Method for simultaneous measurement of mass loading and fluid property changes using a quartz crystal microbalance

A method, using a quartz crystal microbalance, to obtain simultaneous measurement of solid mass accumulation and changes in liquid density-viscosity product. The simultaneous real-time measurements of electrical parameters yields that changes in surface mass can be differentiated from changes in solution properties. Two methods to obtain the admittance/frequency data are employed.

BACKGROUND OF THE INVENTION 
This invention relates generally to the field of microchemical sensors, and 
more particularly to using electrical parameters to differentiate changes 
in surface mass from changes in chemical solution properties using a 
quartz crystal microbalance. 
The quartz crystal microbalance (QCM) is commonly configured with 
electrodes on both sides of a thin disk of AT-cut quartz. Because of 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 
resonance when the excitation frequency is such that the crystal thickness 
is an odd multiple of half the acoustic wavelength. At these frequencies, 
a standing shear wave is generated across the thickness of the plate for 
the fundamental and higher harmonic resonances. 
QCMs were originally used in vacuo to measure deposition rates. As shown by 
Sauerbrey, Z. PHYS., Vol. 155, pp. 206-222 (1959), changes in the resonant 
frequency are simply related to mass accumulated on the crystal, and this 
teaching has been implemented in U.S. Pat. No. 4,788,466, entitled 
"Piezoelectric Sensor Q-loss Compensation," to Paul et al., Nov. 29, 1988; 
and U.S. Pat. No. 4,561,286, entitled "Piezoelectric Contamination 
Detector," to Sekler et al., Dec. 31, 1985; and U.S. Pat. No. 4,391,338, 
entitled "Microbalance and Method for Measuring the Mass of Matter 
Suspended Within a Fluid Medium," to Patashnick et al., Jul. 5, 1983. Lu 
et al., J. APPL. PHYS.Vol. 43, pp. 4385-4390 (1972) showed that the QCM 
typically may be used as an instrument in the frequency-control element of 
an oscillator circuit; a precise microbalance is realized by monitoring 
changes in oscillation frequency. More recently, QCMs have been shown to 
operate in contact with fluids by Numura et al., NIPPON KAGAKU KAISHI, pp. 
1121(1980) enabling their use as solution phase microbalances. This 
microbalance capability has facilitated a number of solution measurements, 
as in, for instance, U.S. Pat. No. 4,741,200, entitled "Method and 
Apparatus for Measuring Viscosity in a Liquid Utilizing a Piezoelectric 
Sensor," to Hammerle, May 3, 1988. Other examples include deposition 
monitoring as taught by Schumacher, ANGEW. CHEM. INT. ED. ENGL., Vol. 29, 
pp. 329-343 (1990), and U.S. Pat. No. 4,311,725, entitled "Control of 
Deposition of Thin Films," by Holland, Jan. 19, 1982; species detection by 
Deakin et al., ANAL. CHEM., Vol. 61, pp. 290-295 (1989); immunoassay by 
Thompson et al., ANAL. CHEM. Vol. 58, pp. 1206-1209 (1986), and U.S. Pat. 
No. 4,999,284, entitled "Enzymatically amplified piezoelectric specific 
binding assay," to Ward et al., Mar. 12, 1991; fluid chromatographic 
detection shown by Konash et al., ANAL. CHEM., Vol. 52, pp. 1929-1931 
(1980); corrosion monitoring by Seo et al., EXTENDED

DESCRIPTION OF THE INVENTION 
FIG. 1 depicts the cross-sectional geometry of the QCM 10 loaded from above 
by a surface mass layer 20 and a contacting fluid 22. Excitation 
electrodes 24 and 26 are also located at the upper and lower quartz 
surfaces, 28 and 30, respectively. The mass layer 20 is on top of the QCM 
10 and may or may not be derived from the contacting fluid 22. The mass 
layer 20 is thin compared to the acoustic wavelength, it is solid and 
rigidly attached to the QCM 10, ensuring synchronous motion with the 
oscillating surface. The mass layer 20 may be, for example, metals, metal 
alloys, salts, some rigid polymers, or ice. The mass layer 20 may be 
applied to the QCM 10 by evaporation, electroplating, precipitation, or 
other chemical or thermodynamic reaction. When the contacting fluid 22 
contacts this oscillating surface, a damped shear wave is radiated into 
the fluid, as shown in FIG. 2. QCM surface displacement causes synchronous 
motion of the surface mass layer and entrainment of the contacting fluid. 
