Quartz crystal microbalance (QCM or QCM-D) is widely used for studying soft (e.g., biological) interfaces in liquid environments. An advantage of this technique over many others is that it provides information about amount of material at an interface as well as its organization, and is therefore useful for studying interfaces undergoing morphological transitions (including protein conformational changes and liposome to bilayer transitions). Quantitative interpretation of QCM data remains difficult, however, in particular in the case of heterogeneous films. In this study, we will consider a simple case of lipidic vesicles adsorbing to the surface of titania. Typically, changes in the resonance frequency and bandwidth of a quartz crystal measured as a function of surface coverage are interpreted in terms of a model, that takes into account adsorbed mass and layer viscoelastic properties:¹

, (1)

where f and G are frequency and bandwidth, respectively, Z_q is the acoustic impedance of quartz (a real number), h, ρ, η, and J are respectively thickness, density, viscosity, and complex shear compliance, and subscripts q, f, and liq refer to quartz, film, and liquid, respectively.

A long-standing issue concerns the frequency dependence of the vicoelastic parameters (J_f in (1)) entering into the model. While causality considerations dictate that elastic and viscous compliances be frequency-dependent, in many studies, the data are fit with frequency-independent expressions, not in the least because introducing frequency dependence increases the number of fitting parameters. We have performed QCM measurements on supported vesicular layers composed of various lipids as a function of surface coverage at frequencies ranging from 15 MHz to 95 MHz. These measurements demonstrate that the shear-elastic compliance of the vesicular film depends on frequency. Furthermore, our measurements demonstrate, that viscoelastic model can not describe the experimental observations unless the elastic compliance is postulated to depend on surface coverage. Such a dependence, however, implies a hydrodynamic interaction between the surface-adsorbed vesicles. Implications of our observations for interpreting QCM(-D) data are discussed.

1. Johannsmann, D., Studies of Viscoelasticity with the QCM. In Piezoelectric Sensors, 1 ed.; Steinem, C.; Janshoff, A., Eds. Springer: 2007; pp 49 - 110.