The relationship between network morphology and conductivity in nanotube films

We have characterized both the direct current conductivity and morphology of a wide range of films made from bundled nanotubes, produced by a selection of commercial suppliers. The conductivity increases with increasing nanotube graphitization but decreases with increasing film porosity $P$ and mean bundle diameter $⟨D⟩$⁠. Computational studies show that the network conductivity is expected to scale linearly with the number density of interbundle junctions. A simple expression is derived to relate the junction number density to the porosity and mean bundle diameter. Plotting the experimental network conductivities versus the junction number density calculated from porosity and bundle diameter shows an approximate linear relationship. Such a linear relationship implies that the conductivity scales quadratically with the nanotube volume fraction, reminiscent of percolation theory. More importantly it shows the conductivity to scale with $⟨D⟩−3$⁠. Well-defined scaling with diameter and porosity allows the calculation of a specific conductivity expected for films with porosity of 50% and mean bundle diameter of 2 nm. This predicted specific conductivity scales well with the level of nanotube graphitization, reaching values as high as $1.5×107S/m$ for well graphitized HiPCO single walled nanotubes.