Langmuir 1993,9, 1990-1994
1990
Surface Morphology and the Response of the Thickness-Shear Mode Acoustic Wave Sensor in Liquids Mengsu Yangt and Michael Thompson* Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 1A1, Canada Received January 19,1993. I n Final Form: June 15,1993 The surface morphologiesof gold electrodeson unpolished and polished quartz crystals were characterized by scanning electron microscopy (SEM)and scanning tunneling microscopy (STM). The effects of surface roughness on the response of the series resonant frequency of the thickness-shear mode (TSM) acoustic wave sensor under various liquid conditions are described. Individual components resulting from viscous damping, rigid mass entrapment, surface stress, and nonshear coupling interactions are distinguished through network analysis. The contributions of these componentsto the frequency changes are discussed.
Introduction It has been shown that a piezoelectric quartz crystal oscillating in the thickness-shear mode (TSM) can be operated in the liquid phase. The TSM provides an interesting tool for the study of liquid properties, the microstructure of the electrode surface, and interfacial phenomena at the solid-liquid interface. Recent studies have focused on the development of chemical sensors,1*2 evaluation of polymer film pr0perties,3*~ and examination of electrochemical proce~ses.”~In most of these investigations, frequency changes were interpreted in terms of rigid mass changes, based on the Sauerbrey equation.* However, in the liquid phase the response of the TSM device depends on various factors such as thin film viscoelasticity, interfacial liquid properties, electrode morphology, and mechanisms of acoustic coupling. In many cases TSM devices do not behave ideally as predicted by the Sauerbrey equation and the results become ambiguous, which prevents this technique from being widely accepted. In the present paper, we report the use of the network analysis method to investigate the effects of surface roughness on the response of the series resonant frequency of TSM devices under various conditions. This study demonstrates that the complex frequency response can be deconvoluted to components reflecting the effects of viscous damping, rigid mass loading, surface stress, and other acoustic interactions. Experimental Section Materials. Analytical grade reagents were used as received. Doubly distilledwater was used. AT-cut quartzcrystals(9-MHz) (unpolished and polished) with gold electrodeswere supplied by International Crystal Manufacturing (Oklahoma City). Equipment. An HP4195A network/spectrumanalyzer with an HP41951 impedance test kit (Hewlett-Packard)was used to characterize TSM devices in liquid. The equivalent circuit elements of the impedance measurements were calculated internally by the analyzer. The crystal was clamped in a cell
* Author to whom correspondence should be addressed.
+ Present address: Department of Molecular Biology,The Scripps Research Institute, La J o b , CA 92037. (1) Thompson, M.; Kipling, A. L.; Duncan-Hewitt,W. C.; RajakoviC, Lj. V.; Cavib-Vlaeak, B. A. Afdy8t 1990, 116, 881. (2) Eberaole, R. C.; Ward, M. D. J. Am. Chem. SOC.1988,110,8623. (3) Reed, C. E.; Kanazawa, K. K.; Kaufman, J. H. J.Appl. Phys. 1990,
68,1993. (4) Borjas, R.; Buttry, D. A. Chem. Mater. 1991,3,872. (5) Deakin, M. R.; Buttry, D. A. A d . Chem. 1989,61,1147A. (6)Schumacher,R. Angew. Chem., Int. Ed. EngZ. 1990,29,329. (7) Buttry, D. A.; Ward, M. D. Chem. Rev. 1992,92,1335. (8)Sauerbrey, G. 2.Phys. 1969,155, 206.
with O-ringson both sides. One side of the crystal was immersed in about 50 rL of liquid. The cell was kept at a constant temperature of 25 “C. The crystal was plasma-cleaned under nitrogen prior to the measurement. Scanning electron microscopy (SEM)of the electrode surfaces was performed on a Joel 36 CF electron microscope. Scanning tunneling microscopy (STM) was performed with a Nanoscope I1 (Digital Instruments).
