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Analytical advantages of monitoring a particular characteristic frequency in a thickness shear mode acoustic wave sensor
Sensors and Actuators B 78 (2001) 331±336
Analytical advantages of monitoring a particular characteristic frequency in a thickness shear mode acoustic wave sensor M.T.S.R. Gomes*, M.I.S. VerõÂssimo, J.A.B.P. Oliveira Department of Chemistry, University of Aveiro, 3810-193 Aveiro, Portugal
Abstract The oscillator or active method, where just the series resonance frequency (fs) can be measured, has been the method of choice for analytical applications of bulk acoustic wave sensors. However, the present work shows that an increase in the analytical signal can be obtained if the frequency at minimum impedance (fn) is measured. An example is given, where quantitative analysis is only possible if fn is measured instead of fs. Sensitivity of a particular analysis can be improved if a previous study is performed in order to select the most suitable characteristic frequency (fs, fn or fp) to be monitored. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Piezoelectric quartz crystals; Passive method; Ethanol; Fructose; Glycerol
1. Introduction Most of the applications involving sensors based on piezoelectric quartz crystals rely on the monitoring of the oscillator resonant frequency changes, which are correlated with gravimetric changes. Sauerbrey equation [1] is used to correlate those frequency changes with added mass. 2f 2 Dm Df p mQ rQ A However, the acoustic wave sensor, especially when operated in liquid phase, is affected by other interfacial properties. Nomura and Minemura [2] were the ®rst to verify that the frequency depended on the density and conductivity of the solution. Nomura and Okuhara [3] suggested in 1982 that the frequency of a crystal immersed in an organic liquid containing no electrolyte is in¯uenced only by the density (d) and the viscosity (Z) of the solution: DF ad1=2 bZ1=2 and verified that the crystal did not oscillate in liquids of high density and viscosity. Yao and Zhou [4] veri®ed that for mixtures of water/ organic solvents, the frequency depended also on the dielectric constant of the liquid. In 1985, the ®rst physical models were developed by Bruckenstein and Shay [5], and Kanasawa and Gordon [6]. *
Corresponding author. E-mail address: [email protected] (M.T.S.R. Gomes).
Bruckenstein and Shay [5] used dimensional analysis to develop the following equation: DF
2:26 106 nf 3=2 Zl dl 1=2
where n 1 or 2 depending on whether one or two faces of the crystal contact the solution. Kanasawa and Gordon [6] treated the quartz (Q) as a lossless elastic solid and the liquid as a purely viscous fluid. The frequency shift arose from coupling the oscillation of the crystal, a standing shear wave, with a damped propagating shear wave in the liquid. The derived expression for the frequency shift: Zl dl 1=2 3=2 DF f pmQ dQ was similar to the one of Bruckenstein and Shay, and both predict that density and viscosity are the relevant parameters for the operation of a quartz crystal in a liquid. Kurosawa et al. [7] showed that the circuit in¯uenced the frequency changes measured in solutions and that the equations of Bruckenstein and Shay and Kanasawa and Gordon did not hold for electrolyte or polymer solutions. Schumacher et al. [8±10] introduced a new factor, surface roughness, in the parameters that affect the oscillation frequency. Frequency became a function of DmL, the mass per unit area of the liquid con®ned in the cavities of the roughness surface, a function of e, the mean diameter of the hemicylinders with liquid entrapments. 2f0 2 Dml Dfs p mQ d Q
0925-4005/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 4 0 0 5 ( 0 1 ) 0 0 8 3 5 - 8
Dml 12 dl e
332
M.T.S.R. Gomes et al. / Sensors and Actuators B 78 (2001) 331±336
Heusler et al. [11] considered surface stress influence on the resonant frequency. Hager and Verge [12], and Hager [13] developed a model based on hydrodynamic coupling between the oscillating crystal and adjacent liquid. Liquid dielectric constant is considered, and the empirical equation contains constants dependent on the crystal equivalent circuit and the working conditions. DF
k1 D dl Zl 1=2 f Del
Shana et al. [14] presented an equation for thin films of viscous liquid of height h, where k2 is the wave number in the crystal in the y-direction. 1=2 Zl dl 3=2 DF f jtanh k2 hj pdQ C 66 If h is suf®ciently large, the equation is similar to the one of Kanasawa and Gordon if the piezoelectric effect is neglected. Thompson et al. proposed that the changes in interfacial surface structure [15] and interfacial properties such as free energy and slippage were related to the resonance frequency of a crystal in contact with a liquid, and reviewed the theoretical aspects of operation of a thickness shear mode acoustic wave sensor in contact with a liquid [16]. In the oscillator method, the crystal is part of the oscillating circuit, and a sole parameter, the series resonant frequency, is measured. Besides the fact that a sole parameter cannot completely characterise the sensor, the resonant frequency depends on the capacitance in series with the crystal and in some instances on the type of oscillator used, and the crystal does not oscillate in solutions of high viscosity [16,7]. An impedance analyser measures the voltage applied across the crystal, at several frequencies, and the current ¯owing through it. The series resonant frequency is the same as that measured by the oscillator method, but impedance is also known. Some of the limitations associated with the oscillator method can be circumvented, as other frequencies, for instance the frequency at minimum impedance (fn) can be measured when series frequency does not exist. Besides, series frequency, parallel frequency and frequency at minimum impedance, among others, show different dependence on equivalent circuit parameters [17±19], and are expected to change in a different manner with solution properties [16,19,20]. This different dependence on solution properties is here explored from an analytical point of view. An analyst always seeks to improve the signal to noise ratio and sensitivity. Measurements of series resonant frequency (fs), parallel frequency (fp) and frequency at minimum impedance (fn) were obtained for a bare crystal in contact with a few analytes. The results are here presented and discussed in terms of the analytical performance of the sensor.
