88 1 ANALYST, SEPTEMBER 1991, VOL. 116 Thickness-shear-mode Acoustic Wave Sensors in the Liquid Phase A Review Michael Thompson,* Arlin L. Kiplingt and Wendy C. Duncan-HewittS Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S ?A I , Canada Ljubinka V. Rajakovic and Biljana A. Cavic-Vlasak Faculty of Technology and Metallurgy, University of Belgrade, Carnegie Street 4, I 1000 Belgrade, Yugoslavia Summary of Contents Introduction Theoretical Aspects The TSM Sensor in the Gas Phase The TSM Sensor in the Liquid Phase Measurement Methods Applications Detectors for Liquid Chromatography Determination of Inorganic Species Development of Biosensors Properties of Thin Films Conclusions Appendix References Introduction The use of piezoelectric acoustic wave devices as chemical sensors has its origins in the work of Sauerbreyl and King2 who carried out microgravimetric measurements in the gas phase.In their work, they assumed that a thin film applied to a thickness-shear-mode (TSM) device could be treated in sensor measurements as an equivalent mass change of the quartz crystal itself. Accordingly, a shift in the resonance frequency of an oscillating AT-cut crystal could be correlated quantita- tively with a change in mass added to or removed from the surface of the device. This concept has been exploited extensively in the fabrication of chemically selective sensors for the gas phase, where a binding agent is incorporated into a film which is then deposited onto the TSM device. In recent times, there has been an increasing amount of attention paid to the operation and applications of the TSM sensor when it is exposed to the liquid phase.3-29 Studies have been made of: in situ deposition of films on the sensor surface, interfacial chemistry and bulk liquid phase properties such as density, viscosity and conductivity. Where deposition or removal of surface species has been involved, frequency shifts have invariably been interpreted in terms of Sauerbrey-like alteration of acoustic wavelength as postulated for the gas phase.In contrast, Thompson et 01.17 proposed that the possibility of changes of interfacial properties such as free energy and slippage were related to the behaviour of the liquid-phase TSM sensor. In this present paper the theoretical aspects are reviewed and measurement methods and applications are suggested for the TSM device operated in the liquid phase.Particular emphasis is placed on the role of interfacial parameters, a * To whom correspondence should be addressed. 'F Permanent address: Department of Physics, Concordia Univer- sity, 1455 de Maisonneuve Boulevard, Montreal, Quebec H3G 1M8, Canada. t Permanent address: Faculty of Pharmacy, University of Toronto, 19 Russell Street, Toronto, Ontario M5S 1A1, Canada. number of which are depicted in Fig. 1, in determining the response of the device. It is recognized that other acoustic wave structures, such as plate-mode and surface acoustic wave sensors, have been employed in the liquid phase. However, in order to be concise the present review deals for the most part only with thickness-shear-mode devices.Hydrophobicity , Deposited mass Thickness (LA \ Slip 1 \\ \ \ Electrodes Oscillating quartz crystal Schematic diagram of interfacial factors that govern the Fig. 1 behaviour of the oscillating TSM sensor in the liquid phase882 Theoretical Aspects The TSM Sensor in the Gas Phase In order to consider carefully the behaviour of the TSM structure in the liquid phase, it is necessary to review briefly the physical aspects of the operation of the sensor in the gas phase. For AT-cut piezoelectric crystals, the resonant condition corresponds to a thickness shear oscillation in which the shear wave propagates through the bulk of the material, perpen- dicular to the faces of the crystal. The atomic displacements corresponding to this shear motion are thus parallel to the crystal surface.If material is deposited on either one or both faces of the crystal, the resonant frequency decreases. The first quantitative investigation of this effect was made by Sauerbreyl who derived the relationship for the change in frequency AF (in Hz) caused by the added mass AM (in g): 2F 2 (1) A F = - L X - AM where Fq is the fundamental resonant frequency of unloaded quartz, pq is the shear modulus of AT-cut quartz (2.947 x 10" g cm-1 s-2), pq is the density of quartz (2.648 g cm-3) and A is the surface area in cm2. Note that AM is the total mass added to both faces of the crystal but A is the area of only one face. Collecting constants and letting Am = AM/A gives AF= -CIAm (2) where C1 = 2.26 x 10-6 Fq2 Hz cm2 8-1 and Am is added mass per unit area in g cm-2.Hence AF is linearly related to Am and this simple relationship is the basis for the application of piezoelectric crystals with a detection limit that has been estimated to be of the order of 10-12 8.2 For a 5 MHz crystal, according to eqn. (2) a decrease in frequency of 1 Hz is caused by an added mass of 18 ng cm-2. For a 9 MHz crystal Am = 5.5 ng cm-2 when A F = - 1 Hz, or A FlAm = -0.18 Hz cm2 ng- 1 . The sensitivity of a particular crystal can be defined as AF/AM and, for example, for a 9 MHz crystal with an electrode ANALYST. SEPTEMBER 1991. VOL. 116 diameter of 0.5 cm ( A = 0.20 cmz), AFIAM = 0.9 Hz ng-1, ignoring the minus sign. Sauerbrey's theory has been verified for the application of 'rigid' overlayers up to a mass load of Amlm = 2%3O where m is mass per unit area