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Simultaneous measurement of mass and viscosity using piezoelectric quartz crystals in liquid media
ANALYTIcA CHIMICA
ACL4
ELSEVIER
Analytica Chimica Acta 288 (1994) 179-185
Simultaneous measurement of mass and viscosity using piezoelectric quartz crystals in liquid media G.L. Hayward *, G.Z. Chu School of Engineering,Universityof Guelph, Gue@t, Ontario,NIG 2WI Canada
(Received 10th August 1993; revised manuscript
received8th October 1993)
Abstract An inexpensive mass and viscosity sensor can be constructed from a quartz crystal microbalance using an automatic gain control oscillator. The gain control voltage, which maintains a constant oscillation amplitude, is shown to be affected only by the energy loss to the liquid medium and the crystal mounting. The frequency shift between a loaded and an unloaded crystal operating in the same medium is shown to closely follow the Sauerbrey equation. A viscosity or density correction based on the gain control voltage can be applied to the measured frequency shift to obtain the mass loading. Errors due to the oscillator phase shift and the crystal mounting losses can be removed by calibration.
Z&ywords: Sensors; Piezoelectric methods; Mass and viscosity sensor; Quartz crystals; Viscosity
1. Introduction
The quartz crystal microbalance was originally used in vacuum to measure the mass of surface deposits [l]. The bulk wave devices commonly used were AT cut quartz crystals which oscillate in a thickness shear mode. The resonant frequency of the crystal, which depends on its mass, was measured by connecting the crystal as the frequency determining part of an electrical oscillator. As shown by Sauerbrey [ll, the resonant frequency of a quartz crystal decreases linearly as mass is deposited onto its surface:
Af =
-2.26
* Corresponding
X
10-6fzAm/A
author.
0003-2670/94/$07.00
(1)
where Af is the frequency shift due to the added mass in Hz, f, is the resonant frequency of the quartz crystal in Hz and Am/A is the surface mass loading in g cme2. This model predicts that a mass loading of 5.5 ng cmv2 gives a 1 Hz frequency shift with a crystal operating at 9 MHz, which is easily measured. More recently, the use of the quartz crystal microbalance in liquid media has received increasing attention. Applications include such diverse areas as biosensors for antigens or DNA [2], electrochemical deposition sensors [3], liquid chromatography detectors [4,51 and titration end-point indicators [6,7]. In liquid media, the acoustic coupling between the liquid and the quartz surface causes an additional frequency shift. This frequency shift has been modelled by Bruckenstein and Shay [S], who used a dimensional analysis of a diffusion anal-
0 1994 Elsevier Science B.V. All rights reserved
SSDI 0003-2670(93)E0608-A
G.L. Hayward, G. Z. Chu /Analytica Chimica Acta 288 (1994) 179-185
180
ogy, by Kanazawa and Gordon [93 as a viscous shear wave propagating into the liquid and by Shana et al. [lo], who included a piezoelectric term in the crystal stiffness. These three models were of the form:
Af =
-kf;/2(/.q)1'2
shear wave propagating into the liquid [17,181. All of these models were of the form: z vrscous = 2mrf,“(
ppp2(
1 +j)
(3)
is the viscous impedance, u is a where ZWOUS coupling coefficient and j is the square root of - 1. Beck et al. [16] pointed out that the Cl+ j) term breaks the viscous impedance term into a resistance or energy dissipation and an inductance or energy storage as fluid inertia. These, with an inductance corresponding to the inertia of mass deposited onto the crystal surface may be added to the Buttenvorth-van Dyke (BVD) electrical equivalent model of a quartz crystal 1193as shown in Fig. lb. Since the resistance and induc-
(2)
where p is the liquid viscosity, p is the liquid density and k is a constant. The form of this equation agrees with experimental data [ll-131 although some deviation in very viscous media has been observed [14]. The viscous impedance has been calculated from an electrical analogy of mechanical shear [15,16] and from a solution of Stokes viscous
DIRLICCIIC 8*oaAaz
(b)
(cl Fig. 1. Quartz crystal equivalent circuits. (a) Butteworth-van Dyke quartz crystal equivalent circuit. (b) Extended quartz crystal equivalent circuit. (c) Equivalent circuit with calibration resistor.