Fig. 1. Experimental layout.
2. Experimental 2.1. Apparatus Fig. 1 shows the experimental layout. A constant nitrogen pressure of 0.1 bar is maintained inside two reagent bottles. The pressure is controlled by a pressure regulator (OMNIFIT 3101) and is the driving force for the displacement of the liquids from the bottles into the crystal cell. One of the bottles contains water (Milli-Q) and the other the sample. A three-way valve selects the ¯uid that enters the crystal cell (International Crystal Manufacturing Co. Inc. Ð ICM). The bottle and tubes (0.8 mm i.d. made of Te¯on) were immersed in a thermostatic bath set to 208C, as temperature variations would affect both density and viscosity. Although the crystal cell is not thermostated no signi®cant temperature variations are expected due to the short liquid residence times and the fact that room temperature is close to 208C. The piezoelectric crystals were 9 MHz, polished AT-cut HC-6/U with gold electrodes (International Crystal Manufacturing Co. Inc. Ð ICM). An HP 4395A network/spectrum analyser coupled to an HP 43961A impedance test kit was used to measure the impedance and phase of the quartz crystal at several frequencies. Measurements were initially made with a frequency span that extended over the entire region of interest of the crystal (from 8995000 to 9025000 Hz). Then the network analyser scanned 801 points around each of the measured frequencies, with 100 Hz bandwidth. Each measurement is an average of eight scans. 2.2. Reagents Ethanol absolute (Merck 1.00983) p.a. grade, glycerol (Merck 104093) and fructose (Panreac 142728), both purissimum grade, were all used without further puri®cation. All solutions were prepared weighting pure compounds and Milli-Q water. Nitrogen was N45 grade from ``ArLõÂquido''.
M.T.S.R. Gomes et al. / Sensors and Actuators B 78 (2001) 331±336
2.3. Procedure Milli-Q water was ¯owing through the crystal cell until constant frequency readings were obtained. Those readings were recorded and used as reference values. A solution of ethanol, glycerol or fructose was then allowed to ¯ow over the piezoelectric crystal and the difference between the parameter readings and reference readings was computed. After each experiment, water was passed over the crystal until complete recover was achieved and reference values were restored. 3. Results and discussion Table 1 shows the observed frequency decreases, obtained by the passive method, for solutions of 8% and 14% (w/w) in ethanol, fructose or glycerol. For each solution, the values for the frequency shifts for the series resonant frequency (Dfs), parallel frequency (Dfp) and frequency at minimum impedance (Dfn) are all different. However, each of the mentioned frequencies shifts, Dfn, Dfs, and Dfp, increase with the product of density (d) and viscosity (Z) of the solution. This correlation between frequency and bulk
Table 1 Frequency decrease at minimum impedance (Dfn), series frequency decrease (Dfs) and parallel frequency decrease (Dfp), for solutions of ethanol, fructose or glycerol, with the correspondent square root of the product of density (d) and relative viscosity (Z) Dfn Glycerol 8% (w/w) Fructose 8% (w/w) Ethanol 8% (w/w) Glycerol 14% (w/w) Fructose 14% (w/w) Ethanol 14% (w/w)
321 351 495 576 688 840
Dfs
10 7 6 6 7 8
278 315 403 468 574 678
(dZ)1/2
Dfp
8 12 6 9 7 6
157 184 251 254 360 427
11 5 5 7 9 8
Fig. 2. Frequency shifts observed with ethanol solutions.
1.1138 1.1267 1.1676 1.2204 1.2509 1.3110
333
Table 2 Sensitivity of the sensor to ethanol, and coefficient of determination, when the frequency at minimum impedance (fn), series frequency (fs) or fp were measured
fn fs fp
Slope (Hz/ethanol % (w/w))
r2
56.7 2.4 46.8 3.0 29.7 2.5
0.999 0.997 0.995
properties of the liquid is here observed regardless the different number of hydroxy groups, chain length or structure of the mentioned compounds. Several aqueous ethanol solutions were prepared, and the frequency shifts, relative to water, are shown in Fig. 2. The quartz crystal used for these measurements was different from the one used in the experiments of Table 1 and, as frequency depends on the surface roughness [10], results are not necessarily comparable to the ones displayed on Table 1. Comparing the frequency shifts for fs, fp and fn versus the ethanol content, it can be concluded that although, the shape of the curves is similar for all the measured frequencies, the highest shifts were observed for fn. Table 2 shows the slope of the linear calibration lines, obtained with the ®rst piezoelectric quartz crystal, for ethanol in the range from 8 to 14% (w/w). Those experiments showed that ethanol, within the range of the normal content of table wines, can be determined measuring any of the three frequencies although, sensitivity is highest when fn is the monitored parameter. Fig. 3 shows Dfn, Dfs and Dfp for solutions of fructose within the normal contents for white wines produced from Portuguese grapes of varieties maria gomes and bical, and Table 3 shows the slopes of the linear calibrations for these data. For fructose, an increase in the analytical signal is also observed if fn is monitored instead of fs. Besides, Table 3 shows than an increase in sensitivity is obtained, if fn or fs are measured instead of fp.