of the unloaded quartz.Several attempts have been made to expand Sauerbrey's theory by including a number of other parameters associated with deposited thin films. These are collected together in ,Table 1 for reference. Stockbridge31 applied a perturbation analysis to the loaded crystal. His mathematically rigorous approach was not, however, of immediate practical utility. Miller and Bolef32.33 applied a continuous acoustic wave analysis to a resonator formed by the quartz crystal and a deposited film. Provided that the acoustic losses in the quartz and thin film are small, it can be shown that the frequency is dependent on the shear wave velocity and density of both the film and quartz.Behrndt34 pointed out that the multiple oscillation period measurement technique is superior to the frequency measure- ment. Lu and Lewis35 and Lu36 have shown that for a metal film the acoustic impedance of the film is an important factor in determining the frequency response. Glassford37.38 made the first attempt to analyse the frequency response associated with an imposed liquid film and droplet deposit. By using the Navier-Stokes equation and a Rayleigh perturbation analysis Glassford was able to derive a relationship which included liquid viscosity, droplet size, velocity distribution and mass loading. Mecea and Bucur39 developed an energy transfer model which constitutes the most complex theory describing the functioning of the TSM acoustic wave device in the gas phase.They considered the mechanism of thin film interaction with the elastic properties of the resonating quartz crystal. The analogy of electrical reactance in series for two components has been applied to a coated piezoelectric crystal by Crane and Fisc her. 40 The TSM Sensor in the Liquid Phase In 1984, the view was expressed that liquid phase operation of the TSM device would not be possible because of oscillation Table 1 Gas phase theories of TSM acoustic wave quartz sensors* Equation AuthorsRef Mathematical model Sauerbre y 1 AM AF= -2.26 X 10-6 Fq2 - (1) A Miller and B 01 e f32.33 (2) ( 3 ) B e h ~ - n d t ~ ~ Lu and Lewis35 and Lu36 (4) ( 5 ) GI assf or d37.38 Mecea and Bucu1-3~ (6) tan = - z, Zf tan (2) AF F4 OL tan Ib(1- tan h2kb) + fi tanh kb (1 + tan%) npqVq (1 + tanh2kb tan2lb) - - _ Crane and Fischer40 - (7) * A glossary of the symbols used is given in the Appendix. Comments Only the effect of added mass is considered Propagation of the acoustic wave from the quartz into the deposited film is considered considered The change of period is The acoustic impedance of the film is considered Mass loading by a liquid film is considered Effects of electrode, film and quartz diameters on the sensitivity of a crystal coated with a thin or non-dissipating film are considered Bulk modulus, viscosity, density, and film thickness are consideredANALYST, SEPTEMBER 1991, VOL.116 883 suppression caused by viscous damping effects,41 despite an earlier study which demonstrated that a coated TSM device could be employed as a detector for liquid chromatography.The subsequent successful measurements in the liquid phase that involved new experimental techniques, spawned attempts to provide theories for coupling of the oscillating surface to a liquid medium. In this area attempts have continued to the present time; the various theories are summarized in Table 2. The first argument, based upon an empirical formulation was presented by Nomura and Minemura.5 The change in the resonant frequency that occurs on coupling one face of a piezoelectric crystal to an aqueous solution is ascribed to the density, p ( g cm-3), and specific conductivity, K ( Q - 1 cm-1) of the solution. For organic liquids the resulting change in frequency for total immersion of the device arises from the density (p) and viscosity [q(cP)] of the liquid.7 Although good agreement with experimental results was obtained, the disadvantages of these relationships are obvious; the numerical constants are characteristic of each particular crystal and the relationships are not based on a physical model. In 1985 two simple physical models were developed by Bruckenstein and Shay13 and Kanazawa and Gordon14 which predict the change of frequency of a sensor immersed in a liquid medium.The latter theory treats the quartz as a lossless elastic solid, and the liquid as a purely viscous fluid. The frequency shift arises from coupling the oscillation of the crystal, involving a standing shear wave, with a damped propagation shear wave in the liquid. A simple relationship was derived which expresses the change in resonant frequency of a piezoelectric crystal, due to the total contact of one face of the crystal with liquid, in terms of parameters that are characteristic of the crystal and the liquid phase [eqn.