Determination of the storage modulus, G', loss modulus, G", and, consequently, the shear moduli, G (G = G' + jG" ), of polymer and polymer/solvent systems was conducted in this study using a thickness-shear mode (TSM) quartz resonator. The polymer poly(isobutylene) was spin-coated as a film of approximately 13 micron thickness on the surface of the TSM device and, upon inducing oscillation of the device at its resonance frequency (several mega-Hertz), the impedance characteristics were measured. In addition, the poly(isobutylene) was exposed to known weight concentrations, up to 20%, of benzene, hexane, dichloroethane, and chloroform vapors diluted in nitrogen gas, and the impedance characteristics were measured. These data sets collected from the impedance analyzer were then examined by modeling the polymer and polymer/solvent loaded TSM device with an electrical equivalent circuit model to yield the shear moduli, which enters as a parameter in the mathematical theory describing this circuit model. Initially, a three-term Taylor series expansion of the expression modeling the additional motional impedance generated by the polymer/solvent film was utilized to determine the storage and loss moduli; however, due to the complexity of the expansion and its limitation as merely an approximation, a rigorous optimization program was created to calculate these moduli directly from the motional impedance model. Additionally, using the optimized storage and loss moduli data, the free volume of the polymer/solvent film was rigorously extracted in this study from the combination of the frequency superposition principle, the Doolittle equation, and published storage and loss moduli data for a pure poly(isobutylene) film.

References:

[1] Hossenlopp, J.; Jiang, L.; Cernosek, R.; Josse, F. J. Polym. Sci. B: Appl. Phys. 2004, 42, 2373.

[2] Ballantine, D. S., Jr.; Martin, S. J.; Ricco, A. J.; Frye, G. C.; Wohltjen, H.; White, R. M.; Zellers, E. T. Acoustic Wave Sensors: Theory, Design, and Physico-Chemical Applications; Academic Press: San Diego, 1997; Chapter 3, Section 3.1.

[3] Martin, S. J.; Frye, G. C. Ultrasonics Symposium 1991, 394.

[4] Ferry, J. D. Viscoelastic Properties of Polymers, 3rd Ed; Wiley: New York, 2004.