Anal. Chem. 1991, 63,615-621
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Mediation of Acoustic Energy Transmission from Acoustic Wave Sensors to the Liquid Phase by Interfacial Viscosity Ljubinka V. Rajakovib,‘ Biljana A. Cavib-Vlasak,’ Vida Ghaemmaghami, Krishna M. R. Kallury, Arlin L. Kipling? and Michael Thompson* Department of Chemistry, University of Toronto, 80 S t . George Street, Toronto, Ontario, Canada M5S 1Al
Frequency measurements In water for bulk acousilc wave (thickness shear mode) sensors wlth gold, alumlnum, and sllanlzed aluminum electrodes have been obtained by the osclllator method. Statlc and time-course responses for particular electrode-to-water Interface conditions correlate with changes In hydrophoblcity. The water-Instigated alteration of the structure of silane films on aluminum electrodes has been studied by X-ray photoelectron spectroscopy, secondary Ion mass spectroscopy, gas adsorptlon experlments, and determlnatbn of advanclng contact angle wlth respect to water. The sensor responses are dlscussed in terms of perturbation of Interfacial viscosity and the slgnlflcance of this parameter In medlatlon of transfer of acoustic energy Into a Ilquld.
INTRODUCTION Bulk acoustic wave sensors of the thickness shear mode (TSM) type and surface acoustic wave (SAW) sensors have been used extensively in the gas phase ( I , 2) but much less in the liquid phase. The relatively few liquid-phase studies which have been reported have for the most part involved TSM structures. Indeed, the view was expressed in 1984 that such experiments would not be possible because of suppression of oscillation caused by viscous damping effects ( 3 ) ,despite an earlier study which demonstrated that a coated TSM device could be employed as a detector for liquid chromatography ( 4 ) . Since this work, a number of measurements, invariably employing the series resonant frequency of the TSM sensor, have been made in relation to in situ deposition of films on the sensor surface and bulk liquid-phase properties such as density, viscosity, and conductivity (5-16). An acoustic wave sensor for direct operation in the aqueous phase with an antibody immobilized to the device surface could permit an attractively facile and inexpensive detector for antigenic species. Such a device was first described by Roederer and Bastiaans (17) who performed immunochemical reactions on the quartz area of a SAW Rayleigh wave sensor. With regard to this type of measurement, subsequent doubt has been cast on the principle of surface wave propagation for SAW devices immersed in liquid (18). Since the appearance of the SAW experimental method, several studies involving immunochemistry a t the TSM electrode-to-water interface have been described in the literature (1%23). In nearly all this work and in that involving in situ deposition of materials mentioned above, it is almost universally accepted that the TSM device operates through a Sauerbrey-type microgravimetric response. Here, an applied thin film in gas-phase work is treated as an equivalent addition of quartz mass resulting in increased wavelength for the confined acoustic wave (24,W). The microgravimetry idea has also been proposed for the liquid case on an exclusive level despite the fact that explicit correlation of added mass to frequency rePresent address: Department of Analytical Chemistry, Faculty of Technology and Metallurgy, University of Belgrade, Carnegie Street 4,11OOO Belgrade, Yugoslavia. *Present address: Department of Physics, Concordia University, 1455 de Maisonneuve Blvd, Montreal, Quebec, Canada H3G 1M8.
sponse given by the Sauerbrey expression has not been demonstrated. Moreover, there is no reason, a priori, to expect that the only mechanism for frequency shift responses should involve an alteration of the acoustic wavelength (associated with deposited material) when, unlike the case for the gas phase, a significant amount of acoustic energy is being propagated into and absorbed by the liquid under investigation. In this respect it is interesting to note that theories derived to account for TSM response in liquids are essentially dimensional equivalents of the Sauerbrey expression (26,27). In the present paper, we examine the role of the deviceto-water acoustic interaction and, accordingly, the part played by interfacial viscosity in determining the frequency response. Here, it is strongly implied that the usually stated “no slip” boundary condition does not hold. This condition states that at the solid-liquid interface, the tangential components of velocity of the solid surface and liquid surface are the same, that is, the particles (atoms or molecules) on the surface of the solid and liquid are rigidly connected. The normal components of velocities of each medium at the interface are the same in all cases (no slip, partial slip, and complete slip) because otherwise the solid and liquid would not remain in contact at all times. The failure of the no-slip condition with respect to the operation of TSM devices in liquids has been alluded to previously by this group (19,23,28)and by others in connection with the performance of plate-mode devices (29-31 ).
