Numerical Computations of Conductivities over Agglomerated Continuum Percolation Models

TL;DR

This paper numerically investigates how particle agglomeration influences the conductivity in continuum percolation models, revealing that agglomeration mainly affects the size of the analyzed region and discussing shape effects on universal properties.

Contribution

It introduces a simple numerical algorithm to model particle agglomeration and analyzes its impact on conductivity in continuum percolation models, extending previous shape effect studies.

Findings

Agglomeration significantly influences conductivity through size effects.

Shape of agglomerated clusters affects universal properties.

Numerical modeling clarifies agglomeration's role in real materials.

Abstract

In order to clarify how the percolation theory governs the conductivities in real materials which consist of small conductive particles, e.g., nanoparticles, with random configurations in an insulator, we numerically investigate the conductivities of continuum percolation models consisting of overlapped particles using the finite difference method as a sequel of our previous article (Int. J. Mod. Phys. 21 (2010), 709). As the previous article showed the shape effect of each particle by handling different aspect ratios of spheroids, in this article we numerically show influences of the agglomeration of the particles on conductivities after we model the agglomerated configuration by employing a simple numerical algorithm which simulate an agglomerated configuration of particles by a natural parameter. We conclude that the dominant agglomeration effect on the conductivities can be interpreted as the size effect of an analyzed region. We also discuss an effect of shape of the agglomerated clusters on its universal property.