<title>Use of piezoelectric resonators for the characterization of mechanical properties of polymers</title>

Abstract

In this paper a variety of techniques to characterize the mechanical properties of polymers in the MHz frequency range based on the impedance analysis of thickness and thickness shear composite resonators will be presented. The analysis is based on inverting the impedance data of the composite resonator to find the best fit using the material coefficients of the piezoelectric resonator and attached polymer layer. Mason's equivalent circuit is used along with standard acoustic circuit elements to generate the impedance of the composite resonators and interpret the experimental data. Inversion techniques will be presented which allow for the direct determination of the acoustic load if the material properties of the resonator are known before being joined to the polymer. A specific example of this technique, the quartz crystal microbalance will be presented and it will be shown how the model can be extended to include all the acoustic elements of the experimental setup including the acoustic load of the solution. In the model all elements are treated as complex to account for loss mechanisms (viscous effects, electric dissipation etc.). If the free resonator is modeled prior to deposition a transform is presented that allows for the determination of the acoustic load directly. The advantage being that one no longer has to assume a functional form of the acoustic load (eg. mass damping) since it can be measured directly and compared to the various models. In addition the transform allows for an easy determination of the mass sensitivity and bandwidth for the system. The theory can be extended to account for electrode mass changes (adsorption/condensation and desertion/evaporation) or for use in chemical monitoring by the addition of a chemically sensitive layer (artificial noses and tongues). The technique has also applications for the direct determination of the elastic coefficients of polymer materials.