Identification of vacancy defects in carbon nanotubes using vibration analysis and machine learning

Abstract

Point vacancies are the most common defects in a carbon nanotube (CNT) lattice. However, there is no standard technique to identify these defects. Moreover, the effect of such vacancies on the vibrational properties of CNTs is unknown. Therefore, this paper presents the first-ever technique for identification of vacancy defects in single-walled carbon nanotubes (SWCNT) using their vibrational analyses and machine learning. 240 SWCNT samples were modelled using molecular-structural-mechanics-approach and their modes obtained using finite element analyses. Then, an analytical expression for fundamental vibration frequency of a vacancy defective SWCNT was derived using log-linear multiple regression. This frequency is found to decrease with: (i) increase in the magnitude of point vacancies; (ii) decrease in diameter; and (iii) increase in length. A polynomial support vector machine (SVM) was developed that successfully classifies pristine and vacancy defective SWCNT samples at test accuracy greater than 90%. The proposed technique for identification of point vacancies combines the developed SVM classification with inverse estimation using the derived expression. This technique will be useful for the most crucial characterization of SWCNTs, i.e., characterizing pristine and vacancy defective samples. The derived expression will be useful in predicting vibration response of vacancy defective SWCNTs, and deciding their applications.