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Determination of Nano-sized Adsorbate Mass in Solution using Mechanical Resonators: Elimination of the so far Inseparable Liquid Contribution

Assumption-free mass quantification of nanofilms, nanoparticles, and (supra)molecular adsorbates in liquid environment remains a key challenge in many branches of science. Mechanical resonators can uniquely determine the mass of essentially any adsorbate; yet, when operating in liquid environment, the liquid dynamically coupled to the adsorbate contributes significantly to the measured response, which complicates data interpretation and impairs quantitative adsorbate mass determination. Employing the Navier-Stokes equation for liquid velocity in contact with an oscillating surface, we show that the liquid contribution can be eliminated by measuring the response in solutions with identical kinematic viscosity but different densities. Guided by this insight, we used quartz crystal microbalance (QCM), one of the most widely-employed mechanical resonator, to demonstrate that kinematic-viscosity matching can be utilized to accurately quantify the dry mass of systems such as adsorbed rigid nanoparticles, tethered biological nanoparticles (lipid vesicles), as well as highly hydrated polymeric films. The same approach applied to the simultaneously measured energy dissipation made it possible to quantify the mechanical properties of the adsorbate and its attachment to the surface, as demonstrated by, for example, probing the hydrodynamic stablization induced by nanoparticles crowding. Finally, we envision that the possibility to simultaneously determine the dry mass and mechanical properties of adsorbates as well as the liquid contributions will provide the experimental tools to use mechanical resonators for applications beyond mass determination, as for example to directly interrogate the orientation, spatial distribution, and binding strength of adsorbates without the need for complementary techniques.