Anal. Chem. 2007, 79, 7078-7086
Measuring the Mass of Thin Films and Adsorbates Using Magnetoelastic Techniques Rong Zhang,† M. Isabel Tejedor-Tejedor,* Craig A. Grimes,‡ and Marc A. Anderson
Environmental Chemistry and Technology Program, University of Wisconsin, Madison Madison, Wisconsin 53706
Magnetoelastic sensor techniques have the unique characteristics of being able to wirelessly detect resonant frequency shifts of a magnetoelastic foil in response to differences in the foil mass. However, the mathematical expression that links the resonant frequency shift with the change in the mass of the magnetoelastic foil is rarely reported. Furthermore, this relationship is not easy to ascertain due to potential changes in the Young’s modulus of the sensor upon a change in mass loading. In this paper, we have shown that adsorption of water vapor from the gas phase by magnetoelastic ribbons coated with a two layer porous thin film (SiO2/Pt-TiO2) induces large changes in the effective Young’s modulus of the sensor. We also demonstrated that the change in Young’s modulus upon mass loading can be eliminated from the relationship between mass loading and shifts in resonant frequency by using a technique that we refer to as the two different length sensor method (TDLS). This methodology permits the conversion of the magnetoelastic sensor into a microbalance. From data presented in this paper, we illustrate that the sensitivity for the same sensor can range between 214 Hz/mg for mass loadings of Au to 438 kHz/ mg for acetone. In the case of water adsorption, frequency shifts varies from 20.0 kHz/mg when ∆m e 0.01 mg to 2.00 kHz/mg for ∆m values between 0.05 and 0.10 mg. Magnetoelastic sensor techniques have the unique characteristics of being able to wirelessly detect resonant frequency changes of a magnetoelastic foil in response to differences in physical parameters including stress, pressure, temperature, flow velocity, liquid viscosity, magnetic field, and mass loading.1 The response of the magnetoelastic sensor to mass loading allows the device to function as a gas sensor. After the magnetoelastic foil is coated with suitable nanoporous thin films, the sensitivity of the sensor is enhanced by increasing the surface area of adsorption reaction per unit geometric area of the foil. This film can also provide specificity to the sensor by modifying the adsorption properties of the thin film to be sensitive to a targeted adsorbate. The use of magnetoelastic foils coated with porous films of metal * Corresponding author. Phone: +1 608 262-2674. Fax: +1 608 262-0454. E-mail address:
[email protected]. † Current address: Jackson State University, Electron Microscopy Core Laboratory, College of Science, Engineering and Technology, Jackson, MS, 39217. ‡ Current address: Pennsylvania State University, Materials Science and Engineering Department, University Park, PA 16802. (1) Grimes, C. A.; Mungle, C. S.; Zeng, Z. F.; Jain, M. K.; Dreschel, W. R.; Paulose, M.; Ong, K. G. Sensors 2002, 2, 294-313.
