Effective electrical conductivity of random resistor networks generated using a Poisson--Voronoi tessellation

TL;DR

This paper investigates the effective electrical conductivity of dense, random resistor networks generated by Poisson-Voronoi tessellations, deriving an analytical relationship with the number of edges per area using a mean-field approach.

Contribution

It introduces an analytical model for conductivity in Poisson-Voronoi resistor networks, highlighting the proportionality to the square root of edge density.

Findings

Conductivity scales with the square root of edge density for high densities.

Networks are isotropic and homogeneous on average but have local fluctuations.

The mean-field approach provides a simple analytical dependency.

Abstract

We studied the effective electrical conductivity of dense random resistor networks (RRNs) produced using a Voronoi tessellation when its seeds are generated by means of a homogeneous Poisson point process in the two-dimensional Euclidean space. Such RRNs are isotropic and in average homogeneous, however, local fluctuations of the number of edges per unit area are inevitably. These RRNs may mimic, e.g., crack-template-based transparent conductive films. The RRNs were treated within a mean-field approach (MFA). We found an analytical dependency of the effective electrical conductivity on the number of conductive edges (resistors) per unit area, $n_\text{E}$. The effective electrical conductivity is proportional to $\sqrt{n_\text{E}}$ when $n_\text{E} \gg 1$.