Electric Field and Frequency Dependence of the Dielectric Storage, Loss, and Conductivity of Multi-Wall Carbon Nanotubes

The dielectric storage ($\epsilon'$) and loss ($\epsilon''$) of the complex dielectric constant ($\epsilon*$) are reported for multi-wall carbon nanotubes (MWCNT) up to $10^5$~Hz as a function of ac-electric field amplitude $E_{rot}$ (in-phase and same frequency as the measurement) and $E_{ac}$ (fixed phase and frequency with respect to the measurement). A slow relaxation process (mode-1) is observed that increases in peak frequency with increasing $E_{rot}$ but is independent of $E_{ac}$. A fast relaxation process (mode-2) is also observed that is independent of $E_{rot}$ and shifts to higher frequency with increasing $E_{ac}$ (opposite to that seen for mode-1). A conductivity analysis of MWCNT reveals possible mechanisms for how $E_{rot}$ and $E_{ac}$ can effect the dielectric dissipation differently.