Quartz Crystal Microbalance Model for Quantitatively Probing the Deformation of Adsorbed Particles at Low Surface Coverage

Characterizing the deformation of nanoscale, soft-matter particulates at solid-liquid interfaces is a demanding task, and there are limited experimental options to perform quantitative measurements in a nonperturbative manner. Previous attempts, based on the quartz crystal microbalance (QCM) technique, focused on the high surface coverage regime and modeled the adsorbed particles as a homogeneous film, while not considering the coupling between particles and surrounding fluid and hence resulting in an underestimation of the known particle height. In this work, we develop a model for the hydrodynamic coupling between adsorbed particles and surrounding fluid in the limit of a low surface coverage, which can be used to extract shape information from QCM measurement data. We tackle this problem by using hydrodynamic simulations of an ellipsoidal particle on an oscillating surface. From the simulation results, we derived a phenomenological relation between the aspect ratio r of the absorbed particles and the slope and intercept of the line that fits instantaneous, overtone-dependent QCM data on (δ/a, -Δf/n) coordinates where δ is the viscous penetration depth, a is the particle radius, Δf is the QCM frequency shift, and n is the overtone number. The model was applied to QCM measurement data pertaining to the adsorption of 34 nm radius, fluid-phase and gel-phase liposomes onto a titanium oxide-coated surface. The osmotic pressure across the liposomal bilayer was varied to induce shape deformation. By combining these results with a membrane bending model, we determined the membrane bending energy for the gel-phase liposomes, and the results are consistent with literature values. In summary, a phenomenological model is presented and validated in order to show for the first time that QCM experiments can quantitatively measure the deformation of adsorbed particles at low surface coverage.