Results and Discussion The microscopic structure of the electrode surface plays an important role in determining the response of the TSM device in the liquid phase. It has been reportedg-ll that the frequency responses are drastically affected by changes in surface roughness of the electrodes and that the differences were interpreted as changes of the mass rigidly trapped in surface cavities. The morphologies of the gold electrodes on unpolished and polished quartz surfaces were characterized by SEM and STM. Both SEM (Figure 1) and STM (Figure 2) show that the unpolished surface is sigtlificantly rougher than the polished surface. An SEM micrograph of an unpolished surface (Figure la) indicates that the surface is covered with irregular cracks and pits. The sizes of the cracks range from 1 to 3 pm. An STM image (Figure 2a) reveals similar features as observed by the former technique. This shows that large flattened spheroids are separated by trenches several hundred nanometers deep. The average depth of the crevices obtained from STM is approximately0.8 pm. On the other hand, the SEM micrograph (Figure lb) and STM images (Figure 2b,c) reveal that the polished surface is relatively flat compared to the unpolished surface. Single line scans obtained by using the STM show that the surface features of the polished crystal are approximately 0.01-0.02 pm in depth. The series resonant frequencies (Table I) of both the unpolished and polished crystals in contact with several organic liquids and water are depicted in Figure 3. The solid line represents the theoretical values expected from the relationship derived by Kanazawa and Gordon:12
where n is the number of faces in conhct with the liquid, (9) Schumacher,R.; Borges, G.; Kanazawa, K. K. Surf. Sci. 1986,163, L621. (10)Muller, A.; Wicker, M.; Schumacher, R.; Schindler, R. N. Ber. Bunsen-Ge8. Phys. Chem. 1988,92,1395. (11) Beck, R.; Pittermann, U.; Weil, K. G. J. Electrochem. SOC.1992, 139, 453. (12) Kanazawa, K. K.; Gordon, J. Anal. Chim. Acta 1986,175,99.
0743-7463/93/2409-1990$04.00/0 0 1993 American Chemical Society
Langmuir, Vol. 9,No. 8,1993 1991
I
.
.
,
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Figure 1. SEM micrographs of the gold electrodes on the unpolished and polished quartz crystals. Magnification x3.00k.
fo is the fundamental frequency, p~ and PQ are the shear
modulus and density of quartz, respectively, and p~ and VL are the density and viscosity of the bulk liquid, respectively. It is apparent that the responses of the unpolished crystal are significantly greater than both the responses of the polished crystal and the expected values. The responses of the polished crystal under less viscous liquids (open circles 1-4 in Figure 3) are also considerably larger than the predicted values. The small frequency
Figure 2. STM images of the gold electrodes on the unpolished and polished quartz crystals: (top) 10 X 10 pm image of the unpolished surface, z-range 1.5 pm; (middle) 10 X 10 pm image of the polished surface, z-range 1.5 pm; (bottom) 1 X 1 p m image of the polished surface, z-range 0.15 pm.
shift for ethylene glycol (open circle 6 in Figure 3) is due to the large amount of energy loss resulting from highly viscous damping.13 The discrepancies for the polished device cannot be interpreted purely as mass rigidly trapped in surface cavities. For example, the frequency difference between the measured data and the predicted value is 472 Hz for ethanol (see Table I). Based on a simplified "hemicylinder" modelg the size of the surface cavities is estimated at about 0.07 pm, which is much greater than the average size obtained from STM. TSM devices respond to changes in the surrounding environment, including the mass rigidly trapped in surface crevices, surface stress due to hydrostatic pressure, liquid loading and mechanical damping (clamping),enhanced interfacial viscosity due to different liquid structures, and acoustic couplingmechanisms other than shear coupling. The total frequency changes comprise the contributions from these (13) Yang, M.;Thompson, M. Anal. Chem. 1993,65,1158.
1992 Langmuir, Vol. 9, No. 8,1993
Letters
Table 11. Frequency Components of the Responms of Polished and Unpolished 9-MHa TSM Resonators in Liquids
loo00 b
polished0 4 d+
Cov~ed
no. 1 2 3 4 5 6
O Y 0
.
