Percolation-to-hopping crossover in conductor-insulator composites

TL;DR

This paper investigates how the electrical conductivity in conductor-insulator composites transitions from percolation to tunneling regimes based on particle size, tunneling length, and microstructure, revealing a crossover influenced by these parameters.

Contribution

It identifies the key parameters governing the crossover between percolation and tunneling regimes in conductor-insulator composites and characterizes the conditions for each regime.

Findings

Percolation occurs at large D/ξ in lattice-like microstructures.

Tunneling regime dominates at low D/ξ regardless of microstructure.

A crossover from percolation to tunneling behavior is observed as D/ξ decreases below approximately 5.

Abstract

Here, we show that the conductivity of conductor-insulator composites in which electrons can tunnel from each conducting particle to all others may display both percolation and tunneling (i.e. hopping) regimes depending on few characteristics of the composite. Specifically, we find that the relevant parameters that give rise to one regime or the other are $D/\xi$ (where $D$ is the size of the conducting particles and $\xi$ is the tunneling length) and the specific composite microstructure. For large values of $D/\xi$, percolation arises when the composite microstructure can be modeled as a regular lattice that is fractionally occupied by conducting particle, while the tunneling regime is always obtained for equilibrium distributions of conducting particles in a continuum insulating matrix. As $D/\xi$ decreases the percolating behavior of the conductivity of lattice-like composites gradually crosses over to the tunneling-like regime characterizing particle dispersions in the continuum. For $D/\xi$ values lower than $D/\xi\simeq 5$ the conductivity has tunneling-like behavior independent of the specific microstructure of the composite.