EXPERIMENTAL SECTION Apparatus. Piezoelectric AT-cut quartz crystals (Leigh Instruments, Don Mills, Ontario) resonant at 5 and 9 MHz with aluminum and gold electrodes were incorporated in cells designed to operate either in the gas phase or in liquid media. For the latter case, one surface of the operating device was generally exposed to liquid of 50-pL volume in an overall measurement configuration described elsewhere (23). Gas-phase probe experiments on the sensor surface were performed in the flow-through train shown in Figure 1. This system included hydrocarbon and moisture traps in addition to sample evaporators fitted with dispersion frits to ensure maximum vapor saturation (32). The remainder of the setup in both situations incorporated an oscillator consisting of two TTL inverters connected in series (discussed later) and a universal counter (Hewlett-Packard 5228A) for frequency measurements. The data were collected by a computer (IBM-compatible PC) connected to the counter by a general purpose interface bus (National Instruments GPIB-PC IIA). X-ray photoelectron spectroscopy (XPS) measurements were obtained on either a Surface Science Laboratory SSX-100 or Leybold LH-DS 100 spectrometer with excitation by monochromatic A1 K a radiation. Secondary ion mass spectroscopy (SIMS) spectra were obtained on the former instrument by employing, as the source, 2.5 kV Xe ions of current 1.3 nA. The surface free energy of a number of sensor surfaces was examined by water contact angle measurements. Viscosities of various water-glycerol solutions at 22 “C were determined by using an automatic capillary viscometer (Eco Plastics Ltd., Toronto, Ontario). Reagents. (Aminopropy1)triethoxysilane (APTES) and dichlorodimethylsilane(DCDMS)were obtained from a commercial source (Aldrich, Milwaukee, WI). All other common laboratory chemicals were of reagent grade.
0003-2700/91/0363-0615$02.50/00 1991 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL.
63,NO. 6, MARCH 15, 1991 AMPLl F l ER
QUARTZ WAFER
M L D ELECTRODE
PIEZOELECTRIC CRYSTAL\
11
,DETECTOR
CELL
Flgure 2. Flgure 1. Flow-through train for exposure of sensor surfaces to gas-phase probes.
Procedures. A number of aluminum electrode-based sensors were silanized by using the agents APTES and DCDMS. After treatment with chloroform and acetone followed by vacuum drying, the devices were subjected to 100 mg of silanizing agent in 20 mL of dry toluene under nitrogen and under various reaction conditions including the use of the base catalyst triethylamine (TEA). Measurements of frequency response for 50 g L of water or aqueous solutions were obtained when steady values (A2 Hz) were reached. The results were always referenced to the frequency of the same device operating in air. Two types of experiments were performed. First, the response of gold and aluminum sensors to solutions of different viscosity was measured, and second, the frequency-time-course for silanized aluminum electrodes was assessed. Such experiments with APTES-coated sensors were performed at least 20 times. In the latter case, XPS and SIMS spectra were recorded before and after exposure of the sensor to water and, in addition, an analogous time course for variation in contact angle was also obtained. The surface chemistry of aluminum electrodes coated with about 10 gg of APTES was also probed before and after exposure to water by measuring, as a function of time, the frequency response of the sensor to various gases in the flow-through train mentioned above. This technique, which has been employed previously ( 3 2 ) ,involves measurement of the maximum (steady state) response that occurs after sufficient duration of exposure to concentrations of organic species. The latter are calculated from vapor pressure data and in certain cases confirmed by gas chromatographic analysis after appropriate trapping.
RESULTS AND DISCUSSION Oscillator Method. In view of the fact that previous papers in this field have given only a cursory treatment of the principles of the oscillator method without any reference to the fundamental limitation of the method, we include a discussion of this point in the present paper. First, the basic circuit of the oscillator will be analyzed, and then the behavior of the quartz crystal sensor in terms of its equivalent circuit will be explained. The oscillator circuit used in this work is essentially two TTL inverters in series and the quartz crystal sensor connected from the output of the second inverter to the input of the first, as in ref 11, for example. Other types of oscillators have been used in studies employing the oscillator method, but all are functionally the same as the TTL-inverter-type oscillator. An oscillator is an amplifier that produces an output without an input. Figure 2 is the basic circuit of an oscillator. The amplifier has a voltage gain, A, which is defined as the ratio of the output voltage, v,, and input voltage, vi: A = u,/ui. In general, u, and vi are not in phase and so A is a complex number. 2 is the feedback impedance which represents one or more circuit elements. 2 has a resistive part, R,, and a
Basic oscillator circuit.