As long as the fluid thickness is large compared to the decay length of 
the radiated shear wave, the fluid may be considered semi-infinite. 
Coupling between mechanical displacement and electrical potential in the 
piezoelectric quartz causes mechanical interactions between the QCM and 
contacting media to influence the electrical characteristics of the QCM, 
particularly near resonance, where the amplitude of crystal oscillation is 
greatest. The QCM electrical characteristics can be evaluated using the 
electrical admittance. Admittance is defined as the ratio of current flow 
to applied voltage, and may be considered to be the reciprocal of 
impedance. This parameter contains information about the energy stored and 
the power dissipated in both the QCM and the perturbing media. The 
admittance of the QCM is obtained by solving a boundary-value problem that 
includes the mass layer and contacting fluid. 
FIG. 3 shows an equivalent circuit model that describes the electrical 
admittance of the QCM simultaneously loaded by mass and a contacting 
liquid. The impedance elements in the equivalent circuit model can be 
related to the properties of the QCM, the mass layer, and the contacting 
liquid. The current flow out of the lower electrode and into the upper 
electrode is known. Thus, the QCM admittance can be described in terms of 
its physical properties, surface mass layer, and contacting fluid. 
The method of the invention described herein involves characterizing the 
unperturbed QCM and comparing the differences of those characterizations 
after the QCM has been loaded with mass and/or liquid. An interesting 
feature is that the elements that arise from mass and fluid loading are 
related to the unperturbed QCM parameters. The parasitic capacitance, 
C.sub.p, depends upon the geometry of the test fixture and the QCM 
electrode patterns. The static capacitance, C.sub.o, arises from internal 
fields across the quartz, which also excite the mechanical response of the 
QCM, but C.sub.p arises from fields external to the QCM. Therefore, by 
measuring the resonance and broadband admittance characteristics, C.sub.o 
can be separated from C.sub.p. The total admittance, Y, can be found from 
an inspection of the equivalent circuit model and, including the parasitic 
contribution C.sub.p, where Z.sub.m is the motional impedance, is: 
EQU Y=j.omega.(C.sub.o +C.sub.p)+1/Z.sub.m 
This equation assumes that the mass and fluid are contacting only a single 
side of the QCM; for two-sided contact, certain resistive and motional 
inductance factors are doubled and the conduction current between 
electrodes must be considered. 
The influence of the mass and fluid perturbations arise from a change in 
QCM stored energy caused by the perturbation, i.e., resulting from the 
kinetic energy of the bound mass and/or entrained fluid layer, and the 
power dissipation because of the radiation of a damped shear wave into the 
fluid by the oscillating QCM surface, but moving mass does not cause power 
dissipation. Fluid loading causes an increase in both the motional 
inductance as well as resistance. In contrast, mass loading increases only 
the motional inductance. 
It has also been determined from the analysis that the effect of mass and 
fluid loading on charging the resonant frequency is additive and that it 
is impossible to differentiate changes in surface mass from fluid 
properties when monitoring only the resonant frequency. The maximum 
admittance, Y.sub.max, is affected by fluid loading, with the maximum 
admittance diminishing with .rho..eta. where .rho. and .eta. are fluid 
density and viscosity, respectively, but is unaffected by surface mass 
areal .rho..sub.s. When the unperturbed QCM has been fully characterized, 
.rho..sub.s and .rho..eta. can be simultaneously determined from 
measurements of .DELTA.f.sub.s and Y.sub.max. Moreover, QCM sensitivity to 
surface mass can be emphasized over fluid sensitivity by operating at a 
higher harmonic. 