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oxides, such as Al2O3, TiO2, In2O3/SiO2, zeolites, and Li-Fe2O3, have been reported in the literature.2-9 Thin films of TiO2 have been shown to provide these sensors with very large sensitivities with respect to the measurement of humidity.2,9,10 Gas sensors with thin films of SnO2 and Cu-phthalocyanine have been used to measure chlorine and oxygen.11,12 Most of the research on thin-film coated magnetoelastic sensors has been directed toward the design of coating materials in order to optimize sensor properties such as sensitivity, selectivity, linearity, speed, etc. In most instances, the calibration of a coated foil is limited to defining its frequency response to changes in the concentration of target species. However, the relationship between resonance frequency and mass of adsorbate is rarely reported and, furthermore, this relationship is not easily obtained.13 The objective of this paper is to develop a methodology capable of unequivocally relating the contribution of mass loading to a change in the resonance frequency of the magnetoelastic sensor. The ability to establish a link between frequency and mass of the resonator should open new windows of opportunities and applications for these magnetoelastic techniques. Such a magnetoelastic sensor should be a very sensitive balance capable of measuring the quantity of material composing the porous thin films and the adsorption of gases in these films. Measurement of gas adsorption in porous thin films is not an easy task. Most of the analytical methods commonly used in this field can be generally divided into five areas: volumetric/ manometric, gravimetric, carrier gas, FTIR spectroscopic, and calorimetric. However, most of these methods lack sensitivity for such a small sample as we have in the case of adsorption in porous thin films. A typical case scenario for gas adsorption in porous (2) Traversa, E.; Gnappi, G.; Montenero, A.; Gusmano, G. Sens. Actuators, B 1996, 31, 59-70. (3) Grimes, C. A.; Kouzoudis, D. Sens. Actuators, A 2000, 84, 205-212. (4) Arshak, K.; Twomey, K. Sensors 2002, 2, 205-218. (5) Li, Y.; Yang, M. J.; She, Y. Chin. J. Polym. Sci. 2002, 20, 237-241. (6) Dickey, E. C.; Varghese, O. K.; Ong, K. G.; Gong, D. W.; Paulose, M.; Grimes, C. A. Sensors 2002, 2, 91-110. (7) Zoppi, R. A.; Trasferetti, B. C.; Davanzo, C. U. J. Electroanal. Chem. 2003, 544, 47-57. (8) Suga, Y.; Hiramatsu, T.; Kaneko, F.; Nanba, N. J. Ceram. Soc. Jpn. 2003, 111, 100-103. (9) Neri, G.; Bonavita, A.; Milone, C.; Pistone, A.; Galvagno, S. Sens. Actuators, B 2003, 92, 326-330. (10) Zorn, M. E.; Rahne, K. A.; Tejedor, M. I.; Anderson, M. A. Anal. Chem. 2003, 75, 6223-6230. (11) Nicoletti, S.; Dori, L.; Certicelli, F.; Leoni, M.; Scardi, P. J. Am. Ceram. Soc. 1999, 82, 1201-1206. (12) Miyata, T.; Kawaguchi, S.; Ishii, M.; Minami, T. Thin Solid Films 2003, 425, 255-259. (13) Schmidt, S.; Grimes, C. A. IEEE Trans. Magn. 2001, 37, 2731-2733. 10.1021/ac0708036 CCC: $37.00
© 2007 American Chemical Society Published on Web 08/22/2007
thin films can be described as follows: 1 cm2 of a submicrometer thick porous film, with a specific surface area between 100 and 200 m2/g, is expected to have a mass e 0.1 mg. The resulting surface area should be in the range of 0.01∼0.02 m2/cm2, and the mass of an adsorbed monolayer of simple molecules (ethanol, acetone, ethylene, water, etc.) should be in the range of tens of nanograms per cm2 of film. Hence, only very sensitive mass detecting techniques are capable of measuring the adsorption isotherms of gases in these films. Currently, only quartz crystal microbalances (QCM) are capable of sensing changes of mass within this range. QCM devices have been used for decades to monitor thin-film deposition in a vacuum or gas1,14,15 and more recently to measure the adsorption of gases, including the adsorption of N2 at 76 K in both polymeric and inorganic thin films.16-18 As its sensitivity is in the range of nanograms, the QCM has become a powerful in situ tool for characterizing thin-film properties such as microstructure, layer thickness, thermodynamics, and kinetics of interactions with vapor phase adsorbates, etc. In the QCM balance, the quartz disk crystal with two electrodes becomes a resonator by applying an ac voltage across its electrodes. The quartz crystal is inserted in an electronic circuit, which delivers the signal. However, a magnetoelastic foil can be remotely excited to oscillation by applying a magnetic field, and the change in frequency, responding to a perturbation in the media, can be remotely detected without wires. This wireless capability of magnetoelastic devices adds some advantages over the QCM balance, even if the sensitivity in the former is slightly lower than that of the latter. Some literature data as well as simple calculations from our own studies suggest that the magnetoelastic technique should provide enough