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Behavior of Quartz Crystal Microbalance in Nonadsorbed Gases at High Pressures V. Tsionsky, L. Daikhin, M. Urbakh, and E. Gileadi” School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel Received June 15, 1994. In Final Form: October 17, 1994@ The purpose of this work is to determine experimentallythe frequency shift of a quartz crystal resonator in contact with an inert gas, over a wide range of density of the gas, and to evaluate the various factors allowing a wide affecting this observed behavior. Four different gases were used (Ar, Nz, He, and Hz), range of densities to be studied, over a range of pressure of 0.5-50 atm. Three types of surfaces were used: gold, as obtained from the manufacturer of the quartz crystal; the same electroplatedwith a rough layer of nickel; the same nickel surface polished mechanically. Hydrogen was not studied in combination with nickel because absorption of the gas occurs spontaneously at room temperature. The total frequency shift observed can be divided into contributionsdue to added mass, to the pressure, and to the product of density and viscosity. Under the present experimental conditions the effect of added mass is negligible, since adsorption does not occur. The effects ofpressure,density, and viscosity have been calculated from equations given in the literature. When all these are corrected for, there is a residual effect associated with the interaction of the fluid with a rough surface. A detailed analysis of the effect of roughness on frequency cannot be made, since the roughness is of a random nature. Theories developed for a number of limiting cases indicated that the frequency shift associated with surface roughness should be proportional to the density of the fluid. This relationship was found to hold experimentally. The roughness affecting the frequency of the quartz crystal resonator cannot be related in a simple manner to the surface roughness determined by standard electrochemical methods or by STM. Nevertheless, it will be possible to detect changes in surface morphology by their effect on the frequency in most cases.
Introduction The fundamental frequency of a quartz crystal resonator is determined, besides its own properties, by the properties ofits metal electrodes and by those ofthe medium in which it is immersed. An expression for the shiR of frequency observed when the crystal is immersed in a fluid can be written in the general form
where Afm reflects the effect of additional mass, caused by adsorption or film formation, Afp is the compression effect, due to the pressure of the fluid, Af,, is the viscous effect, which describes the interaction ofthe ideally smooth vibrating crystal with the viscous fluid, and Afr accounts for the additional interaction between the vibrating crystal and the medium, resulting from the roughness of the surface of the crystal. The mass-effect is given by
where Am is the change of mass of the crystal, per unit surface area (resulting from adsorption or deposition on the surface), fo is its fundamental resonance frequency in vacuum, and pq = 2.947 x 1011gcm-l@ and .oq= 2.648 are the shear modulus and the density of the crystal, respectively. The parameter n is assigned a value of 1if only one face of crystal is exposed or 2 if both faces are exposed. Equation 2is written under the assumption that both faces are identical and their areas equal to the area of the quartz plate undergoing oscillation between the two electrodes on opposite faces. Such a simple correlation between the shift of frequency and Am was first given by Sauerbery.l It applies only if the added mass is much ~~
@
Abstract published in Advance ACS Abstracts, January 1,1995.
(1) Sauerbery, G. 2. Phys. 1959,155, 206.
less than the mass of the crystal and if this mass is firmly attached to the surface, so that it moves rigidly with it. It is very probable that these conditions are fulfilled in the case of monolayer adsorption of small molecules. The compression effect, caused by the pressure of the fluid, increases the frequency of the quartz crystal resonator linearly, as shown by Stockbridge2for the case of gases up to pressures of 1atm and by Susse3for liquid up to lo4atm. The slope ofthis dependence is independent of the nature of the fluid and is proportional to the fundamental frequency of the crystal, f o
Wp = [(1.06 x
10-6)folP
(3)
where the pressure is expressed in atmospheres. The third term of eq 1, Af,,, describes the interaction of the vibrating crystal with a viscous medium. This interaction leads to an additional loading of the crystal, expressed by a decrease in frequency, which is proportional to the square root of the product of viscosity, vfl, and density, efl,ofthe fluid in which the resonator is immersed. For a Newtonian fluid, the frequency shift can be expressed214by the equation
(4) The last equation applies for gas pressures exceeding about 300 Torr. This limitation, which depends somewhat on the nature of the gas, is imposed by the relaxation time needed for the gas molecules to equilibriate thermally, after having gained (or lost) momentum upon impact on the surface of the vibrating crystal. In liquids this relaxation time is evidently very short compared to the period of vibration of the crystal, but in gases it depends on pressure and becomes small enough only when P I (2) Stockbridge, C.D.In Vacuum Microbalance Techniques;Behrndt, K. H., Ed.; Plenum Press: New York, 1966; Vol. 5, p 147. ( 3 ) Susse, C. J.Phys. Rad. 1955,16, 348. (4)Kanazawa, K. K.; Gordon, J. Anal. Chim. Acta 1986,175, 99.
