Anal. Chem. 1993, 65, 1158-1168
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Multiple Chemical Information from the Thickness Shear Mode Acoustic Wave Sensor in the Liquid Phase Mengsu Yang and Michael Thompson' Department of Chemistry, University of Toronto, 80 S t . George Street, Toronto, Ontario, M5S IA1 Canada
The effects of viscosity, density, and dielectric constant of a liquid on the response of a thickness shear mode (TSM) bulk acoustic wave sensor are examined with respect to frequency response and the electrical properties of the equivalent circuit. The different behaviors of the characteristic frequencies upon perturbation of the equivalent circuit parameters are studied and the complementary nature of the motional inductance and motional capacitance discussed. The physical significance of the equivalent circuit parameters is described theoretically, and the relationship between the motional inductance and resistance of the TSM sensor and the density-viscosity product of the bulk liquid as well as that between the static capacitance of the TSM sensor and the dielectric constant of the liquid is demonstrated experimentally with a network analyzer. The composite responses of the resonant frequencies upon liquid loading can be interpreted in terms of the kinetic energy transfer, acoustic energy dissipation, and formation of interfacial structures in the sensing system. The properties of the surface adjacent liquid layer at the solid-liquid interface are estimated from the responses of the respective parameters.
thickness of the decay length of the acoustic wave. An important element of this model is the assumption that the transverse velocity of the quartz surface is identical to that of the adjacent liquid layer (nonslip boundary condition). Other theories have considered the influences of surface stress,,j viscous energy losses and dielectric and surface roughness.8 The effect of surface free energy and interfacial viscosity on the response of the TSM device has been examined by Thompson and co-w~rkers.~-l~ It is considered that the resonant frequency response arises from the perturbation of acoustic energy transmission caused by a partial-slip boundary condition a t the solid-liquid interface. Using the molecular theory of viscosity proposed by Krausz and Eyring,l* Duncan-Hewitt and Thompson15 have developed a four-layer model which provides a link between measurable bulk liquid properties such as density, viscosity, surface tension, and contact angle and the TSM sensor response. The predicted results for the model are quantitatively similar to those observed e~perimental1y.l~ There are two methods used to characterize an acoustic wave sensor on an electrical basis. Previous studies of TSM devices in liquid have almost exclusively used the active method, which is more commonly known as the oscillator method. In this method the quartz crystal is part of an oscillator circuit. It is connected between the output and input of the oscillator amplifier and provides positive feedback to cause oscillation of the circuit. The conditions of oscillation are that the magnitude of loop gain is unity and the phase shift around the loop is zero. The quartz crystal is active in the sense that it is continuously oscillating at a frequency controlled by the crystal itself. The resonant frequency of the quartz crystal is measured by a standard frequency counter. There are some serious limitations associated with the oscillator method: (i) as the series resonant frequency is the only parameter measured, the method only partially characterizes the device; (ii) the resonant frequency depends on the components of the oscillator circuit; and (iii) the oscillator does not function in certain situations, such as heavy mass loading or highly viscous damping. On the other hand, in the passive method, the quartz crystal is connected externally to an instrument which applies an alternating voltage at various frequencies across the crystal. The frequencies of the voltages are not determined by the crystal. The network analysis method is a passive method that has been recently developed to more completely characterize acoustic wave devices. The values of the magnitude and phase of the impedance of the quartz crystal can be determined at each frequency from the voltages and currents, and electrical
INTRODUCTION The extensive use of the piezoelectric bulk acoustic wave (BAW) device as a microgravimetric sensor for the gas phase has its origins in the work of Sauerbrey,' which demonstrated that a shift in the resonant frequency of an oscillating AT-cut crystal is related to a change in mass at the surface of the device. More recently, there has been an increasing amount of attention paid to the operation and application of BAW sensors of the thickness shear mode (TSM)type in the liquid phase.* A number of theories have been proposed to interpret the frequency shifts that arise from coupling of the oscillating surface to a liquid medium. Two similar models were developed by Kanazawa and Gordon3and Bruckenstein and Shay4 which allow the prediction of frequency changes of TSM devices from the properties of quartz and the bulk liquid. The oscillation of the crystal in liquid results in a damped propagating shear wave. The decay length of the propagating wave is a function of viscosity and density of the bulk liquid. The former theory treats the quartz as a lossless elastic solid and the liquid as a purely viscous fluid. The surface-adjacent liquid layer is regarded as a rigid sheet. The frequency of the TSM device responds to the mass of the liquid layer with a
(5)Heusler, E;. E.; Grzegorzewski, A , ; ,Jackel, K.; Pietrucha. J Aer. Aunsengea. P h y s . Chern. 1988, 92, 1218. (6) Yau. S.-2.; Zhou, T:A. Anal. Chirn. Acla 1988, 212, 61 t i i Hager, H.E. C h e m . Eng. Comrnun. 1986, 43, 25. ( 8 ) Schumacher, R. A n g e u . Chern., Int. Ed. Eng. 1990, 29, 329. ( 9 ) Thompson, M.: Dhaliwal, G . K.; Arthur, C. L.; Calabrese. G. Y. IEEE T r a n s . I:ltrason. Ferroelectr. Frey. Control 1987, UFFC-34. 127. (10) Kipling, A . L.; Thompson, M. A n a l . Chern. 1990, 62, 1514. ( 11) Rajakovif, Lj. V.; (?avit-Wasak. B. A,; Ghaemmaghami, V.; Kallury, h.1. R . K . : Kipling. A. I,.. Thompson, M. A n a l C h e m . 1991. 63, 615.