reactive part, X,:Z = R, + jX,. R is a resistance connected between the input of the amplifier and common, and it includes the input resistance of the amplifier. 2 and R form a voltage divider, and so the feedback voltage, uf, is a fraction of the output voltage, u,: vf = Pv, where P = R / ( R + 2). The fraction, 6 , is a complex number since 2 is complex. Let the input of the amplifer be connected to an external voltage source, point 1 in Figure 2. The input voltage, vi, produces the feedback voltage, uf: uf = flu, = PAui. This equation Uf = PAui
(1) leads to the basic equation of the oscillator. Suppose that there is a frequency of the input voltage from the external source for which uf is exactly the same as ui a t all times: uf = vi, which requires that the frequency, amplitude, and phase of uf and vi are identical. Then, at this frequency, if the input is instantaneously switched from point 1to 2 in Figure 2, the input voltage to the amplifier is unchanged and therefore the output voltage, u, = Aui, remains the same. There is no longer an external input to the amplifier, but there is still an output; the amplifier is oscillating. The condition for oscillation, vf = vi, in terms of the parameters of the circuit is, from eq l PA = 1 (2) The quantity PA is called the loop gain. Since either or A can be a complex number, eq 2 states that the magnitude of PA, IPAl, is 1 and the phase of PA is 0. These are the two criteria that must be satisfied for oscillation to occur. In words, the criteria are (a) the magnitude of loop gain is unity and (b) the phase shift around the loop is zero. Criterion b determines the frequency of oscillation of the circuit. Then at this frequency if A has a value such that criterion a is satisfied, there will be oscillation. In all practical circuits, lPAl > 1 and the amplit,ude of the output voltage is limited by the nonlinearity of operation of the amplifier (as u, approaches the maximum value allowed by the circuit, A decreases). In the oscillator method the amplifier which is always used is noninverting, meaning that the output voltage is in phase with the input voltage, in order to measure the series resonant frequency defined below. So the phase shift through the amplifier is zero (A is a positive real number). In order to satisfy crit,erion b, the phase shift of P must also be zero (@ must be a positive real number) and therefore the phase shift through 2 is zero (2is real since R is real, from the definition of P). 2 is the quartz crystal sensor in the oscillator method. The equivalent circuit of the quartz crystal is given and analyzed by Kipling and Thompson (28). There are two frequencies a t which the phase of the equivalent circuit is zero: f,, called the series resonant frequency, and fp, the parallel resonant frequency (f, is always less than f p ) . So criterion b is satisfied at two frequencies for the quartz crystal. The
ANALYTICAL CHEMISTRY, VOL. 63, NO. 6, MARCH 15, 1991
VISCOSITY, CP
Frequency responses for 5- and 9-MHz sensors with hydrophobic Au and hydrophilic AI electrodes for water-glycerol solutions of varying dynamic viscosity. The frequency change is the frequency measured in air minus the frequency measured in the solution. Figure 3.
variation of the magnitude of 2 with frequency determines at which frequency criterion a is satisfied. 2 is much smaller a t f, than at fp and so fl = R / ( R + 2) is larger at f, than at f,,. As a consequence, criterion a is satisfied a t f, (at fp, PA < 1). If R and 2 are interchanged in Figure 2, by similar reasoning, the circuit would oscillate at frequency fp, but this configuration is not used in the oscillator method. The result of the analysis of the basic circuit of the oscillator method is that the frequency of oscillation of the quartz crystal is the series resonant frequency, f,. But the method will not work for all conditions of the crystal. There is an inherent limitation of the oscillator method which is due to the fact that when the quartz crystal is in a liquid of sufficiently high viscosity, criterion b is never satisfied because the phase of 2 is negative at all frequencies and the circuit will not oscillate (28).
From the preceding theory and the results obtained by using the network analysis method (28), it would appear that the oscillator method could be used for any viscosity if the phase shift of the oscillatory amplifier is judiciously choosen to be some particular positive value, 0,. Indeed, the circuit will oscillate at a frequency for which the phase shift of the quartz crystal is -Ba, neglecting other phase shifts around the loop which may occur in a practical circuit. But when Be # 0, the frequency of oscillation is not f,, which is the frequency in the Sauerbrey theory, but is a frequency lower than f,. Furthermore, the frequency of oscillation will not vary in the same way as f, varies. For example, as viscosity increases, both the oscillation frequency and f, decrease, but the oscillation frequency decreases by a greater amount. This can be visualized by considering a small Ba and noting that (d0/dflfSdecreases as viscosity increases, where 0 is the phase shift of the quartz crystal (28). Electrode Surface. Figure 3 shows measurements of the series resonant frequency of 5- and 9-MHz sensors with gold and aluminum electrodes exposed to water-glycerol solutions of different viscosity. The notation, A1-9, means aluminumelectrode 9-MHz sensor, and similarly for the other notation. Both electrodes of the 9-MHz sensors (Al-9 and Au-9) and only one electrode of the 5-MHz sensors (Al-5 and Au-5) were exposed to the solution. The frequency change is the difference between the frequency measured in air and in the solution. The viscosity is the dynamic (also called absolute) viscosity in units cP, which is g/(cm s). The curves given in Figure 3 exhibit three features of significance. First, there is a considerable difference in frequency change (relative to air) for the aluminum and gold electrodes with the greatest decrease of frequency being recorded for
