Stability analysis of carbon nanotube probes for an atomic force microscope via a continuum model

A continuum model is employed in the stability analysis of carbon nanotubes (CNT) in the application in atomic force microscope (AFM) probes. Current experimental results have observed instability of CNT in the applications in AFM probes. However, a complete study and understanding of the instability of CNT has not yet been conducted so far. The research in the paper provides a complete mechanics analysis on the global and local buckling of both single-walled nanotubes (SWNT) and double-walled nanotubes (DWNT) via an elastic beam model. A cantilever beam model under a tilted compressive load for possible global buckling or local buckling instability of the CNT probe is employed, since a CNT probe interacts with the surface of a probe at an angle relative to the surface normal. A discrete beam model is employed to propose a mechanism of local buckling instability for beam structures. Based on this model, the development of kink instability of CNT is revealed and studied. A benchmark study on the size effect of the CNT on the critical axial force is carefully made for SWNT and DWNT probes. In addition, the global buckling load of CNT under horizontal axial force can be recovered from the current results on local instability by setting a zero tilted angle, and the predicted results are compared with those from a model considering the van der Waals effect to demonstrate the great feasibility of the proposed local instability model for global buckling analysis use. It is hoped this research may provide a benchmark study on a practical and novel design for effective AFM probes with CNT.