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/λ_s, λ _s 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).