Fig. 3. Frequency shifts observed with fructose solutions.
334
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Table 3 Slopes and coefficients of determination for the observed fn, fs and fp, for the fructose solutions displayed in Fig. 3
fn fs fp
Table 4 Frequency shifts observed for three replicate measurements of solutions of equal density (1.03) of fructose and glycerol
Slope (Hz/fructose % (w/w))
r2
Fructose
44.5 2.6 43.7 3.7 21.1 3.0
0.999 0.996 0.994
Dfn
Dfs
Dfp
Dfn
Dfs
Dfp
313 313 315
285 286 286
168 163 164
242 242 239
210 209 212
128 131 128
314 1
286 1
165 3
241 2
210 2
129 2
Mean Standard deviation
Glycerol
Table 5 Shifts in fs, fp and fn with increasing viscosity of the solution Glycerol ! fructose Displacement Displacement Displacement Displacement
Fig. 4. Frequency shifts observed with glycerol solutions.
Fig. 4 shows Dfn, Dfs and Dfp for solutions of glycerol within the range of concentrations usually found in wine. Quanti®cation of glycerol is not possible if fs or fp are monitored. These experiments have shown the analytical importance of choosing a particular frequency for measurements, but no insight into the physical reasons for that choice. Density and
in in in in
Df Dfp Dfn Dfs
Dfp
76 36 73 30
4 8 5 9
viscosity are known to play a major role on the frequency of the piezoelectric quartz crystal, but the polarity and conductivity of the liquid also in¯uence it, mainly fp [19±23]. Interfacial properties viscosity, density and dielectric constant are the important parameters that determine the frequency of the quartz crystal [19]. Unfortunately, these interfacial properties are unknown and only the bulk properties of the liquid, different although related, are easily accessible from literature, or measured. Table 4 shows Dfn, Dfs and Dfp for solutions of fructose and glycerol prepared with quantities appropriate to obtain solutions of the same density, 1.03. A plot of impedance and
Fig. 5. Impedance and phase vs. frequency for Milli-Q water, a glycerol solution 6.08 wt.%, and a fructose solution 7.5 wt.%. Frequencies at minimum impedance (fn), series frequency (fs) and parallel frequency (fp) are marked.
M.T.S.R. Gomes et al. / Sensors and Actuators B 78 (2001) 331±336
335
Table 6 Frequency shifts observed for three replicate measurements of solutions of equal viscosity (relative viscosity to water is 1.25) of ethanol, fructose and glycerol Ethanol
Mean Standard deviation
Fructose
Dfn
Dfs
Dfp
Dfn
Dfs
Dfp
Dfn
Dfs
Dfp
351 355 355
281 283 280
177 178 175
375 381 381
324 326 332
195 202 197
368 360 362
306 310 305
171 176 176
354 2
281 2
177 2
379 3
327 4
198 4
363 4
307 3
174 3
Table 7 Shifts in fs, fp and fn with increasing density of the solution
Displacement Displacement Displacement Displacement
in in in in
Dfs Dfp Dfn Dfs
Dfp
Glycerol
Ethanol ! fructose
Ethanol ! glycerol
46 21 25 25
26 3 10 19
9 10 10 15
8 8 12 11
phase for water, and these particular solutions of fructose and glycerol can be seen on Fig. 5. Besides broadening of the phase curve and decreasing of the intensity of the resonance peaks, a displacement to lower frequencies can be noticed. Table 4 shows that, as before, fn gives the highest frequency shift signals. Observation of data also shows highest frequency shifts for all three frequencies for fructose, which can be explained by the fructose highest viscosity, which is 1.213 in relation to water, at 208C, while relative viscosity for glycerol is only 1.089. Besides, the difference between fn and fp is also greater for fructose than for glycerol, which indicates the importance of viscoelastic changes in the relative shift between these frequencies. Relative shifts on fs and fn, changing from glycerol to fructose are, however, very similar. As a conclusion, one can say that such an increase in viscosity produces a higher shift in fs and fn than in fp (Table 5). Table 6 shows Dfn, Dfs and Dfp for solutions of ethanol, fructose or glycerol prepared with quantities appropriate to obtain solutions of the same relative viscosity of 1.25 (ratio of absolute viscosity at 208C to the absolute viscosity of water). The effect of increasing density, when changing from ethanol to fructose (densities 0.9903 and 1.0342, respectively), or from ethanol to glycerol (densities 0.9903 and 1.0209, respectively), is a broadening of the phase curve, as the distance between Dfs and Dfp showed a small increase. As density increases, changing from ethanol to fructose, or to glycerol, larger shifts in Dfs than in Dfn or Dfp were recorded (Table 7). 4. Conclusions As a conclusion, it can be said that for all solutions, Dfn in relation to water was higher than Dfs or Dfp, which is
