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Quantification of viscoelastic properties using contact resonance atomic force microscopy with U-shaped probes
Contact resonance atomic force microscope (CR-AFM) methods are relatively new measurement techniques used to quantify the elastic and viscoelastic properties of numerous materials such as polymers, elastomers, metallic glasses, asphalt, and biological materials. More recently, AFM thermalevers have been developed to allow local heating of samples and the resonances of these probes are much more complex. These U-shaped probes have one distinct advantage over rectangular AFM probes in that specific modes allow in-plane and out-of-plane tip-sample motion to be excited independently at the same location using a Lorentz force excitation. The CR-AFM approach involves measurement of the resonant frequencies of the AFM probe both for the free case and the case for which the tip is in contact with the sample. Vibration models of the probe and tip-sample contact models are then used to determine the sample properties from the frequency response. A simplified analytical model of these U-shaped probes is described here that is based on two beams clamped at one end and connected with a perpendicular crossbeam at the other end. This three beam model (TBM) for the case in which the tip is not in contact with sample (the free case) is first solved and the results are in good agreement with those from a finite element model (FEM). Then the TBM model is modified to include the sample contact by considering the contact as three orthogonal Kelvin-Voigt elements. Again, the TBM results are compared with FEM and the results agree well with respect to the frequencies and peak widths. Finally, specific applications of such CR-AFM measurements are considered. One application involves the measurement of the in-plane and out-of-plane viscoelastic properties of polymers at the same location. The contact resonant peaks acquired from the experiments are analyzed to obtain the stiffness and damping of the sample. The approach is applied to quantify the material loss tangent for in-plane and out-of-plane behavior simultaneously at local positions on several polymers including high-density polyethylene and polystyrene, as well as biological materials. The results of this dissertation are expected to allow measurements of viscoelastic samples to be interpreted accurately with spatial resolution on the order of tens of nanometers.^
Rezaei, Ehsan, "Quantification of viscoelastic properties using contact resonance atomic force microscopy with U-shaped probes" (2016). ETD collection for University of Nebraska - Lincoln. AAI10103304.