Effect of Film Thickness on the Validity of the Sauerbrey Equation for Hydrated Polyelectrolyte Films
The frequency and energy dissipation change of a quartz crystal microbalance during moisture absorption was measured for films with thickness ranging from 3 to 205 nm. Evidence of the viscoelastic nature of the films was observed for films thicker than 90 nm through the frequency and energy dissipation changes. For sufficiently thin films (t < 40 nm), the frequency change could be effectively modeled as a simple increase in mass, as predicted by the Sauerbrey equation. The viscosity of the swollen films was independent of initial polymer film thickness (93−205 nm). The equilibrium swelling ratio was independent of film thickness for all films examined (3−205 nm). The transition between the observation of a rigid film and a film showing viscoelastic character was found to be at β1D = 0.26 ± 0.10, where β1 = 2π/λs, λs is the shear wavelength, and D is the film thickness. This transition agrees with the predictions of White and Schrag (J. Chem. Phys. 1999, 111, 11192).
Vogt, Bryan, "Effect of Film Thickness on the Validity of the Sauerbrey Equation for Hydrated Polyelectrolyte Films" (2004). Polymer Engineering Faculty Research. 1048.