Resistivity in percolation networks of one-dimensional elements with a length distribution

One-dimensional (1D) nanoelements, such as nanotubes and nanowires, making up percolation networks are typically modeled as fixed length sticks in order to calculate their electrical properties. In reality, however, the lengths of these 1D nanoelements comprising such networks are not constant, rather they exhibit a length distribution. Using Monte Carlo simulations, we have studied the effect of this nanotube and/or nanowire length distribution on the resistivity in 1D nanoelement percolation networks. We find that, for junction resistance-dominated random networks, the resistivity correlates with root-mean-square element length, whereas for element resistance-dominated random networks, the resistivity scales with average element length. If the elements are preferentially aligned, we find that these two trends shift toward higher power means. We explain the physical origins of these simulation results using geometrical arguments. These results emphasize the importance of the element length distribution in determining the resistivity in these networks.