(lo), Table 21. The relationship for the change in frequency, AF, is derived with the assumption that the transverse velocity of the quartz surface is identical with that of the adjacent fluid layer. This simple shear wave model also provides a physical explanation of the fact that the velocity is important for TSM acoustic wave devices operating in the liquid phase. According to this theory the crystal does not drive the entire bulk of the liquid as the transverse displacement decays exponentially in the liquid with a characteristic decay length (Fig.2). This distance (6) varies with (qL)i and is the effective thickness of the liquid when it is treated as a rigid sheet. Accordingly, the added mass of liquid can be derived as 6pL = ( 2 p ~ q ~ h ) ; . Physically this model predicts that only a thin layer of liquid will undergo displacement at the surface of the bulk wave device, and the device response will be a function of the mass of this layer. By using dimensional analysis Bruckenstein and Shayl3 derived a similar although not identical relationship which can be applied to the bulk acoustic wave devices with one or two faces in contact with the liquid. In eqn. (11) (Table 2) AF is the difference between the frequency in air and the frequency in liquid when the liquid is in contact with one or both electrodes of the crystal (AFfor two electrodes in the liquid is twice as large as for one electrode).For a 9 MHz crystal with one electrode ( n = 1) in contact with water (pL = 1 g cm-3, qL = 10-2 g cm-1 s-I), the theory predicts that AF = It appears that both theories introduced new parameters for -6100 Hz. Table 2 Liquid phase theories of TSM acoustic wave quartz sensors* AuthorsRe' Nomura and Minemuras Comments Empirical formulation for aqueous solution. Conductivity and specific gravity are considered Nomura and Okuhara7 Empirical formulation. Viscosity and density are considered Viscosity and density are considered. Interfacial effects are disregarded Kanazawa and Gordon l 4 Bruckenstein and Shayl3 Viscosity and density are considered.Interfacial effects are disregarded Schumacher and co-workers25329 AF= - Surface roughness is considered Schumacher and co-workers25,29 PLE AmL = - 2 Heusler et al. 42 Hagerj4 Surface stress is considered Hydrodynamic coupling analysis. Liquid dielectric constant is considered Resistance of equivalent circuit is considered Muramatsu et a1.22 Similar to Nomura and Okuhara model7 but liquid dielectric constant is considered Yao and Zhou45 Shana et d.46 Piezoelectric effects are considered * A glossary of all the symbols used is given in the Appendix.884 ANALYST, SEPTEMBER 1991, VOL. 116 Fig. 2 sensor into a liquid Propagation of the transverse shear wave from the TSM the mass of a thin boundary film, in this instance a liquid film. Apparently, qL and pL are the parameters which are relevant to the operation and characterization of these devices in the liquid phase.Although experimental verification has been claimed for both theories, these approaches lack considera- tion of the microscopic boundary conditions between the crystal surface and liquid. Specifically, in order to understand the behaviour of acoustic wave sensors operating in the liquid phase, it is important to consider the effect of chemical reactions and processes that change in addition to mass, structure, surface free energy, interfacial viscosity and, possibly, diffusion on the crystal surface. More recent theories have examined some interfacial phenomena. Schumacher and CO-workers25-29 showed that surface roughness can also drastically affect the resonant frequency.They considered a roughened surface made up from hemicylinders with liquid entrapments which can be equivalently represented by a rigidly attached liquid layer. Under these conditions the frequency shift should contain the parameter AmL = pL&/2, where AmL is the mass per unit area of the liquid confined in the cavities of the roughened surface and E is the mean diameter of the hemicylinders. Heusler et al.42 promoted the theory of surface stress influence on the resonant frequency. The internal strains of quartz crystals immersed in a liquid arise as a result of hydrostatic pressure. Parabolic dependence of the resonant frequency, Fq, on the pressure, p , at the oscillator face [eqn. (14), Table 21 could be related to the elastic energy stored in the quartz.Hager and Verge43 and Hagel-44 derived a model using hydrodynamic coupling analysis to determine fluid properties. In their work , viscous energy losses, fluid velocity at the crystal surface and the dielectric effect of the liquid were considered. The frequency shift is described by an empirical equation with constants depending on the crystal equivalent circuit and the working conditions. Considering an electro- mechanical coupling analysis for the computation of equi- valent circuit parameters of piezoelectric devices in, contact with a liquid, Muramatsu et a1.22 developed a linear relation- ship between AF and (vLpL)g for alcohol-water solutions. Shifts from linearity were observed for high-viscosity liquids and when both faces of the crystals were in contact with water.According to Yao and Zhou45 the frequency response of an acoustic wave sensor in the liquid phase depends on the dielectric and conductance effects of the liquid. Based on their experimental measurements an empirical relationship resem- bling the expression of Nomura and Okuhara7 [eqn. (9), Table 21 was derived [eqn. (17), Table 21, As shown by Shana efal.46 a comprehensive analysis including piezoelectric effects could also be used to study a thin film of viscous liquid [eqn. (18), Table 21. When the piezoelectric effect is neglected this theory is similar to that derived by Kanazawa and Gordon.14 Thompson and co-~orkers17,*8 have shown that the response of the sensor can be associated with changes in interfacial surface structure, surface free energy andor interfacial viscosity. From a qualitative analysis of the operation of TSM acoustic wave devices in a liquid, two aspects were introduced.First, chemistry at the interface can lead