important for analytical purposes. Both changes in density and viscosity produced shifts in all of the three measured frequencies, and a broadening of the phase curve. From the experiments for solutions with equal density, it can be concluded that fn followed the decrease in fs and, therefore, viscosity changes, in the range here presented, could be easily detected by measuring fn or fs rather than fp. For solutions with equal viscosity, the change in density produced a larger shift in fs than in fn or fp, and in spite the fact that the biggest signals have been recorded measuring Dfn, sensitivity is improved if fs is the measured frequency. Conductivity was not discussed, although the signi®cant differences between fructose and alcohol solutions can in¯uence the results. Besides, it was not the purpose of this work to relate the characteristic frequencies to physical properties, but to show the analytical importance of measuring a particular characteristic frequency for a sample. The present results must be carefully analysed and each particular system must be studied. Extrapolation to other experiments must be carefully made as, for instance, heavy mass loading or high viscous damping produces an approximation between the fs and fp, until these frequencies cease to exist. References [1] G. Sauerbrey, Verwendung von Schwingquartzen zur WaÈgung duÈnner Schichten und zur MikrowaÈgung, Z. Phys. 155 (1959) 206±222. [2] T. Nomura, A. Minemura, Behaviour of a piezoelectric quartz crystal in an aqueous solution and the application to the determination of minute amounts of cyanide, Nipon Kagaku Kaishi (1980) 1621±1625. [3] T. Nomura, M. Okuhara, Frequency shifts of piezoelectric quartz crystals immersed in organic liquids, Anal. Chim. Acta 142 (1982) 281±284. [4] S.-Z. Yao, T.-A. Zhou, Dependence of the oscillation frequency of a piezoelectric crystal on the physical parameters of liquids, Anal. Chim. Acta 212 (1988) 61±72. [5] S. Bruckenstein, M. Shay, Experimental aspects of the use of the quartz crystal microbalance in solution, Electrochim. Acta 30 (1985) 1295±1300. [6] K.K. Kanasawa, J.G. Gordon II, The oscillation frequency of a quartz resonator in contact with a liquid, Anal. Chim. Acta 175 (1985) 99±105. [7] S. Kurosawa, E. Tawara, N. Kama, Y. Kobatake, Oscillation frequency of piezoelectric crystal in solutions, Anal. Chim. Acta 230 (1990) 41±49.
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[8] R. Schumacher, G. Borges, K.K. Kanazawa, The quartz microbalance: a sensitive tool to probe surface reconstructions on gold electrodes in liquid, Surf. Sci. 163 (1985) L621±L626. [9] W. StoÈckel, R. Schumacher, In situ microweighing at the junction metal/electrolyte, Ber. Bunsenges. Phys. Chem. 91 (1987) 345±349. [10] R. Schumacher, The quartz microbalance: a novel approach to the in situ investigation of interfacial phenomena at the solid/liquid junction, Angewandte 29 (1990) 329±438. [11] K.E. Heusler, A. Grzegorzewski, L. JaÈckel, J. Pietrucha, Measurement of mass and surface stress at one electrode of a quartz oscillator, Ber. Bunsenges Phys. Chem. 92 (1988) 1218±1225. [12] H.E. Hager, P.D. Verge, Multicomponent gas analysis via transient operation of liquid coating piezoelectric crystal detectors, Sens. Actuators 7 (1985) 271±283. [13] H.E. Hager, Fluid property evaluation by piezoelectric crystals operating in the thickness shear mode, Chem. Eng. Commun. 43 (1986) 25±38. [14] Z.A. Shana, D.E. RadtkeTawara, U.R. Kelkar, F. Josse, Theory and application of a quartz resonator as a sensor for viscous liquids, Anal. Chim. Acta 231 (1990) 317±320. [15] M. Thompson, C.L. Arthur, G.K. Dhaliwal, Liquid phase piezoelectric and acoustic transmission studies of interfacial immunochemistry, Anal. Chem. 58 (1986) 1206±1209. [16] M. Thompson, A.L. Kipling, W.C. Duncan-Hewitt, L.V. Rajakovic, B.A. Cavic-Vlasak, Thickness shear mode acoustic wave sensors in the liquid phase, A Review, Analyst 116 (1991) 881±890. [17] M. Thompson, A.L. Kipling, Network analysis method applied to liquid phase acoustic wave sensors, Anal. Chem. 62 (1990) 1514±1519. [18] R. Beck, U. Pittermann, K.G. Weil, Impedance analysis of quartz oscillators, contacted on one side with a liquid, Ber. Bunsenges. Phys. Chem. 92 (1988) 1363±1368.
