The Sauerbrey model describes the linear relationship between frequency shifts and mass changes for thin films.
For a detailed description of the Sauerbrey model, see here.
The simple answer is—as soon as D is larger than zero. Theoretically, as soon as there is any viscoelastic behavior in the adsorbed layers, the mass will not couple 100% to the oscillatory motion of the sensor, and the true mass will be underestimated if the Sauerbrey equation is being used. Putting it the opposite way: as soon as you are able to obtain a stable fit to your data set, it is never wrong to model it. Practically speaking though, it is obvious that small values of D still hold for as a rigid film, especially if the D/f ratio still is very small (for instance, 1:30 or above).
When do I use the extended modeling with overtone dependence?
Yes, you can: measure the non-coated sensor first, so that you get a QCM-D baseline before the treatment of the sensor; then, after the external treatment you measure the processes on the treated sensor, as usual. Remember to use the same medium above the sensor in both measurements to be able to compare data. With QSoft 401, you then merge the two files by using the ‘Stitch files’ function and model the data in QTools the standard way. With QSoft 301 it is a bit more work: you need to un-offset the data in the first measurement file, which means when you open the QSoft file, you do not accept the ‘File transcriber’ suggestions to offsets and scaling; then copy the baseline from the first measurement and insert it in the beginning of the second, non-offsetted, measurement file, to get the right baseline reference in QTools.
Is there a way to estimate the quantity of an adsorbed protein, or similar, with water excluded, even though it is probed in hydrated form?
The QCM-D will give the hydrated mass, i.e. the mass of the molecules adsorbed to the surface and the solvent that is trapped in between. There is no means to extract the mass of only the molecules with the QCM-D technique. However, the dissipation may give a hint on the hydration of the formed layer. For example, if you have a really, really high dissipation with spreading of overtones you may conclude that the molecules have arranged themselves in an extended and sparse fashion which allows plenty of solvent to be trapped. If the dissipation is low and the spreading of overtones is not so significant, the molecules have probably arranged themselves in a more dense and ordered fashion not allowing so much solvent to be trapped. In this case the QCM-D mass will be a closer estimate to the mass of the molecules than the QCM-D mass for the soft layer.
Yes, your thickness will vary depending on L1 density value, since they are correlated. You need to state in your experimental section ‘an estimated L1 density of YYY kg/m3 was used’. You can change the L1 density, the fit should be equally good, but your thickness will change. If you know that your film is 50% hydrated, you can calculate the L1 density:
0.5 · ρdry layer + 0.5 · ρbulk solution
However, this is something that is almost impossible to know. For hydrated biomaterials the density is close to, however slightly larger than, that for water.
Would the viscosity and shear modulus be zero or infinite for a rigid material?
If it is a solid, the elasticity is very high, and the viscosity is very low. Think of the energy losses when sound is transmitted through a material: a good material for sound transfer has low viscosity, and so has quartz almost no viscosity but high elasticity. Maple syrup has high viscosity, which means it is not a good material for sound transfer—it dissipates a lot of energy.
I have difficulties finding a good fit to my data.
There may be several reasons why it is difficult to find a good fit:
If you zoom in your QSoft data, they will appear the same way. It is the averaging function in QSoft that does this: if every single data point would be plotted in QSoft, the software would be too slow, i.e. too much processor time would be spent on updating the plots, which would slow down the acquisition speed drastically. So, instead of plotting all points, only one average of them is plotted for each x-pixel.
I have experienced that thick coatings and/or non-even coatings sometimes results in high overtones being noisy. Are higher overtones less sensitive because they are dampened too much?
The electrical signal strength (voltage) that reaches the instrument decreases as the overtone number goes up. Dampening will decrease the signal strength and when it is low enough, QSoft will lose the overtone.