sensitivity to detect changes in mass below 1 µg10. However, until now there is no straightforward relationship between a change in the resonant frequency of the resonator and a change in its mass. Mass loadings of the QCM can be calculated, because its sensitivity factor is a constant for a wide range of applications.17,18 However, changes in the resonant frequency of a magnetoelastic foil, induced by the deposition of a thin film of material onto the magnetoelastic foil, are largely due to a change in the elastic properties of the coated resonator and cannot be attributed only to a change in mass.13 For example, thin-film coatings of MgO and MgO-Al2O3 onto the foil can induce tensile stresses and cause changes in the elasticity of the coated foil. This change is such a predominant factor controlling the resonance frequency that the frequency may even increase upon coating (addition of mass). On the other hand, coatings of some thin-film materials, such as BaO, SrO-Al2O3 and BaO-Al2O3, have been found to induce a compressive stress on the foils.19 A model for estimating the elastic modulus of these thin films has been proposed.20 Direct measurements of the elastic modulus of the (14) Grimes, C. A.; Jain, M. K.; Singh, R. S.; Cai, Q. Y.; Mason, A.; Takahashi, Y.; Gianchandani, Y. In Proceedings of the 14th IEEE International Conference on Micro Electro Mechanical Systems, Interlaken, Switzerland, January 21-25, 2001; pp 278-281. (15) Grimes, C. A.; Ong, K. G.; Loiselle, K.; Stoyanov, P. G.; Kouzoudis, D.; Liu, Y.; Tong, C.; Tefiku, F. Smart Mater. Struct. 1999, 8, 639-646. (16) Major, J. S.; Blanchard, G. J. Langmuir 2002, 18, 6548-6553. (17) Seo, Y.; Yu, I. Phys. Rev. B 1999, 60, 17003-17007. (18) Hieda, M.; Garcia, R.; Dixon, M.; Daniel, T.; Allara, D.; Chan, M. H. W. Appl. Phys. Lett. 2004, 84, 628-630. (19) Lim, S. H.; Noh, T. H.; Bae, Y. J.; Chae, H. K.; Choi, Y. S. J. Mater. Sci. 1997, 32, 3219-3225.
film using three- and four-point bend tests have also been reported.21 In this paper, a different approach for evaluating the mass loading of a magnetoelastic resonator from a change in resonant frequency is presented. In our technique, the resonant frequencies of two identically fabricated resonators having different lengths are measured. Identically fabricated resonators refer to two different length sensors cut from the same foil, which have been simultaneously subjected to the same treatment (deposition of thin films or exposure to a given partial pressure of a target gas). By comparison of the impact of the perturbation on the frequency of the two foils, the changes in the elasticity of the resonators are eliminated from the equation that relates change in resonant frequency (∆f) to mass load (∆m). EQUATIONS AND MODELS When the frequency of the ac field is equal to the mechanical resonance of the magnetoelastic foil, the conversion of magnetic energy into elastic energy is at a maximum and the sensor is in a state of magnetoelastic resonance. The resonant frequency of a magnetoelastic foil resonator is a function of its length, density, elasticity, and Poisson’s ratio. For a freely oscillating foil vibrating in its basal plane, the resonant frequency fo is given by eq 1,22
fo )
1 2L
x
Es
Fs(1 - σ2)
(1)
where Es is Young’s modulus of elasticity, Fs is the density, σ is the Poisson’s ratio, and L is the length of the bare ribbon. The resonant frequency of a magnetoelastic sensor changes in response to enviromental parameters such as temperature, pressure, change in the superimposed dc bias, and mass load.15 This present study is concerned with the response of the resonant frequency to changes in mass loads caused by either coating the bare ribbon with a thin film of material or by the adsorption of a gas in the porous, high surface area, thin film.20,22 When a bare ribbon is coated with a layer of material evenly deposited on its surface, and the mass change is small compared with the mass of the ribbon, the change in frequency response to changes in mass loading may be expressed as
∆m ∆f ) - fo 2mo
(2)
where mo is the bare ribbon mass, ∆m is the change in mass loading, fo is resonant frequency of the bare ribbon, and ∆f is the change in resonant frequency. Because eq 2 does not account for elastic stress in the applied mass load, this expression is only valid when the coated film is much thinner than the thickness of the bare ribbon.13 If this were not the case, the elasticity of the coated film would have a large effect on the resonant frequency and this effect might likely prevail over that of mass loading. When (20) Schmidt, S.; Grimes, C. A. Sens. Actuators, A 2001, 94, 189-196. (21) Li, H.; Khor, K. A.; Cheang, P. Surf. Coat. Technol. 2002, 155, 21-32. (22) Landau, L. D.; Lifshitz, E. M. Theory of Elasticity; Pergamon Press: New York, 1986. (23) Jain, M. K.; Schmidt, S.; Ong, K. G.; Mungle, C.; Grimes, C. A. Smart Mater. Struct. 2000, 9, 502-510.
