Basics of a Quartz Crystal Microbalance

Transcription

1 Baic of a Quartz Crytal Microbalance Introduction Thi document provide an introduction to the quartz crytal microbalance (QCM) which i an intrument that allow a uer to monitor mall ma change on an electrode. The reader i directed to the numerou review 1 and book chapter 2 for a more in-depth decription concerning the theory and application of the QCM. A baic undertanding of electrical component and concept i aumed. The two major point of thi document are: Explanation of the Piezoelectric Effect Equivalent Circuit Model Explanation of the Piezoelectric Effect The application of a mechanical train to certain type of material (motly crytal) reult in the generation of an electrical potential acro that material. Converely, the application of a potential to the ame material reult in a mechanical train a deformation. Removal of the potential allow the crytal to retore to it original orientation. The igniter on ga grill are a good example of everyday ue of the piezoelectric effect. Depreing the button caue the pring-loaded hammer to trike a quartz crytal thereby producing a large potential that dicharge acro a gap to a metal wire igniting the ga. Quartz i by far the mot widely utilized material for the development of intrument containing ocillator partly due to hitorical reaon (the firt crytal were harveted naturally) and partly due to it commercial availability (ynthetically grown nowaday). There are many way to cut quartz crytal and each cut ha a different vibrational mode upon application of a potential. The AT-cut ha gained the mot ue in QCM application due to it low temperature coefficient at room temperature. Thi mean that mall change in temperature only reult in mall change in frequency. It ha a vibrational mode of thickne hear deformation a hown below in Figure 1. Quartz Crytal No Applied Potential Quartz Crytal Under Applied Potential Figure 1. Graphical Repreentation of Thickne Shear Deformation. The application of an alternating potential (a ine wave in nearly all cae) to the crytal face caue the crytal to ocillate. When the thickne of the crytal (t q ) i twice the acoutical wavelength, a tanding wave can be etablihed where the invere of the frequency of the applied potential i ½ of the period of the tanding wave. Thi frequency i called the

2 reonant frequency, f 0, and i given by the equation ocillation and the reitance repreent energy diipation during ocillation. μq f0 = / 2tq (1) ρq where μ q i the hear modulu (a ratio of heer tre to hear train), ρ q i the denity, and t q i the crytal thickne. The amount of energy lot during ocillation at thi frequency i at a minimum. The ratio of peak energy tored to energy lot per cycle i referred to a the quality factor, Q and i given by the equation Q f c = (2) Δ f FWHM where f c i the center frequency and Δf FWHM i the full width at half max. Thi full width at half max i alo called the bandwidth. For quartz crytal in air, Q can exceed 100,000 while in olution Q decreae to ~3000. Thi i becaue the crytal ha been damped by the olution. Thi damping increae the amount of energy lot per cycle, decreaing Q a hown in Figure 2 below. 30 Figure 3. Quartz Crytal Microbalance Equivalent Mechanical Model. The QCM mechanical model can be electrically modeled in everal different way. The eaiet model to undertand might be an RLC circuit a hown in Figure 4. Figure 4. RLC Circuit. Amplitude Frequency Here R 1 repreent the energy diipated during ocillation, C 1 repreent the energy tored during ocillation, and L 1 repreent the inertial component related to the diplaced ma. At the reonant frequency, f, the impedance of the circuit i at a minimum and i equal in magnitude to R 1 a hown in Figure 5. Figure 2. Comparion of High Q and Low Q. Equivalent Circuit Model The mechanical model (Figure 3) of an electroacoutical ytem conit of a ma (M), a compliance (C m ), and a reitance (r f ). The compliance repreent energy tored during

3 Figure 5. Impedance Spectrum for a Serie RLC Circuit. Making electrical contact to a quartz crytal i mot eaily done be addition of an electrode to each face of the crytal. Thee electrode introduce an additional capacitance (C0) in parallel with the erie RLC a hown in Figure 6. Thi circuit i commonly referred to a the Butterworth van Dyke (BvD) model. Figure 7. Impedance Spectrum for the Butterworth van Dyke Equivalent Circuit Model. Mot commercial QCM that rely upon a phae lock ocillator, manually cancel out C 0, and only report the erie reonant frequency, f ince f ~= f 0 and f i obviouly dependent upon L 1. The eqcm 10M report both frequencie, f and f p, and a relative impedance pectrum. Figure 6. Butterworth van Dyke Equivalent Circuit Model. The circuit hown above now ha two reonant frequencie, f and f p, which tand for the erie reonant frequency (a in the original RLC circuit) and the parallel reonant frequency, repectively. The impedance pectrum for the BvD model i hown below with a minimum at f and a maximum at f p. Since thee two reonant frequencie are dependent upon L 1, ma change on the urface of the electrode will reult in frequency change. When a depoited film i thin and rigid, the decreae in frequency can be directly correlated to the increae in ma uing the Sauerbrey 4 equation f mn Δ f = (3) ( μ ρ ) 1/ 2 q q where f 0 i the fundamental frequency of the crytal a defined in Equation (1), m i the ma added, n i the harmonic number (e.g. n = 1 for a 5 MHz crytal driven at 5 MHz), and μ q and ρ q are a defined above. Equation (3) can be reduced to Δ f = C m (4) f where C f i the calibration contant. The calibration contant for a 5 MHz At-cut quartz crytal in air i 56.6 Hz cm 2 μg -1.

