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AMI. Chem. 1993, 65, 3591-3597
Perturbation of the Electrified Interface and the Response of the Thickness-Shear Mode Acoustic Wave Sensor under Conductive Liquid Loading Mengsu Yang and Michael Thompson. Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 1Al Canada
The behavior of the thickness-shearmode (TSM) acoustic wave sensor under conductive liquid loading has been examined by acoustic network analysis. The response of the TSM sensor arises from the perturbation of the electrified interface, including the acoustoelectric coupling of the surface potential with ionic species and the formation of the electrical double layer. In dilute solutions,dissipation of acoustic energy resulting from acoustoelectric coupling dominates the complete energy-transfer process, which leads to a rapid decrease of the series resonant frequency and an increase in the motional resistance. In concentrated solutions, energy transfer from the quartz dielectric to the interface becomes more important due to increasing energy storage of the double layer, as shown by the continuing increase of the static capacitance and steady decrease of the parallel resonant frequency. In addition, the overall energetics of the dissipation and transfer processes at the interface are reflected in the measurement of the quality factor. INTRODUCTION Most of the applications of the thickness-shear mode (TSM) acoustic wave sensor in the liquid phase involve the use of conductive solutions, such as in biosensor development' and electrochemical ~ t u d i e s . ~In? ~a conductive liquid, the performance of the TSM sensor is influenced by the electrical properties of the solution. The acoustic wave interacts not onlywith additional surface species but also with the charged entities present in the solution. Interaction mechanisms include both viscous and acoustoelectric coupling. The propagation of an acoustic wave in quartz generates a layer of electrical charges at the surface due to the induced electrical polarization of the crystal. The surface potential associated with the acoustic vibration generatesan external electric field which may extend into the adjacent conductive solution. The coupling between the evanescent electric field and ions and dipoles in solution results in changes in the storage and dissipation of the electrical energy. Niemczyk et aL4 have proposed an equivalent circuit model to describe the interaction of the acoustic plate mode (APM) devices with ions and dipoles. The effect of acoustic wave-ion coupling on APM response is estimated by treating the ion motion induced by the evanescent field as a near-surface current. The velocity shift and attenuation of the APM propagation are related to (1) Thompson, M.; Kipling, A. L.; Duncan-Hewitt, W. C.; RajakoviC, Lj. V.; CaviE-Vlasak, B. A. Analyst 1991, 116,881. (2) Schumacher, R. Angew. Chem., Int. Ed. Engl. 1990,29,329. (3) Buttry, D. A.; Ward, M. D. Chem. Reu. 1992,92,1335. (4) Niemnyk, T. M.; Martin, S. J.; Frye, G. C.; Ricco, A. J. J. Appl. Phys. 1988,64, 5002. 0003-2700/93/036535~1$04.00/0
the conductivity
where Kz is the electromechanical coupling factor associated with the mode, eo, 4, and €1 are the dielectric constants of the vacuum, quartz, and liquid, respectively, and u is the conductivity of the liquid. Using a perturbation theory, Jowe and Shana6 obtained similar equations for a Z-cut LiNbOs APM device. For TSM devices, metallic electrodes are depositedon both surfaces of the quartz plate in order to excite the acoustic vibration. Thus the quartz surface is short-circuited. It was suggested that the surface charge associated with the acoustic standingwave may redistribute in a conducting f i i , resulting in the elimination of the evanescent field! Accordingly, the electrical shortening of the surface admittance elements will result in zero power dissipation. However, when an ac voltage is applied across the device, the surface condition is changed. Application of the appropriate boundary conditions at the interface and solution of the characteristic equations in each medium yields an equation for frequency shift of the TSM device with one side immersed in a nonviscous dilute conductive solution:6
