Effect of sample heterogeneity on the interpretation of QCM(-D) data: comparison of combined quartz crystal microbalance/atomic force microscopy measurements with finite element method modeling.

A quartz crystal microbalance was integrated into an AFM in order to monitor the adsorption of biomolecules to the resonator surface with both atomic force microscopy and microgravimetry. The comparison between the two techniques allows the fractional coverage of the surface, theta, to be correlated with the frequency shift of the resonator, deltaf. The adsorbed material was ferritin, which is a spherical protein with a diameter of approximately 12 nm. Even ata coverage below 50%, the protein layer exhibits Sauerbrey-like behavior, meaning that the magnitude in the frequency shift [deltaf] much exceeds the shift in bandwidth and that the normalized frequency shift, deltaf/n (n the overtone order), is similar on the different overtones. The relation between coverage and frequency shift was found to be nonlinear. In order to model this situation, we performed finite element method calculations based on the incompressible Navier-Stokes equation. The comparison between the model and the experiment suggests that the deformation of the protein upon adsorption is small. For low coverage, the volume of the trapped solvent exceeds the volume of the adsorbate itself. The ratio of the two decreases with increasing coverage. This is the cause of the experimentally observed nonlinear relationship between the surface coverage and frequency shift. Comparing frequency shifts at different overtones, one finds that deltaf/n slightly decreases with overtone order. Such a behavior is typically attributed to softness. The model shows that, for the adsorbed spheres, this apparent softness arises through a rocking motion of the spheres at the surface instead of the shear deformation. Also, there is a hydrodynamic contribution (related to roughness) to the overtone dependence of deltaf/n.