Modeling the Responses of Thickness-Shear Mode Resonators under Various Loading Conditions

We develop a general model that describes the electrical responses of thickness-shear mode resonators subject to a variety of surface conditions. The model incorporates a physically diverse set of single-component loadings, including rigid solids, viscoelastic media, and fluids (Newtonian or Maxwellian). The model allows any number of these components to be combined in any configuration. Such multiple loadings are representative of a variety of physical situations encountered in electrochemical and other liquid-phase applications, as well as gas-phase applications. In the general case, the response of the composite load is not a linear combination of the individual component responses. We discuss application of the model in a qualitative diagnostic fashion to gain insight into the nature of the interfacial structure, and in a quantitative fashion to extract appropriate physical parameters such as liquid viscosity and density and polymer shear moduli.