The quartz crystals are 2.54 cm diameter, synthetic AT-cut quartz wafers, 
and those skilled in the art will understand that other crystalline cuts 
of quartz, as well as lithium niobate, and certain cuts of lithium 
tantalate, or any piezoelectric material that allows shear deformations to 
be electrically excited may be used. The QCMs, nominally 0.33 mm thick, 
have planar faces that preferably should be lapped and polished. An 
electrode pattern may be formed by any number of means, including 
vacuum-evaporating a chromium adhesion layer, followed by a gold layer. 
The QCM electrode geometry contains a grounded electrode on one side, 
while the other side contains an electrode at RF potential. Because the 
electric field is largely confined to the quartz region beneath the 
smaller electrode, the QCM active area is approximately this smaller 
electrode area. The larger electrode is contacted by a metal strip that 
wraps around the right edge of the QCM enabling both electrodes to be 
contacted from one side, but other contacting methods including two-sided 
contacts also may be used. 
The surface smoothness of the QCMs is critical for obtaining useful 
admittance measurements. Smoothness is quantified by a measurement of 
average surface roughness (R.sub.a) using a profilometer. Commercial QCMs 
have a wide range of R.sub.a values (0.01 to 0.35 .mu.m). It is 
preferable, however, that the QCM used in the invention have a required 
R.sub.a .ltoreq.0.1 .mu.m. It appears that when surface features are small 
compared to the fluid decay length (.delta.=0.15-1.8 .mu.m with fluids 
tested), the surface behaves as an ideal shear plane interacting with the 
fluid. Otherwise, alternate mechanisms, such as compressional wave 
generation, exist for coupling energy from the QCM into the fluid which 
leads to erroneous results. The QCM roughness leads to increased mass 
loading because of fluid entrainment and increased dissipation. This 
results in increased inductance and resistance. 
To make electrical measurements, the QCM was mounted in an aluminum RF test 
fixture, although other test fixtures may be configured to permit, for 
instance, the fluid to flow across the device. The fixture allows an RF 
connector to be soldered directly to the smaller electrode and a ground 
connection to be soldered to the larger electrode. A solder consisting of 
1:1 Pb:In may be used to avoid amalgamation and removal of the gold 
electrode. Pressure contact alone typically resulted in parasitic contact 
resistance and capacitance, precluding the fitting of measured admittance 
data to an equivalent circuit. The aluminum fixture has an opening which 
permits fluid to contact the grounded electrode of the QCM. Immersing the 
larger electrode in the fluid and keeping that electrode at ground 
potential prevents fringing RF fields from entering the fluid and causing 
electrochemical processes and acoustoelectric interactions. It may be 
necessary to form a fluid seal between the quartz and the test fixture. 
The QCM test fixture may also be temperature regulated. 
A network analyzer measured the complex scattering parameter S.sub.11, 
i.e., reflection magnitude and phase, from which admittance spectra are 
determined. Measurements were made at multiple points centered about the 
fundamental and third harmonic resonant frequencies of the dry QCM. To 
characterize the unloaded QCM at its fundamental resonance, a scan was 
made over a limited bandwidth to capture the sharp resonance peak, as well 
as over a bandwidth range to capture the broad-band characteristics. To 
characterize the unloaded QCM at the third harmonic resonance, scans are 
also made over limited and broad bandwidths. An incident RF power is 
applied and the frequencies are scanned. Each measured S.sub.11 value was 
converted to a complex admittance, Y, using the relation: 
##EQU1## 
where Z.sub.o is the characteristic impedance of the measurement system. 
The admittance, Y, can be decomposed into real and imaginary parts 
(Y=Y.sub.r +jY.sub.i), from which the admittance magnitude 
.vertline.Y.vertline. and phase angle .angle.Y are obtained: 
EQU .vertline.Y.vertline.=(Y.sub.r.sup.2 +Y.sub.i.sup.2).sup.1/2 
EQU .angle.Y=Tan.sup.-1 (Y.sub.i /Y.sub.r) 
For a typical unperturbed QCM in air, the series resonance f.sub.s is 
defined as when .vertline.Y.vertline. is maximum and .angle.Y is zero. 