i l l Sauerbrep, G. Z. P h y s . 1959, 155, 206.
( 2 ) Thompson, M.; Kipling, A. L.; Duncan-Hewitt, W . C.; RajakuviC, Lj. V.; CaviC-Vlasak, B. A. Analyst 1991, 116, 881. i 3 i Kanazawa, K. K.; Gordon, J. G. Anal. Chim. Acta 1985, 175, 99. ( 4 ) Bruckenstein. S.; Shay, M. Electrochim. Acta 1985, 30, 1295. 0003-2700/93/0365-1158$04 0010
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1993 Amerlcan Chemical Society
ANALYTICAL CHEMISTRY, VOL. 65, NO. 9, MAY 1, 1993
quantities can be found from the impedance-frequency curves. Multidimensional information can be obtained to describe the behavior of the TSM devices in liquid phase. The network analysis of the TSM device based on its equivalent circuit and the relationship between several characteristic parameters and the properties of liquids were discussed by Kipling and Thompson.10 Recently, Martin et al.15derived a continuum electromechanical model for an ATcut quartz crystal simultaneously loaded by a surface mass layer and a contacting Newtonian liquid. Admittance analysis resulted in a modified equivalent circuit, and the circuit elements were related to the physical properties of the quartz, surface mass, and contacting liquid. It was suggested that, for a crystal with sufficiently clean and smooth surfaces, the one-dimensional model with bulk viscosity values and the nonslip boundary condition can be used to predict the behavior of the crystal in liquids. Most recently Hayward16 derived a model relating the equivalent circuit elements to the viscous energy dissipation based on the assumptions of continuity and no surface slip. The model overestimates the frequency shifts and the equivalent viscous resistance. It was proposed that the assumptions used are invalid since the surface vibration of the crystal is much smaller than the mean free path between liquid molecules. In the present paper, the responses of the TSM devices in liquid phase are studied with respect to ita characteristic frequencies and the electrical properties of the equivalent circuit. The different behaviors of the frequencies upon perturbation of the equivalent circuit parameters are examined, and the physicochemical significance of the circuit elements is discussed for the first time.
THEORY Background. The piezoelectric crystal resonator is an electromechanical transducer which converts electrical energy to mechanical energy, and vice versa. The circuit of the series combination of a capacitor (C,), an inductor (L,), and a resistor (R,) in parallel with a capacitor (CO)is equivalent electrically to the piezoelectric resonator (Figure 1). The subscript m is used to denote the fact that the RLC series is associated with the motion of the quartz plate. The equivalent circuit responds to an applied voltage in the same way as the quartz crystal itself. The impedance of each circuit element is also given in Figure la, where w is the angular frequency (in rad/s). The impedance of the equivalent zircuit, 2, is a complex quantity resulting from the impedance of Co in parallel with the impedance combination of Rm, L,, and C,:
Z=R+jX (1) where R is the real part of 2, the resistance, and X is the imaginary part of 2, the reactance. Both R and X are functions of the four circuit parameters and w. The magnitude of impedance 1 4 and the phase angle of impedance, 8, are given by
14 = (R2+ X2)l/'
(2)
8 = tan-' ( X I R ) (3) Physically, impedance 2 is the ratio of the applied voltage across the crystal and the current flowing through the crystal. Sinusoidal voltages incident on and reflected from the quartz (12) Krausz, A. S.;Eyring, H. Deformatiue Kinetics;Wiley: New York, 1974. (13) Duncan-Hewitt, W. C.; Thompson, M. Anal. Chem. 1992,64,94. (14) Yang, M.; Thompson, M.; Duncan-Hewitt, W. C. Langmuir, in press. (15) Martin, S. J.; Granstaff, V. E.; Frye, G . L. Anal. Chem. 1991,63, 2272. (16) Hayward, G. Anal. Chim. Acta 1992, 264, 23.
