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arXiv · 2310.03405

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

Yuri Yu. Tarasevich·Irina V. Vodolazskaya·Andrei V. Eserkepov
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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 $n_\text{E} \gg 1$.

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Yuri Yu. Tarasevich, Irina V. Vodolazskaya, Andrei V. Eserkepov. 2023-10-05. Effective electrical conductivity of random resistor networks generated using a Poisson--Voronoi tessellation. https://doi.org/10.1063/5.0181092

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