Atf=!C,I fo
7r2 '8
U2
+ 'I
u2
+ w2(es + 3
2
(3)
The experimental measurements are found to compare well with the' theoretical calculations. Additionalfactors may also affect the response of the TSM device; these include the formation of an electrical double layer at the charged surfaceliquid interface and the fringing of the electrical field. Since the double-layer thicknes~~9~ is much less than the decay length of the electric field (0.01 vs 0.2 pm for a 9-MHz device), the double layer can be treated as an added capacitance to the TSM sensor. However, such a layer may screen the electric field from penetrating into the bulk solution and, thus, affect the acoustoelectric interaction. In addition, it has been reportedgJOthat the fringing of the electric field, particularly in the conductive solution, can significantly influence the TSM sensor response. Recently, the network analysis method hae been developed to characterize the response of the TSM sensor upon viscous (5) Joase, F.; Shana, Z. A. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 1992, UFFC-39, 512. (6) Josse, F.; Shana, Z. A.; Radtke, D.; Haworth, D. IEEE "ram. Ultrason. Ferroelectr. Freq. Control 1990, UFFC-37, 359. (7) Adamson, A. W . Physical Chemistry of Surfaces, 4th 4. Wdey: ; New York, 1982; Chapter 5. (8) Bard, A. J.; Faulkner,L. R. ElectrochemicalMethods; Wiley: New York, 19sO; Chapter 12. (9) Martin, B. A.; Hager, H. E. J. Appl. Phys. 1989,65, 2630. (10) Ward, M. D.; Delawaski, E. J. Anal. Chem. 1991, 63,886. @ 1993 Amcwican Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 65. NO. 24, DECEMBER 15.1993
Chart I. Cell Design for Static-State Liquid-Phase Measurement
To Hp419SA O-ring
1
spacer goldlead liquid loading.”-’4 This method provides multiple chemical information on the bulk properties of the liquid as well as information concerning the sensorliquid interface. The resonant frequencies, impedance characteristics, and equivalent circuit elements can he related to the viscosity, density, and dielectric constant of the contacting liquid.IZJ4 In this report, the effecta of the acoustoelectric coupling on the TSM sensor response upon conductive liquid loading are studied by the network analysis method.
-
EXPERIMENTAL SECTION Apparatus. AT-cut quartz piezoelectric crystals (polished quartz, p X 0.2) coated with gold electrodes were supplied by International Crystal Manufacturing Co., Oklahoma City, OK. Theelectrodeaonhothsideaofthecrystalhavethesamegeometry andoverlapwitheachother. The instrumentusedtocharaeterize theTSMdeviceswasanHP4195ANetwork/SpectrumAnalyzer (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. Reagents. AU the reagents are of analytical grade and used as received. Doubly distilled water was employed. Procedures. Prior to the impedance measurements, the crystals were rinsed with acetone, ethanol, and water and subjected to high radio frequencies in a PD-3XG plasma cleaner (Hanick). Theadvancingconhctangla weremeasuredtoensure the surfaces were completely wetted by water. The TSM device was clamped in a cell with O-rings on both sides. Detailed configurationof the cell design is presented in Chart I. One side of the crystal was immersed in 100 ML of distilled water and a certain volume of 0.5 M KCl solution was added to prepare the desired concentration. The electrode in contact with liquid is connected via the gold lead to the ground port of the HP41951A test kit. The cell was connected to the network analyzer and allowed to stabilize until a constant frequency reading was reached. The network analyzer scanned 401 pointa at a center frequency of 9 MHz (with 120-kHz bandwidth). For each concentration, three frequency scans were averaged for each measurementand 2Omeasurements were recordedtogiveaverage values for a set of parameters.
RESULTS A N D D I S C U S S I O N Impedance Measurement. A number of studies have attempted to relate TSM sensor response to the properties L.;Thompson. M. A w l . Ckcm. 1990.62. 1514. (12) Martin. S. J.; Cranstaff. V. E.;Flye. C . C . A m / Ckem. 1991,653, nn*n * A , *. (13) Yang,M.; Thompson, M.;Duncan-Hewitt, W. C. Longmuir 1993, (11) Kiplmg, A.
9,802. (14) Yang, M.;Thompson, M.Anal. Chem. 1993,65, 1158.
