Anal. Chem. 1996, 68, 2590-2597
Mass Sensitivity of the Thin-Rod Acoustic Wave Sensor Operated in Flexural and Extensional Modes Paul C. H. Li and Michael Thompson*
Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6
The mass sensitivities of the thin-rod acoustic wave sensor in both flexural and extensional acoustic modes are presented. These are based on experiments involving the electrodeposition of a test loading material onto a thin metal fiber (the thin rod) in a delay line configuration. Only small changes in acoustic loss occur when the device is immersed in an electrolyte, particularly in the flexural mode. Copper and lead have been used as test materials to confirm that the effects of elasticity can give rise to positive and negative mass sensitivities, respectively. The experimental and theoretical values all agree in sign and are of the same order of magnitude. This result confirms a refined theoretical model that includes incorporation of the effects of elasticity and inertia. An increase in experimental mass sensitivity with decrease in fiber radius is one of the advantages for the construction of a sensitive chemical sensor based on the thin-rod device. The sensor can be operated with facility in both gas and liquid phases and offers a new technique for the study of interfacial electrochemistry on metal surfaces. The phenomenon of mechanical resonance was observed during a number of experiments. Currently, acoustic wave devices used for chemical sensing include the thickness-shear mode bulk acoustic wave (TSM), surface acoustic wave (SAW), shear-horizontal acoustic plate mode (SH-APM), and flexural plate wave (FPW) sensors.1,2 A thin-rod acoustic wave (TRAW) sensor based on acoustic wave propagation in a thin rod has been developed recently.3,4 In a manner similar to other acoustic wave sensors, any mass loading on the thin rod induces a change in the phase velocity of the acoustic waves propagating in it; this phenomenon provides a means for chemical sensing, as we reported in a previous communication.5 The thin rod refers to a fiber of circular cross section with a radius much smaller than the acoustic wavelength. Piezoelectric transducers, incorporated in various geometries, can generate and receive longitudinal or flexural waves in the thin rod that is arranged in a delay line configuration similar to that employed (1) Grate, J. W.; Martin, S. J.; White, R. M. Anal. Chem. 1993, 65, 940A948A. (2) Grate, J. W.; Martin, S. J.; White, R. M. Anal. Chem. 1993, 65, 987A996A. (3) Jen, C. K.; Oliveira, J. E. B.; Yu, J. C. H.; Dai, J. D.; Bussie`re, J. F. Appl. Phys. Lett. 1990, 56, 2183-2185. (4) Li, P. C. H.; Stone, D. C.; Thompson, M. Anal. Chem. 1993, 65, 21772180. (5) Li, P. C. H.; Thompson, M. Analyst 1994, 119, 1947-1951.
2590 Analytical Chemistry, Vol. 68, No. 15, August 1, 1996
for the SAW, FPW, and SH-APM sensors. The entire rod vibrates in a way analogous to the plate of the FPW sensor. However, it is not necessary to fabricate the device from piezoelectric material, since the propagation of acoustic waves is based entirely on mechanical processes. For the purpose of chemical sensing, the TRAW sensor offers a number of advantages over other acoustic wave devices. In addition to the fact that the material of the thin rod does not have to possess piezoelectric properties, the device can be fabricated in a very small geometric configuration. The thin rod can also be constructed from a metal, which allows its use as an electrode in electrochemical experiments. At a low ultrasonic frequency, the mass sensitivity of the thin-rod acoustic wave sensor is quite high compared to that of the TSM or SAW counterpart, if the radius of the fiber is chosen to be very small. The aforementioned advantages led to the comprehensive examination of the mass sensitivities of the thin-rod device reported in the present paper. THEORY The mass sensitivity, SVm, of an acoustic wave sensor based on phase velocity measurement is defined as3
SVm ) lim
∆msf0
1 ∆V V0 ∆ms
(1)
where ms is the mass per unit area deposited uniformly on the surface of the sensor and ∆V ) (V - V0), in which V0 and V are phase velocities measured before and after a change in the mass per unit area, ∆ms, respectively. From an experimental standpoint it is difficult to measure the phase velocity in our configuration using the continuous wave format. Accordingly, the change in phase is monitored in the present work. Since the phase (in degrees), φ, is defined as follows,
φ ) 360°lf/V
(2)
