A Numerical Study on the Effect of Particle Surface Coverage on the Quartz Crystal Microbalance Response

The quartz crystal microbalance (QCM) is a surface-sensitive measurement technique to characterize adsorption processes at solid-fluid interfaces. While QCM measurements are routinely applied to study homogeneous thin films, characterizing heterogeneous films of adsorbed particles remains challenging because QCM is sensitive to not only the mass of adsorbed particles but also to that of hydrodynamically coupled fluid. To extract information about adsorbed particles, it is necessary to model these hydrodynamic effects, however, current QCM models are restricted to the limit of either a very low surface coverage or to the extrapolated limit of saturation coverage. Herein, we investigated QCM measurement responses in the intermediate surface coverage regime, by conducting lattice Boltzmann simulations of monodisperse, spherical particles that are attached to an oscillating surface. From the simulations, we relate the overtone-dependent QCM frequency and bandwidth shifts to particle size, interparticle distance, and the relevant hydrodynamic length scale. The corresponding results are in qualitative agreement with experimental QCM data for sub-100 nm, gel-phase liposomes. Furthermore, the data provide a theoretical basis for extracting particle sizes from QCM data in the high surface coverage limit.