-I
s4
0.M
8s
9
9.w
901
I
9.m
Frequency(MH4 Figure 1. Magnkude and phase of the impedance of a gMHz TSM device wkh one sMe imm& in KCI solutions.
of the electrolytic soiuti0n.6J”~~ However, these experiments were concerned only with the frequency shiftsobtained from the oscillator method. Beck e t al.M have reported the impedance analysis of the TSM device with one side exposed to concentrated LiCl solutions, but only the effect of density and viscosity of the solution were considered in explaining the frequency response. For diluted electrolytic solutions, the density and viscosity of the solutions are very close to those of water. Thus, when the behavior of the TSM sensor under electrolytic solutions is compared to that under water, the conductivity of the solution becomes dominant in determining the sensor response. In the present work, the magnitude and phase of the impedance of a 9-MHz Au-electrode TSM sensor with one side immersed in a series of KCI solutions (0.0054.1M) were measured. Figure 1 shows the w-0 curves for water and several KCl solutions. It is clear that both the maximum impedance,,,Z , and the maximum phase, Om, decrease as theconductivityincreases. Amore complete pictureis shown in Figure 2 illustrating the response of the impedance characteristies upon KC1 loadings. The changes in Z-, minimum impedance, Zmin,and B,, relatiue to water are plotted against the conductivity of the solutions. The conductivity of water is assumed to be zero. All three parameters decrease as the conductivity increases, although U,i. is much smaller than U ,,.The common feature of the three plots is that the decrease seems to occur a t two different rates. The parameters drop more rapidly a t low conductivities than a t higher conductivities. The turning point is at -0.1 W / m (corresponding to 0.01 M KC1). The significance of this critical value of conductivity will he discussed in the following sections. Since the impedance charactenstiesareintluencedby all theacousticenergystorage anddissipatioupmcessesoccurringinthesystem, it isdifficult (15) Nomura, T.; Iijima, M.Anal. Chim. Acto 1981,131,97.
(16) Nomura, T.; Okuhara, M.Anal. Ckim. Acto 1982,142,281. (17) Bruckenstnin, S.;Shay, M.Electroehim. Acto 1986,30, 1296. (18) Yao, S. 2.;Mo,Z. H . Anal. Chim. Acta 1987,193, 97. (19)Yao, S. Z.; Nie, L. Anal. Roc. 1987,24, 336. (20) Beck, R.;Pittermann, U.;We& K. G . Ber. Bumen-Ges. Phys. Chem. 1988,92, 1363.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 24, DECEMBER 15, 1993
SS3
......
-'I-. -18 O
02
.
,
0.4
0.6
0 , "
0.8
1
1
1.2
Conductivity (mhdm) Flgure 2. Responses of the maxlmum impedance, Z,,, minimum of a 9-MHz TSM device impedance, ZM, and maximum phase,,,e with one side immersed in KCI solutions.
to relate these parameters to any individual properties of the solution. A detailed study of the frequency characteristics and the equivalent circuit elements may provide further information on the acoustoelectric interaction. Series Resonant Frequency. In acoustic network analysis, there are two frequencies at zero phase. The lower frequency is called the series resonant frequency, which is the parameter measured by the oscillator method, whereas the higher value is called the parallel resonant frequency. The change in the series resonant frequency relative to water, Afs, with the solution conductivity u is shown in Figure 3a. Initially an increase in the conductivity results in rapid decrease in fs. However, the effect of u on fs reaches a saturated level a t high conductivities,similar to those observed in the impedancecharacteristics (Figure2). The conductivity value a t which the effect of a becomes minimum is a t -0.1 W/m. The viscosity and density of the solution varies as the concentration changes. The frequency shift due to the change in viscosity and density can be calculated based on Kanazawa's equation.21 At 20 "C, the viscosity and density values for 0.005 M KC1 ( p = 0.9984, q = 1.0017 cP) and 0.1 M KC1 ( p = 1.0029,~= 0.9996 cP)are very similar to those of water ( p = 0.9982, q = 1.0020 cP). The series resonant frequency will decrease only by 0.2 and 5 Hz for 0.005 and 0.1 M KC1, respectively. Therefore,the frequency change due to viscosity and density is considered to be negligible in the concentration range. For conductive liquids, the ionic species in solution redistribute rapidly in response to an applied surface potential. The formation of an electrical double layer a t the solid-liquid interface may block the electric field from penetrating into the bulk solution. However,when the frequency of the applied potential is greater than the dielectric relaxation frequency, ions cannot redistribute fast enough to screen the field. It has been shown that the relaxation frequency,WR, for charged (21) Kanazawa, K. K.; Gordon,J. G. A d . Chin.Acta 1985,175,s.