617
aluminum a t both 5 and 9 MHz. For each electrode the frequency change is about 6 times greater a t 9 MHz than at 5 MHz, but the factor would be 3 instead of 6 if only one electrode of the 9-MHz sensor was in contact with the liquid (26). Secondly, there is an apparent correlation between frequency response and bulk viscosity, and lastly, the slopes of the plots for each electrode are not the same. The latter result has been reported previously by us (28). With respect to the first observation, no electrolyte is present and no mass has been added, and therefore, another factor must be governing the nature of the responses. One possibility is the surface free energy and/or interfacial viscosity of the metal-to-water interface. The advancing contact angle of solvent-cleaned gold and aluminum electrodes was found to be 106 f ' 4 and 10 f ,'Z respectively. The high value obtained for gold represents a discrepancy with the lower value reported by us previously (28). Analysis of the gold surfaces by XPS revealed the expected hydrocarbon contaminants, as evidenced by a C(1s) peak, since no special care was taken to avoid contamination by laboratory air after primary cleaning. (Rigorously cleaned gold is apparently hydrophilic but is very rapidly contaminated by hydrocarbons to yield quite high and variable contact angles (33, 34).) The result for aluminum is clearly related to the hydrophilicity associated with aqueous hydrogen-bonding to the oxide layer on the metal surface. Accordingly, we note that there is a faithful correlation between the degree of acoustic wave coupling to water and interfacial free energy, as reflected in measured contact angles. By inference we conclude that the level of such coupling is determined by the viscosity at the metal-solution interface. In light of the above, we wished to examine this effect further by a study of the time-course of frequency changes for alteration of interfacial free energy without any significant loss or gain of mass at the sensor surface. To achieve this aim, the structure of polymeric APTES a t the aluminum oxide interface, where solvent-instigated reorientation phenomena are known to occur (35),was employed. Before evaluation of the sensor-APTES (and sensor-DCDMS) film response, a study of the behavior of the surface-bound APTES film as a function of water treatment is necessary. Silanized Aluminum Interface. APTES constitutes one of the most extensively used silanizing agents for surface modification. Surfaces treated with this reagent have been examined by a number of techniques including solid-state 13C and NMR spectroscopy (36,37),FTIR spectroscopy (38, 39), XPS (40,41), SIMS (42),and ESR spectroscopy (43). The literature in this area indicates that the surface-bound ATPES forms a polymeric rigid network and is characterized by varying levels of ethoxyl group population, the presence of both free and protonated amino functionalities, and significant increase in siloxane formation (with concomittant increase in hydrophobicity) on exposure to water. The amount of deposited APTES observed on the aluminum electrodes of sensors as a function of reaction condition is given in Table I. The mass values were obtained from conventional gas-phase experiments after silanization and were calculated from the classical Sauerbrey expression. The approximate number of layers of reagent deposited on each side of the sensor is estimated from the total mass area of the sensor surfaces and molecular dimensions of the APTES molecule used in AM1 calculations ( 4 4 ) . (The latter is a semiempirical molecular orbital method that can be employed to study hydrogen bonds of relatively large molecules (45).) Clearly, there is a tendency for this silanizing agent to form polymerized multilayer structures, particularly when base catalyst is employed. The XPS spectra of two aluminum-plated sensors silanized with APTES, one prepared with TEA and the other nonca-
ANALYTICAL CHEMISTRY, VOL. 63, NO. 6, MARCH 15, 1991
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igg2 I
Table I. Frequency Responses for Sensors with APTES Films Deposited under Various Reaction Conditions
5,"
BEFORE WATER TREATMENT
reacn response for conditions device." temp, time, HZ (*2 '2) approximate approximate catalysis "C h 5 MHz 9 MHz mass, pg no.* of layers no no yes yes yes yes yes
21 21 21 110 110 110 110
1
24 24 1 2
3 4
162 308 853 827 1435 1503
679 2478 4700 6150 9050
0.8 1.3 4.1 4.1 7.4 9 15
3
4 14 14 24 30 50
50
a Mean of four measurements. bBased on device area, about 1-cm2 total for 5 MHz and 0.4-cmZtotal for 9 MHz, and APTES dimension from ref 44.
100 DALTONS
52
150
200
TREATMENT
8 Table 11. XPS Data for APTES Films on Sensors before and after Water Treatment
use of catalyst"
water Si(2p):A1(2p) treatmentb ratio
no
no
1.80
no
Yes
1.60
Yes
no
6.0
yes
Yes
7.0
binding energies, (*0.2 N(ls)' Si(2~,,~) 400.1 402.5 400.0 401.5 400.3 402.2 400.2 401.4
(30) (70) (55) (45) (50) (50) (75) (25)
102.0
50
160 DALTONS
150
260
Figure 4. Positive SIMS spectra of APTES films on AI electrodes before and after water treatment. Excitation is by 1.3-nA, 2.5-kV Xe
ions.
101.9
1
102.9
0-NITROTOLUENE
101.9
OReaction overnight a t 21 O C . bSubjected to H 2 0 for 3 h. Intensity contributions for N(1s) in parentheses.
