Phonon Interference in the 1D Array of Carbon Nanotubes

The dynamics of the 1D array of single‐walled carbon nanotubes (CNTs), which interact by van der Waals forces, is considered. The molecular dynamics simulation shows that both the mutual displacements of the nanotubes and the deformations of their walls occur in the low‐frequency oscillations domain. The composite model taking into account both types of the nanotubes’ motions is developed in the framework of the thin elastic shell theory. Such an approach allows us to reduce the problem to the dynamics of the linear lattice with contact interaction. The dispersion relations are represented analytically and the multichannel propagation that results in phonon interference (the acoustical analog of the Fano resonance) is observed in the presence of the array's irregularities. The latter can be formed with redundant nanotubes, which are placed over the array in the grooves between neighbor sites. The calculations of the transmittance have been performed by the transfer matrix method for several typical configurations. The dynamics of the 1D array of carbon nanotubes is defined by the van der Waals forces and the circumferential rigidity of the nanotubes. The redundant nanotube can be placed in the groove between neighboring nanotubes of the regular array that leads to multichannel phonon propagation. The transmittance for the different configurations of the resonant defects calculated.