1770
Anal. Chem. 1905, 57, 1770-1771
ACKNOWLEDGMENT The authors thank R. A. Osteryoung for helpful discussion. Registry No. [R~(bpy)~(vpy)~1~+, 75687-40-0; Bu4NBF4, 429-42-5; Pt, 7440-06-4. LITERATURE CITED Murray, R. W. I n "Electroanalytical Chemistry"; Bard, A. J., Ed.; Marcel Dekker: New York, 1984;Vol. 13,Chapter 3. Brown, A. P.; Anson, F. C. Anal. Chem. 1977, 49, 1589. Brown, A. P.; Koval, C.; Anson, F. C. J. Electroanal. Chem. 1976, 7 2 , 379. Lennox, J. C.; Murray, R. W. J. Am. Chem. SOC. 1978, 100, 3710. Ianniello, R. M.; Lindsay, T. L.; Yacynych, A. M. Anal. Chem., In press. Jester, C. P.; Rocklin, R. D.; Murray, R. W. J. Electrochem. SOC. 1980, 127, 1979. Lane, R. F.; Hubbard, A. T. Anal. Chem. 1076, 48, 1287. Barker, 0. C. Congress on Analytical Chemistry In Industry, St. Andrews, June 1957.
(9) Ramaley, L.; Krause, M. S., Jr. Anal. Chem. 1989, 41, 1362. (IO) Krause, M. S.,Jr.; Ramaley, L. Anal. Chem. 1960,41, 1365. (11) Christie, J. H.; Turner, J. A.; Osteryoung, R. A. Anal. Chem. 1977, 4 9 , 1899. (12) Osteryoung, Janet; Osteryoung, R. A. Anal. Chem. 1985, 57, 101A. (13)Calvert, J. M.; Schmehl, R. H.: Sullivan, B. P.: Facci. J. S.: Mever. T. J.; Murray, R. W. Inorg. Chem. 1083, 2 2 , 2151. (14) O'Dea, J. J.; Osteryoung, J.; Osteryoung, R. A. Anal. Chem. 1081, 53, 695.
Esther Sans Takeuchi Janet Osteryoung* Department of Chemistry State University of New York at Buffalo Buffalo, New York 14214
RECEIVED for review February 12,1985. Accepted March 1, 1985. This work was supported by the National Science Foundation under Grant No. CHE 8305748.
Frequency of a Quartz Microbalance in Contact with Liquid Sir: Several pioneering articles have recently appeared (1-3) which indicate that the high mass sensitivity of the oscillating quartz microbalance, which is routinely used under vacuum, is also available in a liquid environment. Already several potential applications of quartz microbalances as chemical detectors have appeared (1, 2). That stable oscillation can be obtained in contact with a liquid is particularly noteworthy in view of the general impression in the vacuum community (4-6)of the deleterious effects of liquid films. It was thought that the viscous damping would not only cause large frequency shifts but also large losses in the quality factor Q leading to instability and even cessation of oscillation. Quantitative knowledge of the resonator behavior is requisite for a proper interpretation of experimental results. We present here an outline and the results of an analysis which yields a quantitative description of the influence of the liquid properties on the oscillation frequency. The experimental observable in these measurements is the frequency (or period) of oscillation. Under vacuum, the rigid attachment of a film of mass Am to the crystal surface causes a decrease Af in the resonant frequency. That the relationship between Af and Am is linear in the limit of small Am was first derived by Sauerbrey (7)and has been verified experimentally. This relationship Af = - -Am (1) fo
m
where fo is the resonant frequency and m the mass of the unloaded resonator is routinely used today. When the overlayer is thick, the relationship is no longer h e a r and corrections for this case have been developed (8, 9). The coupling of the crystal surface to a liquid also drastically changes the resonant frequency. The observed changes have been ascribed to the liquid density ( 2 ) ,to a combination of density and conductivity ( I ) , and to the mass of solid deposits (3). Recent papers ( 5 , 6 , 9 )have also treated the response of a quartz microbalance to liquidlike deposits. These analyses are appropriate for thin films and partially elastic films but not for the case at hand, viz., the total immersion of one surface of the crystal in a viscous liquid. We have determined the behavior of the crystal/fluid system by examining the coupling of the elastic shear waves in the crystal to the viscous shear waves in the liquid. In this manner, the resonance condition derives directly from the matching of appropriate 0003-2700/65/0357-1770$01.50/0
-I
-2.00.2 0.4 0.6
0.0
0.8
1.0
Distancelrnicrons
Flgure 1. The z profile for the transverse fluid velocity for water at three different times: (solid line) time of peak velocity at the surface; (dotted line) time of zero velocity at the surface; (dashed line) intermediate time.
500 N
-
I
2
400-
-Model Nomura's
w
8 n
300-
5 200u C
'p 100-
E
U
4
"0
8
12
16
Weight Percent Sucrose
Flgure 2. Frequency shift (sucrose in water) vs. sucrose concentration
for a 9-MHz crystal. Circles are Nomura's data. Solid curve is prediction of model.
boundary conditions on the shear waves. Though not as elegant as the previous treatments using the Rayleigh perturbation theory, transmission line analogs, or energy transfer models, this straightforward approach does provide a quantitative and easily grasped physical picture of the way the liquid affects the resonance condition. Details will be presented in a separate publication (10). Here, an outline of the treatment and major results are given. Q 1985 Amerlcan Chemical Society
1771
Anal. Chem. 1985, 57, 1771-1772 600500 -
,
I
,
I
I
-Model
400 -
300 200 -
100 -
.
