Infrared-active modes in finite and infinite double-walled boron nitride nanotubes

The calculation of the infrared spectrum of double-walled boron nitride nanotubes (DBNNT's) is performed in the framework of the force constants model, using the spectral moment's method. The calculation of the DBNNT infrared active modes as a function of the diameter and chirality of the inner and outer tubes allows us to derive the diameter dependence of the wave number of the breathing-like modes, intermediate-like modes and tangential-like modes in a large diameter range. In particular, the diameter dependence of the wave numbers of the two radial breathing-like modes resulting from the in-phase and counterphase coupled motions of the totally symmetric radial breathing mode (the so-called RBM) of the inner and outer tubes is discussed. Depending on the relative lengths of the inner and outer tubes, additional modes are evidenced in the RBM region. These modes must be considered in the analysis of the experimental data.