to a perturbation of acoustic wave transmission caused by alteration of the partial-slip boundary condition at the interface. Secondly, as discussed by many of the workers mentioned above, the continuum viscosity and density of the bulk liquid will be important in determining the frequency response. Using the Navier-Stokes equation for Newtonian fluids and an expression describing transverse damped wave propagation, it was shown that the penetration depth of the wave is about 1 pm. The influence of the interfacial free energy and viscosity within this range of the penetration depth was considered.These effects could be associated with either new material deposited on the interface or by the time required for molecular re-orientation in the interfacial boun- dary layer. As an efficient acoustic bond demands continuity of stress and displacement across the interface, wave propaga- tion could be altered by out-of-equilibrium interfacial effects. For such an example, it was suggested that the frequency of .a crystal exposed to water may increase despite an apparent increase in deposited material. Clearly, in order to accept this argument it is necessary to invoke the controversial slip boundary condition for a solid-liquid interface in which either the solid or the liquid is in motion. Solving the differential equations of motion for the oscilla- tory system, consisting of the TSM device and the liquid with which it is in contact, requires that mathematical continuity be invoked at the interface.In order to accommodate the possibility of interfacial slip at the sensor-liquid interface,47 Duncan-Hewitt and Thompson48 have introduced the concept of additional interfacial regions of finite thickness in the liquid. These layers are endowed with mechanical properties that can be used to explain the experimental finding that coupling with the liquid phase appears to decrease with decreasing surface wettability. The existence of these pro- posed additional fluid layers has been verified by a wealth of experimental and theoretical work.49 In particular, thermodynamic analyses of adsorption isotherms indicate that at vapour saturation the bulk liquid must be at equilibrium with a surface adjacent film.Between this denser and more viscous layer and the bulk is a thin, monomolecular transitional region which is rarified relative to the bulk under incomplete wetting conditions, as in Fig. 3. Under completely non-wetting conditions, it is expected that this region would be indistinguishable from the vapour; acoustic waves would be reflected from this interface and the TSM sensor should behave as though no bulk liquid were present. Using the molecular theory of viscosity proposed by Krausz and Eyring,so Duncan-Hewitt and Thompson48 have provided a link between measurable bulk liquid properties such as density, viscosity, surface tension and contact angle, and the TSM sensor response.The model has provided results that are in agreement with the experimental results obtained to date and obeys the boundary conditions described above.ANALYST, SEPTEMBER 1991, VOL. 116 885 5.95 x 106 FrequencyIHz E c -8 .- - - - -10 C I -i Fig. 3 Four-layer model of the TSM sensor in liquid with predicted impedance-frequency plots for (a) complete wetting and ( b ) incom- plete wetting. Layers depicted from bottom to top are: solid piezoelectric material, interfacial liquid structure, rarified layer and bulk liquid Measurement Methods There are two types of methods used to characterize a quartz crystal sensor electrically, which may be called the active and passive methods. The active method is more commonly known as the oscillator method.In this method the quartz crystal is part of an oscillator circuit. It is connected between the output and input of the oscillator amplifier and provides positive feedback that causes oscillation of the circuit. The resonant frequency of the quartz crystal is measured by an electronic counter. The quartz crystal is active in the sense that it is continuously oscillating at a frequency controlled by the quartz crystal itself. In the passive method the quartz crystal is connected externally to an instrument which applies a sinusoidal voltage at various frequencies across the terminals of the crystal. Voltages are measured and then the electrical characteristics of the crystal, the impedance for example, can be found from the voltages. The crystal does not determine the frequencies at which the measurements are made and in this sense it is passive.(0 C, Fig. 4 (b) impedances of the circuit elements Equivalent circuit of the TSM sensor with (a) parameters and Cadysl was a pioneer in the development of the piezoelec- tric quartz crystal for frequency control in the communications field. His treatment is advanced and difficult to understand, but is one of the milestones in the literature. Bottom52 has presented the fundamentals of the theory of the quartz crystal simply and clearly. This work is recommended for beginners in the subject. Both Bottom52 and Cadys' have derived the equivalent circuit of the quartz crystal (Fig. 4). This circuit is the electrical model of the crystal in a gas, but it is not a good representation of the crystal in a liquid.When the crystal is immersed in a liquid, energy flows out of the quartz into the liquid in the form of acoustic waves and this is dependent on the properties of the sensor-liquid interface which are not included in the