where l is the length of fiber immersed in an electrolyte and f is the frequency of acoustic wave being propagated, accordingly, the change in phase, ∆φ, which is related to the change in velocity, ∆V, can be derived from eq 2 as follows,
∆V/V ) - (∆φ/φ) S0003-2700(96)00034-0 CCC: $12.00
(3)
© 1996 American Chemical Society
Therefore, the theoretical mass sensitivity can be expressed in terms of ∆φ as follows,6
1 ∆φ φ0 ∆ms
SVm ) - lim
∆msf0
(4)
where
φ0 ) 360°lf/V0 For correlation with experimental work, the relative phase, Φ ) φ/φ0, can be obtained by integrating eq 4 as follows,
∫
φ
1
dΦ ) Φ - 1 )
∫
ms
0
- SVm dms
(5)
Mass sensitivities are reported to be
-
1 nFa
(6)
where n ) 1 for the first extensional (radial-axial) mode, n ) 2 for the flexural mode, and F and a are the density and radius of the fiber, respectively.7 This expression ignores the influence of elasticity and inertia of the added deposit on the fiber. These parameters can be incrementally included as follows:6,8
including elasticity -
1 (1 - nCE) nF1a
(7)
Figure 1. Schematic diagram of the thin-rod acoustic wave sensor system in (A) flexural (shown) or (B) extensional mode. The terminals for the reference, counter and working electrodes on the potentiostat are represented by R, C, and W, respectively; whereas the terminals for the source port, reflection test port and transmission test port, on the network analyzer are represented by S, R, and T, respectively.
magnitude in the mass sensitivity of a TRAW device. However, the influence of elasticity (through CE) can give rise to a smaller or larger magnitude in sensitivity. Indeed, depending on the value of [1 - nCE] the actual sign of the mass sensitivity can change. In order to examine the effects of inertia and elasticity on the mass sensitivity of the TRAW device, the electrodeposition of copper and lead onto gold and platinum fibers of varying radii is described in the present work. The use of such a technique has previously been employed in the study of the mass sensitivity of the TSM sensor.9,10
including elasticity and inertia 1 nF1a
(1 - nCE) 2F2h 2nF2h C 1+ 1+ F1a F1a E
(
)(
)
(8)
where subscripts 1 and 2 denote the fiber and the loading material, respectively. The parameter, CE, is a constant related to the influence of elasticity and is given by
CE )
E2/F2 E1/F1
(9)
where E is the Young’s modulus of the deposit on fiber. Based on the assumption of uniform deposition of metal on a cylindrical metal fiber, the thickness, h, in expression 8 can be expressed in terms of ms as follows:
(
h ) a2 +
)
2ams F2
1/2
-a
(10)
Note that expression 8 indicates that the effect of inertia of the deposit (as represented by F2h) always gives rise to a smaller (6) Viens, M.; Li, P. C. H.; Wang, Z.; Jen, C. K.; Thompson, M.; Cheeke, J. D. N. IEEE Trans. Ultrason., Ferroelectr. Freq. Control, in press. (7) Wang, Z.; Cheeke, J. D. N.; Jen, C. K. Electron. Lett. 1990, 26, 1511-1512. (8) Viens, M.; Li, P. C. H.; Wang, Z.; Jen, C. K.; Thompson, M.; Cheeke, J. D. N. IEEE Ultrason. Symp. 1993, 359-364.
EXPERIMENTAL SECTION Reagents. Boric acid, lead(II) oxide, lead wire (1.0 mm in diameter), copper(II) sulfate, sulfuric acid, copper wire (1.0 mm in diameter), gold wire (0.1 mm in diameter), and platinum wire (0.10 mm in diameter) of analytical grade were obtained from Aldrich (Milwaukee, WI). Fluoboric acid (48-50% aqueous solution, purified grade) was obtained from Fisher (Unionville, ON). Gold wire (0.05 mm in diameter) was purchased from Johnson-Matthey (Brampton, ON). Both lead(II) oxide and lead wire are harmful solids and should be handled with care in a fume hood. Moreover, fluoboric acid is a poisonous and corrosive liquid. Equipment. A metal fiber, either of gold, of 25 or 50 µm radius, or of platinum, of 50 µm radius, is configured as an acoustical delay line, as shown in Figure 1. The central portion of the delay line is enclosed within a glass cell, which contains an electrolyte. The fiber passes through two rubber disks at both ends of the glass cell. The aperture of the rubber disk is large enough to allow the acoustic wave to pass through unhindered, but is small enough to avoid any leakage of electrolyte. Acoustic waves were excited in the fiber by using a hollow glass horn that is designed to concentrate the energy of a 2 MHz compressional piezoelectric transducer into the gold fiber. The tips of the glass horns are bonded to the fiber by a glue.5 By choosing the orientation of the glass horns relative to the axis of the fiber, either (A) flexural or (B) extensional modes can be excited and received, (9) Ward, M. D.; Delawski, E. J. Anal. Chem. 1991, 63, 886-890. (10) Ostrom, G. S.; Buttry, D. A. J. Electroanal. Chem. 1988, 256, 411-431.
