Abstract
The properties of polymer composites with nanofiller particles change drastically above a critical filler density known as the percolation threshold. Real nanofillers, such as graphene flakes and cellulose nanocrystals, are not idealized disks and rods but are often modeled as such. Here we investigate the effect of the shape of the particle cross section on the geometric percolation threshold. Using connectedness percolation theory and the second-virial approximation, we analytically calculate the percolation threshold of hard convex particles in terms of three single-particle measures. We apply this method to polygonal rods and platelets and find that the universal scaling of the percolation threshold is lowered by decreasing the number of sides of the particle cross section. This is caused by the increase of the surface area to volume ratio with decreasing number of sides.
| Original language | English |
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| Article number | 054902 |
| Number of pages | 7 |
| Journal | Journal of Chemical Physics |
| Volume | 149 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 7 Aug 2018 |
Funding
This work is part of the D-ITP consortium, a program of the Netherlands Organization for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW). We also acknowledge financial support from an NWO-VICI grant. We thank Bela Mulder, Simonas Grubinskas, Avik Chatterjee, and Claudio Grimaldi for helpful discussions.