Abstract
In this paper, we present an alternative way to study theoretically low-frequency collective modes of DWNTs based on the continuous 2D membrane theory. We obtain aωRBLM (do , di) relation being an equivalent of the conventional formulas established for individual SWNTs. We compare our theoretical predictions with Raman data measured on individual index-identified suspended DWNTs. A good agreement between the experiment and the predictions of the continuous theory is found. We show that the coupling in individual DWNTs strongly depends on the interlayer distance, which is manifested in the frequency shifts of the radial breathing-like modes (RBLMs) with respect to the radial breathing modes (RBM) of the individual inner and outer tubes. In terms of characterization, the combination of Ramanspectroscopy data and the predictions of continuous membrane theory may give additional criteria for the index-identification of DWNTs.