circuit model. However, the equivalent circuit does illustrate the main features of the behaviour of the quartz crystal in liquids of low viscosity. Hence the measurement methods will be described with reference to the impedance of the equivalent circuit in Fig. 4. Most quartz crystals are discs of AT-cut quartz which are TSM devices, that is, the atoms of the quartz oscillate in the plane of the disc. The resonant frequency of the sensors is in the range from 2 to 20 MHz. The impedance, 2, of the quartz crystal is complex: 2 = R + j X , where R is the real part of 2, the resistive part, and Xis the imaginary part of 2, the reactance.For the equivalent circuit (Fig. 4) the expression for the admittance, Y , is simpler than the expression for 2. By definition, Y is the reciprocal of 2 (ie., Y = l/Z) therefore if 2 is complex, so is Y : Y = G + j B ; where the conductance, G, is the real part of Y and the susceptance, B , is the imaginary part of Y . For the circuit shown in Fig. 4, (3) and The quantity, O, is the angular frequency (in rad s-1) and is defined by w = 2nfwherefis the frequency in Hz. For brevity the angular frequency will be called simply the frequency.886 ANALYST, SEPTEMBER 1991, VOL. 116 From Z = l / Y , the real and imaginary parts of Z in terms of G and B can be written as ( 5 ) The magnitude of impedance, 121, and the phase of im- pedance, 8,, are defined as Iz( = V F T Z (7) X 8, = tan-1- R The oscillator method measures the lower of the two frequencies of the quartz crystal for which 8, = 0.The explanation for this is as follows. There are two conditions that must be satisfied for oscillation to occur: the phase shift around the loop should be zero and the loop gain should be unity, the loop being the closed path from the input of the amplifier through the amplifier to its output, and back to the input through the feedback circuit element. The amplifiers used in the oscillator method have a zero phase shift and therefore the crystal must also have a phase shift of zero in order to satisfy the first oscillation condition.When the crystal is connected between the input and output of the amplifier, the loop gain is larger at the low frequency of zero phase and, hence, the second condition of oscillation is satisfied at this frequency. From eqn. (8), X/R = 0 when 8, = 0 and from eqns. ( 5 ) and (6), - B/G = X/R. Equation (4) divided by eqn. (3), with BIG set equal to zero, is a quadratic equation in o and its solution gives the two frequencies of zero phase: LO, called the series resonant frequency, the low frequency of zero phase and therefore the frequency measured by the oscillator method; and cop, called the parallel resonant frequency. If R, = 0, (9) where o,0 is o, when R, = 0 and similarly for oP0. However, Peristaltic Syringe injection in a liquid, assuming that the equivalent circuit is an adequate representation of the crystal, R, is of the order of magnitude of 103 8 hence eqn.(9) is not the frequency measured by the oscillator method. The most often used oscillator consists of two transistor- transistor-logic inverters connected in series to give a non- inverting amplifier (zero phase shift between input and output voltage) with the quartz sensor connected from the output to the input of the amplifier.l0,*3,'5,20 Oscillators with single transistors have also been used.7 A marginal oscillator has been used;17,*8 this is an oscillator with additional feedback applied internally which changes the gain of the oscillator amplifier in response to a change of energy dissipation in the quartz crystal, such that the amplitude of the output voltage of the amplifier remains constant.A wideband marginal ampli- fier is shown in Fig. 5. In order to carry out concurrent electrochemical measure- ments, two different experimental arrangements have been employed. The first is based on a stationary ~onfiguration2~27 in which an immersed quartz crystal in a housing is kept at a fixed position in the cell. The second is a recently developed elegant variant in which a rotating disc electrode was used to measure changes in mass.53 This type of device provides hydrodynamic conditions suitable for the suppression of polarization in experiments with dilute solutions. The oscillator method suffers from three kinds of limita- tions: (a) the method only partially characterizes a quartz crystal sensor because only one quantity, the series resonant frequency, is measured; ( b ) the resonant frequency depends on the capacitance in series with the crystal20 and in some instances on the type of oscillator used;29 and ( c ) the crystal does not oscillate when it is in solutions of high viscosity and if the crystal oscillates when the liquid is in contact with one electrode, it will often not oscillate if both electrodes are exposed to the liquid.Regarding limitation (a), more information can be extrac- ted from this method by measuring the output voltage of the oscillator amplifier,54 and the resonant frequency. The feed- back voltage of the marginal oscillator could also be measured. However, the characterization of the crystal is still incomplete.Limitation ( b ) can be understood in terms of the equivalent circuit of the crystal. A capacitor in series with the equivalent circuit (Fig. 4) will change the zero-phase frequen- cies. Different oscillators may have amplifiers with phase shifts that are not exactly zero and the oscillator circuit may have a capacitance