4 The majority of electrochemical experiment will correpond to a low-loading cae, allowing you to directly correlate change in frequency with change in ma uing the Sauerbrey equation (4). Once a film ha been depoited and the quartz crytal i immered in a liquid, the BvD model can be modified a hown below to include coupling to the liquid. Knowing the liquid vicoity and denity allow one to calculate 3 the expected frequency decreae upon immering the crytal in that liquid uing the equation Δf = 3/ 2 f a ηlρ L πμqρq 1/ 2 (5) where f a i the frequency of the crytal in air, η L i the vicoity of the liquid, ρ L i the denity of the liquid, μ q i the hear modulu of the quartz crytal, and ρ q i the denity of the quartz crytal. Figure 8. Equivalent Circuit Model for a Quartz Crytal Immered in a Liquid Three new component account for the ma loading of the film, L f, and the liquid loading (baed on η L and ρ L ), L l and R l. Both new ma loading L f and L l have the effect of reducing the frequency a indicated with the black arrow in the chart below. The original BvD model (black curve) how reonance approximately 300 khz higher than the modified BvD model (red curve). Notice that the hape of the reonance curve are identical depite the addition of the film and liquid loading. Zmod / Ω BvD modified BvD Serie f / MHz Figure 9. Comparion of BvD and Modified BvD Model. For example, upon immering the crytal in pure water, a frequency decreae of approximately 800 Hz i expected. Equation (4) hold a long a the film i aumed to be thin and rigid. When the film i no longer acoutically thin or i not rigid the BvD model can be modified further a hown below. Quartz Ma Loading (film) η L ρ L η f ρ f Figure 10. One Poible Equivalent Circuit Model for a Quartz Crytal Coated with a Polymer Film and Immered in a Liquid μ f (elaticity) Two new feature have been added Film Loading (η f ρ f ) and Elaticity (μ f ). A vicoelatic polymer will influence the reonant frequencie baed on the film vicoity (η f ), denity (ρ f ) and elaticity (μ f ). If the polymer i rigid or η f ρ f doe not change during the experiment, there will be no change in peak hape and contribution from η f ρ f can be ignored. In cae where η f ρ f doe change during the experiment, the frequency, magnitude and hape of the peak will alo change a hown in Figure 11.

5 Zmod / Ohm BvD Vicou Polymer Modified BvD Serie4 Another way to viualize if η f ρ f i changing during an experiment i to look at the reduced quality factor, Q R a a function of time. Q R ( f + f p ) / 2 = (6) ( f f ) p f / MHz Figure 11. Comparion of BvD and Vicou Polymer Modified BvD Model. Change in Q R correpond to changing η f ρ f. Quantifying change in η f ρ f i challenging mathematically and will not be explored further here. The reader i directed to the literature 5 for additional information at thi time. Reference 1. Hillman, A. R. The EQCM: electrogravimetry with a light touch, J. Solid State Electrochem., 15, 2011, Buttry, D. A. The Quartz Cytal Microbalance a an In Situ Tool for Electrochemitry, in Electrochemical Interface. Modern Technique for In-Situ Interface Characterization, H. D. Abruña, Ed., VCH Publiher, Inc., New York, 1991, Hillman, A. R. The Electrochemical Quartz Crytal Microbalance. In Intrumentation and Electroanalytical Chemitry; Bard, A. J., Stratmann, M., Unwin, P. R., Ed.; Encyclopedia of Electrochemitry; Wiley: New York, 2003; Vol. 3, Glaford, A. P. M. J. Vac. Sci. Technol. 1978, 15, Kanazawa, K. K.; Gordon II, J. Anal. Chem. 1985, 57, Kanazawa, K. K.; Gordon II, J. Analytica Chimica Acta 1985, 175, Sauerbrey, G. Z. Phy. 1959, 155, Muramatu, H.; Tamiya, E.; Karube, I. Anal. Chem. 1988, 60, Hillman, A. R.; Jackon, A.; Martin, S. J. Anal. Chem. 2001, 73, Martin; Hillman; Etchnique Baic of A Quartz Crytal Microbalance. Rev /2/2014 Copyright Gamry Intrument, Inc.