How does a tip tap?

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Abstract
There is a demand for good theoretical understanding of the response of an atomic force microscope cantilever to the extremely nonlinear impacts received while tapping a sample. A model and numerical simulations are presented in this paper which provide a very pleasing comparison with experimental results. The dependence of the cantilever amplitude and phase upon the sample stiffness, adhesion and damping are investigated using these simulations, and it is found that 'topographic' tapping images are not independent of sample properties, nor will it be trivial to measure materials' properties from the tapping data. The simulation can be applied to other probe microscope configurations as well. 1. The demand The intermittent-contact mode atomic force microscope (IC AFM) (1) has been developed to overcome some of the difficulties encountered in contact force microscopy, especially of organic materials. AFM, or alternatively, scanning force microscopy (SFM), provides a way of imaging surfaces with near-atomic resolution, without any constraints on the electrical conductivity. In the contact mode, adhesion between the tip and the sample leads to a certain force between them. When the tip is displaced for scanning, a lateral force is transmitted to the sample. This can lead to distortions of soft samples, and in the worst cases to irreversible damage. In the IC AFM the tip is out of contact with the sample most of the time. Excitation of the base of the cantilever leads to almost free vibrations of the cantilever, and changes in the amplitude or frequency or phase (2) of vibration due to the proximity of the sample are measured, and used in the feedback loop to control the vertical displacement of the sample. This mode of AFM has been used to image a wide range of organic materials with nanometre-scale resolution (3-5).

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