Viscoelastic properties of thin films studied with quartz crystal resonators

We discuss the possibility of determining shear moduli for thin polymeric films coated on quartz resonators by analysing the variation of normalized frequency shift delta f/f with different harmonics. For sufficiently thick films, the elastic compliance can be deduced from the increase in delta f/f with overtone order. However, a correction must be applied to account for a frequency dependence of the Sauerbrey factor relating frequency shift to film mass. Since the elastic effect scales with the square of the film mass, the correction is most important for thin films. Possible sources of frequency dependence of the Sauerbrey factor are the finite thickness of the electrodes, lateral stress components, and insufficient control of the electrical boundary conditions. In order to obtain the shear compliance, the frequency dependence of the Sauerbrey factor was measured and subtracted from the data on polymeric thin films. The correction procedure can be avoided by using electrodeless quartzes and exciting the vibration with external electrodes across an air gap. Since, in this case, the Sauerbrey factor is approximately constant, the shear compliance can be obtained directly from the variation of delta f/f with overtone order.