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Sensing liquid properties with thickness-shear mode resonators
a&
Sensors and Actuators A 44 (1994) 209-218
ELSEVIER
7
PHYSICAL
Sensing liquid properties with thickness-shear mode resonators S.J. Martin,
G.C. Frye, K.O. Wessendorf
Micrmemor Research and Development Deparbnent, Sandia National Laboratories, Albuquerque, NM, UL-4 Received 26 April 1994; accepted 3 May 1994
Abstract The responses of smooth- and textured-surface thickness-shear mode (TSM) resonators in liquid are examined. Smooth devices, which viscously entrain a layer of contacting liquid, exhibit a response that depends on the product of liquid density and viscosity. Textured-surface devices, which also trap liquid in surface crevices, pores, etc., exhibit an additional response that depends on liquid density alone. Combining smooth- and textured-surface resonators in a monolithic sensor enables the liquid density and viscosity to be extracted simultaneously. Keywords:Liquid sensors; Thickness-shear
mode resonators
1. Introduction A thickness-shear mode (TSM) resonator typically consists of a thin disk of AT-cut quartz with circular electrodes patterned on both sides (Fig. 1). Due to the piezoelectric properties and crystalline orientation of the quartz, the application of a voltage between these electrodes results in a shear deformation of the crystal. The crystal can be electrically excited into several resonant modes, each corresponding to a unique stand-
ing shear-wave pattern (eigenmode) across the thickness of the crystal [l]. (The fundamental TSM is shown in Fig. 2.) For each of these modes, displacement maxima occur at the crystal faces, making these devices sensitive to the accumulation of surface mass and contacting fluid properties. The initial sensor application for quartz resonators was as deposition monitors in vacuum evaporations [2]. The linear change in resonance frequency that occurs with mass accumulation allows the device to function as a general-purpose gravimetric detector or ‘microbalance’. The device is easily instrumented as a sensor by incorporating it as the frequency-control element of an oscillator circuit. By monitoring the oscillation
Bottom Electrode
Fig. 1. Top (a) and side (b) views of a quartz thickness-shear (TSM) resonator.
mode
0924-4247/94/$07.00 0 1994 Elsevier Science S.A. All rights resewed SSDI 0924-4247(94)00806-S
Fig. 2. Cross-sectional view of a smooth TSM resonator with the upper surface contacted by a liquid. Shear motion of the smooth surface causes a thin layer of the contacting liquid to be viscously entrained.
210
S.J. Martin et al. I Sensors and Actuators A 44 (1994) 209-218
frequency, changes in surface mass density of roughly 1 ng cm-* can be measured; thus, the TSM resonator is commonly called a quartz-crystal microbalance
(QCM). A major obstacle to adapting piezoelectric resonators to liquid-sensing applications arises from mechanical damping by the liquid medium. Resonators with a surface-normal displacement component generate compressional waves in the contacting liquid. This causes acoustic energy to be radiated away, leading to severe resonance damping. TSMs, however, have only in-plane surface displacement. This results in much less acoustic radiation into a contacting liquid and a significant but tolerable amount of resonance damping. Oscillator circuits have been designed for the TSM resonator that overcome the damping contributed by low-viscosity liquids [3,4]. Since the mass sensitivity of the resonator is nearly the same in liquids as in air or vacuum, the device can be used as a sensitive solutionphase microbalance [5]. Applications include deposition monitoring [6], chemical species detection [7], immunoassay [8], liquid chromatographic detection [9], corrosion monitoring [lo] and electrochemical analysis [ll-131. In addition to functioning as a microbalance, the sensitivity of the TSM resonator to contacting fluid properties enables it to function as a monitor for these properties. Kanazawa and Gordon 1141 have shown that the TSM resonance frequency decreases with liquid immersion as (p#“, where p and q are the liquid density and viscosity, respectively. Muramatsu et al. [15] demonstrated that resonance damping also increases as (pq) lR. Martin et al. [16] derived an equivalent-circuit model to describe the frequency response of the TSM resonator in terms of the contacting liquid properties. This paper will describe the mechanical interactions between smooth- and textured-surface TSM resonators and a contacting liquid. These interactions influence the device response in a way that depends on the liquid properties, providing a means for measuring these properties.
2. Theory 2.1. Liquid coupling to the TSM resonator 2.1.1. Viscous entrainment
When the TSM resonator is operated in contact with a liquid, as shown in Fig. 2, the shear motion of the surface generates plane-parallel laminar flow in the adjacent liquid. The liquid velocity field v,(y), can be determined by solving the one-dimensional Navier-Stokes equation [14]:
(1) where p and n are the liquid density and shear viscosity, respectively, and (‘) denotes a time derivative. With a Newtonian liquid (for which q is independent of amplitude and frequency) and an oscillatory shear displacement at the solid-liquid boundary, the solution to Eq. (1) is [17] v&, t) =v,
1
exp - 7(1+j)y [
expo’4
where v, is the surface particle velocity, y is the distance into the liquid, 6 = (2q/0p)ln, o is the angular frequency (o= 2nj where f is frequency), and j = ( - l)ln. Eq. (2) represents a critically damped shear wave that is radiated into the contacting liquid by the oscillating resonator surface; 6 is the decay length of this shear wave, having, for example, a value of 250 nm in water at 20 “C when the frequency is 5 MHz. The liquid entrained by the oscillating smooth surface, shown in Fig. 2 and described by Eq. (2), is described as ‘viscously coupled’; this liquid does not move synchronously with the surface, but undergoes a progressive phase lag with distance from the surface. The extent to which liquid contact ‘loads’ the resonator, i.e., perturbs the resonance frequency or introduces damping, depends on the surface mechanical impedance 2, contributed by the liquid. The surface shear mechanical impedance arising from viscous entrainment (VE) is
where T, is the shear stress at the solid-liquid interface. Applying Eq. (3) to Eq. (2) yields the surface mechanical impedance due to viscous entrainment of a Newtonian fluid by an ideally smooth surface [18]:
2.1.2. Trapped l&id
Devices with textured surfaces, either randomly rough or regularly patterned, trap a quantity of fluid in excess of that viscously entrained by a smooth surface [19, 201. Vertical features constrain this trapped liquid to move synchronously with the oscillating crystal surface, rather than undergoing a progressive phase lag as occurs with viscously coupled liquid. This trapped liquid thus behaves much like an ideal mass layer contributing an area1 mass density ph. where p is the density and h, the effective thickness of the trapped liquid layer, is dependent upon the vertical relief of the surface texture.
SJ. Martin et al. / Senrors and Achuafors A 44 (1994) 209-218 Y
211
‘unperturbed’ portion of the circuit in Fig. 4. Parasitic capacitance, external to the device, is typically included with the static capacitance and it is denoted C,*. The motional branch of the equivalent-circuit model arises from electrical excitation of a shear-mode mechanical resonance in the piezoelectric quartz. It has beeri shown that surface loading of the resonator (e.g., liquid contact) leads to a change in this (electrical) motional impedance, AZ,,,, in proportion to the surface mechanical impedance Z, contributed by the load [18,22,23]:
Viscously-Entrained Llquld
I 1 Trapped Llquld
Fig. 3. Cmss-sectional view of a textured TSM resonator surface in contact with a liquid; liquid is trapped by surface cavities, in addition to being viscously entrained.
