Frequency- and electric-field-dependent conductivity of single-walled carbon nanotube networks of varying density

We present measurements of the frequency- and electric-field-dependent conductivity of single-walled carbon nanotube (SWCNT) networks of various densities. The ac conductivity as a function of frequency is consistent with the extended pair approximation model and increases with frequency above an onset frequency ${\omega }_0$ which varies over seven decades with a range of film thickness from submonolayer to $200\mathrm{nm}$. The nonlinear electric-field-dependent dc conductivity shows strong dependence on film thickness as well. Measurement of the electric field dependence of the resistance $R\left(E\right)$ allows for the determination of a length scale $L_E$ possibly characterizing the distance between tube contacts, which is found to systematically decrease with increasing film thickness. The onset frequency ${\omega }_0$ of ac conductivity and the length scale $L_E$ of SWCNT networks are found to be correlated, and a physically reasonable empirical formula relating them has been proposed. Such studies will help the understanding of transport properties and benefit the applications of this material system.

Figure 1

SEM of two SWCNT network samples with different densities: (a) submonolayer nanotube film and (b) nanotube film with thickness of about $20\mathrm{nm}$.

Figure 2

(Color online) (a) Real parts of the ac conductance for samples with different densities at room temperature. The black crosses mark the fit onset frequency ${\omega }_0$ for each curve. The magenta (gray) line is the typical fit result of the extended pair approximation model for sample 4 with ${\sigma }_0=3.3\times {10}^{-6}\mathrm{S}$/square, ${\omega }_0=1.1\times {10}^6\mathrm{rad}∕\mathrm{s}$, $k=0.12$, and $s=0.52$. (b) The onset frequencies vs dc conductance of SWCNT networks. The solid line has a slope of 1.

Figure 3

(Color online) The onset frequency vs dc conductance for different SWCNT networks at room temperature. The three solid lines all have a slope of 1.

Figure 4

(Color online) Master scaling curve showing the ac conductance for SWCNT network samples (spray method) with different densities at room temperature. The red (gray) solid line is a fit to the extended pair approximation model $k=0.12$ and $s=0.52$.

Figure 5

(Color online) (a) dc resistance vs electric field for a submonolayer (sample 5) SWCNT network at different temperatures. (b) $E_c$ vs temperature and extracted length scale for this sample.

Figure 6

(Color online) Comparison of the length scale $L_E$ obtained from electric-field-dependent dc conductance data (red dot) and the estimated length scale from frequency-dependent conductance measurement $\sqrt{A∕{\omega }_0}$ (black star) of SWCNT networks of various densities. The line has slope $-1∕2$ in the log-log plot.