  Carbon nanotubes (CTNs) with large aspect-ratios are extensively used to
establish electrical connectedness in polymer melts at very low CNT loadings.
However, the CNT size polydispersity and the quality of the dispersion are
still not fully understood factors that can substantially alter the desired
characteristics of CNT nanocomposites. Here we demonstrate that the electrical
conductivity of polydisperse CNT-epoxy composites with purposely-tailored
distributions of the nanotube length L is a quasiuniversal function of the
first moment of L. This finding challenges the current understanding that the
conductivity depends upon higher moments of the CNT length. We explain the
observed quasiuniversality by a combined effect between the particle size
polydispersity and clustering. This mechanism can be exploited to achieve
controlled tuning of the electrical transport in general CNT nanocomposites.