lbl
1159
100
1
80
h
I !
L 1 8.94
ase
9.02
80 -100 9.06
Frequency (MHz) Flguro 1. Equivalent electrical circuit of the bulk acoustic wave sensor and typical piots of the magnitude (14)and phaseangie @)of impedance for a 9-MHz TSM resonator.
crystal are measured for a large number of frequencies in the resonant frequency region. The experimental values of the magnitude and phase of impedance can be calculated at each frequency and plotted against the frequency to give the impedance-frequency curves. Figure l b shows typical plots of the magnitude and phase angle of impedance of a 9-MHz TSM bulk acoustic wave device. The prominent characteristics from the impedance (magnitude and phase) measurements are the frequencies at the minimum and maximum magnitudes of impedance and the corresponding values of the magnitude of impedance, the frequencies a t zero phase, and the value of maximum phase. The four equivalent circuit parameters (Co, R,, L,, C,) can also be extracted from the impedance measurements by standard circuit analysis. For the equivalent circuit (Figure l a ) the expression for the admittance, Y, is simpler than the expression for impedance, 2. It is more convenient to use the admittance method to derive the characteristic frequencies and demonstrate their relationship. By definition, the admittance Y is the reciprocal of the impedance 2. Since 2 is a complex (eq l),Y can be written as
+
Y = 1/Z = G j B (4) where the real part quantity G is called the conductance and the imaginary part quantity B is called the susceptance:
G=
Rm
Rm2+ (wL, - l/wC,)*
(5)
The mathematical derivation of the characteristic frequencies of the equivalent circuit was developed by Cady17 and presented clearly by Bottom.ls The condition for the circuit to be resonant is that the imaginary part of impedance 2 should be equal to zero. Substituting eqs 5 and 6 into eq 4 (17) Cady, W. G. Piezoelectricity; Dover: New York, 1964. (18) Bottom, V. E. Introduction to Quartz Crystal Unit Design; Van Nostrand Reinhold: New York, 1982.
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and solving the quadratic equation, by assuming R , = 0, we obtain 1 112 (7)
fR=k(&
f,
YL+3
=27r L,C,
1 2
L,C,
where f~ is called the resonant frequency and f A is called the antiresonant frequency. The motional resistance R , relates to the energydissipation of the resonator. In most cases (e.g., gas phase), the effect of energy dissipation can be neglected in determining the resonant frequencies. However, in the cases where the energy losses are significant, e.g., upon liquid loading, the frequencies a t which Z is a pure resistance do depend on R,. When R , is included in solving eq 4, the frequencies are determined as (9) (10)
where r = COIC, and Q = wL,IR,. The series resonant frequency, fs, is the lower frequency at which Z is a pure resistance and the parallel resonant frequency, fp, is the higher frequency at which 2 is a pure resistance. These are also the frequencies a t zero phase. It should be pointed out that in the oscillator method the sole parameter obtained is the series resonant frequency. In addition to the above characteristic frequencies (eqs 7-10), network analysis of the equivalent circuit can also determine the frequencies at which the impedance Z has a minimum and a maximum value. Computing the modulus of the admittance Y and differentiating the expression with respect to X (which is a function of w ) yields (11)
(12)
where fiminis the frequency at minimum impedance and fzmax is the frequency at maximum impedance. In reality, the series and parallel resonant frequencies, fs and fp,and the frequencies at minimum and maximum value of impedance, fimlnand fzmax,are measured directly from the experimental impedancefrequency curves. The resonant and antiresonant frequencies, fR and f,, are calculated by substituting respective equivalent circuit parameters into eqs 7 and 8. An admittance diagram can be constructed to demonstrate the origins of the characteristic frequencies and their relations. The admittance Y of the equivalent circuit of the piezoelectric resonator is the vector sum of the conductance G and susceptance B (eq 4). The admittance diagram is a complex plane with E as the Y-axis and G as the X-axis. Figure 2 shows the admittance diagram of a TSM quartz crystal, which gives an admittance circle with the frequency increasing in clockwise direction. Any given point of the circle represents the vector sum of C and E. The points R and A represent the resonant frequency fR and antiresonant frequency f, at which the imaginary part of admittance (also the imaginary part of impedance) equals zero, while the effect of motional resistance is neglected. The points s and p represent the series resonant frequency fs and the parallel frequency fp at zero phase (pure resistances). The line 0-n on the admittance circle has the maximum length and the line 0-x the minimum length. Therefore the corresponding freuqency a t point n is
freq
-
Figure 2. Admittancediagram of the TSM resonator and the relationship between the characteristic frequencies. See text for details.