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considering changes in elasticity upon coating, the frequency response in terms of mass loading is given by20,23
fc ) fo
x
β2 + mo/∆mc 1 + mo/∆mc
(3)
where fc is resonant frequency of the thin-film coated foil, ∆mc is change in mass loading as a result of coating the foil with thin films of materials, and β is a parameter defined as20
β)
x
Ec/Fc Eo/Fo
N
Ec ) Fc4L2fo2
i)1
(( ) )( ) ∑( ) fci
2
-
fo
mo
mci
N
1-
i)1
1-
mo
mo
mci
2
(5)
mci
where fci and mci are the resonant frequency and mass loading for the foil coated with j numbers of layers, respectively, and i ) 1, 2, ... N, where N is the total number of coating layers. Equation 5 assumes that the density of coated thin films (Fc) is constant. When the Young’s modulus of the coating is independent of the number of layers or the mass load for each layer is equal, it is possible to calculate Ec from eq 5. However, when the mass load for each layer is different or the density of coated thin films varies with the number of layers, Ec cannot be calculated from eq 5. In this case, the parameter β (eq 4) cannot be solved or directly measured. Therefore, the mass load (∆mc) of the coated film cannot be estimated from the change in resonant frequency using eq 3. In this paper, a methodology to measure the change in mass load (∆mc) is developed which is based on the fact that the Young’s modulus of elasticity of a layer of material coated on a magnetoelastic foil is independent of the sensor length.23 Two equally fabricated sensors having different lengths, subjected to the same experimental conditions, have the same effective modulus of elasticity. This concept is mathematically expressed in eq 6 for a one layer coating
()
Ll2fo,l2
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()
mo,l mo,s fc,s 2 mo,l + ∆mc,l fo,s mo,s + ∆mc,s ) Ls2fo,s2 mo,l mo,s 11mo,l + ∆mc,l mo,s + ∆mc,s
fc,l fo,l
2
-
∆mc,s Ls ) ∆mc,l Ll
(7)
(4)
where Eo is Young’s modulus of elasticity of the bare ribbon, Ec is Young’s modulus of elasticity of the coated thin films, Fo is density of bare ribbon, and Fc is the density of the coated thin films. In agreement with Schmidt and Grimes,13 Ec for a coating having multiple layers of the same material can be calculated using the values of resonant frequency of the sensor with different number of layers using the expression20
∑
where fo,l and fo,s are resonant frequencies of the longer and shorter bare ribbons, fc,l and fc,s are resonant frequencies of the mass loaded longer and shorter foils; ∆mc,s and ∆mc,l are the mass loads on the shorter foil and longer foil; and Ls and Ll are the length of the shorter and longer foils, respectively. The ratio of mass loadings on two pieces of magnetoelastic foils subjected to the same mass loading conditions is assumed to be equal to the ratio of their lengths
(6)
Analytical Chemistry, Vol. 79, No. 18, September 15, 2007
With the use of eqs 6 and 7, mass loads for the shorter foil and longer foils can be solved. The beauty of this technique is that the impact of the effective modulus of elasticity of the foil is eliminated from the relationship between frequency and mass load by measuring the frequency change of two pieces of magnetoelastic foils having different lengths that are subjected to the same procedure of mass loading. EXPERIMENTAL SETUP Magnetoelastic Instrument. In this work, an alternating current magnetic field with an amplitude proportional to the applied voltage is generated by a drive coil. The magnetoelastic sensor receives this signal and, in turn, generates a response signal that is acquired by a pickup coil. The electronic components used to generate the magnetic interrogation signal and to detect the emitted magnetoelastic signal are a function of the frequency range in which the sensors operate which is dependent upon the physical size of the sensors. In this study, magnetoelastic sensors having a nominal length of 4.0 cm, with an unloaded characteristic resonance frequency of