Using a Novel Approach to Estimate Packing Density and Related Electrical Resistance in Multi-wall Carbon Nanotube Networks

An efficient procedure for the dispersion and quantification of a network of multi-walled carbon nanotubes (MWCNTs) was developed. The dispersion technique is scalable to wafer-size samples, making the process useful in industrial applications. Using image processing, the fractal dimension factor (D) of the MWCNT network that represents its geometric complexity was determined and correlated to the areal concentration of the CNTs in the network. The less complex network that has a lower density of CNTs had the highest D factor, tending towards 2, which is the characteristic value for a two- dimensional network. The electrical resistance of the thin MWCNT network was found to scale with the areal mass density of MWCNTs by a power law, with a percolation exponent of 1.42 and a percolation threshold of 0.12 micrograms per cm$^{\mathrm{2}}$. The sheet resistance of the highly dense MWCNT networks was about six orders of magnitude lower than that of less dense networks; attributed to a higher number of wire contacts. The dependence of the resistance on the areal density of CNTs in the network and on CNT network complexity was analyzed to validate a two-dimensional percolation behavior.