One challenging aspect of quartz crystal microbalance (QCM) measurements is the characterization of adsorbed particles as the change in resonance frequency (Δf) is proportional not only to the inertia of the adsorbed layer but also to that of the hydrodynamically coupled fluid. Herein, by solving numerically the Navier–Stokes equations, we scrutinize Δf for sparsely deposited, rigid spherical particles that are firmly attached to an oscillating surface. The analysis is shown to be applicable to adsorbed, small unilamellar vesicles (SUVs) of controlled size under experimental conditions in which adhesion-induced vesicle deformation is negligible. The model supports a hydrodynamic explanation for the overtone dependence of Δf, and was fitted to experimental data concerning three monodisperse populations of SUVs with different average sizes ranging between 56 and 114 nm diameter. Using this procedure, we determined the average size of adsorbed vesicles to be within 16% of the size that was measured by dynamic light scattering experiments in bulk solution. In conclusion, this model offers a means to extract the particle size from QCM-D measurement data, with applications to biological and synthetic nanoparticles.

中文翻译：

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从流体动力学模拟中得出的模型，用于从石英晶体微量天平中提取球形颗粒的尺寸

石英晶体微天平（QCM）测量的一项具有挑战性的方面是吸附颗粒的表征，因为共振频率（Δf）的变化不仅与吸附层的惯性成正比，而且与流体动力耦合流体的惯性成正比。在这里，通过数值求解Navier–Stokes方程，我们检查了牢固附着在振动表面上的稀疏沉积的刚性球形颗粒的Δf。该分析显示适用于在可忽略的粘附诱导的囊泡变形的实验条件下，大小受控的吸附式单层小囊泡（SUVs）。该模型支持Δf泛音依赖性的流体动力学解释，并拟合了有关三种单分散SUV的实验数据，这些SUV的平均尺寸在56到114 nm的直径范围内。使用此程序，我们确定吸附的囊泡的平均大小在通过散装溶液中的动态光散射实验测量的大小的16％以内。总之，该模型提供了一种从QCM-D测量数据中提取粒径的方法，并应用于生物和合成纳米颗粒。