Viscoelastic spectra of soft polymer interfaces obtained by noise analysis of AFM cantilevers

The dynamic properties of the environment of an atomic force microscopy (AFM) tip can be probed by observing the cantilever's mechanical noise. In the absence of viscoelastic dispersion, the power spectral density is well approximated by the resonance of a simple harmonic oscillator. By fitting resonance curves to the data, the friction coefficient ξ, the effective mass m and the effective spring constant κ are obtained. The variation of these parameters with the cantilever–substrate distance reflects the hydrodynamic and viscoelastic interactions between the cantilever and the surface. For cantilevers approaching soft polymer brushes, one finds an elastic interaction extending to about the brush height. The viscous interaction, on the other hand, is more long-ranged. For tips deeply immersed into the brush the noise spectra are no longer described by a simple harmonic oscillator. There is an excess noise at low frequencies that we attribute to viscoelastic dispersion. Hydrodynamic interactions, which should also induce deviations from the pure resonance behaviour should be largely screened by the polymer chains. By use of the fluctuation dissipation theorem, the viscoelastic spectrum ξ[ω] can be derived explicitly from the noise power spectrum.