Contribution to the characterization of nanotubes atomic structure: Breathing mode of finite and infinite bundles

Abstract

The Raman spectroscopy is one of the most used tools for the experimental characterization of the atomic structure of bundles of single-wall carbon nanotubes. More particularly, the low frequency range (150–200 cm−1) is dominated by the signature of the resonant fully radial (breathing) mode. A refined evaluation of the parameters that influence the excitation frequencies of these modes is then of primary importance for a reliable interpretation of experimental spectra. In the present contribution, we focus our attention on the effect of the inter-tube interaction. Indeed, we have developed a pair-potential approach for the evaluation of van der Waals interaction between carbon nanotubes in bundles. Starting from a continuum model, we show that the inter-tube modes range from 5 cm−1 to 60 cm−1, depending of the number of tubes in the bundle. We also found that the breathing mode frequency increase by 10% if the nanotubes lie inside a infinite bundle as compared to the isolated tube. The radial-like modes and inter-tube modes of a finite bundles are considered and the transition from an isolated tube to an infinite array of tubes is detailed.