Identifying a single biological nano-sized particle using a quartz crystal microbalance. A mathematical model

Abstract

The effect of a point load on the oscillations of the quartz crystal microbalance (QCM) is represented with a simple one-dimensional model constructed specially for the determination of the basic physical characteristics of solitary nanoparticles. Due to the analytical form of solution, the model is highly selective and sensitive to small mass load and is quite suitable for the identification of solitary viruses. Thickness shear mode in a quartz crystal microbalance is modelled with longitudinal oscillations of a pair of thin elastic strips, with the free parameters calibrated on the basis of experiment. This approach reduces a complicated three-dimensional problem to a one-dimensional one and assesses the effect of distributed and localized mass load on the frequency response of a real QCM. A change of the frequency shift depending on the weight and position of a point body is demonstrated; the ratios of signal intensities at different harmonics accompanying the rupture of the body from the surface due to inertia in the air and in a viscous liquid are considered. The model is developed for the determination of parameters of solitary biological nano-sized bodies: mass, size, and bond rupture force.