0743-7463/95/2411-0674$09.00/0 0 1995 American Chemical Society
Frequency Shift of Quartz Resonator in a n Inert Gas
300 Torr. A review of several approaches to explain this phenomenon in liquids was given recently by Thomson et a1.5 Equation 4 accounts for the reduction in frequency caused by the interaction of the medium with a quartz crystal resonator having an ideally smooth surface. A real surface is, however, invariably rough. In most experimental work published so far, the roughness effect was not taken into account, and its possible influence on the frequency shift observed in different systems has not been discussed at all. However, it was found experimentally that surface roughness can drastically affect the resonance frequency of quartz crystal in contact with liquids.6-11 Quantitative relations between the shift of the resonance and the surface morphology were derived recently for slowly varying interfacial profiles.12 Further development of the theory of this effect is now in pr0gre~s.l~ In order to probe the effect of surface roughness on the QCM data, it is necessary to carry out the measurements over a wide range of the parameter (efll;ld.This cannot be readily done in liquids. In the gas phase the viscosity is essentially independent of pressure, but the density is nearly proportional to it, allowing detailed comparison of theory with experiment. The purpose of this paper is to show experimentallythe dependence of the frequency shift of the quartz crystal resonator, used in our laboratory as a QCM,I4on pressure and density, and in particular to determine the frequency shift on surfaces of different roughness.
Langmuir, Vol. 11, No. 2, 1995 675
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Experimental Section The quartz crystals employed in this study were of the "ATcut" type, with a fundamental resonance frequency off0 = 6 MHz. The quartz crystal disks purchased (diameter of 14 mm) have already been coated by vacuum-sputtered gold on both sides. Measurements were also conducted on rough (Ni,) and bright (Nib)nickel. The first was formed by electroplating on both gold surfaces, from a solution of 50 g/L NiS04 and 40 g/L H3B03, at a cathodic current density of 10 mA/cmz. The thickness of the deposits was about 4 pm. The mirror bright nickel surface was prepared by mechanical polishing the electrodepositedlayer, with diamond paste (1pm). In order to have an independent characterization of the surfaces used in the QCM measurements, scanning tunneling microscope (STM)images have been obtained, as shown in Figure 1. Comparison of the STM images for gold and rough nickel (Ni,) shows that in both cases large-scale roughness is observed, but in the case ofNi, there is an additional small-scale roughness (with the scale 100-200 nm). Measured a t the same resolution, the bright nickel (Nib) surface shows no significant roughness. A Leybold Inficon deposition controller type XTC/2 was used to measure the frequency. Changes in frequency were read through an RS 232 output as described earlier.14 The resolution is 0.15 Hz. The bronze crystal-holder has the form of a pair of tweezers, making several electrical contacts a t the periphery of the crystal, on both sides. The cell containing the crystal and all the connecting capillaries were made of copper. The temperature (25 "C) of the water thermostat containing the cell was controlled to within *0.05 "C, corresponding to a frequency fluctuation of h0.12 Hz.14 The temperature fluctuations of the crystal itself are smaller, due to the thermal inertia of the cell. (5)Thompson, M.; Kipling, A. L.; Duncan-Hewitt, W. C.; Rajakovi, L. V.; Cavic-Vlasak, B. A.Analyst 1991,116,881. (6) Butry, D. A. and Ward, M. D. Chem. Rev. 1992,92,1355. (7) Yang, M.; Thompson, M.; Duncan-Hewitt, W. C. Langmuir 1993, 9,802. (8)Yang, M.; Thompson, M. Langmuir 1993,9, 1990. (9) Schumacher, R.; Borges, G.; Kanazawa, K. K. Surf. Sci. 1985, 163,L612. (10) Schumacher, R.; Gordon, J. G.; Melroy, 0.J.Electroanal. Chem. 1987,216,127. (11)Beck, R.; Pittermann, U.; Weil, K. G. J.Electrochem. SOC.1992, 139,453. (12) Urbakh, M.;Daikhin, L. Phys. Rev. B 1994,49,4866. (13)Urbakh, M.; Daikhin, L. Langmuir 1994,10, 2836. (14)Tsionsky, V.; Gileadi, E. Langmuir 1994,10,2830.