2
1
3
4
I 6
(P q) lr2 Figure 3. Responses of the series resonant frequency of unpolished (closed circles) and polished (open circles) 9-MHz TSM devices under liquids. Solid line represents the theoretical values calculated from eq 1. The shifts are relative to air. Numeric labels correspond to liquids listed in Table I.
Table I. Series Resonant Frequencies and the Motional Resirtances for the Equivalent Circuit of 9-MHa TSM Devices with One Side in Contact with Liauidr polished theory unpolished liauid (~dbullP mmc Mad a m ’ 4, mm methanol 0.464 1174 180 1762 193 4851 235 ethanol 0.946 1676 257 2148 270 5390 308 water 1.002 1725 264 2360 280 6246 322 butanol 2.387 2662 408 2920 423 6296 444 hexanol 4.360 3598 551 3600 569 6836 584 8098 1241 2500 1254 9128 1216 ethylene 22.09 glycol Data taken from Handbook of Chemistry and Physics,61st ed. Calculated from eq 1. Calculated from eq 3. d *lo Hz.8 +2 52.
no. 1 2 3 4 5 6
composite effects
+ Afa + A f x (2) where Afd, Afm, Afa, and Afx refer to frequency changes Afs
Afd
+4
m
caused by viscous damping (energy loss by shear coupling), rigid mass trapping, surface stress, and energy dissipation by nonshear couplings (such as compressional waves), respectively. The trapped mass component does not affect the energy dissipation process. Surface stress mainly results from the mechanical damping by the cell fixture, since the pressure of the loaded liquid is negligible. Frequency changes arising from mechanical clamping are difficult to predict. The mechanical strain upon liquid loading differs from that when the device is dry. In addition, it changes when the crystal is remounted into the cell. For simplicity, it is assumed that this frequency component is constant for a similar set of experiments. Therefore, the energy dissipation processes are limited to shear coupling and nonshear couplings. Through network analysisthe motional resistance Rm of the equivalent circuit is directly related to the energy dissipation of the oscillating system14
where = wBis the angular frequency of the quartz crystal, N is the harmonic number ( N = 1for the fundamental mode),and C1 and L1 represent the unperturbed motional capacitance and inductance, respectively. The changes ~~
(14) Martin,5. J.; Gramtaff, V. E.; Frye, G.L.A d . Chem. 1991,63, 2272.
liquid methanol
(PdW 1.15 1.10 1.12 1.08 1.07 1.02
Unpolished“
4 d
41 41 4 n 1
t
(ccm)
1260 1534 274 2926 0.40 1762 2010 248 2989 0.41 water 1827 2102 275 3763 0.41 butanol 2761 2898 137 3007 0.40 hexanol 3714 3811 97 2634 0.35 ethylene glycolb 8184 7936 801 0.08 a The frequency component for surface stress is determined as 390 170 Hz. The frequency measurement is unreliable due to severe energy dissipation.