which appears in series or in parallel with valve 0-ri'ng I / cry sta I I Voltage controller amplifier amplifier Amplitude Comparator I Reference voltage Fig. 5 Cell design for TSM sensor operation in liquid with wideband marginal oscillator and automatic gain control system. Also shown is the sensor incorporated into a liquid flow-through arrangement (reprinted by kind permission of the Institute of Electrical and Electronics Engineers)ANALYST, SEPTEMBER 1991.VOL. 116 887 the quartz crystal. Finally, the last limitation ( c ) is a fundamental deficiency of the oscillator method due to the fact that at high viscosities both resonant frequencies cease to exist because the phase shift of the crystal is always less than zero.55 Therefore, one of the conditions for oscillation (for an amplifier of zero phase shift) cannot be satisfied and, in principle, the circuit will not oscillate. The network analysis method is a passive method that has been recently developed by Kipling and Thompson55 that completely characterizes a quartz crystal sensor. This method can be used when a liquid of any viscosity is in contact with one or both electrodes of the sensor. Sinusoidal voltages incident on and reflected from the quartz crystal are measured repeatedly for a large number of frequencies in the resonant frequency range, that is, in the range that includes LO, and oP.(For sensors with f, and fp of the order of 107 Hz, f, - fp is of the order 104 Hz, wheref= 03/2n.) The experimental values of magnitude and phase of impedance, for example, can be calculated at each frequency from the measured voltages and then characteristic quantities can be found from the imped- ance-frequency curves. Some characteristic quantities from the phase measurements are: series resonant frequency; parallel resonant frequency; frequency of maximum phase and the value of maximum phase; and the slope of the phase curve at the series resonant frequency. The prominent characteristics from the impedance magnitude measurements are the frequencies at the minimum and maximum magnitudes of impedance and the corresponding values of impedance magnitudes.The theoretical values of 121 and 8, for the equivalent circuit are found by substituting eqns. (3) to (6) into eqns. (7) and (8). Muramatsu and co-workers22,23 used an impedance analyser to partially characterize a quartz crystal. This is a passive method in which, essentially, measurements are made of a voltage applied across the crystal and the current flowing through the crystal. They measured the maximum value of G and the frequency at which G is maximum. From inspection of eqn. ( 3 ) , the maximum value of G, G,,,, is G,,, = 1/R, and the frequency at G,,, is wSO, eqn. (9). They called this frequency the resonant frequency but it is not the resonant frequency measured by the oscillator method, LO,, unless R, = 0 which is certainly not true when the quartz crystal is immersed in a liquid.When R, f 0, LO, is larger than ws0 and cop is smaller than wPO. Both 03, - LO,,, and oPO - cop are proportional to R,2.52 Applications Detectors for Liquid Chromatography Use of the acoustic wave device as a universal mass detector for liquid chromatography was first suggested by Shulz and King.56 In reality these workers did not employ the sensor in an in situ configuration. Liquid samples from the eluent were simply sprayed onto a crystal surface. The first genuine flow-through design was published by Konash and B a ~ t i a a n s . ~ In this work a coated sensor was employed of which only one face was exposed to the liquid eluent.Although stable and mass sensitive detection was achieved, the system exhibited poor reproducibility. Oda and Sawadas7 incorporated a piezoelectric device in a flow cell as a photoacoustic detector in order to monitor chromatographic eluents, but the effects employed were associated with electroacoustic properties rather than piezoelectric operation. Finally, poly- (ethy1enimine)-coated crystals have been used for detecting various species in hydrocarbon solution,58 but in this study it was concluded that response time must be improved in order to cope with the short residence times involved in chromato- graphic detector cells. For the interest of the reader, we should note at this point that acoustic wave devices have been employed successfully as gas chromatographic detectors in a number of areas.5942 Determination of Inorganic Species Over the last several years, a single group, that of Nomura and co-workers,6.~-1~~12,15,63-69 has contributed significantly to the detection of a variety of inorganic species in the liquid phase using a TSM quartz crystal sensor.Generally these moieties were imposed at the sensor-liquid interface by the processes of electrodeposition or adsorption from aqueous solution. A summary of this work is presented in Table 3. Frequency dependence on liquid properties, such as specific conductance of electrolytes in solution70~71 has also been considered. Examples are the determination of micromolar concentrations of Hg" in waste water and microgram amounts of drugs containing iodine in biological material.Finally, Martin et al.72 studied the mass sensitivity of plate mode devices, modified with ethylenediamine ligands, for low concentrations of Cull ions in solution. Development of Biosensors It has been stressed a number of times in the recent literature that direct detection, possibly in an in situ manner, of analytical