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as shown in Figure 1. The excitation of acoustic waves and detection of signals were both accomplished by a network analyzer HP4195A (Hewlett-Packard, Mississauga, Canada). First, longitudinal waves are excited in one transducer by the source of the network analyzer. These are converted into either flexural or longitudinal waves at the junction of the tip of a glass horn and the metal fiber, followed by propagation in the metal fiber to the other end of the delay line. The acoustic waves are then converted back to longitudinal waves, before inducing a signal at the other transducer. Finally, the signal is detected by the detector of the network analyzer. The phase and insertion loss of the signal transmission are internally determined by the network analyzer after a comparison between the signal voltage obtained at the transmission test port (T) and the source voltage obtained at the reflection test port (R), via the power splitter. In fact, Frye and Martin previously employed the network analyzer to study the SAW sensor in the transmission mode.1,11 Although the phase measurement used here is not as sensitive as the frequency measurement commonly used in other acoustic wave sensors,1 the former method does not suffer from the problems of nonoscillation due to high insertion loss and of mode hopping. In addition to the measurement of phase, the network analyzer provides the advantage of obtaining the changes of attenuation as mass is being added on the metal fiber. In order to determine the mass sensitivities of thin-rod acoustic wave sensors in the extensional and flexural modes, a known amount of mass was deposited on or dissolved from a metal fiber, and the influence of the deposition or stripping on the phase of acoustic wave propagation in the thin-rod acoustical delay line was monitored. Electroplating has been chosen as the method of mass loading because it provides a controlled and uniform deposition of mass over a cylindrical substrate. The anodic and cathodic current efficiencies for copper or lead deposition are known to be very close to 100%.12,13 Accordingly, by using Faraday’s law, the current measured during deposition and stripping can be used to determine the amount of loading material deposited. A potentiostat (RDE 4, Pine Instrument Co., Grove City, PA) was used for the controlled-potential deposition and stripping. The metal fiber acts as the working electrode in a three-electrode system. The two other electrodes are an Ag/AgCl reference electrode (Metrohm, Herisau, Switzerland) and a counter electrode made by coiling a lead wire or copper wire for lead or copper plating, respectively. The cylindrical geometry of the counter electrode serves to provide an electric field of cylindrical symmetry for uniform deposition on, and stripping from, the surface of the fiber. Procedures. For lead plating, the electrolyte was a 0.26 M lead(II) tetrafluoroborate solution containing 0.51 M fluoboric acid and 0.12 M boric acid. This was prepared by slowly adding lead(II) oxide into fluoboric acid, because this reaction is highly exothermic. After the reaction subsided, an aqueous solution of boric acid was then added to the mixture. This was sonicated for 15 min for dissolution. Subsequently, it was filtered into a 50 mL volumetric flask and was diluted. For copper plating, the electrolyte is a 0.5 M solution of copper(II) sulfate containing 0.5 M sulfuric acid.
In order to determine the optimal potentials for deposition and stripping of copper or lead, cyclic voltametry was first performed. The potentials for lead are found to be -0.380 and -0.300 V for subsequent potentiostatic deposition and stripping experiments, respectively. The corresponding values for copper are +0.002 and +0.100 V. These values were selected to enable a slow rate of deposition and stripping to occur at a low current density so that any dendritic growth of electrodeposits can be avoided as far as possible. The deposition and subsequent stripping experiments were performed to allow for the examination of the reproducibility of the variation in the phase with the mass of metal deposits on the fiber. No attempt has been made to perform the electroplating on the metal fibers to the same degree in terms of the thickness of the metal deposits. The phase, insertion loss, current, and time were continually monitored during electroplating. A frequency sweep on the network analyzer HP4195A in the network measurement mode was first made. Then, the source voltage of a frequency around 2 MHz with a low insertion loss or a high amplitude was selected. The phase and insertion loss of the thin-rod acoustical delay line at that frequency were continually sampled as deposition or stripping went on. The current flowing between the working and counter electrodes was internally converted into a voltage value, which was measured by a digital multimeter (Model 197, Keithley, Cleveland, OH). Continual measurement of these four parameters during deposition or stripping allows the mass sensitivity to be determined.