ethanol
*
in R m (relative to air) upon liquid loading for both the unpolished and polished TSM devices are listed in Table I. The calculated unperturbed R , is about 0.5 0,while the value measured in the air is about 10 Q, indicative of some energy loss to the cell mounting. The responses of the polished crystal are used as a calibration standard to differentiate the individual frequency components. In this regard, the shear coupling is considered to be the dominant energy dissipation process. are fitted to eq 1 to The changes in series frequency, 4#, give an intercept of 390 f 170 Hz,which is attributed to the frequency component resulting from mechanical strain, Af,,. The large margin of error reflects the fact that the mechanical strain varies under different conditions. To take into account the possibility of an enhanced interfacial viscosity, A R m is substituted into eq 3 togive an “apparent” value of viscosity-density product, (pq)bwaw, to be distinguished from the bulk value, (Pq)bullr. The ratios between (pq)hbrfaceand (&)bullr for various liquids are listed in Table 11. It is interesting to note that the ratios for all the compounds are slightly greater than 1.0. The “apparent” (pq) value is the integrated (pq) value of the liquid region, the thickness of which is the decay length of the propagating acoustic shear wave. This region is much thicker than the possible surface-adjacent layer with ordered liquid structure, which is only a few molecular layers. Viscosity enhancement will likely occur in this surface-adjacent layer. Therefore, the results also suggest that the (pq) values for this interfacial layer should be much greater than the bulk value. Consequently, the frequency component resulting from the shear coupling should be slightly higher than that predicted from eq 1. The “apparent” (pq)hbrfme was used in calculating this component, Afd, and the results are listed in Table 11.The s u m of Afd and Afaaccounts for most of the measured Afs. The discrepancies between Afs and (Afd + 4 d represent less than 7 3’% of the total changes, which can be attributed to a small amount of trapped mass (since the polished surface is not ideally smooth) or the error generated in determining the value of Afa. For the unpolished crystal,the energy dissipation arises from both shear coupling (Afd)..and nonshear coupling interactions (Afx).Following the same treatment as that for the polished crystal, the “apparent” (pq) values for the unpolished system can be estimated from R, measurements and the frequency responses due to energy dissipation can be calculated from eq 1. It is reasonable to assume that A f d is the same for both the unpolished and polished crystals, since the shear coupling interactions for both crystals are similar and the interfacial properties of liquid on the same substrate should be the same. Thus the frequency component of nonshear coupling, Afx, can be extracted for the unpolished crystal. Furthermore, the
Letters
frequency component from rigid mass trapping, Afm, can be discerned by subtracting the energy dissipation components and stress component (Ma,as determined for the polished crystal) from the measured frequency changes. Finally, the size of the surface cavities on the unpolished crystal can be estimated by using the model proposed by Schumacher et al.? in which the roughened surface was assumed to be comprised of hemicylindral corrugations of diameter e. All the results are listed in Table 11. We have demonstrated that it is possible to distinguish the frequency responses of the TSM resonator resulting from various factors. For a polished, relatively smooth crystal, the frequency changes mainly arise from the shear coupling between the liquid and the electrode surface. The surface stress caused by mechanical damping of the cell fixture also contributes to the frequency shifts. The enhancement of the interfacial viscosity-density is also observed to affect the frequency responses. The importance of the interfacial effects due to liquid ordering has been discussed previously.l6J6 However, this effect is less significant for the complete wetting system, probably due to the fact that the decay length of the propagating acoustic wave is much greater than the interfacial region where most of the enhancement occurs. For an unpolished crystal, the kind supplied by most commercial manufacturers, the frequency response is a function of rigid mass trapping, shear coupling, surface stress, and nonshear couplings. The analysis shows that rigid mass entrapment accounts for about 50450% of the total frequencychanges. About 30-40% of the total changes are due to shear coupling and about 5 % of the total changes are due to nonshear coupling mechanisms. Another 5-10% of the total changes are attributed to surface stress effects. In addition, the diameter of the surface cavities is determined to be about 0.4 pm, half the estimated depth from SEM and STM. This is not surprising since the surface features are flattened spheroids without vertical walls. It is also unlikely that the liquid trapped in the cavities will be completely rigid. Nevertheless it gives an indication of the degree of rigid mass confinement. It should be noted that the percentages of each Af term may differ with the particular crystal, especially if manufactured differently. The above observations confirm the importance of surface morphology in determining the TSM resonator performance in the liquid phase. For nonconductive liquids the effect of roughness is mainly due to rigid mass confinement. However, most of the applications of the TSM device involve the use of electrolyte solutions in the development of biosensors and electrochemical studies. The presence of a conductive solution results in acoustoelectric interactions between the surface potential of the piezoelectric substrate and the ionic species. The interaction of the electric field with ions and dipoles for the shear-horizontal acoustic plate model (SH-APM) devices has been studied by Niemczyk et al.17 where the velocity shift and attenuation of the plate mode were found to be perturbed by the conductivity of solutions in contact with the device. For the TSM device, Josse et a1.18 have obtained a similar relationship between frequency shift and the solution conductivity: (15) Duncan-Hewitt,W.C.;Thompson,M. Anal. Chem. 1992,64,94. (16) Yang, M.; Thompson,M.; Duncan-Hewitt,W. C. Langmuir 1993,
9, 802.
