Terahertz Spectroscopy of Single-Walled Carbon Nanotubes in a Polymer Film: Observation of Low-Frequency Phonons

We investigate the dielectric response of single-walled carbon nanotubes dispersed in poly(vinyl alcohol) matrix by using terahertz time domain spectroscopy. Frequency-dependent real and imaginary parts of the complex dielectric function are measured experimentally in the terahertz regime. The low-frequency phonons of carbon nanotubes, though predicted theoretically, are directly observed for the first time at frequencies 0.26, 0.60, and 0.85 THz. Further, a broad resonance is observed at 1.15 THz associated with the longitudinal acoustic mode of vibration of straight-chain segments of the long polymeric molecules in the film. The latter is observed at 1.24 THz for a pristine polymer film and has been used to derive the size of crystalline lamellae in the film