(11) Frye, G. C.; Martin, S. J. Appl. Spectrosc. Rev. 1991, 26, 73-149. (12) Mohler, J. B. Electroplating and related processes; Chemical Publishing Co.: New York, 1969. (13) Kuhn, A. T. The Electrochemistry of Lead; Academic Press: New York, 1979.
(14) Wenzel, S. W.; White, R. M. IEEE Trans. Electron Devices 1988, 35(6), 735-743. (15) Watkins, R. D.; Cooper, W. H. B.; Gillespie, A. B.; Pike, R. B. Ultrasonics 1982, 20, 257-264.
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RESULTS AND DISCUSSION Propagation Losses and Mass Loading. Phase and insertion loss are the parameters measured to characterize the behavior of the TRAW device. A change of phase is induced by an alteration of phase velocity associated with immersion of the fiber in a liquid or change in mass of the metal deposit on a fiber (mass loading). The insertion loss is the ratio of the square of voltages of the output to that of the input, expressed in decibels. It includes both the transduction loss and propagation loss. The former arises from the electrical impedance mismatch between the transducers and the terminals of the network analyzer and from the acoustic impedance mismatch between the transducer, the glass horn, and the metal fiber; the latter is incurred by the attenuation of acoustic waves as they propagate between the two transducers.11 Since, during electrochemical deposition and stripping experiments on a fiber, the only variable is the mass loading, a change in insertion loss simply reflects a perturbation of propagation loss. The phase changes for immersion of a gold fiber of 50 µm radius in electrolyte are +70° and +430° for the flexural and extensional modes, respectively. The corresponding changes in insertion loss are 3 and 7 dB, respectively. The difference between these values is clearly associated with the nature of wave propagation in the two modes. Particle displacement for the flexural wave is perpendicular to the plane of the fiber surface, whereas for the extensional wave, it is in the plane of the device surface. The latter will result in increased viscous coupling to the surrounding liquid.14,15 The fact that, in overall terms, only
Table 1. Change in Insertion Loss (IL) during Deposition in the Extensional and Flexural Modes
deposit Cu plating Pb plating
fiber material
fiber radius (µm)
Au Au Pt Au Au Pt
25 50 50 25 50 50
extensional mode
flexural mode
Ha (%)
IL (dB)
Ha (%)
IL (dB)
1.0 0.4 1.4 14.5 3.2 6.1
+2 +10 +15 0 0 0
1.1 0.8 1.2 21 8.2 14.4
+15 +10 0 +10 +10 +10
a H is the maximum thickness of metal deposit as a percentage of fiber radius.
Table 2. Densities (G) and Young’s Moduli (E) of Various Metals F (103 g cm-3) copper
8.94 8.9 8.96
E (1010 Nm-2)
refs
13.0 12.3 12.98
29 30 31
mean gold
8.93 ( 0.03 19.32 19.3 19.3
12.6 ( 0.4 7.8 8.0 7.85
29 30 31
mean lead
19.31 ( 0.01 11.35 11.3 11.68
7.9 ( 0.1 1.6 1.62 1.61
29 30 31
mean platinum
11.4 ( 0.2 21.45 21.45 21.45
1.61 ( 0.01 16.6 16.8 17.0
29 30 31
mean
21.45
16.8 ( 0.2
small changes in insertion loss occur when the thin rod is immersed in a liquid, particularly in the flexural mode, favors the low-frequency operation of the TRAW sensor in this medium. During deposition, the insertion loss increases to a maximum of 15 dB as shown in Table 1. This is attributed to scattering caused by inhomogeneities in the polycrystalline material coated on the fiber.16 The level of ultrasonic scattering is higher when there is an increased extent of alignment between grains exhibiting high and low moduli of elasticity. As shown in Table 1, the alteration of insertion loss is less for lead than for copper as expected in view of its lower modulus of elasticity. Comparison of Mean Experimental and Theoretical Mass Sensitivity. The experimental mass sensitivity is computed from the relative phase, Φ, (measured phase divided by the absolute phase, Φ0) and the mass of metal electrodeposit per unit area, ms. The latter is calculated from the classical Faraday’s law of electrolysis and the surface area of the fiber. Theoretical values are obtained from eqs 4, 7, and 9 employing the data included in Table 2. A comparison with the mean experimental mass sensitivities for the deposition of copper and lead on various fibers operated in the extensional and flexural modes is given in Table 3. The experimental and theoretical values all agree in sign and are positive or negative for the deposition of copper or lead, respectively. The former result is clearly associated with the (16) Papadakis, E. P. In Methods of Experimental Physics; Edmonds, P. S., Ed.; Academic Press: New York, 1981; Vol. 19, Chapter 5.