pairs such as antibody-antigen complexes and DNA hybrids could offer an attractive alternative to existing procedures. Not surprisingly, the appropriate possibilities for acoustic wave sensors in this area have been explored. Roederer and Bastiaans'l were the first to employ an acoustic wave device in an immunoassay procedure. A surface acoustic wave (SAW) sensor was immersed in an aqueous medium for the detection of an antibody by reaction with an antigen immobilized on the surface of the quartz. Although Table 3 Detection of inorganic species in aqueous solution using a quartz crystal sensor, from the work by Nomura and co-workers Coating on Concentration Analyte Au electrode Procedure range/pmol dm-3 Reference CN- CN- Ag' AE+ Ag' I- I- Pb2+ Pb2+ Fe3+ Fe3+, Al3+ Hg2+ cu2+ None Pt Pt Pt Ag on Pt Ag on Pt Pt Copper(I1) oleate Pt Silicone oil on Pt None Poly(viny1pyridine) Dissolution of Ag, 0.1-10 measurement in air Dissolution of Au 100-1 000 Electrodeposition 0.005-0.05 Internal 1-10 Electrodeposition 0.2-30 Electrodeposition 0.3-10 Electrodeposition 0.5-7 Adsorption 3-50 electrode position Absorption 3-40 Adsorption 10-100 Absorption 5-100 Adsorption 5-35 Electrodeposition 2-30 63 64 6 10 12 8 15 65 66 9 67 68 69888 ANALYST.SEPTEMBER 1991. VOL. 116 the specific binding of the complementary antigen was demonstrated, non-specific adsorption had taken place to a significant extent. Thompson et ul.17 were first to study interfacial immunochemistry by means of a TSM device in the liquid phase. An antigenic component was immobilized on an auxiliary thin film of polyacrylamide gel or directly on the crystal surface. However, the response of the device to the antibody was tentatively ascribed to interfacial perturbation of acoustic energy transmission rather than to a classical mass signal. In subsequent work the same group reviewed, on a qualitative basis, the diffusion-to-capture of interfacial immu- nochemical reactions, acoustic wave propagation through the liquid-solid interface and the characterization of piezoelectric crystal operation in water.18 It was postulated that shear wave devices are capable of generating two distinct types of analytical signals.Firstly, thin films characterized by a shear modulus of elasticity would provide a Sauerbrey-type mass measurement. Secondly, capture at a liquid-solid shearing surface could lead to a differential signal associated with the introduction of new material at the interface. The main idea is that acoustic wave devices operating in the liquid phase respond to a change in interfacial conditions, not to the absolute amount of added mass. A piezoelectric immunosensor for the detection of Cundidu ulbicuns microbes was developed by Muramatsu et ~1.21 Anti-Candidu antibody was covalently bonded on the plated platinum electrodes.The frequency of the crystal was recor- ded before and after dipping into a suspension of Candidu. The frequency change was observed and correlated with a concentration of Cundidu in the range 1 X 106-5 x 108 cells cm-3. Muramatsu et ~1.2’ also measured the response of AT-cut 9 MHz piezoelectric crystals to samples of human IgG under various operational conditions.22 Crystals were modi- fied by immobilizing Protein A on the oxidized palladium layer on the electrode surface with (3-aminopropyl)triethoxy- silane. Shifts in frequency were ascribed to the affinity reaction of Protein A and human IgG. Davis and Leary73 claimed to be able to continuously monitor the reaction of immunoglobulins with Protein A at the sensor surface.A frequency change of approximately 1 Hz for each 10 ng of added immunoglobulin was observed. They pointed out that because frequency decreases were demon- strated for added material at the sensor surface, the Sauerbrey mechanism must be correct. This was postulated despite the fact that no experiments confirming added material at the interface were mentioned. An indirect immunoassay involving polymer particles was developed by Kurosawa et u1.74 In their work the antibody-antigen reaction was carried out on latex and the frequency changes were regarded as being due to viscosity or density changes of bulk solution associated with aggregation of the latex particles.In addition to the TSM-device work outlined above, research has continued on the performance of immunoassays using the SAW device,75 in which the quartz surface of the sensor was etched and treated with (3-glycidyloxypropyl)- trimethoxysilane prior to immobilization of an antibody against influenza virus A. Frequency shifts were observed on exposure of the sensor to the virus. Richards and Bach76 have worked with DNA hybridization systems. In an ingenious experiment a DNA probe-type experiment was performed in which amplification of mass was obtained using iron oxide microparticles. These entities, bearing one of the reacting pairs, were attracted to the sensor surface by a magnetic field. Finally in this section, we should note that a number of studies have been performed in which the final bioanalytical signal has been obtained from the sensor in the gas phase, subsequent to reactions in solution.77-82 In view of the central theme of this review details of this work will not be outlined.Properties of Thin Films As has been the situation for the gas phase, a number of studies have been concerned with the in situ liquid behaviour of organic multilayers in the TSM sensor, both with respect to selective adsorption