[19] M. Yang, M. Thompson, Multiple chemical information from the thickness shear mode acoustic wave sensor in the liquid phase, Anal. Chem. 65 (1993) 1158±1168. [20] M. Yang, H.C.M. Hellas, W. Zhu, Response of a thickness shear mode quartz crystal resonator upon hydrogel formation, Anal. Chim. Acta 351 (1997) 177±187. [21] M. Yang, M. Thompson, Thickness shear mode acoustic wave sensors and flow injection analysis, Anal. Chim. Acta 116 (1991) 881±890. [22] S. Hongbo, M. Thompson, Rheological and interfacial properties of nucleic acid films studied by thickness shear mode sensor and network analysis, Can. J. Chem. 74 (1996) 344±358. [23] M. Yang, M. Thompson, Perturbation of electrified interface and the response of the thickness shear mode acoustic wave sensor under conductive liquid loading, Anal. Chem. 65 (1993) 3591±3597.
Biographies M.T.S.R. Gomes is an associate professor at the University of Aveiro. She received a BS degree in chemical engineering from the University of Coimbra in 1983 and a PhD in analytical chemistry from the University of Aveiro in 1997. Her current research interests are in chemical sensors and environmental analytical chemistry. M.I.S. VerõÂssimo is a PhD student at the University of Aveiro. She received a BS degree in chemistry from the University of Aveiro in 1998. Her current research interests are in mass sensors. J.A.B.P. Oliveira is an associate professor at the University of Aveiro. He received a BS degree in chemical engineering from the Technical University of Lisbon in 1976 and a PhD in analytical chemistry from the University of Virginia, Charlottesville in 1985. His current interests are chemical sensors, chemometrics, and laboratory automation.
Analytical advantages of monitoring a particular characteristic frequency in a thickness shear mode acoustic wave sensor M.T.S.R. Gomes*, M.I.S. VerõÂssimo, J.A.B.P. Oliveira Department of Chemistry, University of Aveiro, 3810-193 Aveiro, Portugal
Abstract The oscillator or active method, where just the series resonance frequency (fs) can be measured, has been the method of choice for analytical applications of bulk acoustic wave sensors. However, the present work shows that an increase in the analytical signal can be obtained if the frequency at minimum impedance (fn) is measured. An example is given, where quantitative analysis is only possible if fn is measured instead of fs. Sensitivity of a particular analysis can be improved if a previous study is performed in order to select the most suitable characteristic frequency (fs, fn or fp) to be monitored. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Piezoelectric quartz crystals; Passive method; Ethanol; Fructose; Glycerol
1. Introduction Most of the applications involving sensors based on piezoelectric quartz crystals rely on the monitoring of the oscillator resonant frequency changes, which are correlated with gravimetric changes. Sauerbrey equation [1] is used to correlate those frequency changes with added mass. 2f 2 Dm Df p mQ rQ A However, the acoustic wave sensor, especially when operated in liquid phase, is affected by other interfacial properties. Nomura and Minemura [2] were the ®rst to verify that the frequency depended on the density and conductivity of the solution. Nomura and Okuhara [3] suggested in 1982 that the frequency of a crystal immersed in an organic liquid containing no electrolyte is in¯uenced only by the density (d) and the viscosity (Z) of the solution: DF ad1=2 bZ1=2 and verified that the crystal did not oscillate in liquids of high density and viscosity. Yao and Zhou [4] veri®ed that for mixtures of water/ organic solvents, the frequency depended also on the dielectric constant of the liquid. In 1985, the ®rst physical models were developed by Bruckenstein and Shay [5], and Kanasawa and Gordon [6]. *
Corresponding author. E-mail address: [email protected] (M.T.S.R. Gomes).
