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.

We describe a new strategy for interpreting frequency responses of thickness shear mode resonators loaded with spatially uniform viscoelastic films. This procedure leads to unambiguous extraction of the four parameters that characterize such a film: its thickness, density and shear modulus components (storage and loss moduli). The interpretational difficulty is that the experimental frequency response (impedance spectrum) can only provide two parameters; thus, the problem is underdetermined. Previous interpretations employed various approximations and assumptions for two (or more) film parameters to effectively reduce the problem to a two-parameter fit. Such approaches are clearly imperfect. Our new strategy splits the problem into two separate two-parameter sub-problems, each of which is solved by the measurement of two different experimental responses. The result is a unique fit to the data without the need to make approximations or assumptions for film parameters. First, in the acoustically thin regime, measured frequency shift and film charge are combined to provide a unique solution for film thickness and density; shear moduli components do not affect the response in this regime. Second, film density is carried forward directly, and the film thickness-charge relationship is extrapolated into the acoustically thick regime. Third, with film density and thickness held fixed, crystal impedance data in the acoustically thick regime provide unambiguous shear modulus components. The method is generalized to any other (nonelectrochemical) probe that provides film thickness data and validated using crystal impedance data for poly(3-methylthiophene) films exposed to propylene carbonate.

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