We can approximate the response of a texturedsurface resonator in liquid by separating the solid-liquid interface into two regions, as shown in idealized fashion in Fig. 3. If we imagine a boundary (dashed line) connecting peaks of the textured surface, then liquid below this boundary is ‘trapped’ and moves synchronously with the surface; liquid above this boundary is viscously coupled (as if by the boundaT) and undergoes a progressive phase lag with distance from the boundary. While this is an extreme simplification of the interaction between an oscillating rough surface and a liquid, it is useful in understanding the process. Consideration of these two regions in calculating the interfacial stress gives a surface mechanical impedance for the textured surface in contact with liquid of
,gw+zy3
(5)
where ZivE) is as given in Eq. (4) and the additional impedance contribution arising from trapped liquid (TL) is Zi=) 4 j&
(7) where N is the resonator harmonic number (N= 1,3,5,. ..); 0,=2& where fa is the unperturbed (dry) series resonance frequency; Z, = (c~qp$~, where kq and pq are the quartz shear stiffness and mass density, respectively; KZ is the electromechanical coupling factor. AT-cut quartz properties [24] are pq=2.947 x 1O’l dyne crnw2, pq =2.651 g cme3, KZ= 7.74X 10e3 and Z,= 8.839 x 10s g cm-* s-l. Eq. (7) indicates that liquid loading contributes additional elements to the motional impedance branch of the equivalent-circuit model of Fig. 4. 2.2.1. Vikous entrainment by a smooth su$ace
For viscous entrainment of liquid by an ideally smooth surface, Eqs. (4) and (7) can be combined to find AZ,. Since Zcve) has both a real and an imaginary component (both Gsitive), AZ,,, can be represented (for o near 0,) by a combination of a motional resistance, Rz, and an inductance, L,: AZ,,,=R,+j&. These elements of the equivalent-circuit model (Fig. 4), arising fromviscous entrainment by a single ideally smooth surface, are [18,25]:
(6)
If the effective thickness of trapped liquid h is small compared to the liquid decay length 6, then the relative response due to liquid trapping is small compared with the response due to viscous entrainment and may be neglected. This defines a criterion for hydrodynamic smoothness [18]: h K 6. If h is comparable to or larger than 6, then a significant additional response arises due to liquid trapping. 2.2. Equivalent circuit model The electrical characteristics of an unperturbed (Le., not contacted by liquid) quartz resonator can be described by a Butterworth-Van Dyke equivalent circuit [21]. This consists of a ‘static’ capacitance C, in parallel with a ‘motional’ branch (L,, C1, R,), as shown in the
I-
t
RI ___ ____________________---_____ Viscously Entrained
Mass Layer or Trapped Liquid
Fig. 4. Equivalent-circuit model to describe the electrical characteristics (for o near 4) of a TSM resonator with liquid loading. Contributions arise from both viscously coupled liquid and liquid trapped by surface asperities.
S.J. Martin et al. i Sensors and Actuators A 44 (1994) 209-218
212
where we note that R2 = o,L, for loading by a Newtonian fluid. For two-sided liquid contact, L, and R, are doubled. Electrical-energy storage in L, arises from the kinetic energy of the viscously entrained liquid layer (with effective thickness s/2); power dissipation in R2 arises from radiation of a critically damped shear wave into the liquid by the oscillating resonator surface. Thus, R, may be regarded as a ‘radiation resistance’. 2.2.2. Liquid trapping The motional impedance element arising from liquid trapping is found by combining Eqs. (6) and (7). Since Zin) is purely imaginary, AZ, can be represented as joL,. Thus, only the inductance LS, indicated in Fig. 4, arises from liquid trapping [16]: L3=
Nnioh
(9)
4K2GX~,~g)‘a
results
3.1. Swept-frequency impedance measurement The equivalent-circuit model of Fig. 4 describes the electrical characteristics of the TSM resonator over a range of frequencies near resonance. The electrical admittance (ratio of current i to applied voltage v in Fig. 2) is Y(n=joC,*+
$
(10)
m where the electrical motional impedance 2, Z,=(R,+R,)+jw(L1+L,+L,)+
90
:
$
60
;
30
E
0
: j
-30
.z & 2 -60 4.965
Electrical-energy storage in L, arises from the kinetic energy of the trapped liquid layer that oscillates synchronously with the device surface.
3. Experimental
-,
&
1
is (11)
3.1.1. Densi~-viscosity product from smooth resonator response
Fig. 5 shows the frequency response measured (points) as several glycerol solutions contacted one side of a TSM resonator. The dashed line indicates the series resonance frequency (f,) for the dry device. As pq increases with glycerol concentration (in water), the admittance magnitude plot shows both a translation of the series resonance peak toward lower frequency, as
4.970
Frequency
4.975
4.900
(MHz)
Fig. 5. Network analyzer measurements of resonator electrical admittance Y measured (points) and calculated (lines) near the fundamental resonance as the density-viscosity product (pq, Table 1) is varied by the concentration of glycerol in water (percentage glycerol is given in legend).
well as a diminution and broadening of the peak. The lines in Fig. 5 are calculated from the equivalent-circuit model (Fig. 4) using best-fit values of L2 and R, (L3 = 0 for a smooth device) along with values of C,,*, L,, C, and R, obtained by fitting measurements made on the dry device. The liquid density-viscosity product (p?7) is determined from L, and R2 using Eqs. (8) and is listed in Table 1. The pi values extracted from L, agree with those extracted from R, within 1% for all cases; these extracted values are 3-28% higher (error column) than the literature values of pq for glycerol solutions. When a textured-surface device is used, yielding a non-zero L, value, then ph can be determined. The major effect of surface texture is to translate the Y-f curves due to the addition of the L, element. 3.2. Oscillator measurements From the equivalent-circuit model, changes in the series resonance frequency Af and motional resistance AR due to viscous coupling and liquid trapping are given by [16]
213
S.J. Martin et al. t Sensors and Actuators A 44 (1994) 209-218 Table 1 Equivalent-circuit Glycerol cont.
elements and liquid density-viscosity product from the literature [27] and extracted from electrical admittance measurements Temperatore
Literature
L1
RZ
Extracted pq
CC)
P9
WI
(W
(2
(9’
(wt.%)
0
40 60 70
21.0 20.4 20.3 20.3
cm -’
Error (%)
s-9
cmw4 s-‘)
0.0097 0.0414 0.129 0.250
0.379 0.736 1.24 1.78
12.1 23.5 39.6 56.8
from L2
from RZ
0.0124 0.0469 0.133 0.274
0.0124 0.0466 0.132 0.273
28 13 3 9
Table 2 Element values for the oscillator circuit of Fig. 6 Value
Element
5V 4.7 PH 220 pF 150 n 100 n 0.01 pF 1kCl 825 n
N-9 The first term of Eq. (12a) and Eq. (12b) arises from viscous entrainment of liquid, while the second term of Eq. (12a) arises from liquid trapping. 3.2.1. Oscillator circuit An oscillator circuit capable of driving the TSM resonator in fairly damped liquid media has been described by Wessendorf [4]. Fig. 6 shows a schematic of this oscillator circuit, with element values given in Table 2. This oscillator tracks the series resonance frequency of the crystal, providing an r.f. output (vor) indicating frequency f,, and a d.c. voltage (V,,) proportional to the motional resistance R = (R, + R,). Measuring changes in these responses upon immersion give
Af and AR; Eqs. (12) can then be used to infer liquid properties. The oscillator circuit of Fig. 6 is essentially a noninverting differential amplifier with positive feedback designed to be controlled by the resonator connected between the base of Q, and ground. The negative feedback provided by Rrmakes the oscillation conditions independent of the transistor /3 and forces the oscillation conditions to be a function of resonator resistance R and transistor transconductance g,,, (g,,,=I&!6 mV, where I, is the bias current in each transistor, Q1 and QZ, at 25 “C). The oscillator loop gain is
R
A=@kn)+g@)
(13)
where
“,c/, Fig. 6. Oscillator circuit designed to operate the TSM resonator in liquid media to provide fwo outputs: Vo, (r.f. output) indicates series resonance frequencyf,; Vo, (d.c. output) is proportional to motional resistance R.
