Quartz crystal microbalance Sauerbrey constant

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 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) ... 

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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