Electrical conductivity of randomly placed linear wires: a mean field approach

TL;DR

This paper develops a mean-field model to predict the electrical conductivity of two-dimensional systems of randomly oriented conducting nanowires, accounting for contact and wire resistance, and compares predictions with numerical simulations.

Contribution

It introduces a new mean-field formula for conductivity that includes contact and wire resistance, validated against numerical models for various orientations.

Findings

Cross-alignment reduces electrical conductivity compared to isotropic arrangements.

The zero-width stick model is adequate for cross-aligned nanowires but overestimates connectivity in isotropic systems.

Network topology differences explain conductivity enhancements in cross-aligned nanowire films.

Abstract

Using the mean-field approximation, a formula for the effective electrical conductivity of a two-dimensional system of randomly arranged conducting sticks with a given orientation distribution was obtained. Both the resistance of the sticks themselves and the resistance of the contacts between them were taken into account. The accuracy in the resulting formula was analyzed. A comparison of the theoretical predictions of mean-field approach with the results of direct electrical conductivity calculations for several model orientation distributions describing systems with crossed sticks demonstrated good agreement. Our study showed that cross-alignment of nanowires should lead to a decreasing in the electrical conductivity compared to electrodes with isotropically arranged nanowires. We suppose that the widely used model with zero-width sticks is quite acceptable for systems of cross-aligned nanowires, but overestimates their connectivity in isotropic systems. Thus, the enhancement of the electrical conductivity of conducting films with cross-aligned nanowires may be due to a significant difference in the network topology.