4
0 -
0.2
0.4
0.6
0.8
1
I
1.2
Conductivity (mhdm) Figure 3. (a)Responseof the series resonantfrequency fs of a 9MHr TSM device with one side Immersed in KCI solutions. Sol# line is the best-fitted curve based on eq 3. (b) First derfvattves of the frequency changes.
species a t an interface is22 OR
= 'J//(EB
+ €1)
(4)
Thus, when W R > w, the effect of the double layer will become evident. On the other hand, analysis of eq 3 shows that the most rapid change in frequency will occur a t a conductivity uc = w(e,
+ el)
(5)
where acis exactly the value at which the relaxation frequency of the ions equals the frequency of the potential. For an aqueous solution (el = 78.54~0,where EO = 8.854 X lW2, assuming the effect of the frequency field is negligible) and an AT-cut quartz (es = 4.55~0)~ the value of acis -0.04 W/m. The first derivatives of the frequency changes are plotted in Figure 3b. Indeed, the rate of the frequency changes depends on the conductivity of the solution. However, the most rapid change occurs a t a much smaller a than the critical value uc. This may be either due to the effects of the metallic electrode or due to the reducing dielectric constant of water a t the charged interface. When u > 0.1 W/m, changes infs become minimal with increasing conductivity, suggesting that the electrical field is screened by the double layer. This is consistent with the observation for the APM device that the acoustoelectric interaction dominates only for the range of conductivities u 5 &T,.~ The solid line in Figure 3a is a best-fit curve based on eq 3 by using the bulk dielectricconstant for water and adjusting the value of K2. The electromechanicalcoupling factor, K2, is determined to be 3.4 X le3.This value is smaller than the theoretical value for a quartz TSM device, K2 = 7.6 X 10-3, calculated from the following equation6 where €26 is the piezoelectric stress constant and CM is the elastic constant of quartz (piezoelectrically stiffened). The analysis of eq 3 was performed with the quartz surfacewithout the electrodes, although the electrical effect of the electrodes (22) Josse, F.; Shana, Z. J . Acoust. SOC.Am. 1989,85, 1666.
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 24, DECEMBER 15, 1993
“”I
i
0
0
0
-2
’b
0.4 06 0.8 i 1.2 Conductivity (mhdm) Figure 4. Response of the motional resistance, R,, of a 9-MHz TSM device with one side immersed in KCI solutions. 0.2
was accounted for in the potential boundary conditions. The results suggest that the presence of the electrode significantly reduces the interaction between the ions in the solution and the electrical field. It has been noted4 that the acoustoelectric interaction between the piezoelectric surface potential and the ions and dipoles would become negligible when the immersed electrode is grounded and a larger electrode in contact with liquid is used to prevent fringingfield from entering the liquid. Several factors could give rise to the response in the series resonant frequency observed in this study. First, the electrical field associated with the metal electrode will lead to the formation of a double layer, which acts as a shunt capacitance in parallel with the resonator. Second, the electrodes on both sides of the resonator have the same diameter. The fringing field may enter the liquid, which again behaves as a shunt conductance. Finally, the sensitive area of the resonator may extend beyond the boundary of the circular electrodes.10The ‘parasitic” capacitance in parallel with the resonator due to the double layer and fringing field will certainly change the parallel resonance condition of the crystal, as will be shown in the following sections. However, the “parallel” branch of the resonator circuit, including the static capacitance and the parasitic capacitance, seems to have little effect on the series resonant frequency.14 On the other hand, the interaction between the bare quartz surface and the ionic species represents a situation similar to that in the APM device. The agreement between the experimental data and the model (Figure 3) implies the presence of the