MC
g(R)= R+R,+Rf
(14)
Two conditions are required for oscillation to occur: A must be real (LA =0) and p] > 1. The second condition is maintained by the automatic level control (ALC) circuit. It varies the bias current in Q1 and Q2, via the voltage-controlled current source Q,, to maintain PI 21. The control voltage Vo, required to maintain oscillation is indicative of crystal damping and is taken as an output. The rate at which V,,varies with resonator resistance (R) is controlled by the negative feedback term g(R), Eq. (14). For low values of R, g(R) is proportional to
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S.J. Martin et al. I Sensors and Actuators A 44 (1994) 205-218
R; this allows V,,, to vary substantially with R, providing good sensitivity to changes in the liquid density-viscosity product (Eq. (12b)). At high values of R, the appearance of R in the denominator of Eq. (14) causes g(R) to saturate. This allows the resonance condition (PI > 1) to remain attainable with high liquid damping (large pq) and oscillation to be sustained over a wide range of liquid properties. When the resonator resistance is large, due to operation in high-pq liquids, the oscillator has a tendency to oscillate at spurious frequencies predominantly determined by the static capacitance of the resonator. The tank circuit consisting of L,, C,, and R, is tuned to the resonator frequency; the a.c. impedance from collector to ground is real and equal to R, at fs.This tank circuit helps reject spurious oscillation modes at frequencies away from the resonator resonance. The oscillation condition also requires the phase of A to be zero. This implies that g(R) is real, i.e., has zero phase also. Since the impedance from the collector to base of Qz is dominated by R, and is thus real, then the resonator impedance must also be real and have zero phase angle. The two frequencies at which the resonator impedance has zero phase are the series (_fJ and parallel (f,) resonances. The series resonance impedance is much lower than the parallel resonance impedance; since the circuit tends to oscillate at the lower-gain condition, it tracks the series resonance. In a refinement of the previous argument, the collector-base capacitance (Cbc) causes the impedance phase from the collector to base of Qz to be slightly negative. It can be shown that if Rr>R,, then the phase of the resonator impedance at oscillation is equal to the phase of the impedance from the collector to base of QZ. Thus, the oscillator will track a resonator impedance phase slightly less than 0” (e.g., -Y). At low values of R, this frequency is very close to fs;at higher R values, the oscillation begins to deviate substantially from fs. The oscillator circuit of Fig. 6 will sustain oscillation for motional resistances up to approximately 2 kfI. From Eq. (12b), this enables resonator operation in liquids with pq values up to 0.34 g’ cme4 s-’ (onesided contact) or 0.086 g” cm-4 s-* (two-sided contact). For a liquid with a density of 1 g cmm3, these translate into viscosity values of 34 and 8.6 CP for one- and twosided contact, respectively. 3.2.2. Liquid density-viscosity product from Af and AR Fig. 7 shows the change in series resonance frequency Af and motional resistance AR measured versus the liquid parameter (pq)lR. Measurements were made using a network analyser [18] on a smooth and a rough device as glycerol solutions contacted one side. The rough resonator was fabricated by polishing the quartz crystal with 10 pm abrasive particles before depositing
3
E
2-
%
-0.0
0.1
0.2
0.3
0.4
0.5
0.6
(p~-#‘~ (g cm-*s-l”) Fig. 7. Changes in series resonance frequency, A& and motional resistance, AR, vs. the liquid parameter (p~)‘~ for TSM resonators with two different surface roughnesses.
the conformal Cr/Au electrodes. The surface roughness was quantified using a Wyko RST (Tucson, AZ) profiler. This instrument uses a vertical-scanning interference microscope to obtain a non-contacting surface profile with a 3 nm vertical resolution and a 0.5 pm lateral resolution. The smooth device has an average roughness < 10 nm, much smaller than the liquid decay length S. For this device, the measured frequency shifts and motional resistance changes are nearly equal to the predictions (dashed lines, Eqs. (12) with h = 0) for an ideally smooth surface. The rough device has an average roughness of 243 nm, comparable to the liquid decay length: 6= 250-1200 nm for the glycerol solutions tested. This device exhibits a large additional frequency shift of approximately 0.87 kHz at (~3)‘” =0 due to liquid trapping in the randomly rough surface. From Eq. (12a), this gives h = 150 nm, or roughly 63% of the optically measured average surface roughness. The rough device also exhibits increased damping over the smooth device, indicating that Z,(TIJ (Eq. (6)) also has a small real component. This implies a slightly higher energy dissipation by the rough surface, thought to arise from the generation of compressional waves by surface asperities [18].
SJ. Martin et al. I Sensors and Actuators A 44 (1994) 209-218
215
3.3. Simultaneous density and viscosity measurement
From Eqs. (8) and (12), the response of a smoothsurfaced TSM resonator depends only on the product (pq) of liquid density and viscosity. Thus, density and viscosity cannot be individually resolved from smooth resonator measurements. However, the introduction of surface texture that traps fluid adds a density-dependent contribution (ph in Eq. (12a)) to the response. Eqs. (12) indicate that a single textured device with a calibrated trapping thickness h could be used to extract density and viscosity. However, due to the uncertain contribution to motional resistance caused by surface texture, we have found that a better determination can be made using a pair of devices, one smooth and one textured [26]. Since the response due to viscous entrainment of liquid is common to both the textured and smooth devices, the difference in response measured upon immersion eliminates this contribution and, in effect, weighs the trapped liquid. From Eq. (12a) (one-sided contact), the liquid density is
%iJ-T-Lxt”rad Resonator
RTD
Fig. 8. Monolithic sensor that includes a smooth and a textured TSM resonator to measure liquid density and viscosity along with an RTD to measure temperature.
where Aft and Afs are the frequency shifts measured upon immersion of the textured and smooth resonators, respectively. Having determined the liquid density, the frequency change of the smooth device can be used (Eq. (12a) with h = 0) to determine the liquid viscosity (one-sided contact):
Alternatively, if the change in motional resistance AR is measured (using the oscillator circuit of Fig. 6, for example), the liquid viscosity can be determined (Eq. (12b)) from this parameter: (17) where AR, is the change in motional resistance of the smooth device upon immersion. 3.3.1. Dual-resonator sensor for simultaneous density and viscosi~ measurement
Fig. 8 shows a monolithic quartz sensor that includes a smooth and a textured TSM resonator to measure liquid density and viscosity. Since these liquid properties (especially viscosity) are temperature dependent, a meander-line resistance temperature device (RTD) is included to measure the liquid temperature. Texture in the form of a surface corrugation is formed on one device by electrodepositing periodic gold ridges on top
OCluark
m Photoresist
0
Au
Fig. 9. Steps in the fabrication of a corrugated-surface TSM resonator: (a) electrode metal deposited; (b) electrodes patterned; (c) periodic photoresist strips patterned; (d) Au electrodeposited; (e) resist removed, leaving corrugated metal.
