Spatially resolved frequency-dependent elasticity measured with pulsed force microscopy and nanoindentation.

Recently several atomic force microscopy (AFM)-based surface property mapping techniques like pulsed force microscopy (PFM), harmonic force microscopy or Peakforce QNM® have been introduced to measure the nano- and micro-mechanical properties of materials. These modes all work at different operating frequencies. However, complex materials are known to display viscoelastic behavior, a combination of solid and fluid-like responses, depending on the frequency at which the sample is probed. In this report, we show that the frequency-dependent mechanical behavior of complex materials, such as polymer blends that are frequently used as calibration samples, is clearly measurable with AFM. Although this frequency-dependent mechanical behavior is an established observation, we demonstrate that the new high frequency mapping techniques enable AFM-based rheology with nanoscale spatial resolution over a much broader frequency range compared to previous AFM-based studies. We further highlight that it is essential to account for the frequency-dependent variation in mechanical properties when using these thin polymer samples as calibration materials for elasticity measurements by high-frequency surface property mapping techniques. These results have significant implications for the accurate interpretation of the nanomechanical properties of polymers or complex biological samples. The calibration sample is composed of a blend of soft and hard polymers, consisting of low-density polyethylene (LDPE) islands in a polystyrene (PS) surrounding, with a stiffness of 0.2 GPa and 2 GPa respectively. The spring constant of the AFM cantilever was selected to match the stiffness of LDPE. From 260 Hz to 1100 Hz the sample was imaged with the PFM method. At low frequencies (0.5-35 Hz), single-point nanoindentation was performed. In addition to the material's stiffness, the relative heights of the LDPE islands (with respect to the PS) were determined as a function of the frequency. At the lower operation frequencies for PFM, the islands exhibited lower heights than when measured with tapping mode at 120 kHz. Both spring constants and heights at the different frequencies clearly show a frequency-dependent behavior.