Modeling the responses of thickness-shear mode resonators under various loading conditions

We develop a general model that describes the electrical responses of thick ness-shear mode resonators subject to a variety of surface conditions. The model incorporates a physically diverse set of single-component loadings, i ncluding rigid solids, viscoelastic media, and fluids (Newtonian or Maxwell ian). The model allows any number of these components to be combined in any configuration. Such multiple loadings are representative of a variety of p hysical situations encountered in electrochemical and other liquid-phase ap plications, as well as gas-phase applications. In the general case, the res ponse of the composite load is not a linear combination of the individual c omponent responses. We discuss application of the model in a qualitative di agnostic fashion to gain insight into the nature of the interfacial structu re, and in a quantitative fashion to extract appropriate physical parameter s such as liquid viscosity and density and polymer shear moduli.