of the gold electrodes. In order to trap liquid and ensure that it moves synchronously with the surface, these ridges are oriented perpendicular to the direction of surface shear displacement, i.e., the +X crystalline direction. In fabricating the dual-resonator device, a Cr/Au (30 nrn/200 nm) metallization layer is tirst deposited on both sides of an optically polished AT-cut quartz wafer (Fig. 9(a)). This metallization layer is photolithographicalIy patterned to form the resonator electrodes (both
216
SJ. Martin et al. I Sensors and Actuators A 44 (1594) 20%218
Fig. 10. SEM micrograph of surface corrugation, formed from electrodeposited gold, for trapping liquid at the surface.
sides) and the meander-line RTD (one side), Fig. 9(b). To form a surface corrugation on one resonator, a periodic resist pattern is formed on both electrodes (Fig. 9(c)). Gold is then electrodeposited, to a thickness of 1.5 pm, onto the electrode between resist stripes (Fig. 9(d)). When the photoresist is removed, a corrugation pattern remains (Fig. 9(e)) with cavities approximately 5 pm wide for trapping liquid. Fig. 10 is an SEM micrograph of the sectioned surface, showing the surface corrugation. In instrumenting the dual-resonator sensor, each resonator is driven by an independent oscillator circuit (Fig. 6). The r.f. outputs (VoJ from the oscillators are read by frequency counters (HP 5384A), while the d.c. voltages (Vo,) and RTD resistance are read by multimeters (HP 3478A). These signals are input to a personal computer. The baseline responses are determined by measuring frequency (f,) and motional resistance (R) for each device before immersion. Changes in responses are then measured for the smooth (Afs, AR,) and textured (Aft, AR,) devices upon immersion. Eqs. (15) and (17) are then used to determine simultaneously the density and viscosity. Fig. 11 illustrates the densitometer function of the dual-resonator sensor of Fig. 8. The difference in responses 1Aft - AfsI measured between the textured and smooth resonators upon immersion (two-sided liquid contact) is shown versus liquid density. The response difference is extremely linear with density, despite variations in viscosity between the test liquids. This indicates that liquid trapping is independent of liquid viscosity, as assumed in the two-region model outlined above (Fig. 3) that led to Eqs. (5) and (6). Once the liquid density is determined, the response of the smooth device gives the viscosity. Fig. 7 illustrates how frequency and motional resistance changes due to viscous entrainment depend on the liquid parameter (PVY.
0.5
0.0
1.0 Liquid
1.5 Density
2.0
2.5
3.0
3.5
(g/cm3)
Fig. 11. The difference in frequency changes 14f,-Af,f,l measured behveen the textured and smooth resonators (Fig. 8) upon immersion vs. liquid density. Liquids tested: (1) hexane, (2) butanol, (3) water, (4) chloroform, (5) carbon tetrachloride, (6) dibromomethane and (7) tetrabromoethane. I-
L
0.3
0.5
3
1 Viscosity
5
10
(CP)
Fig. 12. Scatter diagram comparing the extracted (circles) and literature (squares) values of liquid density and viscosity for organic liquids listed in Table 3.
Fig. 12 shows a ‘scatter diagram’ that compares liquid densities and viscosities extracted from dual-resonator measurements (circles) with literature values (squares). The liquids corresponding to each set of points are indicated in Table 3. For pq>O.O8 g” cme4 s-l (8 CP g crn3) the crystal is damped too severely to sustain oscillation. These data illustrate that the liquid density and viscosity can be extracted from measurements made by a pair of quartz resonators, one smooth and one with surface texture. When compared to the literature
S_J. Martin et al. / Sensors and Actuators A 44 (1994) 209-218 Table 3 Liquids shown in Fig. 12 A B C D E F G
n-Pentane n-Hexane Methanol Ethanol nPropano1 nButano1 n-Pentanol
H n-Hexanol I n-Heptanol J n-Octanol K Dichloromethane L Trichloroethylene M Carbon tetrachloride N Dibromomethane
values,
the average measured density error in this data set was 5.3% and the average viscosity error was 19.5%. Interestingly, the points in Fig. 12 divide into density bands according to chemical class: the lowest set (A-J) are hydrocarbons, the middle set (K-M) are chlorinated solvents, while the upper point (N) is a brominated solvent. These data suggest the possibility of identifying pure liquids on the basis of density and viscosity measurements.
4. Conclusions Quartz resonators with smooth surfaces can be operated in liquids to measure the density-viscosity product of a contacting fluid. Surface texture on the resonator causes fluid trapping and an additional response proportional to liquid density. Comparing the responses of a pair of resonators, one smooth and one textured, enables the liquid density to be extracted. Once the density is known, the response of a smooth device yields the liquid viscosity.
Acknowledgements The authors wish to thank Professor S.D. Senturia of Massachusetts Institute of Technology for helpful discussions and L. Casaus and K. Rice of Sandia National Laboratories for technical assistance. This work was performed at Sandia National Laboratories, supported by the U.S. Department of Energy under contract No. [email protected].
keferences
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VI G. Sauerbrey, Venvendungvon
Schwingquarzen zur Wrigung dunner Schichten und zur Mikrowlgung, Z. Phys., 155 (1959) 206-222. [31 H.E. Hager, Fluid property evaluation by piezoelectric crystals operating in the thickness shear mode, Chem. Eng Commun., 43 (1986) 25-38. The lever oscillator for use in high [41 K.O. Wessendorf, resistance resonator applications, Pmt. IEEE 1993 Frequency Control Symp.., Salt Luke City, UT, USA, pp. 711-711.
217
I51 T. Numura and A. Minemura, Behavior of a piezoelectric quartz crystal in an aqueous solution and its use for the determination of minute amounts of cyanide, Nippon Kugaku K&hi, (1960) 1621-1625. WI R. Schumacher, The quartz microbalance: a novel approach to the in-situ investigation of interfacial phenomena and the solid/liquid junction, Angew. Chem. Int. Ed. En@, 29 (1990) 329-343. [71 M.R. Deakin and H. Byrd, Prussian Blue coated quartz crystal microbalance as a detector for electroinactive cations in aqueous solution, Anal. Chem., 61 (1989) 29fk295. PI P.L. Konash and G.J. Bastiaans, Piezoelectric crystals as detectors in liquid chromatography, Anal. Chem., 52 (1980) 1929-1931. [91 M. Thompson, CL. Arthur and G.K. Dhaliwal, Liquidphase piezoelectric and acoustic transmission studies of interfacial immunochemistry, Anal. Chem., 58 (1986) 1206-1209. M. Seo, I. Sawamura and N. Sata, Study of corrosion of PI copper thin film in air containing pollutant gas by a quartz crystal microbalance, Abstract No. 187, Extended Abstracts, Electrochem. Sot. Fall Meet., Seattle, WA, USA, 1990, p. 272. WI S. Bruckenstein, and M.J. Shay, An in situ weighing study of the mechanism for the formation of the adsorbed oxygen monolayer at a gold electrode, J. Electrounal. Chem., 188 (1985) 131-136. WI A.R. Hillman, DC. Loveday and M.J. Swann, Transport of neutral species in electroactive polymer films, L Chem. Sot. Faraday Tmns., 87 (1991) 2047-2053. P31 M.D. Ward and D.A. Buttty, In situ interfacial mass detection witb piezoelectric transducers,Science, 249(1990) 1000-1007. P41 K.K. Kanazawa and J.G. Gordon II, Frequency of a quartz microbalance in contact with liquid, Anal. Chem., 57 (1985) 1770-1771. P51 H. Muramatsu, E. Tamiya and I. Karube, Computation of equivalent circuit parameters of quartz crystals in contact with liquids and study of liquid properties, Anal. Chem., 60 (1988) 2142-2146. WI S.J. Martin, V.E. Granstaff and G.C. Frye, Characterization of a quartz crystal microbalance with simultaneous mass and liquid loading, Anal. Chem., 63 (1991) 2272-2281. P71 F.M. White, mcous Fluid Flow, McGraw-Hill: New York, 1991, Section 3-5.1. S.J. Martin, G.C. Frye, A.J. Ricca and SD. Senturia, Effect M of surface roughness on the response of thickness-shear mode resonators in Iiquids,Annl. Chem., 65 (1993) 291&2922. P91 R. Beck, U. Pitterman and K.G. Weil, Influence of the surface microstructure on the coupling between a quartz oscillator and a liquid, 1. Electrochem. Sot., 139 (1992) 45Z-461. PO1 R. Schumacher, G. Barges and K.K. Kanazawa, The quartz microbalance: a sensitive tool to probe surface reconstructions on gold electrodes in liquid, Swface Sci., 163 (1985) L621-L626. I211 J.F. Rosenbaum, BuNc Acoustic Wave Theory and Devices, Artech House, Boston, 1988, Section 10.5. WI S.J. Martin and G.C. Frye, Polymer film characterization using quartz resonators, Rot. IEEE 1991 Ultrasonics Symp., Lake Buena Vktu, FL, USA, pp. 393-398. of a thick[231 V.E. Granstaff and S.J. Martin, Characterization ness-shear model quartz resonator with multiple nonpiezoelectric layers, 1 Appl. Phys., 75(3) (1994) 1319-1329. capacitance be[241 A. Ballato. Frequency-temperature-load havior of resonators for TCXO application, IEEE Trans. Sonics Ubmson., SP25 (1978) 185-191.
