Determination of Nanosized 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. including porosity determination (17, 18), monitoring the growth of mesoporous materials (19), probing responsiveness of polymeric coatings (20), and characterization of biomimetic membranes (21, 22). Additionally, QCM has been extensively employed to study discrete adsorates such as aboitic and biological macromolecules and nanoparticles (NPs). These studies included investigation of biomolecular interactions of proteins (23, 24) and viruses (25, 26); structure (27, 28), conﬁrmation (29, 30) and orientation changes (31) of bio-macromolecules; spatial distribution (32), size (33–35), deformation (36, 37) and dissolution (38) of NPs; protein corona formation on amyloids (39); NPs interactions with biomimetic membranes (40, 41); as well as bioanalytical sensors development (42–45), energy and whether it is aﬀected by the properties of the liquid. These results suggest that the mechanically dissipated energy was not aﬀected by the diﬀerent liquid properties within the range of liquids used in this work. If there were a dependency on the liquid properties one would have expected a systematic increase or decrease in ∆ D η = 0 with the increasing D 2 O concentrations in the D 2 O/H 2 O mixtures. On the other side, the possibility to determine ∆ f ρ = 0 and ∆ D η = 0 based on the extrapolation of four couples of data points provides a robust statistical veriﬁcation of the analysis especially for systems with small ∆ f and ∆ D responses. Note that in this work we determine the dry mass and mechanically dissipated energy at θ = 1% of 150 nm SiO 2 NPs, which is equivalent to ∆ f ρ = 0 ≈ − 15 Hz and ∆ D η = 0 ≈ 2 ⋅ 10 − 6 ; − 15 Hz corresponds to the mass of monolayer of small protein of ≈ 5 nm in diameter at the jamming limit ( θ = 54%). Finally, it is also worth noting that one could achieve a sound statistical veriﬁcation of ∆ f ρ = 0 and ∆ D η = 0 , as the one achieved using diﬀerent D 2 O/H 2 O mixtures, by exchanging the same kinematic viscosity matched liquids, e.g., D 2 O and 4.55%wt glycerol in H 2 O, several times before and after the adsorbate. The SPR experiments were conducted using a dual wavelength, 670 and 785 nm, multi-parametric SPR Navi ™ 420A (BioN-avis, Finland) on silica-coated sensors. The sensors were cleaned by bath sonication for 15 minutes in 2%wt. SDS solution, followed by rinsing with Milli-Q water, then drying under a N 2 ﬂow, and ﬁnally treating in a UV/Ozone chamber for 45 minutes directly before use. The temperature and ﬂow rate were kept constant at 25 ℃ and 7 µ l ⋅ min − 1 , respectively. Detailed theoretical derivation; calculation of the physical properties of diﬀerent D 2 O/H 2 O and glycerol/H 2 O mixtures; detailed methods and experimental procedure to measure the response in diﬀerent liquids and for independent mass determination using measurements in air and SEM; experimental results for measurements with reference to air, polymers adsorption to APDMES-coated sensors, adsorption of carboxylated and PEGylated Au NPs, response at diﬀerent overtones and D 2 O concentrations, lipid vesicles characterization and tethering, SPR calculations and results.