TY - JOUR A1 - Labuda, Aleksander A1 - Kocuń, Marta A1 - Meinhold, Waiman A1 - Walters, Deron A1 - Proksch, Roger T1 - Generalized Hertz model for bimodal nanomechanical mapping JF - Beilstein Journal of Nanotechnology PY - 2016/// VL - 7 SP - 970 EP - 982 SN - 2190-4286 DO - 10.3762/bjnano.7.89 PB - Beilstein-Institut JA - Beilstein J. Nanotechnol. UR - https://doi.org/10.3762/bjnano.7.89 KW - bimodal atomic force microscopy KW - bimodal spectroscopy KW - contact mechanics KW - multifrequency KW - nanomechanical mapping KW - nanomechanics N2 - Bimodal atomic force microscopy uses a cantilever that is simultaneously driven at two of its eigenmodes (resonant modes). Parameters associated with both resonances can be measured and used to extract quantitative nanomechanical information about the sample surface. Driving the first eigenmode at a large amplitude and a higher eigenmode at a small amplitude simultaneously provides four independent observables that are sensitive to the tip–sample nanomechanical interaction parameters. To demonstrate this, a generalized theoretical framework for extracting nanomechanical sample properties from bimodal experiments is presented based on Hertzian contact mechanics. Three modes of operation for measuring cantilever parameters are considered: amplitude, phase, and frequency modulation. The experimental equivalence of all three modes is demonstrated on measurements of the second eigenmode parameters. The contact mechanics theory is then extended to power-law tip shape geometries, which is applied to analyze the experimental data and extract a shape and size of the tip interacting with a polystyrene surface. ER -