acoustoelectric effect. The smaller value of K2 suggests that the quartz beyond the electrode boundary is less sensitive toward external perturbation than that under the electrodes. Motional Resistance and Quality Factor. The conductive metallic electrodes on the TSM devices tend to eliminate the evanescent field and power dissipation. However, the interactions that cause the change in the series resonant frequency will also lead to energy dissipation by the same mechanisms. The piezoelectric resonator can be represented by the equivalent circuit of the series combination of acapacitor, an inductor, andaresistor (the motional branch) in parallel with a capacitor (the parallel branch).11-14 The motional resistance R, is intrinsically related to the power attenuation of the TSM device. Changes in R, with the conductivity can be viewed as an indicator of the energy loss of the TSM sensor into the solution due to ion-acoustic wave interaction. Figure 4 shows the energy dissipation as determined from R , measurements. Initially, R, rises to a maximum value a t the same value of conductivity where f s has the most rapid shift. Subsequently R, declines rapidly until reaching a saturated level at u = 0.1 W/m. The decrease
0
0
0.4
0.2
0
0.6
0.8
1
Conductivity (mhdm) Figure 5. Response of the quality factor of a 9-MHz TSM device with one side immersed in KCI solutions.
- 1 4 %
0 0
0 0 0 0
0
0.2
0.4
0.6
0.8
1
iI
1.2
Conductivity (mho/m) Figure 6. Response of the parallel resonant frequency, fp, of a 9-MHz TSM device with one side immersed in KCI solutions. in R, relative to water seems to indicate that there is less energy loss into solutions with high conductivities than into water. This may result from the screening of the electrical field by the double layer. Trace amounts of ions in water may also alter the position of the R,-o curve. R, increases slightly at concentrated solutions,likely due to small increases in the viscosity-density value of the solutions. Despite the small changes in fs and R,, the quality factor shows continuous decrease as the conductivity increases (Figure 5). The quality factor of a quartz crystal is determined by the overall energy storage and dissipation of the resonant system. The result suggests that there is a net energy loss from the quartz crystal into the surrounding media. Therefore, the effect of the conductive liquid loading on the ‘parallel” branch of the impedance peak must be considered. Parallel Resonant Frequency. Unlike the series resonant frequency, the parallel resonant frequency is strongly influenced by conductive properties of the liquid. The shift in the parallel resonant frequency with the conductivity of the solutions is depicted in Figure 6. The behavior of A f p differs drastically from that of Afs (Figure 3a). First,fp shows a much greater sensitivity toward the conductive properties of the solution. Under the same conditions, Afp is more than 10 times that of Afs. Second, f p decreases continuously with increasing u without the occurrence of a saturation level. At the low-conductivity region, fp does not exhibit the rapid decrease observed in fs. A common feature between f p and fs is that both curves show a change of slope at u = 0.1 W/m. The difference between f s and f p has been demonstrated by circuit analysis.23 It has been shown that the response of (23) Bottom, V. E. Introduction to Quartz Crystal U n i t Design; Van Nostrand Reinhold: New York, 1982.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 24, DECEMBER 15, 1993
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5 1.6 0 0
0 0
0
0
0.4
Conductivity (mhdm) Flguro 7. (a) Potential variation according to the Stern model. (b) Total capacity of the electrified interfaceas given by the Helmholtz and Gouy capacitles in series.
fs is related to the energy dissipation, while the response of
Flgure 8. Response of the static capacltance & of a 9-MHr TSM device with one side immersed in KCI solutions. The total capacitance of the electrified interface(line) as a function of the conductivity of the solution is calculated on the basis of eq 7.
