Continuum Modeling and Analysis of the Frictional Interaction Between a CNT and a Substrate During Dragging

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. An analysis of the steady-state 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 paper continuum level modeling of the frictional interaction is used to determine the relationship between the steady-state deformed 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.