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 (sigma) 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 sigma 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) approximately 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.