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(251 S.J. Martin, V.E.Granstaff and G.C. Frye, Characterization of a quartz crystal microbalance with simultaneous mass and liquid loading, Anal. Chem., 63 (1991) 2272-2281. [26] S.J. Martin, K.O. Wessendorf, C.T. Gebert, G.C. Frye, R.C. Cernosek, L. Casaus and M.A. Mitchell, Measuring
liquid properties with smooth- and textured-surface resonators, Proc. IEEE 1993 Frequency Control Symp., Salt L&e City, UT, USA, pp. 603-608. [27] R.C. Weast (ed.), Handbook of Chem&y and Physics, CRC Press, Boca Raton, FL, 1984, p. D-236.
Sensors and Actuators A 44 (1994) 209-218
ELSEVIER
7
PHYSICAL
Sensing liquid properties with thickness-shear mode resonators S.J. Martin,
G.C. Frye, K.O. Wessendorf
Micrmemor Research and Development Deparbnent, Sandia National Laboratories, Albuquerque, NM, UL-4 Received 26 April 1994; accepted 3 May 1994
Abstract The responses of smooth- and textured-surface thickness-shear mode (TSM) resonators in liquid are examined. Smooth devices, which viscously entrain a layer of contacting liquid, exhibit a response that depends on the product of liquid density and viscosity. Textured-surface devices, which also trap liquid in surface crevices, pores, etc., exhibit an additional response that depends on liquid density alone. Combining smooth- and textured-surface resonators in a monolithic sensor enables the liquid density and viscosity to be extracted simultaneously. Keywords:Liquid sensors; Thickness-shear
mode resonators
1. Introduction A thickness-shear mode (TSM) resonator typically consists of a thin disk of AT-cut quartz with circular electrodes patterned on both sides (Fig. 1). Due to the piezoelectric properties and crystalline orientation of the quartz, the application of a voltage between these electrodes results in a shear deformation of the crystal. The crystal can be electrically excited into several resonant modes, each corresponding to a unique stand-
ing shear-wave pattern (eigenmode) across the thickness of the crystal [l]. (The fundamental TSM is shown in Fig. 2.) For each of these modes, displacement maxima occur at the crystal faces, making these devices sensitive to the accumulation of surface mass and contacting fluid properties. The initial sensor application for quartz resonators was as deposition monitors in vacuum evaporations [2]. The linear change in resonance frequency that occurs with mass accumulation allows the device to function as a general-purpose gravimetric detector or ‘microbalance’. The device is easily instrumented as a sensor by incorporating it as the frequency-control element of an oscillator circuit. By monitoring the oscillation
Bottom Electrode
Fig. 1. Top (a) and side (b) views of a quartz thickness-shear (TSM) resonator.
mode
0924-4247/94/$07.00 0 1994 Elsevier Science S.A. All rights resewed SSDI 0924-4247(94)00806-S
Fig. 2. Cross-sectional view of a smooth TSM resonator with the upper surface contacted by a liquid. Shear motion of the smooth surface causes a thin layer of the contacting liquid to be viscously entrained.
210
S.J. Martin et al. I Sensors and Actuators A 44 (1994) 209-218
frequency, changes in surface mass density of roughly 1 ng cm-* can be measured; thus, the TSM resonator is commonly called a quartz-crystal microbalance
(QCM). A major obstacle to adapting piezoelectric resonators to liquid-sensing applications arises from mechanical damping by the liquid medium. Resonators with a surface-normal displacement component generate compressional waves in the contacting liquid. This causes acoustic energy to be radiated away, leading to severe resonance damping. TSMs, however, have only in-plane surface displacement. This results in much less acoustic radiation into a contacting liquid and a significant but tolerable amount of resonance damping. Oscillator circuits have been designed for the TSM resonator that overcome the damping contributed by low-viscosity liquids [3,4]. Since the mass sensitivity of the resonator is nearly the same in liquids as in air or vacuum, the device can be used as a sensitive solutionphase microbalance [5]. Applications include deposition monitoring [6], chemical species detection [7], immunoassay [8], liquid chromatographic detection [9], corrosion monitoring [lo] and electrochemical analysis [ll-131. In addition to functioning as a microbalance, the sensitivity of the TSM resonator to contacting fluid properties enables it to function as a monitor for these properties. Kanazawa and Gordon 1141 have shown that the TSM resonance frequency decreases with liquid immersion as (p#“, where p and q are the liquid density and viscosity, respectively. Muramatsu et al. [15] demonstrated that resonance damping also increases as (pq) lR. Martin et al. [16] derived an equivalent-circuit model to describe the frequency response of the TSM resonator in terms of the contacting liquid properties. This paper will describe the mechanical interactions between smooth- and textured-surface TSM resonators and a contacting liquid. These interactions influence the device response in a way that depends on the liquid properties, providing a means for measuring these properties.