-I H
talytically prepared, and in each case under anhydrous conditions and after water treatment, are summarized for the N(1s) and Si(2p3/J regions in Table 11. These results show that there is no major change in the intensity ratios of the Si(2p):A1(2p) signals subsequent to water treatment, which indicates that no significant loss of surface silane takes place. Both the protonated amino N(1s) (from 402.5 eV) and Si(2p3,,) signals exhibit a downward shift of about 1 eV on treatment of the catalytically prepared surface with water. We attribute the latter result to increased siloxane conversion, whereas the former reflects changes in the nature of hydrogen bonding of the amino function (less positive charge on the nitrogen atom). The positive SIMS spectra for water-treated and anhydrous silanized (by using TEA) surfaces in Figure 4 are virtually identical with respect to mass peaks, again demonstrating no gross perturbation is caused by the liquid. The same ion currents for the various masses appear at the same intensity ratios for the two spectra. However, the total ion current is approaching a 2-fold higher value for the former surface than the latter. We attribute this difference to the formation of hydrogen-bonded structures of lower bond strength upon water treatment. This hypothesis stands in agreement with the N(1s) binding energy changes discussed above. The results outlined so far clearly point to structural changes in the APTES film rather than material loss caused by exposure to water. An excellent probe of the surface condition of the APTES layer is the tendency of the bound reagent to selectively adsorb various organic species to the amino functionality through hydrogen bonding. In the present work, a number of gases at saturation level in carrier Nzat 20 "C were introduced to the above-mentioned flow-through acoustic wave cell in which a 9-MHz APTES-coated sensor was incorporated. Typical reversible responses for o-nitrotoluene and benzaldehyde are depicted in Figure 5. The response of the sensor, before (curve 1) and after (curve 2)
W
v,
z
2
v, W
E
>
V
z
ll
BENZALDEHYDE
W
2 0 W
E LL
I
I
I
I
ANALYTICAL CHEMISTRY, VOL. 63, NO. 6, MARCH 15, 1991
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Table 111. Gas-Phase Probe Responses and Sensitivities for A P T E S Films on 9-MHz Sensors before and after Water Treatment
compd
concn," mmol L-l
benzene
4.1 0.013 1.2 0.009 0.009 0.0096 0.19c 0.06 0.035
nitrobenzene toluene o-nitrotoluene m-nitrotoluene p-nitrotoluene phenol
benzaldehyde aniline
after water treatment sensitivity of A, Hz mmo1-l response, Hz L
before water treatment sensitivity of B, Hz mmol-' response, Hz L 122
125 224 165 156 204 182 135 518 201
29 8600 87 12400 10600 9300 590 17100 4900
112 105 112 95 84 112 1024 172
"From the following formula: concentration (mmol L-l) = [vapor pressure (mmHg)/760 (mmHg)] X
0.9 l.O
c
7 7
f
30 17200 137 17300 22700 20200 710 8600 5700 41.6.
ratio of sensitivities AIB 1.0 2.0 1.6 1.4 2.1 2.2
1.2 0.5 1.2
*For 60 "C. CFor50
"c.
r h j e c r i o n of HzO
i
L
+ APTES
ia
DCDMS
0.2 0.3
0.1 : 0
60
120
180
TIME, minutes Figure 6. Cosine of advancing contact angle versus time for exposure of APTES-coated and DCDMS-coated sensors to water.
L--
0
of multilayered APTES. Accordingly, we can conclude reasonably that surface site saturation is not reached for any of the compounds, with the possible exception of benzaldehyde. Thus, the results shown in Table I11 confirm that compounds containing the nitro group interact selectively with APTES amine functionalities through a hydrogen-bonding configuration (44). A further important observation is that the same compounds are detected with significantly increased sensitivity after treatment of the APTES film with water (the ratios of sensitivities are greater than unity in Table 111). As discussed above, this observation is clearly associated with a structural change in the silane polymer which results in increased population by the free amino group. We now turn to an examination of the surface free energy of the APTES-coated sensors and their liquid-phase frequency response. Figure 6 shows plots of cos (contact angle) versus time, from the measurement of advancing contact angle, for exposure to water of APTES and DCDMS surfaces. Both systems depict a relatively slow but significant decrease in surface free energy with time. We attribute this rise in hydrophobicity to water-instigated reorientation of APTES polymer bonds to yield fewer polar groups a t the polymerliquid interface ( 3 5 , 4 7 ) . This argument is highly consistent with the measurements outlined above. Oscillation of the APTES- and DCDMS-coated TSM sensors in water resulted in the typical frequency responses shown in Figure 7 . The imposition of water mass load begins a t 20 min. This causes a large frequency drop, which is followed first by a period of stabilization and secondly by a significant increase in frequency (about 200 Hz).In terms of mass, such an increase would correspond to a loss of about 1Fg of material (for a 5-MHz device). Since this figure is higher than the
TIME, minutes Flgure 7. Typical frequency responses with time for exposure of uncoated, APTEScoated, and DCDMScoated sensors to water. These plots are for 5-MHz Al-electrode devices treated in a single step with 50 FL of water on one side of the sensor. The experiment witfi APTES was repeated 20 times.
original amount of APTES, which was coated noncatalytically in this experiment (and considering the results outlined above), it is necessary to look for an alternative explanation other than mass loss for the increase in frequency. It is particularly noteworthy that the latter effect follows a similar time-course to the surface free energy changes discussed previously. Furthermore, the direction of the frequency change is identical with that in Figure 3 for the two uncoated electrode surfaces, that is, increased hydrophobicity correlates with a rise in frequency (less acoustic energy transmitted to the liquid). It now behooves us to consider the origin of this phenomenon. Acoustic Transmission, Interfacial Viscosity, and Molecular Slip. Taken together, the results for the bare electrode surface and silanized sensors clearly imply that the sensor-to-water interface mediates the amount of acoustic energy that is transmitted to the liquid and in turn the resonant frequency of the device. Accordingly, we must consider the motions of the surface of the TSM sensor and corresponding adjacent layer of water and, in particular, how these relate to the flow of energy into the liquid, the link between interfacial free energy and viscosity, the structure of water at hydrophilic-hydrophobic interfaces, and the concept of slip versus stick boundary conditions. In this analysis we must assume that possible changes in surface morphology are included in contributions to the alteration of interfacial free energy.
