Stratified rod network model of electrical conductance in ultrathin polymer–carbon nanotube multilayers

Abstract

The electronic conductance of polymer--carbon nanotube multilayered composite films assembled by the spin-spray layer-by-layer method is investigated. Our measurements show that the film conductance per bilayer ${\ensuremath{\sigma}}_{1}$ vanishes for film thickness below a critical value, and above this threshold it grows logarithmically with the number of polyelectrolyte bilayers ${k}_{\mathrm{l}}$. The results of our experiments are interpreted using a stratified quasi-two-dimensional conducting-network model, in which the junction resistance between nanotubes deposited in different bilayers is a function of the interlayer distance. Using scaling arguments and numerical simulations, we show that the linear dependence of the junction resistance on the layer separation leads to the logarithmic behavior ${\ensuremath{\sigma}}_{1}\ensuremath{\sim}\mathrm{log}{k}_{\mathrm{l}}$ for large ${k}_{\mathrm{l}}$, as observed in our experiments. Properties of our stratified-network model are investigated, and we show that with proper rescaling, different sets of experimental measurements can be collapsed onto a master curve. The overall shape of the master curve is determined by a single dimensionless parameter characterizing the slope of the junction-resistance function.