Figure 22.

The frequency response induced by thin adsorbates is proportional to an integral of the response function from Equation (59). The z-range, in which ρ(z) and η(z) are significantly different from the corresponding bulk values, must be much below the depth of penetration of the shear wave, δ, in order to let the integral formulation be applicable. The displacement profile is sketched at the bottom. For most polymers, ρ(z) is similar to ρ_bulk. The dependence of the viscosity, $\tilde{\mathsf{\eta }}\left(z\right),$ on the polymer volume fraction, ϕ(z), is strong and not easily guessed based on simple models.