G.L. Hayward, G.Z. Chu /Analytica Chimica Acta 288 (1994) 179-185
tance terms are additive, the individual values can not be determined from a single frequency measurement. Network analysis provides a means to determine the values of the BVD parameters [14,17,20]. As before, the individual inductance and resistance components can not be resolved, but shifts from those of a dry, clean crystal can be attributed to viscous and mass loading. The increase in the resistance is due to viscosity, and since the viscous impedance contains the (1 +j) term, the viscous inductance can be calculated from 1161:
R v1sc0us
= ~“foJkIsco”s
(4)
remaining inductance increase may be attributed to the mass deposited on the crystal surface [20]. A mass determination, therefore, requires three measurements to resolve the three inductances of Fig. lb. These are the unperturbed crystal inductance, the viscous inductance from Eq. 4 and the measured overall inductance. An alternative to the network analyzer, which is a large and expensive research tool, is the automatic gain control (AGC) oscillator. This has been used in several studies [15,18,21,22] to measure the energy dissipation as well as the resonant frequency shift. Since the resistance is the only energy loss element, the AGC voltage required to maintain the oscillator output level may be calibrated against the resistance [18]. The measured frequency shift may be used to calculate the overall inductance change, and the mass calculated by subtracting the viscous inductance from Eq. 4. The mass and liquid loadings can, therefore, be obtained simultaneously from data provided by an AGC oscillator. The
2. Experimental The AGC oscillator used in the present study was designed by Simpson [151. The oscillator section consists of a Motorola MC1350 amplifier and an NPN transistor. A biased comparator and an integrator form the AGC feedback loop. When the output amplitude decreases due to energy loss from the crystal, the duty cycle of the com-
silo
-250
-200
-150
181
-100
-50
Aoc Vdma (mv)
Fig. 2. Crystal resistance vs. AGC voltage calibration. Solid lines are regression fits.
parator output decreases, reducing the output of the integrator which is connected to the AGC input of the oscillator. At lower AGC voltages, the gain of the MC1350 increases restoring the amplitude of the oscillator output. The oscillation frequency was measured with a Hewlett Packard 5330B frequency counter. To improve the stability, a Raltron TF65OlOB oven controlled external time base was used. A bias amplifier was used to set the AGC reading to zero with a dry crystal connected to the oscillator. Fig. 2 presents a calibration relating the crystal resistance to the AGC voltage. A series of fiied resistors were placed in series with dry crystals and the AGC voltage change and frequency shift were measured. These resistances were outside the BVD network as shown in Fig. lc. The difference between the real part of the impedances of the BVD and calibration networks increased with the resistance, giving a maximum error of 2.5 Ohm for the present study. Using this circuit, Hager [21] and Simpson [15] report that the AGC voltage is linear with the viscous loss, however the gain of the MC1350 changes non-linearly with the AGC voltage [23]. Their AGC voltage changes were of the order of 0.045 V, which were small enough to approximate a linear relationship. A second order AGC calibration equation was obtained by a least squares fit. The correlation coefficient CR*>was 0.9999 and the standard error of the resistance estimated from the AGC
182
G.L. Hayward, G.Z. Chu /Analytica Chin&a Acta 288 (1994) 179-185
U
U
Fig. 3. Crystal support assembly.
voltage was 1.3 Ohm. Both of these errors were less than the dry crystal mounting resistance of approximately 4.9 Ohm, measured using a Hewlett Packard 4195A network analyzer. The crystals used were 9.00 MHz AT-cut crystals 1.4 cm in diameter with 7 mm diameter gold electrodes (Lap-Tech, Bowmanville). The support assembly, made of a clear acrylic plastic, is shown in Fig. 3. The crystal was clamped between two O-rings with gold foil connections to the crystal electrodes. The entire assembly plugged directly into the oscillator module to reduce the length of the lead wiring. Liquid was passed across the top of the crystal. The entire system, including liquid samples and syringes was placed in a temperature controlled box at 30°C (kOS”C). Five liquids were used, water and 5, 10, 15 and 20% glycerol (ACS grade, Fisher Scientific Co., Fair Lawn, NJ) by weight in water. The density and viscosity of these solutions were taken from Miner and Dalton [241. The crystal surface mass was increased in steps by plating silver onto the wet electrode. The plating was performed by passing approximately 100 PA from a silver wire anode through a 0.01 M silver nitrate (ACS reagent grade, Aldrich, Milwaukee, WI) electrolyte. The crystal was not removed from the support assembly during the plating. The plating current was obtained from the voltage drop across a sense resistor and the plating time measured by a stopwatch. The deposited mass was calculated from the total charge passed through the cell. Two crystals were plated. Each experiment was performed by measuring the frequency and
AGC signal for each liquid. Sufficient liquid was passed across the crystal to ensure the glycerol concentration and the frequency was allowed to stabilize before data were recorded. After the five liquids were used, the cell was flushed with deionized water followed by silver nitrate solution and the plating was done. The silver wire anode was passed through one of the sample tubes to the space near the crystal. After plating, the crystal was again flushed with deionized water. This process was repeated 15 times for the first crystal and 18 times for the second.