approximately 59.0 kHz, were used. The computer controlled instrument utilized a Waetek function generator to produce the interrogation signal, which was subsequently amplified by a Mackie power amplifier. The output from the amplifier was passed to a coil that was used to generate the magnetic interrogation field. Here, a Helmholtz coil configuration was used with a 16-turn coil of radius 15 cm, generating a field amplitude of approximately 50 mOe. The magnetoelastic ribbon was tuned to its optimal operating point (maxiumum amplitude ) peak voltage) by application of a dc magnetic biasing field ) HDCmin (dc power supply: BOP 50-2, Kepco, Inc., Flushing, NY) of approximately 4 Oe intensity to overcome the anisotropy of the ribbon. The resulting magnetic flux change of the magnetoelastic ribbon was detected using a closely placed pickup coil, the output of which is fed into a lock-in amplifier (SR 830 DSP, Stanford Research Systems, Sunnyvale, CA). The output of the lock-in amplifier was collected by the computer to provide the amplitude-frequency spectrum of the sensor, thus enabling determination of resonance frequency. A rough schematic of the operational aspect of this instrumentation is shown in Figure 1. However, for a more complete description of this apparatus, the reader is referred to the paper by Schmidt and Grimes.13 As shown in Figure 1, the magnetoelastic ribbons were placed in a Teflon chamber (inside dimensions 5 cm × 4.5 cm × 2 cm) which allowed control over the ambient humidity of the environment, and the chamber was placed inside the field.
Figure 1. Experimental apparatus designed to measure water adsorption by magnetoelastic sensors.
Magnetoelastic Sensors. Bare ribbons of Metglas 2826 MB from Metglas Inc. were used in this study as the material with magnetoelastic properties. Metglas is an alloy of composition Fe40 Ni38 Mo4 B18. The bare ribbon has a thickness of 30 µm and a width of 13 mm. Segments of bare ribbon were used to fabricate the sensors. These segments of Metglas bare ribbon were subjected to two treatments in this study: coated with Pt or Au and coated with porous ceramic thin films. The bare ribbons were cleaned using the following sequential steps in an ultrasonic bath before coating: detergent solution, MQ water, ethanol, and MQ water. The bare ribbons were rapidly dried in a stream of dry air to avoid corrosion after washing. Pt and Au were deposited by vacuum sputtering using a Denton Vacuum sputtering device. Pt and Au targets were purchased from Denton Vacuum Inc. The current densities used in the sputtering were 45 mA for Pt and 30 mA for Au. The quantity of metal deposited was controlled by the sputtering time. The metal was deposited on both sides of the foil. Thin layers of both SiO2 and a platinized TiO2 (Pt-TiO2) were deposited in both sides of the clean bare ribbons and fired at 300 °C. The SiO2 layer was deposited prior to depositing the Pt-TiO2 layer. Deposition was performed by dip-coating the ribbon segments in aqueous sols of either metal oxide. Thickness and density of the film in dip-coating techniques are a function of the viscosity of the sol and speed of withdraw which are both constant in these experiments. The pair of dip-coated magnetoelastic foils (long and short) in each experiment were pieces cut from a longer coated foil. The sols produced coated ceramic thin films with high specific surface areas (obtained from surrogate studies involving N2 adsorption measurements of unsupported xerogels fired at 300 °C: 312 m2/g for SiO2 and 231 m2/g for Pt-TiO2). The preparation of SiO2 and TiO2 sols are described elsewhere,24,25 and the method of doping the TiO2 with Pt(0) is a part of a paper in preparation. Both ceramic layers have a nanoporous structure. The SiO2 layer is coated to protect the alloy from the corrosion induced by coating with Pt-TiO2. The SiO2 has a pH between 8 and 9. At this pH, the sol is stable for years.24 Likewise, the Pt-TiO2 sol is stable at (24) Xu, Q. Y.; Anderson, M. A. J. Am. Ceram. Soc. 1993, 76 (8), 2093-2097. (25) Chu, L.; Tejedor-Tejedor, M. I.; Anderson, M. A. Mater. Res. Soc. Symp. Proc. 1994, Vol. 346.
