Abstract
The peak forces exerted on soft and rigid samples by a force microscope have been modeled by performing numerical simulations of the tip motion in liquid. The forces are obtained by using two contact mechanics models, Hertz and Tatara. We present a comparison between the numerical simulations and three analytical models for a wide variety of probe and operational parameters. In general, the forces derived from analytical expressions are not in good quantitative agreement with the simulations when the Young modulus and the set-point amplitude are varied. The only exception is the parametrized approximation that matches the results given by Hertz contact mechanics for soft materials and small free amplitudes. We also study the elastic deformation of the sample as a function of the imaging conditions for materials with a Young modulus between 25 MPa and 2 GPa. High lateral resolution images are predicted by using both small free amplitudes (less than 2 nm for soft materials) and high set-point amplitudes.
Highlights
The high-resolution imaging of heterogeneous materials, in particular soft materials in liquid, by amplitude modulation atomic force microscopy (AM-AFM) is an active area of research in nanotechnology [1,2,3,4,5,6,7,8,9,10,11]
The numerical simulation of the tip motion in amplitude modulation AFM provides a comprehensive description of the factors that control the peak force and the lateral resolution in liquid
The parametrized model resembles the results given by Hertz for soft materials and small free amplitudes but its quantitative accuracy decreases by increasing the Young modulus
Summary
The high-resolution imaging of heterogeneous materials, in particular soft materials in liquid, by amplitude modulation atomic force microscopy (AM-AFM) is an active area of research in nanotechnology [1,2,3,4,5,6,7,8,9,10,11]. The peak forces exerted on soft and rigid samples by a force microscope have been modeled by performing numerical simulations of the tip motion in liquid. The only exception is the parametrized approximation that matches the results given by Hertz contact mechanics for soft materials and small free amplitudes.
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