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.
Acoustic wave resonators are used to explore the relationship between ion and solvent populations (composition) and shear moduli (dynamics) for poly(3-methylthiophene) Ðlms. The Ðlms were electropolymerized from monomer solutions in and subsequently characterized in a acetonitrileÈLiClO 4 monomer-free electrolyte. Crystal impedance spectra provide a diagnostic for the rigid vs. viscoelastic behaviour. Very thin Ðlms contain two types of zone, with di †erent electrochemical responses and solvation characteristics. The more compact type of zone signiÐcantly inÑuences the characteristics of very thin Ðlms. The more open, solvated type of zone dominates the characteristics of thicker Ðlms. Gravimetric interpretation of resonator frequency response shows that redox driven ion and solvent transfers exhibit compensatory motion : anions driven into the Ðlm to maintain electroneutrality displace some of the solvent present in undoped Ðlms. These transfers can be temporally resolved by variation of the potential scan rate in cyclic voltammetric experiments : solvent transfers more slowly. Resonator responses for thicker Ðlms are interpreted using a model in which a Ðnite viscoelastic Ðlm contacts a semi-inÐnite Newtonian Ñuid. Compensatory motion of anions and solvent is again manifested through redox state independent Ðlm thickness ; replacement of some solvent by denser dopant anions results in increased Ðlm density. Film shear moduli at 10 MHz are characteristic of lossy, viscoelastic materials. The storage shear modulus increases signiÐcantly (almost by a factor of two) upon p-doping of the Ðlm. The loss shear modulus, which is the larger component of the two, increases only marginally upon Ðlm doping.
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