Bimodal atomic force microscopy uses a cantilever that is simultaneously driven at two of its eigenmodes (resonant modes). Parameters\nassociated with both resonances can be measured and used to extract quantitative nanomechanical information about the sample\nsurface. Driving the first eigenmode at a large amplitude and a higher eigenmode at a small amplitude simultaneously provides\nfour independent observables that are sensitive to the tipââ?¬â??sample nanomechanical interaction parameters. To demonstrate this, a\ngeneralized theoretical framework for extracting nanomechanical sample properties from bimodal experiments is presented based\non Hertzian contact mechanics. Three modes of operation for measuring cantilever parameters are considered: amplitude, phase,\nand frequency modulation. The experimental equivalence of all three modes is demonstrated on measurements of the second eigenmode\nparameters. The contact mechanics theory is then extended to power-law tip shape geometries, which is applied to analyze\nthe experimental data and extract a shape and size of the tip interacting with a polystyrene surface.
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