Influence of nanotube length on the optical and conductivity properties of thin single-wall carbon nanotube networks

We study the optical and electrical properties of transparent conducting films made from length-sorted single-wall carbon nanotubes (SWCNT). Thin films of length-sorted SWCNTs, formed through filtration from a dispersing solvent onto a filter substrate (buckypaper), exhibit sharp changes in their optical properties and conductivity (a) with increasing SWCNT surface concentration. At a given surface concentration, tubes longer than 200 nm are found to form networks that are more transparent and conducting. We show that changes of a with SWCNT concentration can be quantitatively described by the generalized effective medium (GEM) theory. The scaling universal exponents describing the percolation transition from an insulating to a conducting state with increasing concentration are consistent with the two-dimensional (2D) percolation model. Shorter tubes and mixed length tubes form 3D networks. Furthermore, we demonstrate that the conductivity percolation threshold (x(c)) varies with the aspect ratio L as, x(c) similar to 1/L, a result that is also in accordance with the percolation theory. These findings provide a framework for engineering the optical and electrical properties of SWCNT networks for technological applications where flexibility, transparency, and conductivity are required.