3. Results The resistance data obtained from the two plating experiments are shown in Fig. 4. The data
0
5 &Mass(rn&m,
Fig. 4. Series resistance data. 0, Water. *, 5% Glycerol. A, 10% Glycerol. l , 15% Glycerol. +, 20% Glycerol.
G.L. Hayward, G.Z. Chu /Analytica Chimica Acta 288 (1994) 179-185
*
1
0.9
OS
1
1.06
1.1
1.15
1.2
1.25
I 1.3
w~~~~w(kg/m*=')
Fig. 5. Series resistance vs. liquid properties. 0, Present data. A, Previous data [IS].
are grouped as 5 horizontal lines, each corresponding to a different liquid medium. It is apparent from this that the amount of mass plated onto the crystal electrode has little effect on the viscous resistance. The increase at 9 pg observed in the data from one of the crystals can be attributed to surface roughness. At the end of each experiment, the crystal was examined. The silver was not deposited uniformly, but rather was concentrated in a few active areas on each crystal. Yang et al. [25] have shown that surface roughness increases the viscous resistance. Fig. 5 presents these data as a function of the liquid properties. The data are linear in (pp)i/‘. The regression gave R* = 0.968with a standard error of the resistance estimate of 2.6 Ohm. This is in agreement with equation 3. An electrode area correction from the resistance model derived by Hayward [18] was applied to data from that study. These data, also shown in Fig. 5, agree well with the present data. The effect of deposited mass on the frequency shift is shown in Fig. 6. Here the frequency shift is the difference between the operating frequency of a plated crystal and that of the unplated crystal operating in the same liquid medium. The relationship is linear CR*= 0.998) and is in reasonable agreement with the Sauerbrey equation [ll. The difference in slopes suggests that the plating current efficiency was about 96%. This may be
183
due to current leakage across the plating cell, or to the decomposition of water. The plating voltage was not controlled. No effect of the medium viscosity was noted in these data. These plating experiments have shown that the equivalent resistance of a crystal is related to the viscosity and density of a liquid medium. The deposition of mass onto a crystal causes a frequency shift, but does not affect the equivalent resistance of the crystal. Moreover, when the frequency shift caused by mass loading is calculated from the frequency of a crystal operating in a particular medium, the properties of the medium do not affect the relationship between the mass and the frequency shift. These conditions are necessary, but not sufficient for the design of a mass and viscosity sensor to operate in an unknown medium. The resistance of the crystal in an unknown solution can be used to obtain the frequency shift from a crystal operating in air by calculating (pp)‘/* from the regression of Fig. 5 and then applying Eq. 2. To test this, data from 5 crystals, including those used in the plating experiments, are presented in Fig. 7. Two complicating factors emerge from these data. The first factor is the oscillator phase shift. At high phase shifts, the crystal operating frequency is greatly affected by the crystal resistance 1181. The oscillator used in this study had a phase shift
Fig. 6. Frequency shift due to deposited mass. 0, Water. * ,
5% Glycerol. A, 10% Glycerol. n , 15% Glycerol. +, 2Q% Glycerol.
