BVD model for QCM loaded by viscoelastic film in gas phase application

As an ultra-sensitivity sensor, a quartz crystal microbalance (QCM) could be used to quantitatively characterize the relation between QCM parameters and the characteristics of viscoelastic films. When a QCM coated with a viscoelastic thin film is in the gas phase, based on the constructive equation of the quartz crystal and ignoring the capacitance effect, the equivalent Butterworth-Van Dyke (BVD) model of the QCM and the explicit expression for its frequency shift are derived. The "extra mass effect" deduced by the complex modulus is also obtained. It is found that the tendency of the BVD model in this work agrees well with that of Voinova's model, although both are derived in different ways. Meanwhile, it can be seen that the two above-mentioned models exhibit different characteristics when compared with Sauerbrey's model and Arnau's model. The BVD model will help analyze the properties of viscoelastic films in the gas phase.