2kT where N Ais Avogadro’s number, c is the concentration of the electrolyte, k is Boltzmann’s constant, z is the charge of the electrolyte, e is electron charge density, and 90is the surface potential. At low potential, CG = 2.28(cz2)’I2F/m2 can be
derived for aqueous electrolyte a t 25 Thus, the total capacitance of the double layer at the electrode surface can be calculated as a function of the electrolyte concentration by taking into account the surface area of the electrode on a TSM sensor (0.2 cm2for a 9-MHz device). The values of CD calculated on the basis of eq 7 are depicted in Figure 8. Because of the linear relationship between the concentration and the conductivity of the solvent, CD is plotted against Q for consistency. It can be seen that, at sufficiently low concentration, CH >> CG,so that CD= CG. The double-layer capacity is effectively equal to the capacity of the GouyChapman region. While at concentrated solutions, CH 2.5 pF, the energy storage of the (d I n double layer becomes the primary interaction mechanism. The energy dissipation becomes negligible except for a small increase due to increasing density and viscosity of the solution. However, the capacity of the double layer increases with the 0 concentration due to the formation of a contact-adsorbed 0 layer. Thus, there is increasing energy transfer from the 0 0 quartz to the electrified interface and the Q-factor decreases 2 -2 0 d steadily with CO. d . , . . . . . . . It has been shown4that, in the operation of APM devices, 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 the contribution from interfacial capacitance was negligible, Co (pF) since the double-layer capacitance is so large that the Flgure 9. (a) Relationship between the parallel resonant frequency associated impedance is negligibly small compared with the and the static capacitance. (b) Changes in the quality factor revealing three steps of overall energeticprocess for a 9-MHz TSM device under electrolytic resistance. Nevertheless, the presence of the KCI solutions. electrical field associated with the metal electrodes on the TSM device may introduce different coupling mechanisms the capacity between the electrode and the OHP remains governing the energetic processes at the interface. Although constant in concentrated solutions. However, a more complete the mechanisms of these interactions are not fully understood, treatment involves the hydrated ions coming into contact the correlation between the double-layer structure and the with the electrodes and forming a so-called inner Helmholtz sensor response offers a possible explanation for the experplane (IHP).24 The formatim of such a contact-adsorbed imental observations. layer depends on water-electrode, ion-electrode, and ionwater interactions. It is known that chloride ions are CONCLUSION energetically favorable to form an IHP. Therefore, the total The network analysis method has been applied to study capacity of this 'triple layer" (electrode + IHP + OHP) is the behavior of the TSM sensor with one side in contact with affected by contact-adsorbed ions populating the IHP. conductive liquids. This method provides multidimensional Analysis shows that increasing the ionic population will result information on the sensor responses. The magnitude and in an increase in the total capacity of the electrified interface.24 phase of the impedance of the TSM sensor can be measured This explains the observation that COsteadily increases with under various concentrations of electrolyte. Impedance the conductivity even under concentrated solutions. characteristics, resonant frequencies, equivalent circuit elThe above analysis serves to interpret the observed ements, and quality factor of the device can be related to the responses of the parallel resonant frequency and the quality conductive properties of the solution. factor. As mentioned earlier,f p is predominantly determined The interaction between the TSM sensor and the conby the capacitive effects. A plot of the changes in f p against ductive liquid involves the acoustoelectric coupling of the the changes in COis shown in Figure 9a. It is evident that f p electrical field associated with the acoustic wave and the ions is inversely proportional to CO. Therefore, a change in f p is and dipoles in the solution, and the formation of an electrical directly related to a change in the total capacity and thus the double layer. In diluted solutions, the energy dissipation from structure of the charged interface. A plot of the changes in the TSM sensor into the liquid resulting from the acoustothe quality factor vs Coillustrates the overall energetic process electric coupling dominates the whole energetic process, which for the TSM sensor under conductive liquid loading. As is reflected in a rapid decrease of the series resonant frequency depicted in Figure 9b, the Q-factor undergoes three different and an increase in the motional resistance. In concentrated stages of change as COincreases. Initially, for CO
