The problem of uniqueness of fit for viscoelastic films on thickness-shearmode resonator surfaces

We describe a new strategy for interpreting frequency responses of thicknes s shear mode resonators loaded with spatially uniform viscoelastic films. T his procedure leads to unambiguous extraction of the four parameters that c haracterize such a film: its thickness, density and shear modulus component s (storage and loss moduli). The interpretational difficulty is that the ex perimental frequency response (impedance spectrum) can only provide two par ameters; thus, the problem is underdetermined, Previous interpretations emp loyed various approximations and assumptions for two (or more) film paramet ers to effectively reduce the problem to a two-parameter fit. Such approach es are clearly imperfect. Our new strategy splits the problem into two sepa rate two-parameter subproblems, 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 parame ters. First, in the acoustically thin regime, measured frequency shift and film charge are combined to provide a unique solution for film thickness an d density; shear moduli components do not affect the response in this regim e. Second, film density is carried forward directly, and the film thickness -charge relationship is extrapolated into the acoustically thick regime. Th ird, 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 pro vides film thickness data and validated using crystal impedance data for po ly(3-methylthiophene) films exposed to propylene carbonate.