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

Abstract

A continuum model is employed in the stability analysis of carbon nanotubes (CNT) in theapplication in atomic force microscope (AFM) probes. Current experimental resultshave observed instability of CNT in the applications in AFM probes. However, acomplete study and understanding of the instability of CNT has not yet beenconducted so far. The research in the paper provides a complete mechanics analysison the global and local buckling of both single-walled nanotubes (SWNT) anddouble-walled nanotubes (DWNT) via an elastic beam model. A cantilever beam modelunder a tilted compressive load for possible global buckling or local bucklinginstability of the CNT probe is employed, since a CNT probe interacts with thesurface of a probe at an angle relative to the surface normal. A discrete beammodel is employed to propose a mechanism of local buckling instability for beamstructures. Based on this model, the development of kink instability of CNT isrevealed and studied. A benchmark study on the size effect of the CNT on thecritical axial force is carefully made for SWNT and DWNT probes. In addition,the global buckling load of CNT under horizontal axial force can be recoveredfrom the current results on local instability by setting a zero tilted angle, and thepredicted results are compared with those from a model considering the van derWaals effect to demonstrate the great feasibility of the proposed local instabilitymodel for global buckling analysis use. It is hoped this research may provide abenchmark study on a practical and novel design for effective AFM probes with CNT.