Determination of power-law attenuation coefficient and dispersion spectra in multi-wall carbon nanotube composites using Kramers–Kronig relations

Abstract

Using a broadband through-transmission technique, the attenuation coefficient and phase velocity spectra have been measured for a set of multi-wall carbon nanotube (MWCNT)-nylon composites (from pure nylon to 20% MWCNT by weight) in the ultrasonic frequency band from 4 to 14 MHz. The samples were found to be effectively homogeneous on spatial scales from the low end of ultrasonic wavelengths investigated and up (>0.2 mm). Using Kramers-Kronig relations, the attenuation and dispersion data were found to be consistent with a power-law attenuation model with a range of exponents from y=1.12 to y=1.19 over the measurement bandwidth. The attenuation coefficients of the respective samples are found to decrease with increasing MWCNT content and a similar trend holds also for the dispersion. In contrast, the mean phase velocities for the samples rise with increasing MWCNT content indicating an increase in the mechanical moduli.