Parallel resonance f.sub.p occurs when .vertline.Y.vertline. is minimum 
and .angle.Y is zero. The parameters related to extrinsic QCM properties, 
i.e., dependent upon QCM geometry, such as thickness h and area A), are 
determined. The intrinsic properties of the AT-cut quartz are: .rho..sub.q 
=2.651 g/cm.sup.3, c.sub.66 =2.947.times.10.sup.11 dyne/cm.sup.2, K.sup.2 
=7.74.times.10.sup.-3, and .eta..sub.q =3.5.times.10.sup.-3 g/cm-s. The 
QCM operated in air is nearly unperturbed, but has a small resistive and 
inductive contribution because of the non-zero density and viscosity of 
air. 
The invention actually contemplates two methods of obtaining 
admittance/frequency data. The first method would be to apply an 
oscillating signal to the QCM at its resonant frequency, and then while 
oscillating at the resonant frequency, measure the magnitude of the 
admittance of the QCM. When the mass and/or liquid loading is added, the 
resonant frequency and maximum admittance are remeasured. From the change 
in resonant frequency, .DELTA.f, and loaded maximum admittance magnitude, 
Y.sub.max, we can simultaneously determine the surface mass density 
p.sub.2 and contacting liquid density-viscosity product, .rho..eta.. This 
model assumes an "ideal" mass layer that has infinitesimal thickness and 
stiffness, a condition that is approximated in a number of circumstances. 
According to the model, the resonant frequency depends on a linear 
combination of mass and liquid loading terms, while the peak admittance 
depends only on the liquid loading: 
##EQU2## 
These equations can be solved for surface mass density, .rho..sub.s 
=.rho..sub.f h, where .rho..sub.f and h are the density and thickness of 
the mass layer, and the liquid density-viscosity product .rho..eta., where 
.omega..sub.o is the angular frequency of 2.pi.f, N is the harmonic 
number, the c.sub.66 factors are quartz stiffness parameters, K.sup.2 is 
an electromechanical coupling factor, .rho..sub.Q is the quartz density 
and k.sub.1 is the wavenumber which is related to the thickness of the 
quartz: 
##EQU3## 
Therefore, a measurement of the change in resonant frequency and the 
admittance at resonance can be used to extract the surface mass density, 
.rho..sub.s, and the viscosity-density product, .rho..eta., of the 
solution. This result, showing how the surface mass and liquid properties 
can be obtained from the resonant frequency and the admittance, is a 
crucial part of the technique and has not been previously demonstrated. 
A second method contemplates measuring the phase and magnitude of 
admittance over a frequency range centered around a fundamental or 
harmonic resonant frequency of the QCM. The data is then fit to the 
equivalent circuit model of FIG. 3. Fitting the admittance/frequency data 
to the model allows for determination of equivalent circuit parameters 
which in turn can be correlated to obtain a solid mass accumulation and 
the density-viscosity product. A complete theoretical analysis and 
solution of the boundary value problem for the admittance within a QCM 
contacting a solid mass layer and a fluid is given in Martin et al., 
"Characterization of a Quartz Crystal Microbalance with Simultaneous Mass 
and Liquid Loading," ANAL. CHEM., Vol. 63, No. 20, pp. 2272-2281 Oct. 15, 
1991), which is hereby incorporated by reference. 
It is to be appreciated that either of the two methods above may be used to 
measure either the solid mass accumulation and the liquid properties; or 
both simultaneously. For example, if no solid mass accumulates onto the 
surface of the QCM, then an accurate measurement of the density-viscosity 
product is obtained. And if the properties of the fluid do not change or 
if there is no fluid contacting the QCM, solid mass accumulation may be 
measured. 