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ANALYTICAL CHEMISTRY, VOL. 63, NO. 6, MARCH 15, 1991
At the macroscopic level, a sensor in a liquid corresponds to the following system: a liquid occupies the space on one side of a rigid plane wall as the wall oscillates sinusoidally in its own plane (48,49). A transverse wave propagates into the liquid in a direction perpendicular to the wall with an amplitude that decreases with distance from the wall. By use of the notation and results of Landau and Lifshiftz (49),the characteristics of the wave motion in the liquid, including the energy flowing into the liquid, are presented. The no-slip boundary condition is used in this analysis. The wall is in the y z plane with the liquid in the region x > 0. The y axis is taken as the direction of oscillation of the wall. The displacement, y, of a particular point on the wall is
(6)
locity of sound in air is about 340 m/s.) Finally, the term ( w ~ 7 p / 2 ) ' /in ~ the energy expression, eq 6, for 5 MHz in water is 400 g/(cm2 s) and for glycerol, 18700 g/(cm2s). So at 5 MHz, about 47 times more energy flows into glycerol than into water. The same point is true at 9 MHz. The energy propagation into a particular liquid a t 9 MHz is (9/5)1/2= 1.35 times greater than at 5 MHz if uo,the amplitude of u (maximum velocity) of the wall, is the same at both frequencies. If the maximum displacement of the wall, yo, is the same at both frequencies, then since uo = coyo, the amount of energy that flows into the liquid at 9 MHz is (9/5121.35= 4.35 times greater than at 5 MHz. Note that the energy transmitted at different frequencies into the same liquid is not directly related to the change of resonant frequency, which varies as PI2according to the Sauerbrey theory for the liquid phase (28). Neither yo nor uo can be controlled by the oscillator method. Furthermore, the energy dissipation given by eq 6 is not measured by the oscillator method; only resonant frequency is measured. But the network analysis method (28) can measure energy dissipation and so uocan be calculated from eq 6 and then yo from uo = wyo. The experimental evidence presented earlier implies that this argument must be modified to include perturbation of the system associated with the interfacial properties of the "wall", that is, the no-slip boundary condition cannot be invoked. (It is, in fact, usually employed by fluid dynamicists as a convenience in solving the equations of motion.) The concept of interfacial viscosity is an old one going back to the classical paper of Moore and Eyring (50). They viewed this parameter as involving an activation energy for flow of liquid over a solid, which implies the severing of bonds to allow the molecules of the liquid to move from one surface position to another. This is why a connection between interfacial free energy and viscosity can be expected and why a correlation between frequency response and contact angle was observed in this work. The same chemical forces are, in part, responsible for the development of interfacial free energy and resistance to flow at an interface. Indeed, such a link was introduced by Tolstoi (51) in his earlier theory regarding slip between a liquid and solid. The concept of slip boundary conditions at interfaces has been evaluated a t the microscopic and theoretical level by Oppenheim and co-workers (52, 53) and has recently been reviewed by Blake (54). A crucial point to emerge from those arguments is that the true boundary condition is ultimately governed by both wall forces (chemical bonds) and the structure of the liquid formed at a particular interface. With respect to the latter it is particularly interesting to note that in recent years there has been increasing attention paid to the difference between water structures present a t hydrophilic and hydrophobic interfaces (47,55-57). The work presented in this paper appears to constitute an additional technique for examination of such interfacial structures.
where 7 is the absolute viscosity and p is the density of the liquid. (By definition, kinematic viscosity, u , is Y = v / p . ) The energy, E , is kinetic energy transmitted into the liquid which is then dissipated (converted into thermal energy) in the liquid. It is instructive to consider the two liquids, water and glycerol, and the two TSM quartz crystals, 5 and 9 MHz. The kinematic viscosity and density of water are u, = 1mm2/s and p , = 1 g/cm3 and for glycerol, vg = 1400 mmz/s and pg = 1.26 g/cm?. The penetration depth, 6 in eq 5 is, for water at 5 MHz, bw5 = 0.25 pm and, for water a t 9 MHz, 6,, = 0.19 pm. Similarly for glycerol, b,, = 9.4 pm and 6,, = 7.0 pm. The wavelength, 2 ~ 6 for , 5 MHz in water is 1.6 gm and in glycerol, 59 pm. The phase velocity, w6, for 5 MHz in water is 7800 m / s and in glycerol, 295000 m/s. (For comparison, the ve-