184
G.L. Hayward, G.Z. Chu /Analytica Chimica Acta 288 (1994) 179-185
of +77.8 degrees. This value was obtained by measuring the operating frequency of three calibrated reference crystals and is in good agreement with the frequency response measurement reported previously [18]. The frequency shifts calculated from the model of JSanazawa and Gordon [81 were corrected by adding the frequency shifts calculated from the BVD equivalent circuit with resistances taken from Fig. 5. The result overprediets the frequency shift by about 1500 Hz. The second complicating factor is the mounting resistance. When a crystal is clamped between two O-rings, the energy lost to the O-ring depends on the orientation of the O-ring on the crystal and on the clamping pressure. The effect of these is enhanced when liquid increases the coupling between the O-ring and the crystal. From the BVD model at 77.8 degrees phase shift, a resistance of 30.4 Ohm will give a 1500 Hz frequency shift. This resistance is not unreasonable for mounting since the reference crystals mounted with two small spring clips had a measured resistance of 8 to 10 Ohm. Much more energy may be expected to be dissipated by O-ring mountings. The discrepancy between the curves shown in Figure 7 may, therefore, be attributed to mounting losses. By changing the reference frequency to that of an unplated crystal operating in pure water, the subtraction to get frequency shift values compen-
-1
2
Fig. 8. Frequency shift from operation in water. A, Crystal 1 (before plating). n , Crystal 2 (before plating). *, Crystal 3. +, Crystal 4. 0, Crystal 5.
sates for the mounting resistance. These frequency shift data are shown in Fig. 8. Since the absolute values of the frequency shift are smaller, the nonlinearity of the oscillator phase shift component of the frequency shift is emphasized. A quadratic equation fitted the data well (R* = 0.987 with a standard error of frequency shift estimate of 40.2 Hz). The unplated frequency in an unknown medium can be obtained from (pp)‘/’ which in turn is related to the resistance or to the AGC voltage. This may then be subtracted from the measured oscillation frequency to obtain the mass loading. As in the network analyzer method, three measurements are required, the unplated frequency in water, the AGC voltage and the oscillation frequency.
4. Conclusions
Fig. 7. Frequency shift from dry crystal operation. A, Crystal 1 (before plating). l , Crystal 2 (before plating). *, Crystal 3. + , Crystal 4. 0, Crystal 5.
An inexpensive mass and viscosity sensor based on an AGC oscillator can be designed to operate in an unknown medium. The AGC voltage is affected only by the liquid medium so that a viscosity or density correction can be applied to the measured frequency shift to obtain the mass loading from the Sauerbrey equation [ll. Errors due to the oscillator phase shift and the crystal mounting losses can be removed by calibration.
G.L. Hayward, G.Z. Chu /Analytica Chimica Acta 288 (1994) 179-185
5. List of symbols
A fo
i k L viscous
R2 R viscous
z viscous Af
Am CL P c-r
Crystal electrode area, cm2 Crystal frequency, Hz Square root of - 1 Frequency shift constant, cm2 g-’ Viscous inductance, Henry Correlation coefficient from linear regression Viscous resistance, Ohm Viscous impedance, Ohm Frequency shift, Hz Change in surface mass, g Liquid viscosity, g cm-’ s-l Liquid density, g cmW3 Acoustic coupling coefficient, Ohm cm2 g-’
6. Acknowledgement The authors would like to thank Dr. M. Thompson at the University of Toronto for allowing the use of the Hewlett Packard network analyzer. The financial support of the National Science and Engineering Research Council of Canada is gratefully acknowledged. 7. References 111G. Sauerbrey, Z. Phys., 155 (1959) 206. [21M. Thompson, A.L. Kipling, W.C. Duncan-Hewitt, L.V. Rajakovic, and B.A. C&c-Vlasak, Analyst, 116 (1991) 881. 131 R. Schumacher, R., Angew. Chem. Int. Ed. Engl., 29 (1990) 329.
