Connectedness percolation of hard deformed rods

TL;DR

This study uses connectedness percolation theory and Monte Carlo methods to show that shape deformations in nanorods minimally impact the percolation threshold, supporting the robustness of idealized rod models.

Contribution

It demonstrates that shape imperfections in nanorods have little effect on percolation thresholds, validating the use of idealized models for nanofiller analysis.

Findings

Deviations from perfect rod shape have minimal impact on percolation threshold.

Universal scaling of percolation threshold is weakly affected by particle shape.

Shape deformations only significantly affect percolation at strong deformations.

Abstract

Nanofiller particles, such as carbon nanotubes or metal wires, are used in functional polymer composites to make them conduct electricity. They are often not perfectly straight cylinders, but may be tortuous or exhibit kinks. Therefore we investigate the effect of shape deformations of the rodlike nanofillers on the geometric percolation threshold of the dispersion. We do this by using connectedness percolation theory within a Parsons-Lee type of approximation, in combination with Monte Carlo integration for the average overlap volume in the isotropic fluid phase. We find that a deviation from a perfect rodlike shape has very little effect on the percolation threshold, unless the particles are strongly deformed. This demonstrates that idealized rod models are useful even for nanofillers that superficially seem imperfect. In addition, we show that for small or moderate rod deformations, the universal scaling of the percolation threshold is only weakly affected by the precise particle shape.