2. Theory 2.1. Liquid coupling to the TSM resonator 2.1.1. Viscous entrainment
When the TSM resonator is operated in contact with a liquid, as shown in Fig. 2, the shear motion of the surface generates plane-parallel laminar flow in the adjacent liquid. The liquid velocity field v,(y), can be determined by solving the one-dimensional Navier-Stokes equation [14]:
(1) where p and n are the liquid density and shear viscosity, respectively, and (‘) denotes a time derivative. With a Newtonian liquid (for which q is independent of amplitude and frequency) and an oscillatory shear displacement at the solid-liquid boundary, the solution to Eq. (1) is [17] v&, t) =v,
1
exp - 7(1+j)y [
expo’4
where v, is the surface particle velocity, y is the distance into the liquid, 6 = (2q/0p)ln, o is the angular frequency (o= 2nj where f is frequency), and j = ( - l)ln. Eq. (2) represents a critically damped shear wave that is radiated into the contacting liquid by the oscillating resonator surface; 6 is the decay length of this shear wave, having, for example, a value of 250 nm in water at 20 “C when the frequency is 5 MHz. The liquid entrained by the oscillating smooth surface, shown in Fig. 2 and described by Eq. (2), is described as ‘viscously coupled’; this liquid does not move synchronously with the surface, but undergoes a progressive phase lag with distance from the surface. The extent to which liquid contact ‘loads’ the resonator, i.e., perturbs the resonance frequency or introduces damping, depends on the surface mechanical impedance 2, contributed by the liquid. The surface shear mechanical impedance arising from viscous entrainment (VE) is
where T, is the shear stress at the solid-liquid interface. Applying Eq. (3) to Eq. (2) yields the surface mechanical impedance due to viscous entrainment of a Newtonian fluid by an ideally smooth surface [18]:
2.1.2. Trapped l&id
Devices with textured surfaces, either randomly rough or regularly patterned, trap a quantity of fluid in excess of that viscously entrained by a smooth surface [19, 201. Vertical features constrain this trapped liquid to move synchronously with the oscillating crystal surface, rather than undergoing a progressive phase lag as occurs with viscously coupled liquid. This trapped liquid thus behaves much like an ideal mass layer contributing an area1 mass density ph. where p is the density and h, the effective thickness of the trapped liquid layer, is dependent upon the vertical relief of the surface texture.
SJ. Martin et al. / Senrors and Achuafors A 44 (1994) 209-218 Y
211
‘unperturbed’ portion of the circuit in Fig. 4. Parasitic capacitance, external to the device, is typically included with the static capacitance and it is denoted C,*. The motional branch of the equivalent-circuit model arises from electrical excitation of a shear-mode mechanical resonance in the piezoelectric quartz. It has beeri shown that surface loading of the resonator (e.g., liquid contact) leads to a change in this (electrical) motional impedance, AZ,,,, in proportion to the surface mechanical impedance Z, contributed by the load [18,22,23]:
Viscously-Entrained Llquld
I 1 Trapped Llquld
Fig. 3. Cmss-sectional view of a textured TSM resonator surface in contact with a liquid; liquid is trapped by surface cavities, in addition to being viscously entrained.
We can approximate the response of a texturedsurface resonator in liquid by separating the solid-liquid interface into two regions, as shown in idealized fashion in Fig. 3. If we imagine a boundary (dashed line) connecting peaks of the textured surface, then liquid below this boundary is ‘trapped’ and moves synchronously with the surface; liquid above this boundary is viscously coupled (as if by the boundaT) and undergoes a progressive phase lag with distance from the boundary. While this is an extreme simplification of the interaction between an oscillating rough surface and a liquid, it is useful in understanding the process. Consideration of these two regions in calculating the interfacial stress gives a surface mechanical impedance for the textured surface in contact with liquid of
,gw+zy3
(5)
where ZivE) is as given in Eq. (4) and the additional impedance contribution arising from trapped liquid (TL) is Zi=) 4 j&
(7) where N is the resonator harmonic number (N= 1,3,5,. ..); 0,=2& where fa is the unperturbed (dry) series resonance frequency; Z, = (c~qp$~, where kq and pq are the quartz shear stiffness and mass density, respectively; KZ is the electromechanical coupling factor. AT-cut quartz properties [24] are pq=2.947 x 1O’l dyne crnw2, pq =2.651 g cme3, KZ= 7.74X 10e3 and Z,= 8.839 x 10s g cm-* s-l. Eq. (7) indicates that liquid loading contributes additional elements to the motional impedance branch of the equivalent-circuit model of Fig. 4. 2.2.1. Vikous entrainment by a smooth su$ace
For viscous entrainment of liquid by an ideally smooth surface, Eqs. (4) and (7) can be combined to find AZ,. Since Zcve) has both a real and an imaginary component (both Gsitive), AZ,,, can be represented (for o near 0,) by a combination of a motional resistance, Rz, and an inductance, L,: AZ,,,=R,+j&. These elements of the equivalent-circuit model (Fig. 4), arising fromviscous entrainment by a single ideally smooth surface, are [18,25]:
(6)
If the effective thickness of trapped liquid h is small compared to the liquid decay length 6, then the relative response due to liquid trapping is small compared with the response due to viscous entrainment and may be neglected. This defines a criterion for hydrodynamic smoothness [18]: h K 6. If h is comparable to or larger than 6, then a significant additional response arises due to liquid trapping. 2.2. Equivalent circuit model The electrical characteristics of an unperturbed (Le., not contacted by liquid) quartz resonator can be described by a Butterworth-Van Dyke equivalent circuit [21]. This consists of a ‘static’ capacitance C, in parallel with a ‘motional’ branch (L,, C1, R,), as shown in the
I-
t
RI ___ ____________________---_____ Viscously Entrained
Mass Layer or Trapped Liquid
Fig. 4. Equivalent-circuit model to describe the electrical characteristics (for o near 4) of a TSM resonator with liquid loading. Contributions arise from both viscously coupled liquid and liquid trapped by surface asperities.
S.J. Martin et al. i Sensors and Actuators A 44 (1994) 209-218
212
where we note that R2 = o,L, for loading by a Newtonian fluid. For two-sided liquid contact, L, and R, are doubled. Electrical-energy storage in L, arises from the kinetic energy of the viscously entrained liquid layer (with effective thickness s/2); power dissipation in R2 arises from radiation of a critically damped shear wave into the liquid by the oscillating resonator surface. Thus, R, may be regarded as a ‘radiation resistance’. 2.2.2. Liquid trapping The motional impedance element arising from liquid trapping is found by combining Eqs. (6) and (7). Since Zin) is purely imaginary, AZ, can be represented as joL,. Thus, only the inductance LS, indicated in Fig. 4, arises from liquid trapping [16]: L3=
Nnioh
(9)
4K2GX~,~g)‘a
results
3.1. Swept-frequency impedance measurement The equivalent-circuit model of Fig. 4 describes the electrical characteristics of the TSM resonator over a range of frequencies near resonance. The electrical admittance (ratio of current i to applied voltage v in Fig. 2) is Y(n=joC,*+
$
(10)
m where the electrical motional impedance 2, Z,=(R,+R,)+jw(L1+L,+L,)+
90
:
$
60
;
30
E
0
: j
-30
.z & 2 -60 4.965
Electrical-energy storage in L, arises from the kinetic energy of the trapped liquid layer that oscillates synchronously with the device surface.