the frequency of maximum admittance (or minimum impedance), and the frequency a t point x is the frequency of minimum admittance (or maximum impedance). The relative positions of these six characteristic frequencies are shown graphically (not to scale) in Figure 2. Effect of the Static Capacitance, Co. At frequencies far from the resonant frequency, the quartz plate is equivalent to a simple parallel-plate capacitor with a capacitance
C, = kco(A/e) (13) where A is the area of the electrodes, e is the thickness of the quartz plate, t o is the permitivity of space, and k is the dielectric constant of the quartz. The dielectric constant is determined by the direction of the field and should be corrected for the fringing of the field unless the plate is infinitely large. It alsodepends on whether the quartz crystal is clamped or loose, since the externally applied stress on the crystal upon clamping affects the dielectric constant as well. In addition, when the crystal is loaded with polar liquids or conductive electrolyte solutions, the formation of electrical double layers will behave as an added capacitor to the quartz plate and thus change the value of the static capacitance C,. The charge distribution on the surface and the fringing of the electric field will also contribute to the change. Figure 3a shows the effect of the static capacitance on the magnitude and phase angle of the impedance. Cois increased from 5.0 to 10.0 pF and the impedance-frequency curves are simulated where the solid curves (CO= 5.9 pF) represent the real measurement of an unperturbed 9-MHz TSM device. It can be seen from the magnitude-frequency curve that, as Co increases, the peak a t which the impedance has a maximum value moves toward lower frequency, while the peak a t which the impedance has a minimum value does not change. The same effect is observed from the phase-frequency curve. As Co increases, the 'parallel" branch of the resonance band translates toward lower frequency while the 'series" branch of the resonance band remains unaffected. The net result is a reduction of the resonant bandwidth and thus an increase of energy storage in the quartz crystal. From eqs 7-12 it follows that the resonant frequency fR is independent of the static capacitance. When the effect of energy dissipation is considered, the term involving CO( r = C0/C,) is included in the expressions for the series resonant frequency fs and the frequency a t minimum impedance fZmln.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 9, MAY 1, 1993
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is also inversely proportional to the electrode area A and to the square of the piezoelectric stress constant t. However, it is difficult to estimate the absolute value of R, since a is assumed to contain all mechanisms of the energy dissipation, including internal dissipation, air damping, surface friction, and mounting losses. Muramatau et al.20 used an analogy between a mechanical model and the electrical circuit and showed that, for a quartz crystal in contact with a liquid,
1
'4
Y
where p~ and )IL are the liquid density and viscosity, respectively. However, the use of the electromechanical coupling factor K is arbitrary and ita value is unknown. Martin et al.15 have derived the analytical expression for the equivalent circuit admittance, and the resulting motional resistance is
9005 fR
fs
f m
Because of the high Q of the piezoelectric crystal and the relatively small change of Co, the effect of COon fs and fzmin is insignificant (although not negligible). However, the antiresonant frequency fA does depend on CO.It can be shown that fR(1 1/2r) = f ~thus, ; from eqs 10 and 12 the parallel resonant frequency fp and the frequency a t maximum impedance fzmaxare directly related to fA. Therefore, when the crystal is operated in the frequency region near the antiresonance, fA, fp, and fzmardepend not only on the quartz crystal but also on the associated circuit and all capacitances in parallel with the device. However, the measurement of fp can be very useful in determining specific properties of the media surrounding the quartz crystal, especially in the case of electrolytes.1g The effect of the static capacitance on the characteristic frequencies is illustrated in Figure 3b. Effect of the Motional Resistance, %. The value of the motional resistance depends on the energy dissipation of the oscillating system. Complete treatment of the equation of crystal motion and the electrical potential function resulting from the piezoelectric effect gives the expression of R, for an infinitely large, unperturbed TSM quartz plate:'*
+
R, = e3a/8At2
(14) It shows that R, is directly proportional to the damping constant u and the cube of the thickness of the plate, e3.R, (19) Yang, M.; Thompson, M. Anal. Chirn. Acta 1992,269, 167.