CONCLUSIONS The results presented here show that the interfacial physical condition at the surface of a bulk acoustic wave (thickness shear mode) sensor in liquid can mediate the flow of acoustic energy into the surrounding medium. This process can affect the frequency response of the sensor that is being operated by the oscillator method. Hydrophobic sensor surfaces display lower interfacial viscosity, which has its origins in increased molecular slip, than hydrophilic surfaces. Accordingly, it is important to consider this effect in liquid-phase TSM sensor systems that are responding to added (or lost) material imposed a t the device-to-liquid interface. Such responses will clearly be governed by both extension (or contraction) of the acoustic wavelength (the so-called mass response) and the alteration of interfacial viscosity. The domination of response
y = yo sin (ut)
(3)
where w = 27rf is the angular frequency, f is the frequency, and t is the time. This point on the wall is a t the origin of the coordinate system at t = 0. The velocity of all points on the wall is the same since the wall is rigid. So the velocity of the wall, u , is u = dy/dt and from eq 3 u = uo cos ( a t )
(4)
where uo = wyo. The constants yo and uoare the amplitudes (maximum values) of y and u , respectively. The Navier-Stokes equation is solved for the velocity of the liquid, u, a t any time, t , and any distance from the wall, x . The boundary condition u = u for x = 0 is used, that is, the liquid in contact with the wall moves with the same velocity as the wall, the no-slip boundary condition. The velocity of the liquid, u, is everywhere in the y direction. The result is u = uoe-x/6cos ( x / 6
- ut)
(5)
where 6 = ( ~ Y / W ) ' / ~and Y is the kinematic viscosity. In order to visualize the wave motion, consider a snapshot of the wave at t = 0 (assume the wall has been oscillating for a long time before t = 0). A t t = 0, u has local maxima at x / 6 = 0, 2 ~ , 47r, ... but the amplitude of velocity, uoe-x/6, decreases exponentially with x . For example, at x = 0, 6, 27r6 (one wavelength from the wall), and 47r6 (two wavelengths), the amplitudes are, respectively, uo,u0/2.7, u0/535, and 3.5 x 1O4uW The quantity 6 is called the depth of penetration, since it is a measure of the thickness of the liquid into which the wave travels before it is dissipated. From inspection of the cosine term in eq 5, the frequency of the wave, f = w/27r, is the same as the frequency of oscillation of the wall, the wavelength, A, is X = 2 4 and the phase velocity of the wave, up, is up = w6. The energy per unit time per unit area of the wall, E, which flows from the wall into the liquid is
E ='/2u0"4a
ANALYTICAL CHEMISTRY, VOL. 63, NO. 6, MARCH 15, 1991
by one of these factors will depend in a complex manner on the properties of the new film a t the interface. For example, a metal layer deposited on the sensor surface will not yield the same behavior as the same mass of a deformable, highly hydrated protein layer. Finally, we are in agreement with the statement of Schumacher (58) that the TSM sensor presents interesting new possibilities for the examination of interfacial physical chemistry, but not for the same reasons. We believe that perturbation of interfacial viscosity offers additional scope for device development, particularly in the area of biosensor technology, which is hitherto unexplored.
ACKNOWLEDGMENT We are grateful to E. Yang for assistance with the gas-phase adsorption experiments and to D. C. Stone and W. C. Duncan-Hewitt of the University of Toronto and G. Blackburn of IGEN Inc. for much helpful discussion. LITERATURE CITED (1) McCallum, J. J. Analyst 1989, 174, 1173. (2) Nieuwenhuizen, M. S.; Venema. A. Sens. Mater. 1989, 5 , 261. (3) Guilbault, G. G. I n Applications of Pieroelectric Ouartz Crystal Microbalances; Lu, C., Czanderna. A. W., Eds.; Methods and Phenomena, Their Applications to Science and Technology, Vol. 7; Elsevier: New York, 1984: p 251. (4) Konash, P. L.; Eastiaans, G. J. Anal. Chem. 1980, 5 2 , 1929. (5) Nomura. T.; Iijima, M. Anal. Chim. Acta 1981, 137, 97. (6) Nomura, T.; Okuhara, M. Anal. Chim. Acta 1982, 742, 281. (7) Nomura. T.; Mimatsu, T. Anal. Chim. Acta 1982, 742, 237. (8) Nomura, T.; Maruyama, M. Anal. Chim. Acta 1983, 747, 365. (9) Nomura, T.; Nagamune. T. Anal. Chim. Acta 1983, 755,231. (10) Nomura, T.; Tsuge, K. Anal. Chim. Acta 1985, 769, 257. (11) Nomura, T.; Watanabe, M.; West, T. S.Anal. Chim. Acta 1985, 175, 107. (12) Yao, S.