A model derived from hydrodynamic simulations for extracting the size of spherical particles from the quartz crystal microbalance‡

One challenging aspect of quartz crystal microbalance (QCM) measurements is the characterization of adsorbed particles as the change in resonance frequency (Δf) is proportional not only to the inertia of the adsorbed layer but also to that of the hydrodynamically coupled fluid. Herein, by solving numerically the Navier–Stokes equations, we scrutinize Δf for sparsely deposited, rigid spherical particles that are firmly attached to an oscillating surface. The analysis is shown to be applicable to adsorbed, small unilamellar vesicles (SUVs) of controlled size under experimental conditions in which adhesion-induced vesicle deformation is negligible. The model supports a hydrodynamic explanation for the overtone dependence of Δf, and was fitted to experimental data concerning three monodisperse populations of SUVs with different average sizes ranging between 56 and 114 nm diameter. Using this procedure, we determined the average size of adsorbed vesicles to be within 16% of the size that was measured by dynamic light scattering experiments in bulk solution. In conclusion, this model offers a means to extract the particle size from QCM-D measurement data, with applications to biological and synthetic nanoparticles.