Carbon nanotubes (CNTs) have been widely used to improve the electrical conductivity of polymers. However, not all CNTs actively participate in the conduction of electricity since they have to be close to each other to form a conductive network. The amount of active CNTs is rarely discussed as it is not captured by percolation theory. However, this amount is a very important information that could be used in a definition of loading efficiency for CNTs (and, in general, for any nanofiller). Thus, we develop a computational tool to quantify the amount of CNTs that actively participates in the conductive network. We then use this quantity to propose a definition of loading efficiency. We compare our results with an expression presented in the literature for the fraction of percolated CNTs (although not presented as a definition of efficiency). We found that this expression underestimates the fraction of percolated CNTs. We thus propose an improved estimation. We also study how efficiency changes with CNT loading and the CNT aspect ratio. We use this concept to study the size of the representative volume element (RVE) for polymers loaded with CNTs, which has received little attention in the past. Here, we find the size of RVE based on both loading efficiency and electrical conductivity such that the scales of “morphological” and “functional” RVEs can be compared. Additionally, we study the relations between particle and network properties (such as efficiency, CNT conductivity and junction resistance) and the conductivity of CNT/polymer composites. We present a series of recommendations to improve the conductivity of a composite based on our simulation results.
Mora, A., Han, F., & Lubineau, G. (2018). Estimating and understanding the efficiency of nanoparticles in enhancing the conductivity of carbon nanotube/polymer composites. Results in Physics, 10, 81–90. https://doi.org/10.1016/j.rinp.2018.05.019