-2.: Mo, Z.-H. Anal. Chim. Acta 1987, 793, 97. (13) Muramatsu, H.; Tamiya, E.; Karube, I. Anal. Chem. 1988, 6 0 , 2142. (14) Muramatsu, H.; Tamiya, E.; Suzuki, M.; Karube, I.Anal. Chim. Acta 1988, 215. 257. (15) Muramatsu. H.; Kajiwara, K.; Tamiya, E.; Karube, I.Anal. Chim. Acta 1986, 787, 257. (16) Shana, 2 . A.; Radtke. D. E.; Kelkar, U. R.; Josse, F.; Haworth. D. T. Anal. Chlm. Acta 1990, 231. 317. (17) Roederer, J. E.; Eastiaans, G. J. Anal. Chem. 1983, 55. 2333. (18) Calabrese, G. S.;Wohltjen, H.: Roy, M. K. Anal. Chem. 1987, 59, 837. (19) Thompson, M.; Dhaliwal, G. K.; Arthur, C. L.; Calabrese, G. S. I€€€ Trans. Uitrason ., Ferroeiec ., Freq . Contr . 1987, UFFC-34, 127. (20) Muramatsu, H.; Dicks, J. M.: Tamiya, E.; Karube, I. Anal. Chem, 1987, 5 9 , 2670. (21) Ebersole, R. C.;Ward, M. D. J . Am. Chem. SOC. 1988, 710, 8623. (22) Davis, K. A.; Leary, T. R. Anal. Chem. 1989, 6 1 , 1227. (23) Thompson, M.; Dhaliwal, G. K.; Arthur, C. L. Anal. Chem. 1986, 58, 1206. (24) Sauerbrey, G. 2.Phys. 1959, 155, 206. (25) Sauerbrey, G. Z . Phys. 1964, 778, 457. (26) Bruckenstein, S.; Shay, M. €lectrochim. Acta 1985, 3 0 , 1295
621
Kanazawa. K. K.; Gordon, J. G. Anal. Chim. Acta 1985, 175, 99. Kipling, A. L.;Thompson, M. Anal. Chem. 1990, 6 2 , 1514. White, R. M.; Wenzel, S. W. Appi. Phys. Left. 1988, 5 2 , 1653. Martin, S.J.; Ricco, A. J.; Niemczyk. T. M.; Frye, G. C. Sens. Actuators 1990, 2 0 , 253. (31) Hughes, R. C.; Martin, S. J.; Frye, G. C.; Ricco, A. J. Sens. Actuators 1990, A22, 712. (32) RajakoviE, Lj. V.; Ghaemmaghaml, V.; Thompson, M. Anal. Chim. Acta 1989, 2 1 7 , 111. (33) Schneegans, M.; Menzei, E. J . Colloid Interface Sci. 1982, 88, 97. (34) Bain, C. D.; Troughton, B. E.; Tao, Y.-T.; Evall, J.; Whitesides, G. M.; Nuzzo, R. G. J . Am. Chem. SOC. 1989, 7 1 1 , 321. (35) Furukawa, T.; Eib, N. K.; Mittal, K. L.; Anderson, H. R. J . Colloid Interface Sci. 1983, 9 6 , 322. (36) Caravajal, G. S.;Leyden, D. E.; Quinting, G. R.; Maciel, G. E. Anal. Chem. 198E96 0 , 1776. (37) Huijgen, T. P.; Angad Gaur, H.; Weeding, T. L.; Jenneskens, L. W.; Schuurs. H. E. C.; Huysmans, W. G. 8.; Veeman, W. S. Macromolecules 1990, 2 3 , 3063. (38) Leyden, D. E.; Murthy, R. S. S.;Atwater. J. B.; Blitz, J. P. Anal. Chim. Acta 1987, 200. 459. (39) Rangnekar. V. M.; Oldham, P. 8. Spectrosc. Left. 1989, 2 2 , 993. (40) Moses, P. R.; Wier, L. M.; Lennox, J. C.; Finklea, H. 0.; Lenhard, J. R.; Murray, R. W. Anal. Chem. 1978, 50, 576. (41) Kallury, K. M. R.; Krull, U. J.; Thompson, M. Anal. Chem. 1988, 6 0 , 169. (42) Garbassi, F.; Ochiello, E.; Bastoli, G.; Romano, G.; Brown, A. I n Composite Interfaces, Proceedings of the First International Conference on Composite Interfaces; Ishida, J., Koenig, J. L., Eds.; Elsevier: New York, 1986; p 241. (43) Cukman. D.; Jednacak-Biscan, J.; Venksli, Z.; Haller, W. J . Colloid Interface Sci. 1987, 115, 357. (44) Heckl, W. M.; Marassi, F. M.; Kailury, K. M. R.; Stone, D. C.; Thompson, M. Anal. Chem. 1990, 6 2 , 32. (45) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J . Am. Chem. SOC. 1985, 107, 3902. (46) Van Velzen, P. N. T. Surf. Sci. 1984, 746, 319. (47) Wiggins. P. M. Prog. Polym. Sci. 1988. 13, 1. (48) O'Neiii, M. E.; Chorlton, F. Viscous and Compressible Fiuid Dynamics: Eiiis Horwood: Chichester, U.K., 1969; p 95. (49) Landau, L. D.; Lifshitz, E. M. FiuidMechanics; Pergamon Press: Oxford, U.K., 1987; p 83. (50) Moore, W. J.; Eyring, H. J . Chem. Phys. 1938, 6 , 391. (51) Tolstoi, D. M. Dokl. Akad. Nauk. SSSR 1952, 85. 1089. (52) Ronis, D.; Kovac, J.; Oppenheim, I.Physica 1977, 88A, 215. (53) Dekker, H.; Oppenheim, I.Physica 1983, 177A, 1. (54) Blake, T. D. Coiloids Surf. 1990, 4 7 , 135. (55) Parsonage, G. I n Trends in Interfacial Nectrochemistry; Silva, A. F., Ed.; Reidel: Dordrecht, Netherlands, 1986. (56) Rossky, P. J.; Lee, H. S. Chem. Scripta 1989, 29A, 93. (57) Ahistrom, P.; Teleman, 0.; Jonsson, B. Chem. Scripta 1989, 29A, 97. (58) Schumacher, R. Angew. Chem., Int. Ed. Engl. 1990, 2 9 , 329. (27) (28) (29) (30)
RECEIVED for review July 31,1990. Accepted November 30, 1990. Support for this work from IGEN Inc., Rockville, MD, the Natural Sciences and Engineering Research Council of Canada, and the Ontario Center for Materials Research is gratefully acknowledged. In addition, we are particularly appreciative for the award of fellowships to Lj.V.R. and B. A.C.-V. by the Serbian Research Council of Yugoslavia.