3. Experimental
-,
&
1
is (11)
3.1.1. Densi~-viscosity product from smooth resonator response
Fig. 5 shows the frequency response measured (points) as several glycerol solutions contacted one side of a TSM resonator. The dashed line indicates the series resonance frequency (f,) for the dry device. As pq increases with glycerol concentration (in water), the admittance magnitude plot shows both a translation of the series resonance peak toward lower frequency, as
4.970
Frequency
4.975
4.900
(MHz)
Fig. 5. Network analyzer measurements of resonator electrical admittance Y measured (points) and calculated (lines) near the fundamental resonance as the density-viscosity product (pq, Table 1) is varied by the concentration of glycerol in water (percentage glycerol is given in legend).
well as a diminution and broadening of the peak. The lines in Fig. 5 are calculated from the equivalent-circuit model (Fig. 4) using best-fit values of L2 and R, (L3 = 0 for a smooth device) along with values of C,,*, L,, C, and R, obtained by fitting measurements made on the dry device. The liquid density-viscosity product (p?7) is determined from L, and R2 using Eqs. (8) and is listed in Table 1. The pi values extracted from L, agree with those extracted from R, within 1% for all cases; these extracted values are 3-28% higher (error column) than the literature values of pq for glycerol solutions. When a textured-surface device is used, yielding a non-zero L, value, then ph can be determined. The major effect of surface texture is to translate the Y-f curves due to the addition of the L, element. 3.2. Oscillator measurements From the equivalent-circuit model, changes in the series resonance frequency Af and motional resistance AR due to viscous coupling and liquid trapping are given by [16]
213
S.J. Martin et al. t Sensors and Actuators A 44 (1994) 209-218 Table 1 Equivalent-circuit Glycerol cont.
elements and liquid density-viscosity product from the literature [27] and extracted from electrical admittance measurements Temperatore
Literature
L1
RZ
Extracted pq
CC)
P9
WI
(W
(2
(9’
(wt.%)
0
40 60 70
21.0 20.4 20.3 20.3
cm -’
Error (%)
s-9
cmw4 s-‘)
0.0097 0.0414 0.129 0.250
0.379 0.736 1.24 1.78
12.1 23.5 39.6 56.8
from L2
from RZ
0.0124 0.0469 0.133 0.274
0.0124 0.0466 0.132 0.273
28 13 3 9
Table 2 Element values for the oscillator circuit of Fig. 6 Value
Element
5V 4.7 PH 220 pF 150 n 100 n 0.01 pF 1kCl 825 n
N-9 The first term of Eq. (12a) and Eq. (12b) arises from viscous entrainment of liquid, while the second term of Eq. (12a) arises from liquid trapping. 3.2.1. Oscillator circuit An oscillator circuit capable of driving the TSM resonator in fairly damped liquid media has been described by Wessendorf [4]. Fig. 6 shows a schematic of this oscillator circuit, with element values given in Table 2. This oscillator tracks the series resonance frequency of the crystal, providing an r.f. output (vor) indicating frequency f,, and a d.c. voltage (V,,) proportional to the motional resistance R = (R, + R,). Measuring changes in these responses upon immersion give
Af and AR; Eqs. (12) can then be used to infer liquid properties. The oscillator circuit of Fig. 6 is essentially a noninverting differential amplifier with positive feedback designed to be controlled by the resonator connected between the base of Q, and ground. The negative feedback provided by Rrmakes the oscillation conditions independent of the transistor /3 and forces the oscillation conditions to be a function of resonator resistance R and transistor transconductance g,,, (g,,,=I&!6 mV, where I, is the bias current in each transistor, Q1 and QZ, at 25 “C). The oscillator loop gain is
R
A=@kn)+g@)
(13)
where
“,c/, Fig. 6. Oscillator circuit designed to operate the TSM resonator in liquid media to provide fwo outputs: Vo, (r.f. output) indicates series resonance frequencyf,; Vo, (d.c. output) is proportional to motional resistance R.
MC
g(R)= R+R,+Rf
(14)
Two conditions are required for oscillation to occur: A must be real (LA =0) and p] > 1. The second condition is maintained by the automatic level control (ALC) circuit. It varies the bias current in Q1 and Q2, via the voltage-controlled current source Q,, to maintain PI 21. The control voltage Vo, required to maintain oscillation is indicative of crystal damping and is taken as an output. The rate at which V,,varies with resonator resistance (R) is controlled by the negative feedback term g(R), Eq. (14). For low values of R, g(R) is proportional to
214
S.J. Martin et al. I Sensors and Actuators A 44 (1994) 205-218
R; this allows V,,, to vary substantially with R, providing good sensitivity to changes in the liquid density-viscosity product (Eq. (12b)). At high values of R, the appearance of R in the denominator of Eq. (14) causes g(R) to saturate. This allows the resonance condition (PI > 1) to remain attainable with high liquid damping (large pq) and oscillation to be sustained over a wide range of liquid properties. When the resonator resistance is large, due to operation in high-pq liquids, the oscillator has a tendency to oscillate at spurious frequencies predominantly determined by the static capacitance of the resonator. The tank circuit consisting of L,, C,, and R, is tuned to the resonator frequency; the a.c. impedance from collector to ground is real and equal to R, at fs.This tank circuit helps reject spurious oscillation modes at frequencies away from the resonator resonance. The oscillation condition also requires the phase of A to be zero. This implies that g(R) is real, i.e., has zero phase also. Since the impedance from the collector to base of Qz is dominated by R, and is thus real, then the resonator impedance must also be real and have zero phase angle. The two frequencies at which the resonator impedance has zero phase are the series (_fJ and parallel (f,) resonances. The series resonance impedance is much lower than the parallel resonance impedance; since the circuit tends to oscillate at the lower-gain condition, it tracks the series resonance. In a refinement of the previous argument, the collector-base capacitance (Cbc) causes the impedance phase from the collector to base of Qz to be slightly negative. It can be shown that if Rr>R,, then the phase of the resonator impedance at oscillation is equal to the phase of the impedance from the collector to base of QZ. Thus, the oscillator will track a resonator impedance phase slightly less than 0” (e.g., -Y). At low values of R, this frequency is very close to fs;at higher R values, the oscillation begins to deviate substantially from fs. The oscillator circuit of Fig. 6 will sustain oscillation for motional resistances up to approximately 2 kfI. From Eq. (12b), this enables resonator operation in liquids with pq values up to 0.34 g’ cme4 s-’ (onesided contact) or 0.086 g” cm-4 s-* (two-sided contact). For a liquid with a density of 1 g cmm3, these translate into viscosity values of 34 and 8.6 CP for one- and twosided contact, respectively. 3.2.2. Liquid density-viscosity product from Af and AR Fig. 7 shows the change in series resonance frequency Af and motional resistance AR measured versus the liquid parameter (pq)lR. Measurements were made using a network analyser [18] on a smooth and a rough device as glycerol solutions contacted one side. The rough resonator was fabricated by polishing the quartz crystal with 10 pm abrasive particles before depositing
3
E
2-
%
-0.0
0.1
0.2
0.3
0.4
0.5
0.6
(p~-#‘~ (g cm-*s-l”) Fig. 7. Changes in series resonance frequency, A& and motional resistance, AR, vs. the liquid parameter (p~)‘~ for TSM resonators with two different surface roughnesses.
the conformal Cr/Au electrodes. The surface roughness was quantified using a Wyko RST (Tucson, AZ) profiler. This instrument uses a vertical-scanning interference microscope to obtain a non-contacting surface profile with a 3 nm vertical resolution and a 0.5 pm lateral resolution. The smooth device has an average roughness < 10 nm, much smaller than the liquid decay length S. For this device, the measured frequency shifts and motional resistance changes are nearly equal to the predictions (dashed lines, Eqs. (12) with h = 0) for an ideally smooth surface. The rough device has an average roughness of 243 nm, comparable to the liquid decay length: 6= 250-1200 nm for the glycerol solutions tested. This device exhibits a large additional frequency shift of approximately 0.87 kHz at (~3)‘” =0 due to liquid trapping in the randomly rough surface. From Eq. (12a), this gives h = 150 nm, or roughly 63% of the optically measured average surface roughness. The rough device also exhibits increased damping over the smooth device, indicating that Z,(TIJ (Eq. (6)) also has a small real component. This implies a slightly higher energy dissipation by the rough surface, thought to arise from the generation of compressional waves by surface asperities [18].