185
[4] P.L. Konash and G.J. Bastiaans, Anal. Chem., 52 (1980) 1929. [5] T. Nomura, T. Yanagihara and T. Mitsui, Anal. Chim. Acta., 248, (1991) 329. [6] S.-Z. Yao, Z.-H. MO and L.-H. Nie, Anal. Chim. Acta, 229 (1990) 205. [7] S.-Z. Yao, Z.-H. MO and L.-H. Nie, Anal. Chim. Acta, 230 (1990) 51. [S] S. Bruckenstein and M. Shay, Electrochim. Acta, 30 (1985) 1295. [9] KK. Kanazawa and J.G. Gordon, Anal. Chim. Acta, 175 (1985) 99. [IO] Z.A. Shana, D.E. Radtke, U.R. Kelkar, F. Josse and D.T. Haworth, Anal. Chim. Acta, 231, (1990) 317. [ll] T. Nomura and A. Minemura, Nippon Kagaku Kaishi, 1980 (19801 1621. [12] T. Nomura and M. Okuhara, Anal. Chim. Acta, 142 (1982) 281. [13] S.-Z. Yao and T.-A. Zhou, Anal. Chim. Acta, 212 (1988) 61. [141 A.L. Kipling and hf. Thompson, Anal. Chem., 62 (1990) 1514. [151 R.L. Simpson, Ph.D. Thesis, University of Washington, 1985. [I61 R. Beck, U. Pittermann and KG. Weil, KG., Ber. Bunsenges. Phys. Chem., 92 (1988) 1363. 1171 H. Muramatsu, E. Tamiya and I. Karube, Anal. Chem., 60 (1988) 2142. Dl G.L. Hayward, Anal. Chim. Acta, 264 (1992) 23. [191 V.E. Bottom, Introduction to Quartz Crystal Unit Design, Van Nostrand Reinhold, New York, 1982. 1201J. Martin, V.E. Granstaff and G.C. Frye, Anal. Chem., 63 (1991) 2272. [211H. Hager, Chem. Eng. Commun., 43 (1986) 25. f221M. Thompson, C.L. Arthur and G.K Dhaliwal, Anal. Chem., 58 (1986) 1206. [231Motorola Inc., Linear and Interface Integrated Circuits, Motorola Inc., Phoenix, 1983. [Ul C.S. Miner and N.N. Dalton, Glycerol, Reinhold, New York, 1953. [H M. Yang, M. Thompson and W.C. Duncan-Hewitt, Langmuir, 9 (1993) 802.
ACL4
ELSEVIER
Analytica Chimica Acta 288 (1994) 179-185
Simultaneous measurement of mass and viscosity using piezoelectric quartz crystals in liquid media G.L. Hayward *, G.Z. Chu School of Engineering,Universityof Guelph, Gue@t, Ontario,NIG 2WI Canada
(Received 10th August 1993; revised manuscript
received8th October 1993)
Abstract An inexpensive mass and viscosity sensor can be constructed from a quartz crystal microbalance using an automatic gain control oscillator. The gain control voltage, which maintains a constant oscillation amplitude, is shown to be affected only by the energy loss to the liquid medium and the crystal mounting. The frequency shift between a loaded and an unloaded crystal operating in the same medium is shown to closely follow the Sauerbrey equation. A viscosity or density correction based on the gain control voltage can be applied to the measured frequency shift to obtain the mass loading. Errors due to the oscillator phase shift and the crystal mounting losses can be removed by calibration.
Z&ywords: Sensors; Piezoelectric methods; Mass and viscosity sensor; Quartz crystals; Viscosity
1. Introduction
The quartz crystal microbalance was originally used in vacuum to measure the mass of surface deposits [l]. The bulk wave devices commonly used were AT cut quartz crystals which oscillate in a thickness shear mode. The resonant frequency of the crystal, which depends on its mass, was measured by connecting the crystal as the frequency determining part of an electrical oscillator. As shown by Sauerbrey [ll, the resonant frequency of a quartz crystal decreases linearly as mass is deposited onto its surface:
Af =
-2.26
* Corresponding
X
10-6fzAm/A
author.
0003-2670/94/$07.00
(1)
where Af is the frequency shift due to the added mass in Hz, f, is the resonant frequency of the quartz crystal in Hz and Am/A is the surface mass loading in g cme2. This model predicts that a mass loading of 5.5 ng cmv2 gives a 1 Hz frequency shift with a crystal operating at 9 MHz, which is easily measured. More recently, the use of the quartz crystal microbalance in liquid media has received increasing attention. Applications include such diverse areas as biosensors for antigens or DNA [2], electrochemical deposition sensors [3], liquid chromatography detectors [4,51 and titration end-point indicators [6,7]. In liquid media, the acoustic coupling between the liquid and the quartz surface causes an additional frequency shift. This frequency shift has been modelled by Bruckenstein and Shay [S], who used a dimensional analysis of a diffusion anal-
0 1994 Elsevier Science B.V. All rights reserved
SSDI 0003-2670(93)E0608-A
G.L. Hayward, G. Z. Chu /Analytica Chimica Acta 288 (1994) 179-185
180
ogy, by Kanazawa and Gordon [93 as a viscous shear wave propagating into the liquid and by Shana et al. [lo], who included a piezoelectric term in the crystal stiffness. These three models were of the form:
Af =
-kf;/2(/.q)1'2
shear wave propagating into the liquid [17,181. All of these models were of the form: z vrscous = 2mrf,“(
ppp2(
1 +j)
(3)
is the viscous impedance, u is a where ZWOUS coupling coefficient and j is the square root of - 1. Beck et al. [16] pointed out that the Cl+ j) term breaks the viscous impedance term into a resistance or energy dissipation and an inductance or energy storage as fluid inertia. These, with an inductance corresponding to the inertia of mass deposited onto the crystal surface may be added to the Buttenvorth-van Dyke (BVD) electrical equivalent model of a quartz crystal 1193as shown in Fig. lb. Since the resistance and induc-
(2)
where p is the liquid viscosity, p is the liquid density and k is a constant. The form of this equation agrees with experimental data [ll-131 although some deviation in very viscous media has been observed [14]. The viscous impedance has been calculated from an electrical analogy of mechanical shear [15,16] and from a solution of Stokes viscous
DIRLICCIIC 8*oaAaz
(b)
(cl Fig. 1. Quartz crystal equivalent circuits. (a) Butteworth-van Dyke quartz crystal equivalent circuit. (b) Extended quartz crystal equivalent circuit. (c) Equivalent circuit with calibration resistor.