(17) Niemczyk, T. M.; Martin, S. J.; Frye, G. C.; Ricco, A. J. J. Appl.
Phys. 1988,64,5002.
(18)Josse, F.;Shana, Z.; Radtke, D.; Haworth, D. IEEE Trans. Ultrason., Ferroelec., Freq. Contr. 1990, UFFC-37, 359.
Langnuir, Vol. 9,No. 8,1993 1993
0.2
0.0
0.4
0.6
0.8
1 .o
1.2
Conductivity (11 R m)
Figure 4. Responses of the series resonant frequency of unpolished (closed circles) and polished (open circles) 9-MHz TSM devices under KCl(aq). The shifts are relative to water. Solid curves are best-fit values from eq 4.
%=---K2
e22
fo
+ e22 a2
P2 CL
a2
+ &EL + e22)2
(4)
where K2 is the electromechanical coupling factor, €22 and EL represent dielectric constants for quartz and liquid, respectively, and Q is the liquid conductivity. The intrinsic properties of AT-cut quartz are K2 = 7.74 X 10-3 and e22 = 4.34~0(eo is permittivity of free space). For dilute aqueous solution the dielectric constant was taken as that of the deionized water and EL = 78eo. The effect of the frequency field on the water dielectric constant is negligible. The frequency changes of the unpolished and polished crystals were measured for a series of KCl(aq) solutions. The changes relative to water are plotted against the solution conductivity (Figure 4). The density and viscosity of the solutions are very similar to those of water. Therefore, the amount of solution trapped in the cavities should be very similar to the amount of trapped water; Le. an increase in ionic concentration does not change the trapped mass component. However, the frequency changes for the unpolished crystal are still much greater compared to those for the polished crystal under identical electrolyte conditions. This strongly indicates the presence of interfacial effects other than rigid mass loading. These effects may arise from increasing surface area on the roughened electrode which changesthe capacitive loading of the liquid. The electromechanical coupling factor, Kz, can be obtained by fitting the experimental data to eq 4. The values of K2 are 2.3 X for the unpolished crystal for the polished crystal, respectively. The and 3.5 X latter value is smaller than the calculated value from properties of the quartz, possibly due to the presence of the electrode in contact with the liquid. Nevertheless, the K2 ratio between the unpolished and polished devices is about 6.6, indicating that the acoustoelectric interactions for the unpolished crystal are 6 times stronger than those for the polished crystal. It has been noted17 that the acoustoelectric effect (coupling between the piezoelectric surface potential and the ions and dipoles) will diminish in the presence of a metal electrode for a common TSM configuration. In this study, the electrode in contact with liquid is grounded while the electrodes on both sides of the crystal have the same geometry and overlap with each other. The fringing electrical field may enter the liquid and generate a parasitic conduction path. In this case, varying solution conductivity can change the oscillating frequency. Indeed the
1994 Langmuir, VoE. 9,No. 8,1993 parallel resonant frequency f, and the static capacitance COchange as the conductivity of the solution changes. However the shifts in fp and COare the same for both the polished and unpolished crystals (data not shown). Therefore it is unlikely that the difference in Afs between the polished and unpolished crystals is caused by the difference in the parasitic capacitance. The term “acoustoelectric interaction” used in this report serves to indicate the fact that the sensor response is affected by interactions other than the capacitive effect. Although the mechanisms of these interactions are not fully understood, the results
Letters unequivocally indicate the existence of other interfacial effects resulting from changing surface morphology, in addition to trapped mass.
Acknowledgment. We thank D. C, Stone for help in performing the SEM experiments and D. Snetivy for assistance in performing the STM experimenta. Support for this research from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.
