Continuum modeling and analysis of the frictional interaction between a CNT and substrate during dragging

Abstract

A simple method to determine the frictional interaction between a carbon nanotube (CNT) and a substrate is analyzed for feasibility. In this technique an atomic force microscope (AFM) tip is used to drag a CNT along a substrate. Then the deformed shape of the CNT can be viewed either with the AFM or in a Scanning Electron Microscope (SEM). An analysis of the deformed shape allows the determination of the frictional interactions which occurred during dragging. It is important to quantify these interactions in a variety of potential applications of nanotechnology. In one such example, a CNT based nanoswitch consists of a CNT bridging over a trench. Actuation of the CNT causes it to stretch and can lead to partial slip at the interface. This slip causes hysteresis which has been observed in the mechanical actuation of a CNT bridge. In this work continuum level modeling is used to determine the relationship between the shape of the CNT and the frictional interaction which occurred between the CNT and substrate during dragging. The model and analysis indicate that this method should be feasible for CNTs with aspect ratios approximately in the 100?250 range. The modeling is extended to determine the frictional interaction between a CNT and an anisotropic substrate. Anisotropy is the property of being directionally dependent, as opposed to isotropy, which is homogeneity in all directions. In this context the shear stress offered by the substrate will vary with respect to orientation. Results of anisotropic substrate indicate the dependence of orientation of nanotube with respect to substrate and also the effect of various substrates for the same value of applied load and orientaton. For both cases results are of high resolution if the AFM tip is away from the midpoint of the nanotube. For high values of the frictional interaction and a very long CNT there is insufficient change in the final shape of the CNT to accurately resolve the shear stress. For low values of frictional interaction CNT is apt to roll rather than slide.