effects caused by the Young’s modulus and density for copper compared to the analogous values for the metal composing the fiber. Furthermore, this observation explains the unusual variation in phase with respect to mass of copper deposits obtained in previous work.4 The agreement between the experimental and theoretical numbers expressed in Table 3 is reasonable given the nature of the values employed for the theoretical equations and the type of experiment being conducted. With respect to theory, differences in the mass sensitivities can have contributions from errors in the values used for the fiber radius and the density and acoustic wave velocities of the metals. The fiber radii are definitely not a factor, since this parameter was found to be close to the nominal values in all cases. The fiber radii were obtained by the measurement of fiber diameter against a calibration grid of size of 5 µm under an optical microscope, and they were found to be 25.4, 52.9, and 53.9 µm for the 25 µm gold, 50 µm gold, and 50 µm platinum fibers, respectively. However, the acoustic wave velocities do depend on the values of the density, F, and Young’s modulus, E. Here, it is important to note that these parameters may well be quite different for the experiment described in the present work, when compared to the values quoted in Table 2, which apply to cold-rolled wrought metal samples. For example, it has been reported that columnar structures of electrodeposits are formed from simple acidic solutions of ions such as sulfate or fluoborate, if a low current density is utilized.17 These structures will clearly give rise to lower strength and hardness of the deposits. Furthermore, voids are often found during electroplating and their presence will obviously reduce the elastic modulus and density of the deposit.14 In contrast, it is not expected that the presence of ultrasonic vibrations in our experiments will cause changes in the hardness, elasticity, porosity, and internal stress of metal electrodeposits reported in other areas.18,19 This observation is accurate with the use of very low acoustic power in our experiments, which in turn results in small acoustic amplitude.20,21 Finally, from the experimental view, it is difficult to measure the extensional velocity in the continuous-wave mode, at least employing the configuration we adopted. However, the flexural velocity can be determined by measuring the phase change associated with a change in the length of the delay line, which is the distance between the two tips of the glass horns. Nevertheless, since the bond between the tip of one glass horn and the metal fiber must be removed to effect the necessary movement of the glass horn, this procedure led to a less stable signal and unreliable phase measurement. Therefore, the velocities are computed using the physical parameters given in Table 2. Relative Phase and Deposition-Stripping Cycles. The phase collected from the network analyzer recurs every 180°. Accordingly, an integral number of 360° was added to the collected phase value when an increasing trend was observed; or subtracted when a decreasing trend was found. An example of the result of this procedure for cycles of deposition and stripping of copper on a gold fiber (flexural mode) is shown in Figure 2. The relative phase versus deposited mass per unit area for plating of copper on a gold fiber of radius 50 µm in the extensional mode is depicted (17) Dini, J. W. Electrodeposition: The Material Science of Coatings and Substrates; Noyes Publications: Park Ridge, NJ, 1993. (18) Kochergin, S. M.; Vyaseleva, G. Y. Electrodeposition of metals in ultrasonic fields; Consultants Bureau: New York, 1966. (19) Yeager, E.; Hovorka, F. J. Acoust. Soc. Am. 1953, 25, 443-455. (20) Engan, H. E.; Kim, B. Y.; Blake, J. N.; Shaw, H. J. J. Lightwave Technol. 1988, 6(3), 428-436. (21) Roth, W.; Rich, S. R. J. Appl. Phys. 1953, 24, 940-950.