where V Q is the effective quartz viscosity, p g is the density of quartz, PQ is the quartz elastic constant, N is the harmonic number ( N = 1 for fundamental mode), and C1 and L1 represent the unperturbed motional capacitance and inductance, respectively. Although eqs 15 and 16 are similar, the value of R, can be predicted from the properties of the quartz and liquids from eq 16. As a result, an increase of the densityviscosity product of the liquid resulta in an increase in energy dissipation and thus a proportional increase of R,. The effect of the motional resistance on the magnitude and phase angle of the impedance is demonstrated in Figure 4a. R, is increased from 10 to 2000 s1 and the impedancefrequency curves are simulated, where the curves at which R, = 10 s1 represent an unperturbed 9-MHz TSM resonator. Increasing R, causes the "damping" of both the magnitudefrequency and phase-frequency curves. The results are an increase in the magnitude of the minimum impedance (qmin and a decrease in the magnitude of the maximum impedance lArnax and the maximum phase angle, e,,,. The broadening and diminishing of the resonance peaks arises from the power dissipation due to increasing R,. An important observation is that when R, reaches a certain value, as in the case where R, = 2000 s1, emax becomes negative. The consequence is that the frequencies at zero phase, fs and fp, no longer exist. This is one of the limitations of the oscillator method. However, several quantities can still be obtained from the impedance analysis to describe the behavior of the quartz crystal under these extreme conditions, including other characteristic frequencies. The effect of the motional resistance on the characteristic frequencies is shown in Figure 4b. It is clear from eqs 7-12 that the resonant and antiresonant frequencies are independent of R,. With increasing R, the series resonant frequency and the parallel resonant frequency converge and eventually coincide. The critical value of R, above which fs and fp do not exist can be calculated by solving eqs 9 and 10:
On the other hand, with increasing R, the difference between fzmin and fzmax increases, reflecting the broadening of the resonance peak. Both fZminand fzmaxare strongly influenced by R, and they always exist regardless of the value of R,. Relationship between L,,, and C,. The values of the motional inductance and the motional capacitance for an unperturbed quartz crystal are determined by electro(20) Muramatsu, H.; Dicks,J. M.; Tamiya, E.; Karube, I. Anal. Chern. 1987,59, 2760.
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M
24
28
32
36
do
Crn (fF) Flgure 5. Relationship between the motional inductance L, and the
motional capacitance C, (at 9 MHz).
94
8%
898
9
Sa2
frequency span. The values of L , and C, which best fit the experimental curves may not explicitly relate to their respective mechanical counterparts due to the complementary nature ofL, and C,. In order to circumvent this complexity, by taking into account the assumption that the elasticity of the system remains unchanged upon Newtonian liquid loading, a simplified treatment of L , and C, provides results which are easier to interpret. The motional capacitance is obtained for an unperturbed TSM sensor and treated as constant upon liquid loading. The values of L, and C, for the loaded TSM sensor from experimental measurement can then be used to calculate a corrected value of the motional inductance:
90)
Frequency [MHr) 9cb
9
I
4
Rrn [ohm)
Effect of the motional resistance R, on (a,top)the magnitude and phase of the Impedance and (b, bottom) the characteristic frequencies of the TSM sensor. The series and parallel resonant frequencies( f s and f,) cease to exist when the maximum phase angle is below zero. Figure 4.