'6 5
10
15
20
25
'
30
Weight Percent Glucose
Figure 3. Frequency shift (glucose in water) vs. glucose concentration for a 5-MHz crystal. Circles are experimental data. Solid curve is prediction of model.
The differential equation describing the steady-state shear waves in the AT cut quartz resonator is the Helmholtz equation, yielding as solutions undamped sinusoidal shear strains traveling in the direction perpendicular to the crystal surface. When one surface of the resonator (the surface not in contact with the liquid) is unconstrained, standing waves result. In the liquid, the differential equation describing the shear waves is the diffusion equation, having as solutions highly damped sinusoidal shear waves traveling in the z direction, away from the resonator. This shear wave can be written in terms of the instantaneous velocity of the liquid layer located at z, u,(z,t) u,(z,t) = Ae-k(r-l)cos [K(z - 1) - u t ] (2) where A is the amplitude of the wave at the interface z = 1. The characteristic distance describing the envelope of the decay function is l / k , the reciprocal of the propagation constant. The propagation constant can be written in terms of the density p and the absolute viscosity 7 of the liquid K = (op/29)'/2 (3) Shown in Figure 1is the z profile of u,, where values of p and 11 are those for water at 20 "C, namely, 0.9982 g cm-3 and 1.0022 cP, respectively. The characteristic decay length is 2500 A. This wave is so strongly damped that ita sinusoidal character is not apparent. Requiring that the transverse velocity of the surface of the quartz resonator at z =: 1 be identical with that of the adjacent liquid, and that the force exerted by the liquid on the crystal be equal and opposite to the force exerted by the crystal on the liquid, leads to the condition for the shift Af in the resonant frequency f o Af = ~ O ~ / ~ ( ~ P / V U $ P Q ) ~ / ~ (4) ' Here PQ and /.LQ are the density and shear modulus of quartz
having the values PQ = 2.648 g cm-3 and PQ = 2.947 X 10" g cm-l s - ~ , respectively. We have tested this relation with Nomura's data (1). These are shown in Figure 2 where the frequency shift between pure water and water/sucrose solutions as reported by Nomura (circles) is plotted against the weight percent of sucrose. The solid line is calculated from eq 4 using values for the density and viscosity of sucrose/water solutions from ref 11and assuming an unloaded crystal frequency of 9 MHz. The agreement is remarkable, especially as there are no adjustable parameters. Results of experiments performed in our laboratory on solutions containing up to 23 wt % glucose are similar and are shown in Figure 3. They clearly demonstrate the importance of viscosity since the density changes only from 0.998 to 1.09 while the viscosity increases by a factor of 2.2. These experiments used a 5-MHz crystal, a frequency nearly half of that of Nomura's. Thus, the quantitative agreement also substantiates the frequency dependence indicated in eq 4. The oscillation frequency also seems to be sensitive to strains induced by mounting and hydrostatic pressure. We believe the deviations at high glucose concentration are due to an increase in the hydrostatic pressure. These measurements were taken in a flow cell driven by a constant velocity pump, and the driving pressure certainly increased as the viscosity increased. Registry No. Glucose, 50-99-7. LITERATURE CITED (1) Nomura, T.; Minemura, A. Nippon Kagaku Kelshl 1980, 7980, 1261. (2) Konash, P. L.; Bastiaans, G. J. Anal. Chem. 1980, 5 2 , 1929. (3) Bruckenstein, S.; Shay, M. 1983 Abstracts, 1983 Pittsburgh Conference and Exposltion, Atlantic City, NJ, March 1983, Paper 763. (4) Hiavay, J.; Guiibauit, G. G. Anel. Chem. 1977, 49, 1890. (5) Glassford, A. P. M. J . Vac. Sci. Techno/. 1978, 75, 1836. (6) Crane, R. A.; Fischer, 0. J . fhys. D : Appl. f h y s . 1979, 72, 2019. (7) Sauerbrey, G. Z . fhys. 1959, 755, 206. (8) Lu, Chih-shun; Lewis, Owen J . Appl. f h y s . 1972, 43, 4385. (9) Mecea, V.; Bucur, R. V. Thln Solid Films 1979, 60, 73. (10) Kanazawa, K. Keiji; Gordon, J. G., unpublished results. (11) "Handbook of Chemistry and Physics", 63rd ed.; CRC Press: Boca Raton, FL, 1982.
K. Keiji Kanazawa* Joseph G. Gordon I1 IBM Research Laboratory, K33-281 5600 Cottle Road San Jose, California 95193
RECEIVED for review September 29, 1983. Resubmitted October 4, 1984. Accepted October 29, 1984.
Dehalogenation Reactions in Californium-252 Plasma Desorption Mass Spectrometry Sir: A recent communication (1) calls attention to the extensive dehalogenation with concomitant incorporation of hydrogen encountered by a series of nucleosides and thyroxine during fast atom bombardment (FAB) mass spectrometry. Through the use of deuterated glycerol, all hydrogens of the matrix were shown to be involved in the reduction process. Ease of replacement followed the general order I > Br > C1
> F, i.e., inverse to the order of bond strength, and a radical mechanism was suggested. Californium-252 plasma desorption mass spectrometry (PDMS) (2) is a similar particle-induced ionization method with the distinction that 100-MeV fission fragments are employed rather than 6-keV xenon atoms. More important to this-discussion is that, because a time-of-flight spectrometer
This article not subject to U.S. Copyright. Published 1985 by the American Chemical Society
