Bulk wave resonator solutions in the regime for viscoelastic polymers

Abstract

The frequency shifts and resonant resistances for films of a model polymer coating a 5 MHz AT-cut quartz crystal have been calculated using the complete electromechanical model. The density has been takento have a value of 1200 kgm m-3 and a shear modulus of 5×107 Pascals. The inelasticity of the film is described in terms of a loss factor. For loss factors in the range from 0 to 1×10-2, the films can be considered to be very nearly elastic, having frequency changes indistinguishable from that of elastic films. However, the resonant resistance is extremely sensitive to the viscosity, particularly for film thicknesses which are nearly a quarter wavelength of the shear wave. Films having a loss factor greater than 10 can be treated as liquid-like. Interpretation of data for polymers whose viscosity may be changing (say via cross-linking) must be done with care, since the resonator resistance decreases with increasing viscosity. The intermediate range with loss factors in the range from 0.1 to 1 are the most complex and those cases require detailed computations in order to interpret data. Both the frequency shift and resistance behavior show striking changes in the neighborhood of the thickness region which corresponds to a quarter wavelength of the shear wave. The thickness dependence of the frequency shift and the resistance should serve as a useful experimental tool to study the rheological properties of polymers.