Quartz crystal microbalance Sauerbrey equation

The first application of the quartz crystal microbalance in electrochemistry came with the work of Bruckenstein and Shay (1985) who proved that the Sauerbrey equation could still be applied to a quartz wafer one side of which was covered with electrolyte. Although they were able to establish that an electrolyte layer several hundred angstroms thick moved essentially with the quartz surface, they also showed that the thickness of this layer remained constant with potential so any change in frequency could be attributed to surface film formation. The authors showed that it was possible to take simultaneous measurements of the in situ frequency change accompanying electrolysis at a working electrode (comprising one of the electrical contacts to the crystal) as a function of the applied potential or current. They coined the acronym EQCM (electrochemical quartz crystal microbalance) for the technique. 

Mercury binding leads to an increase of mass of the gold layer which can be detected by electro-acoustic transducers based on quartz microbalance (QMB the abbreviation QCM = quartz crystal microbalance is also widely used), surface acoustic waves (SAW)—devices [20] or microcantilevers [21,22], Adsorption of mercury vapour increases resonance frequency of shear vibrations of piezoelectric quartz crystals (Fig. 12.2). This process can be described by Sauerbrey equation [23]. For typical AT-cut quartz, this equation is... 

The Electrochemical Quartz Crystal Microbalance (EQCM) The resonant frequency of a quartz crystal oscillator is perturbed from its base value (f ) by attached overlayers. For thin, rigid films the measured change in resonant frequency (Af) with attached mass (AM) is described by the Sauerbrey equation (10) ... 

Electrochemical quartz crystal microbalance (EQCM) is a powerful tool for elucidating interfacial reactions based on the simultaneous measurement of electrochemical parameters and mass changes at electrode surfaces. The microbalance is based on a quartz crystal wafer, which is sandwiched between two electrodes, used to induce an electric held (Fig. 2.21). Such a held produces a mechanical oscillation in the bulk of the wafer. Surface reactions, involving minor mass changes, can cause perturbation of the resonant frequency of the crystal oscillator. The frequency change (A/) relates to the mass change (Am) according to the Sauerbrey equation ... 

If the electrodes on both sides of the quartz disk are connected to an oscillator circuit, frequencies / can be measured with a frequency counter. The changes of superficial mass can be calculated from changes of the frequency A/ using the Sauerbrey-equation (-> quartz crystal microbalance). Changes at the sensitivity level of 0.1 Hz at a fundamental frequency of 10 MHz correspond to a mass of about 0.4 ng cm-2. 

Saturated calomel electrode calomel electrode Sauerbrey-equation -> quartz crystal microbalance Scan rate potential sweep rate... 

The quartz crystal microbalance (QCM) is a very sensitive technique allowing measurements of mass changes in the nanogram range. " Under high vacuum conditions, the attachment to the quartz crystal surface of a foreign layer of mass dm yields a frequency shift Sfrn which follows the Sauerbrey equation... 

The quartz crystal microbalance (QCM) is an excellent tool for these investigations since the frequency change produced by the adsorption on the surface of a piezoelectric crystal can be used to assess the mass (to a few ng/cm ) of the adsorbent using the Sauerbrey equation. Since the adsorbed protein layers can have some degree of structural flexibility or viscoelasticity that is undetectable by the determination of the resonance frequency alone, the energy loss, or dissipation factor (D), due to the shear of the adsorbent on the crystal in aqueous solution must also be determined.The technique is termed QCM-D and as well as representing an improvement in the study of biomolecular-surface interactions, it presents an opportunity to observe the adsorption of AFP and PVP, on a model nucleator with a hydrophilic surface. 

The photoswitchable complexation/dissociation properties of n donor-acceptor complexes between xanthene dyes and photoisomerizable bipyrid-inium salts have been used to generate an optoelectronic interface [97] (Fig. 28). Eosin isothiocyanate (52) was covalently linked to an electrode surface via a thiourea bond (Fig. 28A). The electron acceptor 3, 3 -bis(N-methylpyridinium) azobenzene 53 was used as the photoisomerizable component. The association constants of the n donor-acceptor complexes generated between eosin and 53a or 53b in solution correspond to Ka — 8.3 x 103 M-1 and Ka — 3.4 x 103 M 1, respectively. The analysis of complexation on the functionalized surface was accomplished by quartz crystal microbalance measurements. The frequency change (Af) of a piezoelectric quartz crystal on which a mass change Am occurs is given by the Sauerbrey equation (Eqn. 1) ... 