SJ. Martin et al. I Sensors and Actuators A 44 (1994) 209-218
215
3.3. Simultaneous density and viscosity measurement
From Eqs. (8) and (12), the response of a smoothsurfaced TSM resonator depends only on the product (pq) of liquid density and viscosity. Thus, density and viscosity cannot be individually resolved from smooth resonator measurements. However, the introduction of surface texture that traps fluid adds a density-dependent contribution (ph in Eq. (12a)) to the response. Eqs. (12) indicate that a single textured device with a calibrated trapping thickness h could be used to extract density and viscosity. However, due to the uncertain contribution to motional resistance caused by surface texture, we have found that a better determination can be made using a pair of devices, one smooth and one textured [26]. Since the response due to viscous entrainment of liquid is common to both the textured and smooth devices, the difference in response measured upon immersion eliminates this contribution and, in effect, weighs the trapped liquid. From Eq. (12a) (one-sided contact), the liquid density is
%iJ-T-Lxt”rad Resonator
RTD
Fig. 8. Monolithic sensor that includes a smooth and a textured TSM resonator to measure liquid density and viscosity along with an RTD to measure temperature.
where Aft and Afs are the frequency shifts measured upon immersion of the textured and smooth resonators, respectively. Having determined the liquid density, the frequency change of the smooth device can be used (Eq. (12a) with h = 0) to determine the liquid viscosity (one-sided contact):
Alternatively, if the change in motional resistance AR is measured (using the oscillator circuit of Fig. 6, for example), the liquid viscosity can be determined (Eq. (12b)) from this parameter: (17) where AR, is the change in motional resistance of the smooth device upon immersion. 3.3.1. Dual-resonator sensor for simultaneous density and viscosi~ measurement
Fig. 8 shows a monolithic quartz sensor that includes a smooth and a textured TSM resonator to measure liquid density and viscosity. Since these liquid properties (especially viscosity) are temperature dependent, a meander-line resistance temperature device (RTD) is included to measure the liquid temperature. Texture in the form of a surface corrugation is formed on one device by electrodepositing periodic gold ridges on top
OCluark
m Photoresist
0
Au
Fig. 9. Steps in the fabrication of a corrugated-surface TSM resonator: (a) electrode metal deposited; (b) electrodes patterned; (c) periodic photoresist strips patterned; (d) Au electrodeposited; (e) resist removed, leaving corrugated metal.
of the gold electrodes. In order to trap liquid and ensure that it moves synchronously with the surface, these ridges are oriented perpendicular to the direction of surface shear displacement, i.e., the +X crystalline direction. In fabricating the dual-resonator device, a Cr/Au (30 nrn/200 nm) metallization layer is tirst deposited on both sides of an optically polished AT-cut quartz wafer (Fig. 9(a)). This metallization layer is photolithographicalIy patterned to form the resonator electrodes (both
216
SJ. Martin et al. I Sensors and Actuators A 44 (1594) 20%218
Fig. 10. SEM micrograph of surface corrugation, formed from electrodeposited gold, for trapping liquid at the surface.
sides) and the meander-line RTD (one side), Fig. 9(b). To form a surface corrugation on one resonator, a periodic resist pattern is formed on both electrodes (Fig. 9(c)). Gold is then electrodeposited, to a thickness of 1.5 pm, onto the electrode between resist stripes (Fig. 9(d)). When the photoresist is removed, a corrugation pattern remains (Fig. 9(e)) with cavities approximately 5 pm wide for trapping liquid. Fig. 10 is an SEM micrograph of the sectioned surface, showing the surface corrugation. In instrumenting the dual-resonator sensor, each resonator is driven by an independent oscillator circuit (Fig. 6). The r.f. outputs (VoJ from the oscillators are read by frequency counters (HP 5384A), while the d.c. voltages (Vo,) and RTD resistance are read by multimeters (HP 3478A). These signals are input to a personal computer. The baseline responses are determined by measuring frequency (f,) and motional resistance (R) for each device before immersion. Changes in responses are then measured for the smooth (Afs, AR,) and textured (Aft, AR,) devices upon immersion. Eqs. (15) and (17) are then used to determine simultaneously the density and viscosity. Fig. 11 illustrates the densitometer function of the dual-resonator sensor of Fig. 8. The difference in responses 1Aft - AfsI measured between the textured and smooth resonators upon immersion (two-sided liquid contact) is shown versus liquid density. The response difference is extremely linear with density, despite variations in viscosity between the test liquids. This indicates that liquid trapping is independent of liquid viscosity, as assumed in the two-region model outlined above (Fig. 3) that led to Eqs. (5) and (6). Once the liquid density is determined, the response of the smooth device gives the viscosity. Fig. 7 illustrates how frequency and motional resistance changes due to viscous entrainment depend on the liquid parameter (PVY.
0.5
0.0
1.0 Liquid
1.5 Density
2.0
2.5
3.0
3.5
(g/cm3)
Fig. 11. The difference in frequency changes 14f,-Af,f,l measured behveen the textured and smooth resonators (Fig. 8) upon immersion vs. liquid density. Liquids tested: (1) hexane, (2) butanol, (3) water, (4) chloroform, (5) carbon tetrachloride, (6) dibromomethane and (7) tetrabromoethane. I-
L
0.3
0.5
3
1 Viscosity
5
10
(CP)
Fig. 12. Scatter diagram comparing the extracted (circles) and literature (squares) values of liquid density and viscosity for organic liquids listed in Table 3.
Fig. 12 shows a ‘scatter diagram’ that compares liquid densities and viscosities extracted from dual-resonator measurements (circles) with literature values (squares). The liquids corresponding to each set of points are indicated in Table 3. For pq>O.O8 g” cme4 s-l (8 CP g crn3) the crystal is damped too severely to sustain oscillation. These data illustrate that the liquid density and viscosity can be extracted from measurements made by a pair of quartz resonators, one smooth and one with surface texture. When compared to the literature
S_J. Martin et al. / Sensors and Actuators A 44 (1994) 209-218 Table 3 Liquids shown in Fig. 12 A B C D E F G
n-Pentane n-Hexane Methanol Ethanol nPropano1 nButano1 n-Pentanol
H n-Hexanol I n-Heptanol J n-Octanol K Dichloromethane L Trichloroethylene M Carbon tetrachloride N Dibromomethane
values,
the average measured density error in this data set was 5.3% and the average viscosity error was 19.5%. Interestingly, the points in Fig. 12 divide into density bands according to chemical class: the lowest set (A-J) are hydrocarbons, the middle set (K-M) are chlorinated solvents, while the upper point (N) is a brominated solvent. These data suggest the possibility of identifying pure liquids on the basis of density and viscosity measurements.
4. Conclusions Quartz resonators with smooth surfaces can be operated in liquids to measure the density-viscosity product of a contacting fluid. Surface texture on the resonator causes fluid trapping and an additional response proportional to liquid density. Comparing the responses of a pair of resonators, one smooth and one textured, enables the liquid density to be extracted. Once the density is known, the response of a smooth device yields the liquid viscosity.
Acknowledgements The authors wish to thank Professor S.D. Senturia of Massachusetts Institute of Technology for helpful discussions and L. Casaus and K. Rice of Sandia National Laboratories for technical assistance. This work was performed at Sandia National Laboratories, supported by the U.S. Department of Energy under contract No. [email protected].
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