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Table 3. Comparison of Meana Experimental and Theoretical Mass Sensitivities, SVm (cm2 g-1), for TRAW Devices Operated in the Extensional and Flexural Modes extensional mode deposit
fiber
fiber radius (µm)
Cu Cu Cu Pb Pb Pb
Au Au Pt Au Au Pt
25 50 50 25 50 50
a
Hb
(%)
1.0 0.4 1.4 14.5 3.2 6.1
theor
SVm
53.9 26.9 8.2 -13.5 -6.7 -7.6
flexural mode expt
SVm
6.5 ( 0.1 26.9 ( 7.3 11.2 ( 3.0 -13.4 ( 2.4 -13.1 ( 0.9 -8.2 ( 0.7
Hb
(%)
1.1 0.8 1.2 21 8.2 14.4
theor SVm
expt SVm
64.2 32.1 12.9 -3.1 -1.6 -3.0
41.6 ( 17.5 30.9 ( 4.0 7.5 ( 0.5 -4.6 ( 0.7 -3.2 ( 0.3 -4.1 ( 0.8
Mean value from both deposition and stripping experiments. b H is the maximum thickness of metal deposit as a percentage of fiber radius.
Figure 2. Variation in phase and insertion loss (IL) of flexural wave in a gold fiber (50 µm radius) with time during deposition (from 80 to 350 s) and stripping (from 360 to 430 s) of copper.
Figure 3. Variation in relative phase for the extensional (a, top) and flexural (b, bottom) waves in a gold fiber of 50 µm radius with mass of copper deposit per unit area during deposition (x) and stripping (y). Other curves represent theoretical values based on mass only (A), mass plus elasticity (B), and mass together with both elasticity and inertia included (C) models.
in Figure 3a together with computed theoretical curves. The latter includes the three scenarios discussed above, that is, the massonly values and those incorporating the effects of elasticity and 2594 Analytical Chemistry, Vol. 68, No. 15, August 1, 1996
elasticity with inertia. The corresponding results for the flexural mode are shown in Figure 3b. A hysteresis between the deposition and stripping curves (four in all) is observed for the experiment involving propagation of the extensional acoustic wave (Figure 3a). This result is reflected in the large confidence limit for the mass sensitivity given in Table 2. The hysteresis effect is less pronounced for the case involving the flexural mode (Figure 3b). These results are undoubtedly associated with the difference between the rates of deposition and stripping, since the potential, rather than the current density, was controlled during the various experiments. The results exhibit a further interesting feature for the flexural mode experiment. At very low values of ms, there is a correspondence with the “mass-only” model, whereas with rising ms the effect of elasticity becomes increasingly pronounced. It is conceivable that the effect of elasticity of the copper deposit on acoustic wave propagation in the metal fibers is less effective if there is less adhesion between the deposit and the substrate surface. Furthermore, the adhesion between the deposit and the substrate surface is less effective if there is a high internal (intrinsic or residual) stress within the deposit resulting from electroplating.17,22 It has been reported that the high initial internal stress of a copper electrodeposit is reduced to a steady value as the thickness of the deposit increases.17 Accordingly, this explains why the effect of elasticity of a copper deposit on acoustic wave propagation in metal fibers increases as the mass or thickness of deposits increases. The analogous experiments for the plating of copper on a platinum fiber of radius 50 µm are given in Figures 4. In both cases, the data fit the mass-only scenario at low values of ms and similar hysteresis curves for deposition and stripping are exhibited. Finally, the experimental data for plating of lead on a platinum fiber of 50 µm radius are presented in Figures 5. A striking feature of the curves is the conformity between the results during deposition and stripping, at least compared to the case for copper outlined above. The explanation for this result lies in the close agreement between the two rates of change of lead loading (depositions24.3 × 10-6 cm-2 s -1 and strippings19.5 × 10-6 cm-2 s-1). It is well-known that lead possesses a higher exchange current density and, therefore, exhibits greater reversibility with respect to kinetics than the case for copper.23 Such an electrochemical property tends to yield nonuniform dendritic growth in (22) Weil, R. In Properties of electrodeposits-their measurement and significance; Sard, R., Leidheiser, H., Jr., Ogburn, F. Eds.; Electrochemical Society: Pennington, NJ, 1975; Chapter 19. (23) Cheh, H. Y.; Cheng, T. In Proceedings of the Symposium on Electrodeposition Technology; Romankiw, L. T., Turner, D. R., Eds.; Electrochemical Society: Pennington, NJ, 1987; pp 555-564.