Bruckenstein and Shay [5] used dimensional analysis to develop the following equation: DF
2:26 106 nf 3=2 Zl dl 1=2
where n 1 or 2 depending on whether one or two faces of the crystal contact the solution. Kanasawa and Gordon [6] treated the quartz (Q) as a lossless elastic solid and the liquid as a purely viscous fluid. The frequency shift arose from coupling the oscillation of the crystal, a standing shear wave, with a damped propagating shear wave in the liquid. The derived expression for the frequency shift: Zl dl 1=2 3=2 DF f pmQ dQ was similar to the one of Bruckenstein and Shay, and both predict that density and viscosity are the relevant parameters for the operation of a quartz crystal in a liquid. Kurosawa et al. [7] showed that the circuit in¯uenced the frequency changes measured in solutions and that the equations of Bruckenstein and Shay and Kanasawa and Gordon did not hold for electrolyte or polymer solutions. Schumacher et al. [8±10] introduced a new factor, surface roughness, in the parameters that affect the oscillation frequency. Frequency became a function of DmL, the mass per unit area of the liquid con®ned in the cavities of the roughness surface, a function of e, the mean diameter of the hemicylinders with liquid entrapments. 2f0 2 Dml Dfs p mQ d Q
0925-4005/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 4 0 0 5 ( 0 1 ) 0 0 8 3 5 - 8
Dml 12 dl e
332
M.T.S.R. Gomes et al. / Sensors and Actuators B 78 (2001) 331±336
Heusler et al. [11] considered surface stress influence on the resonant frequency. Hager and Verge [12], and Hager [13] developed a model based on hydrodynamic coupling between the oscillating crystal and adjacent liquid. Liquid dielectric constant is considered, and the empirical equation contains constants dependent on the crystal equivalent circuit and the working conditions. DF
k1 D dl Zl 1=2 f Del
Shana et al. [14] presented an equation for thin films of viscous liquid of height h, where k2 is the wave number in the crystal in the y-direction. 1=2 Zl dl 3=2 DF f jtanh k2 hj pdQ C 66 If h is suf®ciently large, the equation is similar to the one of Kanasawa and Gordon if the piezoelectric effect is neglected. Thompson et al. proposed that the changes in interfacial surface structure [15] and interfacial properties such as free energy and slippage were related to the resonance frequency of a crystal in contact with a liquid, and reviewed the theoretical aspects of operation of a thickness shear mode acoustic wave sensor in contact with a liquid [16]. In the oscillator method, the crystal is part of the oscillating circuit, and a sole parameter, the series resonant frequency, is measured. Besides the fact that a sole parameter cannot completely characterise the sensor, the resonant frequency depends on the capacitance in series with the crystal and in some instances on the type of oscillator used, and the crystal does not oscillate in solutions of high viscosity [16,7]. An impedance analyser measures the voltage applied across the crystal, at several frequencies, and the current ¯owing through it. The series resonant frequency is the same as that measured by the oscillator method, but impedance is also known. Some of the limitations associated with the oscillator method can be circumvented, as other frequencies, for instance the frequency at minimum impedance (fn) can be measured when series frequency does not exist. Besides, series frequency, parallel frequency and frequency at minimum impedance, among others, show different dependence on equivalent circuit parameters [17±19], and are expected to change in a different manner with solution properties [16,19,20]. This different dependence on solution properties is here explored from an analytical point of view. An analyst always seeks to improve the signal to noise ratio and sensitivity. Measurements of series resonant frequency (fs), parallel frequency (fp) and frequency at minimum impedance (fn) were obtained for a bare crystal in contact with a few analytes. The results are here presented and discussed in terms of the analytical performance of the sensor.
Fig. 1. Experimental layout.
2. Experimental 2.1. Apparatus Fig. 1 shows the experimental layout. A constant nitrogen pressure of 0.1 bar is maintained inside two reagent bottles. The pressure is controlled by a pressure regulator (OMNIFIT 3101) and is the driving force for the displacement of the liquids from the bottles into the crystal cell. One of the bottles contains water (Milli-Q) and the other the sample. A three-way valve selects the ¯uid that enters the crystal cell (International Crystal Manufacturing Co. Inc. Ð ICM). The bottle and tubes (0.8 mm i.d. made of Te¯on) were immersed in a thermostatic bath set to 208C, as temperature variations would affect both density and viscosity. Although the crystal cell is not thermostated no signi®cant temperature variations are expected due to the short liquid residence times and the fact that room temperature is close to 208C. The piezoelectric crystals were 9 MHz, polished AT-cut HC-6/U with gold electrodes (International Crystal Manufacturing Co. Inc. Ð ICM). An HP 4395A network/spectrum analyser coupled to an HP 43961A impedance test kit was used to measure the impedance and phase of the quartz crystal at several frequencies. Measurements were initially made with a frequency span that extended over the entire region of interest of the crystal (from 8995000 to 9025000 Hz). Then the network analyser scanned 801 points around each of the measured frequencies, with 100 Hz bandwidth. Each measurement is an average of eight scans. 2.2. Reagents Ethanol absolute (Merck 1.00983) p.a. grade, glycerol (Merck 104093) and fructose (Panreac 142728), both purissimum grade, were all used without further puri®cation. All solutions were prepared weighting pure compounds and Milli-Q water. Nitrogen was N45 grade from ``ArLõÂquido''.
M.T.S.R. Gomes et al. / Sensors and Actuators B 78 (2001) 331±336
2.3. Procedure Milli-Q water was ¯owing through the crystal cell until constant frequency readings were obtained. Those readings were recorded and used as reference values. A solution of ethanol, glycerol or fructose was then allowed to ¯ow over the piezoelectric crystal and the difference between the parameter readings and reference readings was computed. After each experiment, water was passed over the crystal until complete recover was achieved and reference values were restored. 3. Results and discussion Table 1 shows the observed frequency decreases, obtained by the passive method, for solutions of 8% and 14% (w/w) in ethanol, fructose or glycerol. For each solution, the values for the frequency shifts for the series resonant frequency (Dfs), parallel frequency (Dfp) and frequency at minimum impedance (Dfn) are all different. However, each of the mentioned frequencies shifts, Dfn, Dfs, and Dfp, increase with the product of density (d) and viscosity (Z) of the solution. This correlation between frequency and bulk
Table 1 Frequency decrease at minimum impedance (Dfn), series frequency decrease (Dfs) and parallel frequency decrease (Dfp), for solutions of ethanol, fructose or glycerol, with the correspondent square root of the product of density (d) and relative viscosity (Z) Dfn Glycerol 8% (w/w) Fructose 8% (w/w) Ethanol 8% (w/w) Glycerol 14% (w/w) Fructose 14% (w/w) Ethanol 14% (w/w)
321 351 495 576 688 840
Dfs
10 7 6 6 7 8
278 315 403 468 574 678
(dZ)1/2
Dfp
8 12 6 9 7 6
157 184 251 254 360 427
11 5 5 7 9 8
Fig. 2. Frequency shifts observed with ethanol solutions.
