Amplitude Response of Single-Wall Carbon Nanotube Probes during Tapping Mode Atomic Force Microscopy:  Modeling and Experiment

Abstract

Imaging of surfaces with carbon nanotube probes in tapping mode results frequently in complex behavior in the amplitude-distance curves monitored. Using molecular mechanics simulations, we calculate the force exerted on a nanotube pressed against a smooth surface as it undergoes deformation and buckling. This nonlinear force is then used in a macroscopic equation, describing the response of a damped harmonic oscillator, to predict the amplitude response of a nanotube AFM probe. Similarities between the prediction and experiment suggest that the complex amplitude response seen in the experiment may be explained by the nonlinearity in the force exerted on the nanotube and thus must not necessarily be related to the structure of the surface.

Frequency Function in Atomic Force Microscopy Applied to a Liquid Environment

“…In the following calculation, the total height of a CNT-tip is set to 10 μm, and the rest of the probe geometry is the same as in previous calculations. The carbon-carbon interaction potential is F ( z ) = 4 επnσ 2 [−( σ / z ) 10 /5+ ( σ / z ) 4 /2], where the parameters are assumed to be ε = 4.751×10 −22 eV, n = 0.114 Å −3 , and σ = 3.407 Å [23]. To study the jumps, the microcantilever length was set sequentially to L = 125, 250, and 500 μm ( k 0 distribution ratio is 1/8:1:8) as shown in Figure 3b.…”

Effects of surface morphology, size effect and wettability on interfacial adhesion of carbon nanotube arrays

“…As the indenter tip was pushed further into the CNT array, the force increased linearly until a turning point [step (b)] was the stress relaxation caused by deformationpromoted reactivity [55][56][57][58][59][60]. At the turning point, the force varied a somewhat non-linear as the penetration depth was increased slightly; indicating a bending [61,62] and pre-buckling deformation of the CNTs [63][64][65][66]. From observation, the collapse force for the present CNT array was found to be approximately 3.38 μN, in which our present result is higher than that reported in buckling instabilities of CNTs under uniaxial compression by Waters et al (~2.5 μN) [67,68].…”

Competition of elastic and adhesive properties of carbon nanotubes anchored to atomic force microscopy tips

“…However, let assume a linear relationship between force and position for repulsive and attractive interaction, corresponding to compression (in repulsive regime) and elongation (in attractive regime) of the CNT interacting with the surface, as depicted in gure 3. The slope of the force curves denes two nanotube stiness : an equivalent repulsive one k r for the elastic repulsive force and an equivalent attractive one for the extension part.Therefore, other parameters that may be relevant will not be considered here, for instance, the inuence of the nanotube angle as respect to the surface as developed by other authors [19,20,21] or else change of the contact area as a function of the vertical displacement.…”