Figure 4. Variation in relative phase for the extensional (a, top) and flexural (b, bottom) waves in a platinum fiber of 50 µm radius with mass of copper deposit per unit area during deposition (x) and stripping (y). Other curves represent theoretical values based on mass only (A), mass plus elasticity (B), and mass together with both elasticity and inertia included (C) models.
lead deposits if no additives are employed. However, since the current densities used in the present work are low (4-30 mA cm-2) compared to the limiting current density, dendritic growth is not expected to be a major factor in determining the variation of Φ with ms.24 In a manner analogous to that described above for copper, there is a tendency for operation of the device in both vibrational modes to correlate with the mass only model at low values of ms. Moreover, a comparison of parts a and b of Figure 5 clearly indicates that the effect of elasticity is a much more important influence during propagation of the extensional wave. Mechanical Resonance of the Thin-Rod Acoustical Delay Line during Deposition and Stripping. For a number of experimental curves of phase with time, occasional abrupt changes in the phase are observed. This effect has been found previously, but remained unexplained (see Figure 6 in reference 4). As shown in Figure 6, the abrupt change in phase corresponds to a sudden increase in the insertion loss curve. Since an increase in insertion loss implies an increase in propagation loss, it was first believed that the change must be caused by a type of propagation loss due to absorption or scattering introduced by the foreign metal deposit. Nevertheless, since the decrease is momentary, and does not persist as the mass of metal deposit continues to change, there is a strong suggestion that a transition must have taken place. This unexpected phenomenon can be explained through an (24) Vallotton, P. H.; Matlosz, M.; Landolt, D. J. Appl. Electrochem. 1993, 23, 927-932.
Figure 5. Variation in relative phase for the extensional (a, top) and flexural (b, bottom) waves in a platinum fiber of 50 radius µm with mass of lead deposit per unit area during deposition (x) and stripping (y). Other curves represent theoretical values based on mass only (A), mass plus elasticity (B), and mass together with both elasticity and inertia included (C) models.
Figure 6. Variation in phase and insertion loss of extensional wave in a gold fiber (50 µm radius) with time during deposition (from 700 to 820 s) and stripping (from 880 to 1160 s) of lead. Mechanical resonances occur at the times represented by the dotted vertical lines.
observation made by Miller and Bolef25 in 1969. These authors reported that an abrupt 180° change of phase occurs in the signal presented to the receiver of a delay line as the sweeping frequency of the excitation source passes through the frequency corresponding to the center of a standing wave mechanical resonance.25 The effect occurs when the length of the delay line is equal to an (25) Miller, J. G.; Bolef, D. I. Rev. Sci. Instrum. 1969, 40, 361-363.
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integral number of half-wavelengths of the acoustic wave. At a fixed phase velocity, this condition is satisfied at some frequencies. However, since the frequency was fixed during our experiments, the above condition can also be satisfied at some phase velocity that is varied by a change in mass of the metal deposit on the surface of the thin-rod acoustical delay line. Accordingly, the effect causes an increase in insertion loss due to a conversion of electrical energy to mechanical energy at mechanical resonance. The abrupt phase shift is superimposed on the general phase change induced by a change in mass of metal deposits, resulting in the appearance of the curve. If the rate of deposition or stripping is lower, the rate of change in phase velocity is also lower, and the unusual change in phase at mechanical resonance is not as abrupt. It is interesting to note that the time when a maximum insertion loss occurs corresponds to the time at the point of inflection of the phase change around the region of resonance. Since the phase at mechanical resonance is unusual, the data in this region cannot be used to determine the mass sensitivity. Nevertheless, the segments before and after the point of resonance have the same slope, indicating that the phase response is not affected after mechanical resonance occurs. Care must be taken to avoid using the sensor in such a region, since analytical information can be lost. This mechanical resonance of the delay line should not be confused with the film resonance observed in nonrigid polymeric films coated on SAW sensors, as reported by Ballantine26 and explained in detail by Martin et al.27 The former occurs when the distance of the delay line, is equal to an integral multiple of half-wavelengths of the acoustic wave propagated in the delay line; whereas the latter occurs when film thickness is equal to an integral multiple of half-wavelengths of the acoustic wave propagated across the non-rigid polymeric film. In the ultrasonic community, the phenomenon of mechanical resonance that occurs at certain frequencies has been employed to determine the phase velocity in the continuous-wave mode. The phase velocity, V0, which is a constant value, can be expressed in terms of the difference in frequencies, f, between two successive mechanical resonances28 as follows:
V0 ) 2l′(fp+1 - fp)
(11)
where l′ is the length of the delay line and p is an arbitrary integer. The formula was derived based on the fact that l′ should be equal to an integral number of half-wavelengths of the acoustic wave at mechanical resonance, as given below:
l′ )
p+1 V0 p V0 ) 2 fp+1 2 fp
(12)
In the present work, instead of varying the frequency to attain mechanical resonance, the phase velocity is varied by a change in the mass of metal deposits. Therefore, eq 12 can be expressed (26) Ballantine, D. S., Jr. Anal. Chem. 1992, 64, 3069-3076. (27) Martin, S. J.; Frye, G. C.; Senturia, S. D. Anal. Chem. 1994, 66, 2201. (28) Breazeale, M. A.; Cantrell, J. H., Jr.; Heyman, J. S. In Methods of Experimental Physics; Edmonds, P. S., Ed.; Academic Press: New York, 1981; Vol. 19, Chapter 2. (29) Harrison, R. D. Book of Data; The Nuffield Foundation: London, 1978. (30) Kaye, G. W. C.; Laby, T. H. Tables of Physical and Chemical Constants, 11th ed.; Longmans Green: London, 1957. (31) Brandes, E. A. Smithells Metals Reference Book, 6th ed.; Butterworths: London, 1983.
