Random geometric graph description of connectedness percolation in rod systems

Abstract

The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The probability that an edge (or link) connects any randomly selected pair of nodes depends upon the rod volume fraction as well as the distribution over their sizes and shapes, and also upon quantities that characterize their state of dispersion (such as the orientational distribution function). We employ the observation that contributions from closed loops of connected rods are negligible in the limit of large aspect ratios to obtain percolation thresholds that are fully equivalent to those calculated within the second-virial approximation of the connectedness Ornstein-Zernike equation. Our formulation can account for effects due to interactions between the rods, and many-body features can be partially addressed by suitable choices for the edge probabilities.

7 pages

References in corpus (4)

• Depletion-induced percolation in networks of nanorods
• Geographical threshold graphs with small-world and scale-free properties
• Quasiuniversal connectedness percolation of polydisperse rod systems
• Continuum percolation of polydisperse hyperspheres in infinite dimensions

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• Jammed systems of oriented needles always percolate on square lattices
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• Jammed systems of oriented dimers always percolate on hypercubic lattices
• Rigidity percolation in random 3D rod systems