into such films and to their physical properties. Okahata et ~1.83 argued from studies involving adsorption of hydrophobic alcohols or cholesterol into various synthetic multilayer matrices, that the frequency response could not be correlated with density or viscosity changes of the film. The direct detection of the selective interaction between phospholipid or cholesterol multibilayer films cast on a piezoelectric crystal with cyclodextrins has been reported.84 Depending on their cavity sizes, cyclodextrins form soluble molecular-selective inclusion complexes through interaction with lipidic species. The cast films on crystal surfaces were stable and did not peel off the plate, even under harsh conditions in aqueous solution, which were confirmed by frequency observations of the crystal. Calibration showed that a decrease in frequency of 1 Hz corresponded to an increase in mass of 1.27 ng. Thickness-shear-mode acoustic wave devices have been used successfully to follow phase transitions in liquid crystals and lipid multilayers.85 Rajakovic et ~1.86 examined the role of the device-to-water acoustic interaction and, accordingly, the part played by interfacial viscosity in determining the frequency response.Frequency measurements in water for TSM sensors with gold, aluminium and silanized aluminium electrodes were obtained by the oscillator method. In that paper a number of aluminium electrode-based sensors were silanized using aminopropyltri- ethoxysilane and dichlorodimethylsilane and then exposed to water or aqueous solutions. The results showed that physical conditions at the polymeric silane-water interface can radiate the flow of acoustic energy into the surrounding medium as indicated earlier in this review. Conclusions It is evident from the progress reviewed in this article that the frequency response of the TSM device in liquids is governed by a number of factors.(Indeed the measurement of series resonant frequency produces a less than complete picture of the system.) Among these parameters, significant but hitherto unrecognized for the TSM sensor, is the role played by molecular slip and viscosity at the sensor-liquid interface. This observation opens up a number of new possibilities for application of the technique including, for example, the study of the physics of fluids at interfaces, surface structure of polymer films, extrusion phenomena, flow in porous media, lubrication and the development of a new type of signal for biosensor design. There is evidence in the literature that the above is now being recognized, at least with respect to the physical chemistry of liquids.87-90 Finally, we would like to emphasize that several of the interfacial arguments presented in this review have been discussed by other authors with respect to the different types of acoustic wave devices.In particular, readers are advised to consult the work of Ricco and Martin91 on plate devices and Diller and Frederick92 on torsional structures. The authors are grateful to the Natural Sciences and Engineer- ing Research Council of Canada for support of our work. Additionally, we appreciate the Fellowships provided to two of us, Lj. V. R. and B. A. C-V., by the Serbian Research Council of Yugoslavia.ANALYST. SEPTEMBER 1991, VOL. 116 889 APPENDIX Glossarv of svmbols used: , J Area of the quartz plate Numerical constant Numerical constant Numerical constant Liquid film thickness Numerical constant Numerical constant Numerical constant Numerical constant Numerical constant Numerical constant Stiffened elastic constant due to intrinsic viscosity of the quartz crystal Specific gravity of liquid Ratio of velocity amplitude at z and velocity Numerical constant Frequency change due to film Frequency change due to a liquid film Frequency change due to a solid film Resonant frequency of the quartz crystal with the Resonant frequency of the film amplitude at crystal surface, z = 0 film Fqm Resonant frequency of the quartz crystal without the Change of resonant frequency of the quartz crystal Height of liquid layer Real part of the propagation coefficient of the film Numerical constant Electromechanical coupling constant Imaginary part of the propagation coefficient of the film due to p-pm film Film thickness Quartz crystal thickness Mass per unit area of equivalent liquid layer Mass of the quartz crystal Mass of the film Change in mass due to solid film Number of sides of crystal in contact with liquid (n = Frequency constant of the specific crystal cut Pressure difference between the two sides of the quartz crystal Radius of the film Radius of the electrode Radius of the quartz crystal Resistance of equivalent circuit of quartz crystal Phase velocity of a shear wave in quartz One direction in a rectangular coordinate system Acoustic impedance of the film Acoustic impedance of the quartz Real part of the characteristic impedance of the film Imaginary part of the characteristic impedance of the Mean diameter of hemicylinders Dielectric constant of a liquid Dynamic viscosity of a liquid Specific conductivity of a liquid Shear modulus of quartz Density of the film Density of liquid Density of quartz Period change due to a solid film Phase angle by which the acoustic wave at z lags that at the crystal surface, z = 0 1 or 2) film 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 References Sauerbrey, Ci., Z.Phys., 1959. 155, 206. 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