The use of the quartz crystal microbalance in monitoring resist dissolution rates was first reported in 1985 by W.D. Hinsberg et al. This technique is based on the equation that G. Sauerbrey developed in 1959 as a method for correlating changes in the oscillation frequency of a piezoelectric crystal with the mass... 

In addition to deriving the equation that now bears his name, Sauerbrey also developed a method for measuring the characteristic frequency and its changes by using the crystal as the frequency-determining component of an oscillator circuit. It should be mentioned that the Sauerbrey equation was developed for oscillation in air and only applies to rigid masses attached to the crystal. However, Kanazawa and Gordon have shown that quartz crystal microbalance measurements can be performed in liquid, in which case a viscosity-related decrease in the resonant frequency is observed ... 

The most effective method to measure the adsorbed mass is the quartz crystal microbalance (QCMB). This method goes back to the work of Sauerbrey. ° The apphcation of this method is based on the following equation relating the shift A/of the resonance frequency /o of a quartz crystal to the change of the mass of the crystal Am divided by A (area)... 

An electrochemical quartz crystal microbalance (EQCM) experiment was carried out to determine the mass change on the electrode. The equation of the resonant frequency change for mass change has been presented by the Sauerbrey equation ... 

Sorption of gases in coatings deposited on quartz crystal microbalance (QMB) [29] or on surface acoustic wave (SAW) devices [30, 31] can be monitored by weight changes of the exposed layer. By applying that technique it is important to ascertain that the Sauerbrey equation is valid, i.e. that contributions to the frequency shift other than mass loading are negligible. By combined mass and admittance measurements the concentra-... 

Electrochemical quartz crystal microbalance. To monitor adsorbate accumulation on catalyst surfaces from formic acid electrooxidation and advance mechanistic understanding, an electrochemical quartz crystal microbalance (EQCM) can be used to simultaneously measure current and mass [22, 66, 81-83]. The dampening of the vibration frequency (A/) of an AT-cut 9 MHz piezoelectric crystal is directly proportional to mass accumulation (Am) on the catalyst surface through the Sauerbrey equation (A/ = —/o 2(jUqPq) Am/A) [84], where /o is the base... 

Is the quartz crystal microbalance really a microbalance For one thing, it should rightly be called a nano-balance, considering that the sensitivity of modern-day devices is on the order of 12 ng/cm and could be pushed further, if necessary. More importantly, calling it a balance implies that the Sauerbrey equation applies strictly, namely that the frequency shift is the sole result of mass loading. It is well known that this is not the case, and the frequency shift observed could more appropriately be expressed by a sum of terms of the form... 

Sorption and surface adsorption of chemical agents by a mat of polymer nanofibers can be detected gravimetrically using quartz crystal microbalance (QCM) detectors (Ding et al. 2004b, 2005c Kwoun et al. 2001). The mass sensor is essentially a circular quartz crystal with thin metal elecfiodes deposited on either side of it. The resonant frequency of the piezoelectric crystal in an AC field depends on the crystal characteristics as well as the mass of material deposited on its surface. The Sauerbrey equation predicts a linear relationship... 

When acting as a microbalance, it is sometimes stated that the change in resonant frequency is an absolute measure of the change in mass loading, namely that this device does not require calibration. This statement is only partially true, and one is well advised to calibrate the QCM. Admittedly, the constant C in Eq. (1) can be calculated from the fundamental properties of the quartz crystal, as given by the Sauerbrey equation [see Eq. (9)]. However, for this constant to be applicable for the determination of the added mass, several implicit assumptions must be made. Primarily, it must be assumed that the mass distribution on the surface is uniform. It must also be borne in mind that the Sauerbrey equation only applies to thin films, such that the thickness of the film is small compared to the thickness of the crystal itself. In addition, the EQCM can operate as a true microbalance only if, in the course of the process being studied, the nature of the interface—its roughness, the density and viscosity of the solution adjacent to it, and the structure of the solvent in contact with it—is kept constant. 

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