Tomographic-like reconstruction of the percolation cluster as a phase transition

TL;DR

This paper investigates a phase transition in percolation clusters using atomic force microscopy, revealing connectivity behavior and cluster statistics similar to continuum percolation models.

Contribution

It introduces a tomographic-like reconstruction method to analyze percolation clusters and identifies a phase transition in connectivity on a two-dimensional cross-section.

Findings

Connectivity onset marks phase transition

Cluster statistics match continuum percolation predictions

Electrical connectivity features depend on cut-off current

Abstract

We observed a phase transition-like behavior that is marked by the onset of the realization of the connectivity between two sites on a two-dimensional cross-section of a three-dimensional percolation cluster. This was found using contact-resistance atomic force microscopy on carbon black/polymer composites. The features in the current images, when presented as a function of the cut-off current, or as a function of the total area covered by the electrically connected objects, appear to obey a cluster statistics that is similar to the one predicted and observed in continuum percolation systems.