a pH near 2. This pH can be reached by titrating the sol with HCl or HNO3. Because of the high buffer capacity of the sols, these pH values remain constant for weeks. The mass of ceramic coating was extracted from the difference in the weight of the coated and uncoated foils. Weighing was performed under dry conditions using an analytical balance with 0.01 mg readability. Dip-coating one time in SiO2 sol and four times in the Pt-TiO2 sol generates a mass loading of 0.04 mg/cm2 (average sample size was approximately 50 cm2. With a density for the film of 2 g cm-3 (calculated using the pore volume rendered by BET analysis of N2 adsorption isotherms on X-gels), the thickness of this film is of the order of 200 nm. This thickness is very similar to that obtained from SEM imaging. Gas Adsorption Studies. As noted above, foils coated with ceramic films were housed in a Teflon gas flow through chamber. A carrier gas with known concentrations of the target species (either water or acetone) flowed through the chamber while the resonant frequency of the coated foils was being measured. A constant frequency value was an indication that equilibrium adsorption between the gas and the film had been obtained. The chamber was kept at room temperature (∼20 °C). The response of the resonant frequency to the partial pressure of water was determined by exposing the foils to a stream of N2 having a known relative humidity (RH). The RH of the N2 was controlled by diluting a stream of dry gas with a previously humidified stream (bubbling through a water reservoir). In the studies with acetone, a stream of dry N2 was allowed to flow through the headspace of a bottle containing acetone. The bottle containing the acetone was immersed into a water bath at constant temperature. The concentration of acetone in the stream of N2 was controlled by the temperature of the water bath. Ultrapure MQ water is used to generate the desired %RH in the N2 stream, and HPLC-grade acetone was used in these experiments. Adsorption isotherms of both water and acetone on the thinfilm coated foils were measured in batch experiments. The mass of the coated film was measured for six foils using an analytical balance under dry conditions. The difference in weight between the six uncoated and coated foils produces the average mass of coating material per cm2 of foil. Before measuring the gas adsorption isotherms, these foils were dried in glass bottles of 60 mL at 60 °C for several hours. While still hot, the bottles were sealed with Mininert valves. Aliquots of water or acetone were injected into the bottles and left to reach equilibrium (g12 h at 20 °C). Water and acetone in these experimentes was either adsorbed or in the gas phase as the partial pressure of both gases, under all experimental conditions, were well below the saturation pressure. The amount of water or acetone adsorbed by the thin-film coated foils was determined by the difference in concentration between a blank (empty bottle) and that in the bottle with the coated ribbons. The concentration of both water and acetone was measured by gas chromatography using a GC-2010 (Shimadzu). A flame ionization detector was used for detecting acetone, and a thermal conductivity detector was employed for water. RESULTS Resonant Frequency Response to Mass Loading for ThinFilm Coated Magnetoelastic Foils, Calibration Curves. The Analytical Chemistry, Vol. 79, No. 18, September 15, 2007
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Figure 2. Change in resonant frequency for a magnetoelastic foil coated with a layer of SiO2 and a subsequent layer of Pt-TiO2: (A) upon increasing mass of Au loaded onto the ribbon, the foil is 30 mm long; (B) upon water adsorption, shorter foil is 30 mm long and longer foil is 43 mm long; (C) upon acetone adsorption, shorter foil is 30 mm long and longer foil is 43 mm long.
