# Two-step percolation in aggregating systems

## TL;DR

This study investigates the two-step percolation behavior in aggregating systems like CNT suspensions, combining experiments and Monte Carlo simulations to reveal distinct percolation thresholds related to aggregate structure and formation.

## Contribution

It provides a combined experimental and computational analysis of two-step percolation, highlighting the roles of aggregate structure and particle interactions in electrical conductivity.

## Key findings

- Two percolation thresholds observed experimentally at ~10^{-3} and ~10^{-2} volume fraction.
- Monte Carlo simulations confirm two smoothed percolation transitions corresponding to shells and cores.
- Aggregation significantly influences anisotropy in electrical conductivity measurements.

## Abstract

The two-step percolation behavior in aggregating systems was studied both experimentally and by means of Monte Carlo (MC) simulations. In experimental studies, the electrical conductivity, $\sigma$, of colloidal suspension of multiwalled carbon nanotubes (CNTs) in decane was measured. The suspension was submitted to mechanical de-liquoring in a planar filtration-compression conductometric cell. During de-liquoring, the distance between the measuring electrodes continuously decreased and the CNT volume fraction $\varphi$ continuously increased (from $10^{-3}$ up to $\approx 0.3$% v/v). The two percolation thresholds at $\varphi_{1}\lesssim 10^{-3}$ and $\varphi_{2}\approx 10^{-2}$ can reflect the interpenetration of loose CNT aggregates and percolation across the compact conducting aggregates, respectively. The MC computational model accounted for the core-shell structure of conducting particles or their aggregates, the tendency of a particle for aggregation, the formation of solvation shells, and the elongated geometry of the conductometric cell. The MC studies revealed two smoothed percolation transitions in $\sigma(\varphi)$ dependencies that correspond to the percolation through the shells and cores, respectively. The data demonstrated a noticeable impact of particle aggregation on anisotropy in electrical conductivity $\sigma(\varphi)$ measured along different directions in the conductometric cell.