Different experimental results for the influence of immersion angle on the resonant frequency of a quartz crystal microbalance in a liquid phase: with a comment

This paper presents different experimental results of the influence of an immersion angle (θ, the angle between the surface of a quartz crystal resonator and the horizon) on the resonant frequency of a quartz crystal microbalance (QCM) sensor exposed one side of its sensing surfaces to liquid. The experimental results show that the immersion angle is an added factor that may influence the frequency of the QCM sensor. This type of influence is caused by variation of the reflection conditions of the longitudinal wave between the QCM sensor and the walls of the detection cell. The frequency shifts, measured by varying θ, are related to the QCM sensor used. When a QCM sensor with a weak longitudinal wave is used, its resonant frequency is nearly independent of θ. But, if a QCM sensor with a strong longitudinal wave is employed, the immersion angle is a potential error source for the measurements performed on the QCM sensor. When the reflection conditions of the longitudinal wave are reduced, the influence of θ on the resonant frequency of the QCM sensor is negligible. The slope of the plot of frequency shifts (ΔF) versus (ρη)^1/2, the square root of the product of solution density (ρ) and viscosity (η), may be influenced by θ in a single experiment for the QCM sensor with a strong longitudinal wave in low viscous liquids, which can however, be effectively weakened by using the averaged values of reduplicated experiments. In solutions with a large (ρη)^1/2 region (0-55 wt% sucrose solution as an example, with ρ value from 1.00 to 1.26 g cm⁻³ and η value from 0.01 to 0.22 g cm⁻¹ s⁻¹, respectively), the slope of the plot of ΔF versus (ρη)^1/2 is independent of θ even for the QCM sensor with a strong longitudinal wave in a single experiment. The influence of θ on the resonant frequency of the QCM sensor should be taken into consideration in its applications in liquid phase.