Coverage Effects in Quartz Crystal Microbalance Measurements with Suspended and Adsorbed Nanoparticles

Quartz crystal microbalance (QCM) biosensors often deal with nanoparticles suspended in the solvent at tens of nanometers above the resonator while being linked to some molecular receptor (DNA, antibody, etc.). This work presents a numerical analysis based on the immersed boundary method for the flow and QCM impedance created by an ensemble of spherical particles of radius R at varying surface coverage Θ and particle-surface gap distance Δ. The trends for the frequency Δf and dissipation ΔD shifts against Θ and Δ are shown to be determined by modifications in the structure of the perturbative flow created by the analytes. Simulations are in good agreement with a relatively large experimental database collected from the literature. Qualitative differences between the adsorbed (Δ ≈ 0) and suspended states (Δ > 0) are highlighted. In the case of adsorbed particles, deviations from the linear scaling Δf ∝ Θ are observed above Θ > 0.05 and largely depend on the specific analyte-substrate combination. Moreover, in general, ΔD(Θ) is not monotonous and usually presents a maximum around Θ ∼ 0.2. In the case of suspended analytes, the agreement with the numerical results is quantitative, indicating that the predicted scalings are universal and determined by hydrodynamics. Up to high coverage, the suspended particles present Δf ∼ Θ and ΔD ∼ Θ^β, where β ≈ 0.85 is not largely dependent on R. The present findings should help forecast molecular configurations from QCM signals and have implications on QCM analyses, e.g., in the case of suspended ligands (Δf ∝ Θ), it is safe to use Δf to build Langmuir isotherms and estimate equilibrium constants. Open questions on the transition from the suspended-to-adsorbed state are discussed.