The Dynamic Behaviour of Chiral, Fixed-Free, Single-Walled Carbon Nanotube-Based Nanomechanical Mass Sensors Due to Atomic Vacancies

Abstract

The dynamic analysis of single-walled carbon nanotubes (SWCNTs) with chiralities has been performed using an atomistic finite element method. SWCNTs with different chiral angles are considered for the resonant frequency analysis. The cantilever carbon nanotube (CNT) is modelled by considering it as a space frame structure similar to three-dimensional beams and point masses. The beam element elastic properties are calculated by considering the mechanical characteristics of covalent bonds between the carbon atoms in the hexagonal lattice. The mass of each beam element is assumed as a point mass at nodes coinciding with carbon atoms. This atomistic simulation approach is used to visualize the effect of defects such as atomic vacancies in the CNT on the resonant frequency. The variation of the atomic vacancy is performed along the length and the response is obtained for different chiralities. It is observed that there is a reduction in the simulated natural frequency due to the atomic vacancy. This has a significant effect on dynamic behaviour when the defect is nearer to the fixed end. The change in resonant frequency of such a defective CNT is observed when it is used as a mass sensor. The resonant frequency is also evaluated for various chiralities and numbers of defects. The simulation results indicate that the existence of defects mostly affects the resonant frequency (bending rigidity) of the SWCNT as the number of defects increases. It is quite evident from the simulation results that the effect of atomic vacancies is a maximum when they are situated nearest to the fixed end and the effect diminishes at a mass addition of 10 —2 fg.