Applicability of QCM-D for Quantitative Measurements of Nano- and Microparticle Deposition Kinetics: Theoretical Modeling and Experiments

A new theoretical model is formulated for the quantitative analysis of quartz crystal microbalance (QCM) response for heterogeneous loads consisting of nano- and microparticles. The influence of particle coverage and structure is described using a universal correction function in an ab initio manner. Explicit analytical expressions for the frequency and dissipation shifts are derived for the entire range of particle size under the rigid contact regime. The solvent coupling functions are also calculated to determine the dry coverage using the QCM measurements. These expressions furnish the upper limit of the QCM signal, which can be attained for a sensor providing perfect adhesion of particles. Correction functions accounting for the finite adhesion strength (soft contact regime) are also derived. The theoretical results are confronted with QCM and atomic force microscopy measurements of positively charged polymer particle deposition on silica sensors. The main features of the theoretical model are confirmed, especially the abrupt decrease in the QCM wet mass with the particle coverage and the overtone number. The latter effect is especially pronounced for microparticles under the soft contact regime, where the higher-number overtones produce a negligible QCM signal. These results represent a useful reference data for the interpretation of protein and bioparticles, for example, virus and bacteria attachment processes to various substrates.