Abstract
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.
Highlights
Over the decades since its invention [1] the atomic force microscope (AFM) has been used in a variety of modes to characterize micro- and nanoscale heterogeneous structures in composites and other advanced materials
The sample properties are deduced from changes in the parameters of a driven cantilever that is oscillating in a steady state while interacting with the sample surface
The derivation assumes the eigenmode in question can be modeled as a simple harmonic oscillator (SHO) within the range of interactions explored in the experiment
Summary
Over the decades since its invention [1] the atomic force microscope (AFM) has been used in a variety of modes to characterize micro- and nanoscale heterogeneous structures in composites and other advanced materials. The AFM can provide high resolution topographic and mechanical properties mapping using techniques such as force curves [2,3], contact resonance [4,5], force modulation [6,7], phase imaging [8,9], loss tangent imaging [10], friction force microscopy [11], creep compliance [12], shear modulation force microscopy [13], pulsed force microscopy [14] and torsional approaches [15].
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