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Despite being a fundamental tool in soft matter research, quartz crystalmicrobalance (QCM) analyses of discrete macromolecules in liquid so far lack afirm theoretical basis. Currently, acoustic signals are qualitativelyinterpreted using ad-hoc frameworks based on effective electrical circuits,effective springs and trapped-solvent models with abundant fitting parameters.Nevertheless, due to its extreme sensitivity, the QCM technique pledges tobecome an accurate predictive tool. Using unsteady low Reynolds hydrodynamicswe derive analytical expressions for the acoustic impedance of adsorbeddiscrete spheres. Our theory is successfully validated against 3D simulationsand a plethora of experimental results covering more than a decade of researchon proteins, viruses, liposomes, massive nanoparticles, with sizes ranging fromfew to hundreds of nanometers. The excellent agreement without fittingconstants clearly indicates that the acoustic response is dominated by thehydrodynamic impedance, thus, deciphering the secondary contribution ofphysico-chemical forces will first require a hydrodynamic-reinterpretation ofQCM.

Quantitative reintepretation of quartz-crystal-microbalance experiments with adsorbed particles using analytical hydrodynamics