Continuum percolation of congruent overlapping polyhedral particles: Finite-size-scaling analysis and renormalization-group method

Wenxiang Xu, Zhigang Zhu, Yaqing Jiang, and Yang Jiao
Phys. Rev. E 99, 032107 – Published 6 March 2019

Abstract

The continuum percolation of randomly orientated overlapping polyhedral particles, including tetrahedron, cube, octahedron, dodecahedron, and icosahedron, was analyzed by Monte Carlo simulations. Two numerical strategies, (1) a Monte Carlo finite-size-scaling analysis and (2) a real-space Monte Carlo renormalization-group method, were, respectively, presented in order to determine the percolation threshold (e.g., the critical volume fraction ϕc or the critical reduced number density ηc), percolation transition width Δ, and correlation-length exponent ν of the polyhedral particles. The results showed that ϕc (or ηc) and Δ increase in the following order: tetrahedron < cube < octahedron < dodecahedron < icosahedron. In other words, both the percolation threshold and percolation transition width increase with the number of faces of the polyhedral particles as the shape becomes more “spherical.” We obtained the statistical values of ν for the five polyhedral shapes and analyzed possible errors resulting in the present numerical values ν deviated from the universal value of ν=0.88 reported in literature. To validate the simulations, the corresponding excluded-volume bounds on the percolation threshold were obtained and compared with the numerical results. This paper has practical applications in predicting effective transport and mechanical properties of porous media and composites.

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  • Received 7 June 2018
  • Revised 7 November 2018

DOI:https://doi.org/10.1103/PhysRevE.99.032107

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Wenxiang Xu1,2,*, Zhigang Zhu1, Yaqing Jiang1, and Yang Jiao2,†

  • 1College of Mechanics and Materials, Hohai University, Nanjing 211100, People's Republic of China
  • 2Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA

  • *xwxfat@gmail.com
  • yang.jiao.2@asu.edu

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Vol. 99, Iss. 3 — March 2019

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