Nonlinear dynamics of intermittent-contact mode atomic force microscopy

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Abstract
In intermittent-contact mode atomic force microscopy (AFM), the AFM tip and the harmonically driven sample only spend a brief time in contact, compared to the driving period. As a result the dynamical response of the cantilever to the shocks received on impact can be described and analyzed in terms of an instantaneous impact law specifying the loss of kinetic energy on impact. The simplest such law assumes a constant coefficient of restitution and results in the impact oscillator model. The coefficient-of-restitution law is modified to include an absolute loss of energy on impact, modeling the effects of adhesion. The stability of single-impact orbits for this impact law is analyzed. The analytical results based on these models are found to be in agreement with experiment. A model of the tip-sample interaction based on the Johnson-Kendall-Roberts model of contact incorporating the effects of a liquid meniscus between the tip and the sample is presented. The resulting impact law is found to follow the modified impact law in the presence of adhesion.

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