Physical Interpretation of the Sauerbrey Thickness

The correct interpretation of the frequency shift from QCM experiments in liquids is a challenge. Practitioners often just apply the Sauerbrey equation (Eq. 28) to their data and term the resulting areal mass density Sauerbrey mass and the corresponding thickness Sauerbrey thickness . Even though the Sauerbrey thickness can certainly serve to compare different experiments, it must not be naively identified with the geometric thickness. Here is a fist of considerations  

The QCM always measures an areal mass density, never a geometric thickness (cf. the remarks below Eq. 71). The conversion from areal mass density to thickness usually requires the physical density as an independent input. A density of 1 g cm is often assumed in soft matter experiments. Given the other uncertainties (see below), this is in many cases a fair approximation. 

It is difficult to infer the viscoelastic correction (brackets in Eq. 77) from 

QCM data. However, if the correction factor is significantly different from unity, it may be expected that it also affects the bandwidth, AF, and also that it depends on overtone order. If, conversely, such effects are absent (AT A/, Sauerbrey thickness same on all overtone orders) one may assume (1 - Zj /Z ) 1. 

When the viscoelastic correction as discussed in (2) is insignificant, this by no means implies that the film is not swollen in the solvent. It only means that the (swollen) film is much more rigid than the ambient liquid. The amount of swelling can only be inferred from a comparison of the wet and dry thicknesses. QCM data taken on the wet sample alone do not allow the degree of swelling to be inferred (Sect. 8.3.2). 

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