mechanical snalysis:
L , = e 3 p c ( 8Ac2 ,
(18)
C, = 8Ac'
(19)
a2epuq
The equations show that L , and C, depend on the physical properties of quartz and the dimensions of the quartz plate. L , represents the mass of the plate. External mass loading causes L , to increase due to increase in the thickness of the plate. C, represents the elasticity of the plate. It is assumed that, to a certain degree of accuracy, C, be considered as a constant under liquid loading because a Newtonian liquid does not exhibit any elasticity, although the formation of an interfacial liquid structure may change its elastic property. A t resonance the circuit behaves as a pure resistance. The opposite natures of the reactive elements GwL, and l / ~ u C , ~ ) cancel each other and result in the diminishing of the reactive component. In other words, for a specific resonant frequency there are numerous combinations of L , and C,. Figure 5 depicts the interdependent relationship between L , and C,. It can be seen that any point on the L,,-C, curve will give a resonant frequency of 9 MHz. In reality, the impedance curves of the TSM sensors are measured experimentally and the equivalent circuit elements fitted to yield a minimum deviation between the calculated and experimental values of the impedance over the entire
where the change of the corrected L , directly relates to the change of the environment upon mass deposition or liquid loading. However, it should be pointed out that C, does vary with the viscoelastic properties of the media, as demonstrated in the studies of polymer films." Effect of the Motional Inductance,L,. In the gas phase, the deposition of a thin layer of foreign material onto the crystal surface can be considered as an increase in the thickness of the quartz plate, assuming that the material is rigid and has the same acoustic impedance as that of quartz. In liquid phase, while most of the frequency responses have invariably been interpreted as deposition or removal of surface mass, changes in interfacial properties such as surface free energy and interfacial slip and the surface morphology also influence the response of the sensor.613 For a sufficiently clean and smooth surface, the nonslip boundary condition is applied to give an expression for L, upon liquid 1oading:lj (21)
where the first term is the inductance of the unperturbed resonator and the second term represents the effect of liquid loading. The effect of the motional inductance on the magnitude and phase angle of the impedance is shown in Figure 6a. L , is increased from 12.15 to 12.30 mH where the solid curves ( L , = 12.17 mH) are the actual measurement of an unperturbed 9-MHz TSM quartz crystal. Increasing L,, causes the "translation" of both the magnitude-frequency and phasefrequency curves to lower frequency, while the values of /Amln, ~Z~,ax and Q,,, remain unchanged. The translation of the resonance peaks to lower frequency arises from the increase ofthe vibrating mass corresponding to the increasing motional inductance L,, since the mechanical resonant frequency of i 2 l I Lasky, S. J.: B u t t r y ,
D. A . .4CS SJrnp. S e r . 1989, Yo. 403, 237
ANALYTICAL CHEMISTRY, VOL. 65, NO. 9, MAY 1, 1993 16
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0.00436
P
Y
B
9
(I@) Flgure 7. Relationship between the series resonant frequency fs and the motional inductance L, upon mass loadlngs.
f \I 12 I8
12 22
1226
4
123
Lm (mH)
Fwre 6. Effect of the motionalinductanceLmon(a,top)themagnitude and phase of the impedance and (b, bottom) the characteristic frequencies of the TSM sensor.
a quartz crystal is inversely proportional to the thickness of the quartz plate:
(22) The effect of the motional inductance on the characteristic frequencies is illustrated in Figure 6b. Following eqs 7-12, all six characteristic frequencies depend on L,. Increasing L, significantly reduces the frequencies. However, the distances between fR and fA, fs and fp, and f i m i n and f i m a x remain the same, indicating that the acoustic energy dissipation of the system is not affected by L,.
EXPERIMENTAL SECTION Apparatus. AT-cut quartz piezoelectriccrystals coated with gold electrodes were supplied by International Crystal Manufacturing Co., Oklahoma City, OK. The instrument used to characterize the TSM devices was an HP 4195A network/ spectrum analyzer (Hewlett-Packard). An HP 41951A impedance test kit and HP 16092A spring clip fixture were used to make impedance measurements directly. The values of the equivalent circuit elements of the quartz crystal are calculated internally by the HP 4195A from the measured data. A Perkin-Elmer Model 2400 RF diode sputtering system was used for the vacuum deposition of metal films to study the effect of rigid mass loading. Advancing contact angles of water on the electrode surfaces were measured with a Remy-Hart goniometer at room temperature.
