Measurements of interfacial viscoelasticity with a quartz crystal microbalance: influence of acoustic scattering from a small crystal-sample contact.

We discuss the influence of a limited contact size on measurements of high-frequency interfacial viscoelasticity performed with a combination of a quartz crystal microbalance (QCM) and the Johnson-Kendall-Roberts (JKR) apparatus. In this instrument, a sphere-plate contact is established between an elastomeric lens and a quartz resonator. The analysis is carried out in the frame of the sheet-contact model, which states that both the shift of resonance frequency and the bandwidth are proportional to the contact area as long as the contact area is much smaller than the crystal itself. In particular, the ratio of the shift in bandwidth and the shift in frequency (termed the D-f ratio) is predicted to be constant and independent of geometry. However, the experiment does show a slight increase in the D-f ratio with the contact radius when the contact radius is comparable to the wavelength of sound inside the crystal. This effect can be explained by acoustic scattering.