Quantitative description of the response of finite size adsorbates on a quartz crystal microbalance in liquids using analytical hydrodynamics.

Despite being a fundamental tool in soft matter research and biosensing, quartz crystal microbalance (QCM) analyses of discrete macromolecules in liquids so far lack a firm theoretical basis. Quite often, acoustic signals of discrete particles are qualitatively interpreted using ad hoc frameworks based on effective electrical circuits, effective springs and trapped-solvent models with many fitting parameters. Nevertheless, due to its extreme sensitivity, the QCM technique pledges to become an accurate predictive tool. Using unsteady low Reynolds hydrodynamics we derive analytical expressions for the acoustic impedance of adsorbed discrete spheres. The present approach is successfully validated against 3D simulations and a plethora of experimental results covering more than a decade of research on proteins, viruses, liposomes, and massive nanoparticles, with sizes ranging from a few to hundreds of nanometers. The agreement without fitting parameters indicates that the acoustic response is dominated by the hydrodynamic propagation of the particle surface stress over the resonator. Understanding this leading contribution is a prerequisite for deciphering the secondary contributions arising from the relevant specific molecular and physico-chemical forces.