the energy dissipated per cycle. As previously pointed out by Tessier et al.,20the resonant frequency shift, AA, corresponds to the phase change of the reflected acoustic wave at the sensor-liquid interface (A@), while a decrease of the quality factor is related to the fractional energy loss for each reflection at the interface, (AE). These ultrasonic interfacial parameters are directly related to the solid-liquid reflection coefficient, r, which depends on the respective acoustic impedances (ratio of the stress to the particle velocity) of the quartz, Z,, and the liquid, ZL:
As previously shown, eq 1 can be used to generate the following expressions:*O
where Re(ZL) nd Im(ZL) are the r ~ a land imaginary components of the acoustic impedance of the liquid and n is the harmonic order. The imaginary component corresponds to the kinetic energy stored in the liquid, while the real component corresponds to the radiated energy in the liquid. Martin et ale2' derived expressions similar to eq 2, which explicitly relate ZLand Z, with the electrical elements of the quartz equivalent circuit. Acoustic impedance measurements with AT-cut quartz have been shown to constitute a very useful technique for (19) Ward, M. D.; Buttry, D. A. Science 1990, 249, 1OOO. (20) Tessier, L.; Patat, F.; Schmitt, N.; Lethiecq, M.; Frangin, Y.; Guilloteau, D. Sens. Actuators E 1994, 18-19, 698. (21) Martin, S.J.; Frye, G. C., Ricco, A. J.; Senturia, S.D. Anal. Chem. 1993, 65, 2910.
Analytical Chemistry, Vol. 66, No. 21, November 1, 1994 3569
discriminationof rigid mass deposition from viscosity changes in biological sensing applications.20 This technique has also been applied to characterize bulk hydrodynamical properties of Newtonian where bulk shear acoustic impedance can be expressed as
Clamp
Y
Liquid sample Thermoco
(3)
where o is the angular frequency, TL is the viscosity, and p~ is the density of the bulk liquid. However, one should note that ZL obtained from eq 2 corresponds to the effective impedance seen at the solid-liquid interface, which is usually not equal to the bulk shear acoustic impedance. It has been shown that discrepanciesbetween the theoretical shear acoustic impedance, Zsh, and the effective acoustic impedance arise mostly from interfacial phenomena. In this respect a number of studies have confirmed the influence of various interfacial properties, such as surface r o u g h n e ~ s , ~surface ~ ~ ~ -hydro~~ p h o b i ~ i t y , ~ 9and ~ ~ -the ~ ~ surface-adjacent liquid layer.26 Martin et a1.21have recently proposed, for a rough surface, the classification of the mechanisms of interaction between the sensor and the liquid into two categories: laminar and nonlaminar flow processes. These workers showed that laminar flow generation contributes equally to Re(ZL) and Im(ZL) as ( p ~ v ~ )and ' / ~ enhances viscous damping when surface features become comparable to or larger than the viscous penetration depth, 6 = ( 2 4 w p ~'I2. ) Furthermore, nonlaminar flow contributions arise from surface roughness. Indeed, the liquid trapped by surface microstucturecontributes to the imaginary component, Im(ZL), as p ~ owhile , compressional wave radiation due to surface asperities may account for an additional real term proportional to p ~ However, . as mentioned by Martin et a1.,21 this last point needs to be confirmed by further study. In this paper, the real and imaginary components of the effective acoustic impedance of liquids are determined from shifts in resonant frequency and quality factor caused by a liquid load. These parameters are deduced from the admittance spectrum measured near the resonance of the thicknessshear mode. In a first study, the measurement of the effective acoustic impedance of water at constant temperature allows identification of the different contributions for the various mechanisms of interaction described by Martin et a1.21 In a second experiment, we report variations of the acoustic impedance of water with temperature. The origin of unusual oscillations of acoustic impedance is discussed in terms of the generation of compressional waves. A theoretical expression for the acoustic impedance associated with compressional waves is derived, taking into account the physical size of the measurement cell. The resulting theoretical acoustic impedance curves are compared to the experimental curves obtained for water and organic liquids. EXPERIMENTAL SECTION Equipment. AT-cut quartz crystals (9 MHz) coated with gold electrodes were obtained from Micro Crystal, Moussy (22) Beck, R.; Pitterman, U.; Weil, K. G . J. Electrochem. SOC.1992, 139, 453. (23) Yang, M.; Thompson, M. Langmuir 1993, 9, 1990. (24) Kipling, A. L.; Thompson, M. Anal. Chem. 1990, 62, 1514. (25) Hayward, G. Anal. Chim. Acta 1992, 264, 23. (26) Duncan-Hewitt, W. C.; Thompson, M. Anal. Chem. 1992, 64, 94.
3570
Analytical Chemistry, Vol. 66, No. 21, November 1, 1994
-
I
,
............. ............ ............ ............ ............ ............ ............. ............ ............ ............ ., .........
0-1 ing Ncutial g21\
RF connector, linked to the impedance analyzer Figure 1. Side view of the cell and the sensor used for measurements of the acoustic impedance of liquids.
Lenevf, France. To perform measurements of the effective acoustic impedance of liquids with temperature, the sensor was mounted in a specially designed cell as shown in Figure 1 (for measurements versus temperature the cell was used as is, while for the study at constant temperature, an acoustic absorbent film was deposited at the top of the cell to avoid acoustic compressionalwave reflection). The cell was placed in a controlled-temperature chamber with a thermocouple being inserted as close as possible to the device to minimize errors due to gradients in temperature. The sensor was clamped between two Perspex blocks with O-rings, and the electrodes were linked to a radio frequency connector to allow electrical measurements. The grounded electrode was in contact with the liquid sample, while the other side was held in dry nitrogen to avoid interferences from condensation or evaporation on the quartz surface. A Hewlett-Packard spectrum analyzer, HP 4195A, with an impedance test kit, HP 41951, was used to measure the complex electrical admittance Y(f)at 401 points centered about the resonant frequency fr, i.e., the central frequency of the conductance peak (real part of the admittance). Reagents. All chemicalswere of analyticalgrade, and water was deionized and doubly distilled. In order to avoid interference with microbubbles while the temperature of the cell was raised, all liquids were degassed. Procedures. The frequency response of TSM sensors is significantly influenced by the wetting properties of the electrode-liquid interface. Accordingly, to produce surfaces of high hydrophilicity, the excitation electrodes (100 A Cr/ 1000 A Au) were plasma cleaned just before use. This allows the assumption of "nonslip" coupling between the acoustic shear wave and adjacent liquid l a ~ e r . ~ . ' ~ The conductance data, G vs f, were measured by the spectrum analyzer and then transferred to a personal computer through GPIB connection. The resonant frequency and the quality factor (Q being determined as the ratio of the resonant frequency to the half band width), were then calculated by fitting conductance data to the following Lorentz function:20
To determine Afr and AQ-l and to deduce ZLfrom eq 2, the resonant electrical parameters were measured for the dry
Table 1. Experlmental RewHs of the Shear Acoustlc Impedance Measurements of Water.
acoustic impedance (rayleigh) third overtone
fundamental
real
423
Zrgh
0
Z m d (=zexc 0
5601
ZL Zsb z e x c (=zL- Zsh)
imaginary
real
6186
9402
5178
- Zrgh)
423
fifth overtone
imaginary
real
10082
12353
imaginary 16771
8968 1008 96 1