1.1138 1.1267 1.1676 1.2204 1.2509 1.3110
333
Table 2 Sensitivity of the sensor to ethanol, and coefficient of determination, when the frequency at minimum impedance (fn), series frequency (fs) or fp were measured
fn fs fp
Slope (Hz/ethanol % (w/w))
r2
56.7 2.4 46.8 3.0 29.7 2.5
0.999 0.997 0.995
properties of the liquid is here observed regardless the different number of hydroxy groups, chain length or structure of the mentioned compounds. Several aqueous ethanol solutions were prepared, and the frequency shifts, relative to water, are shown in Fig. 2. The quartz crystal used for these measurements was different from the one used in the experiments of Table 1 and, as frequency depends on the surface roughness [10], results are not necessarily comparable to the ones displayed on Table 1. Comparing the frequency shifts for fs, fp and fn versus the ethanol content, it can be concluded that although, the shape of the curves is similar for all the measured frequencies, the highest shifts were observed for fn. Table 2 shows the slope of the linear calibration lines, obtained with the ®rst piezoelectric quartz crystal, for ethanol in the range from 8 to 14% (w/w). Those experiments showed that ethanol, within the range of the normal content of table wines, can be determined measuring any of the three frequencies although, sensitivity is highest when fn is the monitored parameter. Fig. 3 shows Dfn, Dfs and Dfp for solutions of fructose within the normal contents for white wines produced from Portuguese grapes of varieties maria gomes and bical, and Table 3 shows the slopes of the linear calibrations for these data. For fructose, an increase in the analytical signal is also observed if fn is monitored instead of fs. Besides, Table 3 shows than an increase in sensitivity is obtained, if fn or fs are measured instead of fp.
Fig. 3. Frequency shifts observed with fructose solutions.
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Table 3 Slopes and coefficients of determination for the observed fn, fs and fp, for the fructose solutions displayed in Fig. 3
fn fs fp
Table 4 Frequency shifts observed for three replicate measurements of solutions of equal density (1.03) of fructose and glycerol
Slope (Hz/fructose % (w/w))
r2
Fructose
44.5 2.6 43.7 3.7 21.1 3.0
0.999 0.996 0.994
Dfn
Dfs
Dfp
Dfn
Dfs
Dfp
313 313 315
285 286 286
168 163 164
242 242 239
210 209 212
128 131 128
314 1
286 1
165 3
241 2
210 2
129 2
Mean Standard deviation
Glycerol
Table 5 Shifts in fs, fp and fn with increasing viscosity of the solution Glycerol ! fructose Displacement Displacement Displacement Displacement
Fig. 4. Frequency shifts observed with glycerol solutions.
Fig. 4 shows Dfn, Dfs and Dfp for solutions of glycerol within the range of concentrations usually found in wine. Quanti®cation of glycerol is not possible if fs or fp are monitored. These experiments have shown the analytical importance of choosing a particular frequency for measurements, but no insight into the physical reasons for that choice. Density and
in in in in
Df Dfp Dfn Dfs
Dfp
76 36 73 30
4 8 5 9
viscosity are known to play a major role on the frequency of the piezoelectric quartz crystal, but the polarity and conductivity of the liquid also in¯uence it, mainly fp [19±23]. Interfacial properties viscosity, density and dielectric constant are the important parameters that determine the frequency of the quartz crystal [19]. Unfortunately, these interfacial properties are unknown and only the bulk properties of the liquid, different although related, are easily accessible from literature, or measured. Table 4 shows Dfn, Dfs and Dfp for solutions of fructose and glycerol prepared with quantities appropriate to obtain solutions of the same density, 1.03. A plot of impedance and
Fig. 5. Impedance and phase vs. frequency for Milli-Q water, a glycerol solution 6.08 wt.%, and a fructose solution 7.5 wt.%. Frequencies at minimum impedance (fn), series frequency (fs) and parallel frequency (fp) are marked.
