Mechanical behaviour of films on the quartz microbalance

Abstract

The influence of films on the resonance character of the quartz resonator has been modelled from a variety of points of view. Purely mechanical models, using the notion of the piezoelectrically stiffened modulus, have been very successful in describing the influence of elastic films. Viscoelastic behaviour required another approach and two equivalent methods of dealing with it are possible. The ultimate objective of these is to relate the observed electrical behaviour of the resonance (obtained by impedance analysis, for example) to the physical properties of the film. The focus has then, understandably, been on the description of the electrical parameters of the resonator, as influenced by the materials properties of the film. Here, we focus instead on the mechanical behaviour of the films, using the physical model rather than the equivalent circuit approach. The amplitude of the shear displacements in the quartz and in the overlayer are examined for several cases; the unloaded resonator, the resonator loaded with elastic overlayers, the resonator loaded with a Newtonian fluid and the resonator loaded with a viscoelastic medium. The details of the mathematical analysis are given.