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 σ1 vanishes for film thickness below a critical value, and above this threshold it grows logarithmically with the number of polyelectrolyte bilayers kl. 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 σ1 ∼ log kl for large kl, 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.