Reagents. The liquids were all analytical-grade reagents and used as received. Double distilled water was used. Procedures. Prior to the impedance measurements, the crystals were rinsed with acetone, ethanol, and water and subjected to high rf in a PD-3XG plasma cleaner (Harrick).The advancing contact angles were measured to ensure the surfaces were completely wetted by water. To measure the effectof viscous loading, the impedance measurements were made with various organic liquids and water. The TSM device was clamped in a cell with O-rings on both sides. One side of the crystal was immersed in -50 p L of liquid. The cell was connected to the network analyzer and allowed to stabilizeuntil reaching a constant frequency reading. The network analyzer scanned 401 points at a center frequency of 9 MHz (with 120-kHz bandwidth) and at a center frequency of 10 MHz (with 150-kHz bandwidth) for respective devices. For each liquid, three frequency scans were averaged for each measurement and 20 measurements were recorded to give average values for a set of parameters. The liquid was then removed, and the cell was rinsed with distilled water and blown dry with nitrogen. The next liquid was added, and the same procedure was repeated. Eight liquids were tested in the following order: methanol, ethanol, water, n-butanol, n-hexanol, ethylene glycol, cyclohexanol, and glycerol. To measure the effect of mass loading, iron bismuth oxide films were prepared by simultaneously sputtering from a 99.95 % iron target (Material Research Corp.) and a 99.99% bismuth target (Metron) while rotating the substrate table at -10 rpm. All depositions were done in pure oxygen with a flow rate of 12 mL/s and a chamber pressure of 12 mTorr. Impedance measurementswere performed after every deposition. The deposited mass of the metal oxide was obtained by using the frequencymass relationship of 1.106 ng/Hz for a 10-MHz crystal based on the Sauerbrey equation.
RESULTS AND DISCUSSION Mass Loading and the Motional Inductance, L,,,.The effect of mass loading on the response of a 10-MHzTSM device is examined by depositing layers of rigid metal oxide film on one side of the crystal. The impedance-frequency curves are measured after each layer of deposition. Increasing surface mass causes the impedance curves to shift toward lower frequency, while the magnitudes of the impedance remain unchanged. This is identical to the simulations shown in Figure 6, where an increase in L, results in the impedance curves shifting to lower frequency. The effects of the surface mass loading on the series resonant frequency and the motional inductance (corrected for constant C, based on eq 20) are shown in Figure 7. It is apparent that fs decreases with increasing mass, in accordance with the Sauerbrey relationship. The linear relationship between L, and the surface mass also agrees with the fact that L, represents the mass of the vibrating quartz plate, which reflects in the kinetic energy transfer between the quartz plate and the deposited material. The increase of the surface mass oscillating with
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Table I. Impedance Analysis of a 9-MHz Gold-Electrode TSM Sensor under Different Conditions (20 "C) p4?n q21' o,,, lzlmin Rm Lm /. 11, 1Zim.U p no. compds (Hz) (Hz) (kR) (CP) (deg) (g/cm') (Q) (R) (mH) 1 2 3 4 5 6 7 8
air methanol ethanol water n-butanol n-hexanol ethylene glycol cyclohexanol glycerol
0.001 0.7914 0.7893 0.9982 0.8098 0.8136 1.1088 0.9624 1.2613
0.02 0.597 1.194 1.002 2.948 5.32 19.9 68 1490
1.001 32.63 24.30 78.54 17.80 13.30 37.00 15.00 42.50
8 993 472 8 991 710 8 991 324 8991 113 8 990 552 8 989 872 8 990 972
9 012 754 9 009 241 9 008 951 9 007 137 9 007 931 9 006 896 8 995 105
theTSM device results in an increasing transfer of the kinetic energy. Similarly, all other characteristic frequencies, such as the parallel resonant frequency, the resonant and antiresonant frequencies, and the frequencies a t minimum and maximum impedances, respond linearly with the increasing surface mass. The static capacitance and the motional resistance remain constant regardless of the change of surface mass. It has been shown that increasing surface mass does not cause increasing power dissipation.lj The deposited rigid layers can be regarded as an extension of the surface electrode, which does not alter the dielectric properties of the quartz plate; Le., Co does not change. The explicit relationship between the motional inductance and the added mass demonstrates the ability of the equivalent circuit to calculate the absolute mass, in addition to its use for design purposes. Liquid Loadings. The interfacial slip characteristics can be correlated with the surface free energy reflected in contact angle values. The frequency responses of the TSM devices are significantly influenced by the wetting properties of the solid-liquid interface.l3,I4In order to reduce the number of factors affecting the sensor response, the electrodes of the device were treated to give hydrophilic surfaces which are completely wetted by the liquids (advancing contact angles