Figure 1. STM image of a typical surfaces of the Au (a), Ni, (b), and Nib (c). The surface of the quartz resonator was cleaned by rinsing consecutively in water, methanol, acetone, and petroleum ether. The four gases used in this study were Hz, He, Nz, and Ar. Their viscosities are equal a t 25 "C to 89, 198, 177, and 227 PUP, respective1y.l5J6 Measurements were taken up to a pressure of 50 atm. Hydrogen was not used on nickel surfaces, because of its tendency to be absorbed in this metal.
Results and Discussion In Figure 2 we show the effect of pressure on the frequency of the quartz crystal. The behavior is compared for four gases on gold and for three of them (excludingHz) for nickel. The region up to 10 atm is shown in the inset with an extended vertical scale. To simplify the picture we do not show here the data for polished nickel: Helium on this surface behaves practically the same as on rough nickel, and the data for Nz are between the curves Hemi, and N a i , with the minimum at a pressure of about 0.5 atm. (15)Handbook of Chemistry; Nikolsky, B. P., Ed.; Khimiya: Moscow and Leningrad, 1962; Vol. 1. (16) Handbook of Chemistry and Physics; Weast, R. C., Ed.; CRS Press: Cleveland, OH, 1976.
676 Langmuir, Vol. 11,No.2, 1995 300
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Pressure, a t m Figure 2. Frequency shift, Af, as a function of pressure measured on Au (A, Hz; 0, He; V, Nz; 0 , Ar) and on rough Ni (Ni,) (0,He; V, Nz; W, Ar). For the two light gases the behavior is essentially linear, as expected according to eq 3. The numerical coefficient, calculated from the slope for hydrogen on gold, is 0.97 x atm-l, which agrees well with the value of 1.06 x atm-l obtained from theory. For the two heavier gases, the frequency first decreases and then increases. Similar frequency-pressure dependencies have been observed by Stockbridge2on gold and by Wade et al.17on aluminum (at low pressures, up to 800 Torr) for the same gases, but the values of the pressures corresponding to the minima found in these two papers are very different from those reported here. For example, in the case of argon they are about 600 Torr in ref 2 and 300 Torr in ref 17. In our work the minimum is observed at about 10 atm for Au and 1 atm for Ni, as seen in Figure 2. In order to analyze this effect in detail, we subtract the values of Afp and Afv from the observed frequency shift and plot the resulting function (Af- A f p - Af,,) as a function ofthe total pressure, as shown in Figure 3. The frequency shift corrected in this manner is found to be a linear function of the total pressure. Comparison of the last two figures shows that Afp and Afv constitute a considerable part of the shift of frequency with pressure. For helium and hydrogen the main part of Af is Afp, as a result the function ( A f - Afp - Af,) is essentially independent of pressure, as seen in the inset in Figure 3. In Figure 4 the data are given in a slightly different way. Here we plot N ~ A H $the , difference between Af measured in Nz and in He, corrected for the difference of the calculated viscous effect, as a function oftotal pressure: (17) Wade, W. H.; Allen, R. C . J. Colloid andInterface Sci. 1968,27, 722.
Figure 3. Frequency shift corrected on the compression and viscous effects as a function of pressure. See Figure 2. I
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Pressure, atm Figure 4. Comparison of data obtained with He and Nz on: 1, polished Ni (Nib); 2, rough Ni (Ni,); 3, Au. See the text.