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Table 6 Frequency shifts observed for three replicate measurements of solutions of equal viscosity (relative viscosity to water is 1.25) of ethanol, fructose and glycerol Ethanol
Mean Standard deviation
Fructose
Dfn
Dfs
Dfp
Dfn
Dfs
Dfp
Dfn
Dfs
Dfp
351 355 355
281 283 280
177 178 175
375 381 381
324 326 332
195 202 197
368 360 362
306 310 305
171 176 176
354 2
281 2
177 2
379 3
327 4
198 4
363 4
307 3
174 3
Table 7 Shifts in fs, fp and fn with increasing density of the solution
Displacement Displacement Displacement Displacement
in in in in
Dfs Dfp Dfn Dfs
Dfp
Glycerol
Ethanol ! fructose
Ethanol ! glycerol
46 21 25 25
26 3 10 19
9 10 10 15
8 8 12 11
phase for water, and these particular solutions of fructose and glycerol can be seen on Fig. 5. Besides broadening of the phase curve and decreasing of the intensity of the resonance peaks, a displacement to lower frequencies can be noticed. Table 4 shows that, as before, fn gives the highest frequency shift signals. Observation of data also shows highest frequency shifts for all three frequencies for fructose, which can be explained by the fructose highest viscosity, which is 1.213 in relation to water, at 208C, while relative viscosity for glycerol is only 1.089. Besides, the difference between fn and fp is also greater for fructose than for glycerol, which indicates the importance of viscoelastic changes in the relative shift between these frequencies. Relative shifts on fs and fn, changing from glycerol to fructose are, however, very similar. As a conclusion, one can say that such an increase in viscosity produces a higher shift in fs and fn than in fp (Table 5). Table 6 shows Dfn, Dfs and Dfp for solutions of ethanol, fructose or glycerol prepared with quantities appropriate to obtain solutions of the same relative viscosity of 1.25 (ratio of absolute viscosity at 208C to the absolute viscosity of water). The effect of increasing density, when changing from ethanol to fructose (densities 0.9903 and 1.0342, respectively), or from ethanol to glycerol (densities 0.9903 and 1.0209, respectively), is a broadening of the phase curve, as the distance between Dfs and Dfp showed a small increase. As density increases, changing from ethanol to fructose, or to glycerol, larger shifts in Dfs than in Dfn or Dfp were recorded (Table 7). 4. Conclusions As a conclusion, it can be said that for all solutions, Dfn in relation to water was higher than Dfs or Dfp, which is
important for analytical purposes. Both changes in density and viscosity produced shifts in all of the three measured frequencies, and a broadening of the phase curve. From the experiments for solutions with equal density, it can be concluded that fn followed the decrease in fs and, therefore, viscosity changes, in the range here presented, could be easily detected by measuring fn or fs rather than fp. For solutions with equal viscosity, the change in density produced a larger shift in fs than in fn or fp, and in spite the fact that the biggest signals have been recorded measuring Dfn, sensitivity is improved if fs is the measured frequency. Conductivity was not discussed, although the signi®cant differences between fructose and alcohol solutions can in¯uence the results. Besides, it was not the purpose of this work to relate the characteristic frequencies to physical properties, but to show the analytical importance of measuring a particular characteristic frequency for a sample. The present results must be carefully analysed and each particular system must be studied. Extrapolation to other experiments must be carefully made as, for instance, heavy mass loading or high viscous damping produces an approximation between the fs and fp, until these frequencies cease to exist. References [1] G. Sauerbrey, Verwendung von Schwingquartzen zur WaÈgung duÈnner Schichten und zur MikrowaÈgung, Z. Phys. 155 (1959) 206±222. [2] T. Nomura, A. Minemura, Behaviour of a piezoelectric quartz crystal in an aqueous solution and the application to the determination of minute amounts of cyanide, Nipon Kagaku Kaishi (1980) 1621±1625. [3] T. Nomura, M. Okuhara, Frequency shifts of piezoelectric quartz crystals immersed in organic liquids, Anal. Chim. Acta 142 (1982) 281±284. [4] S.-Z. Yao, T.-A. Zhou, Dependence of the oscillation frequency of a piezoelectric crystal on the physical parameters of liquids, Anal. Chim. Acta 212 (1988) 61±72. [5] S. Bruckenstein, M. Shay, Experimental aspects of the use of the quartz crystal microbalance in solution, Electrochim. Acta 30 (1985) 1295±1300. [6] K.K. Kanasawa, J.G. Gordon II, The oscillation frequency of a quartz resonator in contact with a liquid, Anal. Chim. Acta 175 (1985) 99±105. [7] S. Kurosawa, E. Tawara, N. Kama, Y. Kobatake, Oscillation frequency of piezoelectric crystal in solutions, Anal. Chim. Acta 230 (1990) 41±49.
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Biographies M.T.S.R. Gomes is an associate professor at the University of Aveiro. She received a BS degree in chemical engineering from the University of Coimbra in 1983 and a PhD in analytical chemistry from the University of Aveiro in 1997. Her current research interests are in chemical sensors and environmental analytical chemistry. M.I.S. VerõÂssimo is a PhD student at the University of Aveiro. She received a BS degree in chemistry from the University of Aveiro in 1998. Her current research interests are in mass sensors. J.A.B.P. Oliveira is an associate professor at the University of Aveiro. He received a BS degree in chemical engineering from the Technical University of Lisbon in 1976 and a PhD in analytical chemistry from the University of Virginia, Charlottesville in 1985. His current interests are chemical sensors, chemometrics, and laboratory automation.