To measure the effect of viscous loading on QCM admittance, various 
solutions contacted the grounded side of the QCM. The solutions were 
distilled water and three glycerol/water mixtures having distinct 
viscosity-density products. FIG. 4 shows admittance and frequency data 
(points) measured at the fundamental resonance as solution properties 
alone were changed. Several glycerol/water mixtures of varying density 
.rho. and viscosity .eta. contacted the device: (A) air, 
.rho..eta.=2.times.10.sup.-7 ; (B) water, .rho..eta.=0.010; (C) 43% 
glycerol in H.sub.2 O, .rho..eta.=0.044; (D) 64% glycerol in H.sub.2 O, 
.rho..eta.=0.15; (E) 80% glycerol in H.sub.2 O, .rho..eta.=0.72. With 
increasing .rho..eta., the admittance magnitude plot shows both a 
translation of the series resonance peak toward lower frequency, as well 
as a diminution and broadening of the peak. The parallel or anti-resonant 
dip in .vertline.Y.vertline. also becomes less pronounced as .rho..eta. 
increases. The admittance phase plot indicates that phase shifts occurring 
at f.sub.s and f.sub.p become less sharp and begin to cancel each other as 
.rho..eta. increases. 
The translation of the admittance curves arises from the inductance 
contribution which represents the kinetic energy of the entrained fluid 
layer. The broadening and diminution of the resonance peaks arises from 
the resistance contribution; this element may be called a "radiation 
resistance" because it represents power dissipation arising from the 
radiation of a shear wave into the fluid by the oscillating QCM surface. 
Increasing .rho..eta. causes a proportional increase in both energy 
storage and power dissipation. 
To measure the effect of surface mass on QCM admittance, measurements were 
made before and after the vacuum deposition of a gold film. The gold film 
was evaporated onto the larger electrode to provide a thin adherent mass 
layer. The gold thickness was determined from profilometry to be 124 nm. 
FIG. 5 shows the effect of mass loading on QCM admittance near the 
fundamental resonance: (A) in air before deposition; (B) in water before 
deposition; (C) in air after deposition; and (D) in water after deposition 
of a 124 nm gold layer. It is apparent that the major effect of mass 
deposition is to translate the admittance curves toward lower frequency 
without affecting the admittance magnitude. The increased kinetic energy 
contributed by the mass layer moving synchronously with the QCM surface, 
and the solid lines in FIG. 5 are predicted admittances. The result of 
calculations corresponds to a surface mass density .rho..sub.s =225 
.mu.g/cm.sup.2. Using the bulk density of gold at 19.30 g/cm.sup.3, this 
surface mass density corresponds to a gold thickness of 117 nm, which is 
within 6% of the thickness determined from profilometry measurements (124 
nm). Thus, electrical admittance measurements can be related directly to 
mass accumulation on the QCM. 
In summary, an analytic expression for the admittance of a QCM 
simultaneously loaded by a thin mass layer and/or contacting fluid has 
been derived. Mass and fluid loading lead to distinct admittance/frequency 
curves that can be used to discriminate between these loading mechanisms. 
This capability provides for important QCM applications such as fluid 
phase chemical sensors, viscometers, and plating rate monitors. The 
measurement of .DELTA.f and Y.sub.max is sufficient to determine 
.rho..sub.s and .rho..eta.; these parameters can be extracted from a QCM 
oscillator circuit having automatic gain control. However, the nature of 
the admittance/frequency data leads to greater precision in determining 
.rho..sub.s and .rho..eta., particularly at high .rho..eta., where the 
resonance peak is very broad. 
The method of the invention herein has applications in the field of 
electroless and electrolytic plating, and permits the real-time monitoring 
of the plating rate and solution specific gravity. Because the specific 
gravity of the plating solution can increase with time, particularly if 
the plating bath is overstabilized, it is extremely beneficial to monitor 
both the plating rate to ensure that the plating thickness is adequate and 
that the process is in control, and the specific gravity to determine that 
the mass measurements are accurate. 
The invention is also useful in sensor applications where an analyte is 
deposited as a mass layer onto a substrate from a contacting solution. 
Real-time-in-situ sol-gel viscosity measurements can now be accomplished 
economically because only the very thin layer of fluid contacting the QCM 
will be affected, leaving the bulk fluid unperturbed. 
While the invention has been described with respect to several embodiments, 
and to several applications, it is intended that the invention not be 
limited to the specifics disclosed therein; rather, the invention is 
presented as broadly claimed.