Sauerbrey equation

Any mass changes that occur on the working elechode are reflected in changes in the frequency. The quantitative relationship is given by the 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. 

The Sauerbrey equation predicts a mass sensitivity per unit area of 0.226 Hz cm 2 ng . For a typical crystal the exposed area is c. 0.25 cm2 and the absolute mass sensitivity is 0.904 Hz ng 1. The resolution of modern frequency counters is easily +0,1 Hz in 10 MHz, giving a theoretical mass resolution of c. 9 x 10 10 g in practice this is usually found to be closer to 2 ng. 

Saturation, of organic pigments, 19 427 Saturation temperature, 9 100 SATURN catalyst technology, 11 688-689 Saturn cell, 23 45—46 Sauerbrey equation, 3 804 Saurex, 7 639... 

Although QCM has originally been devised as a mass sensor for operation in vacuum or gas, it also appeared to be suitable for measurements of the mass and visco-elastic changes at a solid-liquid interface. That was possible due to elaboration of the dedicated oscillator circuitry [115]. The Sauerbrey Equation (2) was derived for resonator oscillations in vacuum. However, it also holds for solution measurements provided that (1) the deposited film is rigid and (2) it is evenly... 

This relationship is known as the Sauerbrey equation it is the basic transduction relationship of the QCM when it is used as a chemical sensor. Due to the assumptions made throughout this derivation, the Sauerbrey equation is only semi-quantitative. The assumption of the added rigid mass mentioned earlier is its most serious limitation. The material added to the QCM will invariably exhibit different mechanical characteristics than quartz itself. Thus, the assumption of unified behavior is weak at best. 

Fig. 4.6 Martin and Hager, 1989a, b Hillier and Ward, 1992). The above considerations make the description of the physics of the QCM far more complicated than is apparent from the simple Sauerbrey equation. 

Let us first consider the quartz-metal interface. In deriving the Sauerbrey equation, a pivotal assumption was made, namely that the shear velocities in the crystal and in the film are equal. By this assumption we perform a virtual transformation from thickness to mass. This is the weakest point of Sauerbrey derivation. Here we do not make the same assumption. The shear velocities in the crystal and in the film are... 

In the sensing application, where the interaction of the selective layer with the analyte may lead not only to the mass uptake (i.e., Sauerbrey equation), but also to changes of its mechanical properties (i.e., elasticity and resistance), this form of analysis is the only way to extract meaningful information from QCM measurement. It is not simple, but it adds considerable information about the properties of the interface. 

Can such an approach be used for verification of the Sauerbrey equation Discuss the origin of possible experimental artifacts. 

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... 

Sandwich structure 93 SARS 620-621, e251 Sauerbrey equation 238, 243 SAW 239... 

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) ... 

In this paper we discuss three issues related to our ability to exploit the undoubted attractions of the EQCM technique (a) the extent of mobile species uptake as a function of solution concentration (b) the use of transient measurements to obtain (additional) selectivity and (c) the need to establish that the criteria are satisfied for the Sauerbrey equation (equation [1]) to be used to convert measured frequency changes to mass changes. Of these, (a) and (c) have been demonstrated (see previous paragraph) to be directly relevant to QCM-based biosensors. The concept of using transient measurements in this context has not yet been explored, but is a natural development. 

Finally, we rely on the Sauerbrey equation for the conversion of frequency data to mass data (and thus solution composition). This procedure is only valid for rigid polymer films. We therefore regard establishment of rigidity as vital. 

When a species binds to a crystal it increases its mass by Am, thus causing the resonance frequency to shift by A/, according to the Sauerbrey equation, as follows ... 

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 ... 

Sauerbrey [7] in 1959 related the change in resonance frequency of a piezo-electric quartz crystal with the mass deposited onto or removed from the crystal surface. This approach has been used to perform micro-gravimetric measurements in the gas phase like metal evaporation. For (Afo) the Sauerbrey equation states that ... 

The Sauerbrey equation assumes a rigid film with density and transverse velocity of the acoustic wave identical to those of the quartz crystal (equal acoustic impedance of the quartz and the over-layer). It also assumes that the deposit is uniform while the sensitivity of the QCM is non uniform across the radial direction of the resonant quartz crystal, with maximum sensitivity at the crystal centre [8]. 

The simultaneous negative frequency shift of the EQCM (Fig. 12.1(a)) indicates mass increase in agreement with Takahashi s results [44]. The apparent molar mass of deposited film, M was evaluated from the average initial slope of a linear plot—A/ vs. the anodic charge density, q in Fig. 12.2 and use of the Sauerbrey equation and Faraday s law of electrolysis. 

Differentiation of the Sauerbrey equation (12.1) yields the mass ilux ... 

This reaction requires a stoichiometry of FeOOH to Fe2+ of two-to-one. Analysis of the A/in Fig. 12.1, with the Sauerbrey equation (12.1) and the corresponding molar masses of FeOOH and Fe2+ confirms this hypothesis. It is to be noted that this last result could not have been possible should the EQCM had not been used. 

The EQCM comprises a quartz crystal oscillator, in which one of the Au exciting electrodes is also exposed to the solution and acts as the working electrode in a conventional (here, three electrode) cell. Provided any surface film is rigidly coupled to the underlying electrode changes in inertial mass (Am) of the electrode result in crystal resonant frequency changes (A/) that are described by the Sauerbrey equation [11] ... 

In the event that the film is not rigid, the EQCM response is a function of both the film mass and its rheological characteristics. Application of the Sauerbrey equation under these circumstances is inappropriate it underestimates the mass change, to an extent that is dependent on the viscoelastic properties of the film. Under these circumstances, there are two questions to be addressed first, how does one diagnose film (non-)rigidity and, second, how does one interpret responses from a non-rigid film The answers to both questions can be found from crystal impedance measurements. This is a technique in which one determines the admittance (or impedance) of the loaded crystal as a function of frequency in the vicinity of resonance. Effectively, one determines the shape (width and height) and position (on the frequency axis) of the resonance, rather than just its position (as in the simple EQCM technique). 

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