G.L. Hayward, G.Z. Chu /Analytica Chimica Acta 288 (1994) 179-185
tance terms are additive, the individual values can not be determined from a single frequency measurement. Network analysis provides a means to determine the values of the BVD parameters [14,17,20]. As before, the individual inductance and resistance components can not be resolved, but shifts from those of a dry, clean crystal can be attributed to viscous and mass loading. The increase in the resistance is due to viscosity, and since the viscous impedance contains the (1 +j) term, the viscous inductance can be calculated from 1161:
R v1sc0us
= ~“foJkIsco”s
(4)
remaining inductance increase may be attributed to the mass deposited on the crystal surface [20]. A mass determination, therefore, requires three measurements to resolve the three inductances of Fig. lb. These are the unperturbed crystal inductance, the viscous inductance from Eq. 4 and the measured overall inductance. An alternative to the network analyzer, which is a large and expensive research tool, is the automatic gain control (AGC) oscillator. This has been used in several studies [15,18,21,22] to measure the energy dissipation as well as the resonant frequency shift. Since the resistance is the only energy loss element, the AGC voltage required to maintain the oscillator output level may be calibrated against the resistance [18]. The measured frequency shift may be used to calculate the overall inductance change, and the mass calculated by subtracting the viscous inductance from Eq. 4. The mass and liquid loadings can, therefore, be obtained simultaneously from data provided by an AGC oscillator. The
2. Experimental The AGC oscillator used in the present study was designed by Simpson [151. The oscillator section consists of a Motorola MC1350 amplifier and an NPN transistor. A biased comparator and an integrator form the AGC feedback loop. When the output amplitude decreases due to energy loss from the crystal, the duty cycle of the com-
silo
-250
-200
-150
181
-100
-50
Aoc Vdma (mv)
Fig. 2. Crystal resistance vs. AGC voltage calibration. Solid lines are regression fits.
parator output decreases, reducing the output of the integrator which is connected to the AGC input of the oscillator. At lower AGC voltages, the gain of the MC1350 increases restoring the amplitude of the oscillator output. The oscillation frequency was measured with a Hewlett Packard 5330B frequency counter. To improve the stability, a Raltron TF65OlOB oven controlled external time base was used. A bias amplifier was used to set the AGC reading to zero with a dry crystal connected to the oscillator. Fig. 2 presents a calibration relating the crystal resistance to the AGC voltage. A series of fiied resistors were placed in series with dry crystals and the AGC voltage change and frequency shift were measured. These resistances were outside the BVD network as shown in Fig. lc. The difference between the real part of the impedances of the BVD and calibration networks increased with the resistance, giving a maximum error of 2.5 Ohm for the present study. Using this circuit, Hager [21] and Simpson [15] report that the AGC voltage is linear with the viscous loss, however the gain of the MC1350 changes non-linearly with the AGC voltage [23]. Their AGC voltage changes were of the order of 0.045 V, which were small enough to approximate a linear relationship. A second order AGC calibration equation was obtained by a least squares fit. The correlation coefficient CR*>was 0.9999 and the standard error of the resistance estimated from the AGC
182
G.L. Hayward, G.Z. Chu /Analytica Chin&a Acta 288 (1994) 179-185
U
U
Fig. 3. Crystal support assembly.
