Model-independent analysis of QCM data on colloidal particle adsorption.

Quartz crystal microbalance (QCM) is widely used for studying soft interfaces in liquid environment. Many of these interfaces are heterogeneous in nature, in the sense that they are composed of discrete, isolated entities adsorbed at a surface. When characterizing such interfaces, one is interested in determining parameters such as surface coverage and size of the surface-adsorbed entities. The current strategy is to obtain this information by fitting QCM data--shifts in resonance frequency, DeltaF, and bandwidth, DeltaGamma--with the model derived for smooth, homogeneous films using the film acoustic thickness and shear elastic moduli as fitting parameters. Investigating adsorption of liposomes and icosahedral virus particles on inorganic surfaces of titania and gold, we demonstrate that the predictions of this model are at variance with the experimental observations. In particular, while the model predicts that the ratio between the bandwidth and frequency shifts, DeltaGamma/DeltaF (the Df ratio), should increase with both surface coverage and particle size, we observe that this ratio increases with increasing particle size but decreases with increasing surface coverage, demonstrating that QCM response in heterogeneous films, such as those composed of adsorbed colloidal particles, does not conform with the predictions of the homogeneous film model. Employing finite element method (FEM) calculations, we show that hydrodynamic effects are the cause of this discrepancy. Finally, we find that the size of the adsorbed colloidal particles can be recovered from a model-independent analysis of the plot of the DeltaGamma/DeltaF ratio versus the frequency shift on many overtones.