(545g) Coupled Resonances on the Qcm and the Lumped Equivalent Model

It is well established that the deposition of material onto the surface of a quartz crystal microbalance (QCM) results in a decrease of its resonant frequency. Recent results using particulate loads have resulted in the counter-intuitive observation of an increase in the resonant frequency. An initial explanation of this phenomenon invoked a self resonance in the load itself. This load resonance fL couples to the resonant frequency of the QCM fQ. Under conditions where fL is much greater than fQ, then the usual intuitive condition is observed, where the fQ decreases with increasing load. However, when fL is much less than fQ, then QCM frequency increases. The earlier treatment used a coupled spring and mass analogy to demonstrate this effect. We have incorporated this model into the complete electromechanical model of the QCM and have successfully shown not only the behavior described, but also have been able to obtain quantitative results on the behavior of the QCM at its harmonic resonances as well. We have also developed an equivalent circuit representation for the electrical behavior of the model using the acoustic impedance approach. We believe that this may be of assistance in identifying the physical basis of the origin of the load resonance. This equivalent circuit representation is shown to replicate characteristics of the complete electromechanical solution.