Sauerbrey relationship

Provided that a mass added to electrode surfaces is (i) small compared to the weight of the crystal, (ii) rigidly adsorbed, and (iii) evenly distributed over the active area of the ciy stal, the Sauerbrey relationship has been classically used for quantitative determination of mass deposited on the sensor surface in terms of the following equation (Sauerbrey 1959). 

If the film thickness is negligibly small compared to the resonator thickness, the film has the same acoustic property as the quartz resonator. Then the change of resonance frequency due to surface film foimation can be written as the following equation, which is called the Sauerbrey relationship [8],... 

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 ... 

Deviations between the actual ablation rates and those predicted using Eq. (2) occur at higher fluences. 64 65 Hence, a different rate equation is required to determine the relationship between amax and fluence. According to a rate model proposed by Sauerbrey and Pettit,46 the etch depth per pulse is given by... 

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. 

The first quantitative investigation of the piezoelectric effect was performed by Sauerbrey, who derived the relationship for the change in frequency AF (in Hz) caused by the added mass Am (in g) ... 

The piezoelectric transducers are being used as chemical sensors since the discovery of the relationship between mass of adsorbed films and the resonant frequency by Sauerbrey (2) ... 

The use of piezoelectric devices as potential chemical sensors was realized when Sauerbrey [2] described the relationship between the resonant frequency of an oscillating piezoelectric crystal and the mass deposited on the crystal surface... 

The use of piezoelectric (PZ) devices as potential analytical chemistry sensors was not realized until Sauerbrey (3) described the relationship between the resonant frequency of an oscillating piezoelectric crystal and the mass deposited on the crystal surface. The relationship between the weight of an evenly distributed film of a metal and the resonant frequency of an AT cut crystal vibrating in the thickness shear mode can be expressed by ... 

In 1957 Sauerbrey quantified the relationship between the vibrating frequency and deposition mass in the piezoelectric quartz crystal. The relationship was described as ... 

The essential point is that the resonant frequency decreases when the crystal is loaded with mass, and this change can be determined very acciuntely. Changes of 1 Hz, or even 0.1 Hz, can be measiued when a crystal with a resonance frequency of 10 MHz is used. The relationship between mass change (A/w) and frequency change (A/) was derived by Sauerbrey [150], and is called the Sauerbrey equation ... 

Sauerbrey [70-71] developed the fundamental analysis of the QCM for gas or vacuum operation. The early investigations showed that for small mass changes, the decrease in resonant frequency of a piezoelectric crystal upon which a thin film had been deposited is linearly proportional to the deposited mass. The relationship between the mass of the film and the resonant frequency of a quartz crystal is... 

The Sauerbrey equation gives the relationship between the frequency change and mass change ... 

A mathematical relationship between the mass of material placed upon a bulk wave resonator and frequency shift (equation 14.14) was first derived by Sauerbrey (4) ... 

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... 

For quartz aystals cut in the most common direction (the so-caUed AT cut) and processed in the most advantageous oscillation direction, the Sauerbrey Eq. (2.9) is valid. It describes the relationship between the firequency/ and the mass m of a thin film at the crystal surface ... 

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