Nanoscale contact-radius determination by spectral analysis of polymer roughness images

In spite of the long history of atomic force microscopy (AFM) imaging of soft materials such as polymers, little is known about the detailed effect of a finite tip size and applied force on the imaging performance on such materials. Here we exploit the defined scaling of roughness amplitudes on amorphous polymer films to determine the transfer function imposed by the imaging tip. The finite indentation of the nanometer-scale tip into the comparatively soft polymer surface leads to a finite contact area, which in turn effectively acts as a moving average filter for the surface roughness. In the power spectral density (PSD), this leads to an attenuation of the roughness amplitudes related to the Airy pattern known from light diffraction of a circular aperture. This transfer function is affected by the roughness-induced local modulation of the tip height and contact area, which is studied by performing simulations of the polymer roughness and the imaging process. We find that for typical polymer parameters and sharp tips the contact radius of the tip-sample contact can be recovered from the roughness spectrum. We experimentally verify and demonstrate the method by measuring the nanoscale contact radius as a function of applied load and travel distance on a highly cross-linked model polymer. The data are consistent with the Johnson-Kendall-Roberts (JKR) contact model and verifies its applicability at the nanometer scale. Using the model, quantitative values of the elastic sample parameters can be determined.