voltage was 1.3 Ohm. Both of these errors were less than the dry crystal mounting resistance of approximately 4.9 Ohm, measured using a Hewlett Packard 4195A network analyzer. The crystals used were 9.00 MHz AT-cut crystals 1.4 cm in diameter with 7 mm diameter gold electrodes (Lap-Tech, Bowmanville). The support assembly, made of a clear acrylic plastic, is shown in Fig. 3. The crystal was clamped between two O-rings with gold foil connections to the crystal electrodes. The entire assembly plugged directly into the oscillator module to reduce the length of the lead wiring. Liquid was passed across the top of the crystal. The entire system, including liquid samples and syringes was placed in a temperature controlled box at 30°C (kOS”C). Five liquids were used, water and 5, 10, 15 and 20% glycerol (ACS grade, Fisher Scientific Co., Fair Lawn, NJ) by weight in water. The density and viscosity of these solutions were taken from Miner and Dalton [241. The crystal surface mass was increased in steps by plating silver onto the wet electrode. The plating was performed by passing approximately 100 PA from a silver wire anode through a 0.01 M silver nitrate (ACS reagent grade, Aldrich, Milwaukee, WI) electrolyte. The crystal was not removed from the support assembly during the plating. The plating current was obtained from the voltage drop across a sense resistor and the plating time measured by a stopwatch. The deposited mass was calculated from the total charge passed through the cell. Two crystals were plated. Each experiment was performed by measuring the frequency and
AGC signal for each liquid. Sufficient liquid was passed across the crystal to ensure the glycerol concentration and the frequency was allowed to stabilize before data were recorded. After the five liquids were used, the cell was flushed with deionized water followed by silver nitrate solution and the plating was done. The silver wire anode was passed through one of the sample tubes to the space near the crystal. After plating, the crystal was again flushed with deionized water. This process was repeated 15 times for the first crystal and 18 times for the second.
3. Results The resistance data obtained from the two plating experiments are shown in Fig. 4. The data
0
5 &Mass(rn&m,
Fig. 4. Series resistance data. 0, Water. *, 5% Glycerol. A, 10% Glycerol. l , 15% Glycerol. +, 20% Glycerol.
G.L. Hayward, G.Z. Chu /Analytica Chimica Acta 288 (1994) 179-185
*
1
0.9
OS
1
1.06
1.1
1.15
1.2
1.25
I 1.3
w~~~~w(kg/m*=')
Fig. 5. Series resistance vs. liquid properties. 0, Present data. A, Previous data [IS].
are grouped as 5 horizontal lines, each corresponding to a different liquid medium. It is apparent from this that the amount of mass plated onto the crystal electrode has little effect on the viscous resistance. The increase at 9 pg observed in the data from one of the crystals can be attributed to surface roughness. At the end of each experiment, the crystal was examined. The silver was not deposited uniformly, but rather was concentrated in a few active areas on each crystal. Yang et al. [25] have shown that surface roughness increases the viscous resistance. Fig. 5 presents these data as a function of the liquid properties. The data are linear in (pp)i/‘. The regression gave R* = 0.968with a standard error of the resistance estimate of 2.6 Ohm. This is in agreement with equation 3. An electrode area correction from the resistance model derived by Hayward [18] was applied to data from that study. These data, also shown in Fig. 5, agree well with the present data. The effect of deposited mass on the frequency shift is shown in Fig. 6. Here the frequency shift is the difference between the operating frequency of a plated crystal and that of the unplated crystal operating in the same liquid medium. The relationship is linear CR*= 0.998) and is in reasonable agreement with the Sauerbrey equation [ll. The difference in slopes suggests that the plating current efficiency was about 96%. This may be
183
due to current leakage across the plating cell, or to the decomposition of water. The plating voltage was not controlled. No effect of the medium viscosity was noted in these data. These plating experiments have shown that the equivalent resistance of a crystal is related to the viscosity and density of a liquid medium. The deposition of mass onto a crystal causes a frequency shift, but does not affect the equivalent resistance of the crystal. Moreover, when the frequency shift caused by mass loading is calculated from the frequency of a crystal operating in a particular medium, the properties of the medium do not affect the relationship between the mass and the frequency shift. These conditions are necessary, but not sufficient for the design of a mass and viscosity sensor to operate in an unknown medium. The resistance of the crystal in an unknown solution can be used to obtain the frequency shift from a crystal operating in air by calculating (pp)‘/* from the regression of Fig. 5 and then applying Eq. 2. To test this, data from 5 crystals, including those used in the plating experiments, are presented in Fig. 7. Two complicating factors emerge from these data. The first factor is the oscillator phase shift. At high phase shifts, the crystal operating frequency is greatly affected by the crystal resistance 1181. The oscillator used in this study had a phase shift
Fig. 6. Frequency shift due to deposited mass. 0, Water. * ,
5% Glycerol. A, 10% Glycerol. n , 15% Glycerol. +, 2Q% Glycerol.