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as follows:
l)
p+1 Vp+1 p Vp ) 2 f 2 f
(13)
where l is the length of the delay line immersed in the electrolyte. The difference in masses of metal deposits per unit area, ms, at two successive mechanical resonances can be derived from eqs 13 and 1, and is given as follows:
(ms)p+1 - (ms)p )
Vp+1Vp 2flV0|SVm|
(14)
where V0 is the initial phase velocity; Vp+1 and Vp are the phase velocities at two successive mechanical resonances. This formula can be used to examine the curve for the case of plating of lead on gold fiber 50 µm radius in the extensional mode. This is the only curve in which two successive mechanical resonances are observed, as shown in Figure 6. The left-hand side quantity, [(ms)p+1 - (ms)p], is measured to be 7.12 × 10-4 and 7.63 × 10-4 g cm-2 during deposition and stripping, respectively. Although Vp+1 and Vp are unknown, they can be estimated with a knowledge of V0 (2009 ms-1) and the fact that p is an integer. The righthand side of eq 14 is then evaluated to be 4.80 × 10-4 g cm-2 using the integer, p, determined to be 157 and the experimental SVm (-13.1 cm2 g-1). The left-hand side and right-hand side values in eq 12 are found to be of the same order of magnitude. CONCLUSIONS Electrodeposition of copper and lead has been used as a test protocol to examine the validity of a refined theoretical model for the mass sensitivity of the thin-rod acoustic wave sensor operated in the flexural and extensional modes. Since, as for other acoustic wave sensors, the analytical signal depends on the mass of deposit per unit area, not on the absolute loading mass, a smaller fiber radius increases the mass sensitivity of the device. In addition, the sensitivity is higher when the sensor is operated in the extensional mode. However, smaller changes in insertion loss occur when the thin rodsin the flexural modesis immersed in liquid. Such an operation has constituted a challenge for those working with acoustic wave sensors in liquids because of the effect of attenuation by the matrix. Accordingly, the behavior of the flexural TRAW device complements the use of the FPW and SHAPM devices in the liquid phase. The present work introduces a potential new technique for the study of interfacial electrochemistry: Useful information is stored in the comparison of theoretical versus experimental mass sensitivity, hysteresis between deposition-stripping segments in the plot of relative phase versus mass of deposit per unit area, and in the phenomenon of mechanical resonance. Although the TSM sensor has been used for a similar purpose, there are fundamental differences between the two techniques. The TRAW structure allows the study of curved surfaces and avoids the issues of viscous damping (flexural mode) and the presence of the controversial acoustoelastic effect. Finally, it is clear that the experimental configuration adopted in the present work does not easily lend itself to sensor operation in practical analysis (this is not the case for fundamental electrochemical studies). However, in view of a technical climate
where a suspended mesh, membrane, or cantilever can be easily fabricated in a microelectronic component, the incorporation of a similarly constructed thin rod in a small device structure can be reasonably envisaged. Accordingly, the present work introduces a new strategy to add to the library of acoustic wave devices available to the sensor specialist. ACKNOWLEDGMENT Support from the Natural Sciences and Engineering Research Council, Canada, and the Institute for Chemical Science and Technology, Canada, is gratefully acknowledged. The authors
also thank C. K. Jen of the Industrial Materials Institute, National Research Council, Canada, for helpful suggestion and loan of equipment, and M. Viens from the same organization for useful discussion.
Received for review January 15, 1996. Accepted April 17, 1996.X AC960034I X
Abstract published in Advance ACS Abstracts, June 1, 1996.
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