A Hf =( A P - hpI") - (AfvNz - AfvH")
N2
(5)
On the basis of the data shown in Figure 3 and Figure 4 we conclude that (i) subtraction of the compression and the viscous effects yields a linear dependence of the remaining part of Af on pressure; (ii)the slope of these lines depends drastically on the morphology ofthe surface; (iii) the slope of (Af - A f p - Afv)as a function of pressure depends not only on the nature of metal but also on its surface preparation. Considering eq 1 we can write
Af - Afp - A f v
= Afm iAfy
(6)
Thus, the residual dependence of the function ( A f - A f p - Afv)on pressure, shown in Figure 3 can be interpreted as being due either to the mass effect, Afm, caused by adsorption or to surface roughness, Af,. Mass Effect. The concentration of adsorbed nitrogen is 6 x l O I 4 molecules per cm2of real surface area,18which corresponds to 28 ng/cm2. The sensitivity of our QCM is 6.1ng/Hz.cm2;thus one monolayer of nitrogen on an ideally smooth surface would give rise to a frequency shift of Afm (18)Young, D. M.; Crowell, A. D. Physical Adsorption of Gases; Butterworths: London, 1962; p 226.
Frequency Shift of Quartz Resonator in an Inert Gas
Langmuir, Vol. 11, No. 2, 1995 677
= 4.6 Hz. A similar calculation for Ar leads to a maximum frequency shiR of 13 Hz, if we assume that there can be twice as many Ar atoms per monolayer than Nz molecules. The corresponding shiRs for HZand for He are about an order of magnitude smaller. These values are very small compared to the shift in frequency shown in Figure 3,so it would seem that the mass effect Afmcan be considered negligible, comparedto the changes in frequency observed in the present study. It must be remembered, however, that the values of Afmcalculated above are relevant to an ideally flat surface, i.e. to the real surface area. For a rough surface they would have to be multiplied by the roughness factor and could thus make a larger contribution to the observed frequency shift on very rough surfaces. In our previous work14 we studied the adsorption of several substances (water, alcohols, benzene) from the gas phase on the same gold surface. The isotherms obtained showed a plateau, which corresponds to complete coverage of the surface. For example, in the case of benzene the number of molecules per cm2 of apparent surface area at the plateau was found to be 4 x 1014.From studies of benzene adsorption on graphite19 it is known that one benzene molecule needs a little more than 30 A2. Hence the effective roughness factor on gold is about 1.2. Since the largest effects observed in our work are for a gold surface, it is evident that they cannot be due to chemical or physical adsorption. This is not surprising, since He, Nz, and Ar are not known to be adsorbed to a significant extent at or near room temperature, and H2 is not adsorbed on Au. We conclude that, to a very good approximation, eq 6 can be written in the simple form
w - AfP - Afv = AL
(7)
Thus, Figure 3 represents the effect of surface morphology on the frequency-pressure dependence. RoughnessEffect. The form of the dependence of the frequency of the quartz crystal resonator on the properties of the fluid and on the interface morphology is determined by the relations between the characteristic sizes of surface roughnesses and the length scale defined by the NavierStokes equation for fluid velocities.12J3 The latter is the decay length of fluid velocities
a
Figure 5. Different types of surface roughness: (a) small roughness, 6 >> h; (b) large roughness, 6 1and a16 > 1))the energy dissipation in the fluid is very small.20 Hence the main contribution to the roughness-induced frequency shift, is due to inertial effects and does not depend on
(19) Ross, S.; Olivier, J. P. On Physical Adsorption; Inerscience Publishers: New York, London, Sydney, 1965; p 239.
(20)Landaq L. D.; Lifschitz, E. M. Fluid Mechanics, 2nd ed.; Pergamon: New York, 1987.
(11)
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Tsionsky et al.
678 Langmuir, Vol. 11, No. 2, 1995 5 ,
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the viscosity, vfl. In this case the scaling function Y in eq 9 is proportional to (a/d). For high fluid viscosity and/or small roughness (a/d 1, the roughnessinduced shift of the resonance frequency is proportional to the fluid density efl
as seen in Figure 6. The parameter CDq(a/L,h/a)appearing in eq 12 depends on the morphology of the interface only and can be different for different surface treatments. The function a cPl(a/L,h/a)determines the slope of the dependence of the frequency shift on the fluid density shown in Figure 6. I t should be stressed that eq 12 is applicable only in the limiting cases discussed above. In the general case the roughness-induced frequency shift can become a nonlinear function of the density of the fluid.12J3 The physical meaning of the parameter a cPl(alL,h/a) can be readily understood for the case of a surface having a low density ofinhomogeneities (a