184
G.L. Hayward, G.Z. Chu /Analytica Chimica Acta 288 (1994) 179-185
of +77.8 degrees. This value was obtained by measuring the operating frequency of three calibrated reference crystals and is in good agreement with the frequency response measurement reported previously [18]. The frequency shifts calculated from the model of JSanazawa and Gordon [81 were corrected by adding the frequency shifts calculated from the BVD equivalent circuit with resistances taken from Fig. 5. The result overprediets the frequency shift by about 1500 Hz. The second complicating factor is the mounting resistance. When a crystal is clamped between two O-rings, the energy lost to the O-ring depends on the orientation of the O-ring on the crystal and on the clamping pressure. The effect of these is enhanced when liquid increases the coupling between the O-ring and the crystal. From the BVD model at 77.8 degrees phase shift, a resistance of 30.4 Ohm will give a 1500 Hz frequency shift. This resistance is not unreasonable for mounting since the reference crystals mounted with two small spring clips had a measured resistance of 8 to 10 Ohm. Much more energy may be expected to be dissipated by O-ring mountings. The discrepancy between the curves shown in Figure 7 may, therefore, be attributed to mounting losses. By changing the reference frequency to that of an unplated crystal operating in pure water, the subtraction to get frequency shift values compen-
-1
2
Fig. 8. Frequency shift from operation in water. A, Crystal 1 (before plating). n , Crystal 2 (before plating). *, Crystal 3. +, Crystal 4. 0, Crystal 5.
sates for the mounting resistance. These frequency shift data are shown in Fig. 8. Since the absolute values of the frequency shift are smaller, the nonlinearity of the oscillator phase shift component of the frequency shift is emphasized. A quadratic equation fitted the data well (R* = 0.987 with a standard error of frequency shift estimate of 40.2 Hz). The unplated frequency in an unknown medium can be obtained from (pp)‘/’ which in turn is related to the resistance or to the AGC voltage. This may then be subtracted from the measured oscillation frequency to obtain the mass loading. As in the network analyzer method, three measurements are required, the unplated frequency in water, the AGC voltage and the oscillation frequency.
4. Conclusions
Fig. 7. Frequency shift from dry crystal operation. A, Crystal 1 (before plating). l , Crystal 2 (before plating). *, Crystal 3. + , Crystal 4. 0, Crystal 5.
An inexpensive mass and viscosity sensor based on an AGC oscillator can be designed to operate in an unknown medium. The AGC voltage is affected only by the liquid medium so that a viscosity or density correction can be applied to the measured frequency shift to obtain the mass loading from the Sauerbrey equation [ll. Errors due to the oscillator phase shift and the crystal mounting losses can be removed by calibration.
G.L. Hayward, G.Z. Chu /Analytica Chimica Acta 288 (1994) 179-185
5. List of symbols
A fo
i k L viscous
R2 R viscous
z viscous Af
Am CL P c-r
Crystal electrode area, cm2 Crystal frequency, Hz Square root of - 1 Frequency shift constant, cm2 g-’ Viscous inductance, Henry Correlation coefficient from linear regression Viscous resistance, Ohm Viscous impedance, Ohm Frequency shift, Hz Change in surface mass, g Liquid viscosity, g cm-’ s-l Liquid density, g cmW3 Acoustic coupling coefficient, Ohm cm2 g-’
6. Acknowledgement The authors would like to thank Dr. M. Thompson at the University of Toronto for allowing the use of the Hewlett Packard network analyzer. The financial support of the National Science and Engineering Research Council of Canada is gratefully acknowledged. 7. References 111G. Sauerbrey, Z. Phys., 155 (1959) 206. [21M. Thompson, A.L. Kipling, W.C. Duncan-Hewitt, L.V. Rajakovic, and B.A. C&c-Vlasak, Analyst, 116 (1991) 881. 131 R. Schumacher, R., Angew. Chem. Int. Ed. Engl., 29 (1990) 329.
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