Investigating the influence of surface deviations in double walled carbon nanotube based nanomechanical sensors

Abstract

This manuscript investigates the influence of surface deviations, i.e. curvature in double walled carbon nanotube based nano sensors. A number of papers have been published regarding the sensing characteristics of carbon nanotubes particularly single walled carbon nanotubes. The effect of waviness or curvature has been considered and modeled in single walled carbon nanotubes when used as mass or other types of sensors but very little information is available regarding the deviations in double walled carbon nanotubes and the use of such tubes as sensors. It has been found from the experimental images that double walled carbon nanotubes are not straight and that they have a significant amount of surface deviation associated with them. It is also observed that CNTs do not possess the same wavy thickness throughout their length. Hence a constant curvature or radius model may give uniform thickness in terms of curvature throughout the length which may lead to some what inaccurate results. To model the actual curvature ratio a half sine wave model has been selected which better represents the non-uniform thickness. In this paper resonant frequency of double walled carbon nanotubes (DWCNT) with deviations along it is axis and different boundary conditions namely cantilever and bridged have been investigated. The nonlinear equations of motion of the double-walled carbon nanotubes are derived by using Euler beam theory and Hamilton principle, with considering the nonlinear van der Waals forces. The sensitivity of the apparently deviated double walled carbon nanotubes, different masses (attached to the end of outer tube tip on DWCNT and center outer tube tip of the bridged DWCNT) and different lengths has been explored and presented. The dynamic response of sensors has been explained using orbit plot. The system is seen to be exhibiting an onset of periodic and quasi periodic behavior with the change in the surface deviations. The presented results clearly suggest that change in the stiffness associated with the backed out modulus leads to a frequency shift which is considered as a measure of change in mass. The results obtained have been validated with the published experimental literature as well as shell model and are found in good agreement.