Electrical conductivity of randomly placed linear wires: a mean field approach
arXiv:2511.07021 · doi:10.1088/1361-6528/ae38e8
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.
20 pages, 10 figures, 1 table, 36 refs
References in corpus (9)
- A fast Monte Carlo algorithm for site or bond percolation
- Efficient Monte Carlo algorithm and high-precision results for percolation
- Continuum Percolation Thresholds in Two Dimensions
- Nanowire networks: how does small-world character evolve with dimensionality?
- Anisotropy in finite continuum percolation: Threshold estimation by Minkowski functionals
- Tunneling conductivity in anisotropic nanofibre composites: a percolation-based model
- Effective electrical conductivity of random resistor networks generated using a Poisson--Voronoi tessellation
- Random nanowire networks: Identification of a current-carrying subset of wires using a modified wall follower algorithm
- Lattice model for percolation on a plane of partially aligned sticks with length dispersity