Apparent negative mass in QCM sensors due to punctual rigid loading

Quartz Crystal Microbalances (QCM) are highly sensitive piezoelectric sensors able to detect very small loads attached to them. These devices are widely employed in many applications including process control and industrial and environmental monitoring. Mass loading is usually related to frequency shift by the well-known Sauerbrey's equation, valid for thin rigid homogeneous films. However, a significant deviation from this equation can occur when the mass is not uniformly distributed over the surface. Whereas the effects of a thin film on a QCM have been thoroughly studied, there are relatively few results on punctual loads, even though particles are usually deposited randomly and non-uniformly on the resonator surface. In this work, we have studied the effect of punctual rigid loading on the resonant frequency shift of a QCM sensor, both experimentally and using finite element method (FEM). The FEM numerical analysis was done using COMSOL software, 3D modeling a linear elastic piezoelectric solid and introducing the properties of an AT-cut quartz crystal. It is shown that a punctual rigid mass deposition on the surface of a QCM sensor can lead to positive shifts of resonance frequency, contrary to Sauerbrey's equation.