frequency response of magnetoelastic sensors to mass loading is illustrated in this section. The sensor consisted of a bare ribbon of Metglas 2826 alloy with a “two layer porous coating of SiO2 and Pt-TiO2” described in the experimental section. Figure 2A shows the dependence of ∆f on ∆m upon vacuum sputtering deposition of successive layers of Au on both surfaces of the sensor. In contrast to the prediction from eq 2, ∆f does not have a linear dependency on ∆m over the entire range of this study. For Au loads smaller than 0.30 mg, the value of f (∆f is defined as fc - fo) increases with increasing ∆m. However, for loadings of Au between 0.6 and 1.8 mg, the opposite occurs. Figure 2A also shows that the frequency response to mass loading is linear in the ∆m range of 0.6-1.8 mg, and the calculated sensitivity (i.e., the slope of fitted straight line) is close to that predicted by eq 2 (214 Hz/mg experimental versus 300 Hz/mg calculated). The response of ∆f to ∆m in the magnetoelastic sensor suggests that small loads of sputtered Au change the resonant frequency of the sensor mainly as a result of changing the effective Young’s modulus of elasticity of the multilayer coating. Large changes in 7082 Analytical Chemistry, Vol. 79, No. 18, September 15, 2007
the effective Young’s modulus of the sensor can be predicted either if the sputtered Au atoms fill a fraction of the porosity of the coatings (this changes the density of the preexisting metal oxide coatings) or by the formation in progress of a new Au film for loads below 0.30 mg. To test the applicability of the calibration curve built for Au deposition (Figure 2A) to other targeted species, mass loadings caused by water and acetone adsorption in the coated foils were compared. Figure 2B shows the changes of resonant frequencies of two pieces of thin-film coated magnetoelastic foils having different lengths (43 and 30 mm), upon adsorption of water. From the comparison of parts A and B of Figure 2, one can notice that the frequency response of these foils to mass loadings of Au is very different from the response to water adsorption. In the case of water adsorption, the resonant frequency of both foils decreases with water uptake over the entire mass load range of this study: from 0.003 (under very dry conditions) to 0.140 mg (at 90% relative humidity). However, ∆f does not respond linearly to the mass loading of water. Also, one notes that ∆f follows an exponential rise until finally leveling off. The sensitivity decreases with increasing mass loadings. Since the frequency response to mass loadings of Au is linear over a much larger range of ∆m (Figure 2A), the magnitude of the mass loading in itself should not be the parameter responsible for the decrease in sensitivity with increasing ∆m. There is a large difference in the sensitivity exhibited by these sensors for the different materials. In the case of water adsorption, Figure 2B, the frequency of the shorter foil (which has the same length to the one used in the Au loading studies) shifts downward 20.0 kHz/mg when ∆m e 0.01 mg and 2.00 kHz/mg in the range between 0.05 and 0.10 mg. In contrast, mass loadings of Au induce frequency changes of only 214 Hz/mg (linear part in Figure 2A). The loss of sensitivity with increasing water loading is probably one indication of the influence of water adsorption on the Young’s modulus of the porous films. Figure 2C shows the frequency response of these sensors to the adsorption of acetone. In the mass loading range of this study (
