### Abstract

A recurrent problem in materials science is the prediction of the percolation threshold of suspensions and composites containing complex-shaped constituents. We consider an idealized material built up from freely overlapping objects randomly placed in a matrix, and numerically compute the geometrical percolation threshold pc where the objects first form a continuous phase. Ellipsoids of revolution, ranging from the extreme oblate limit of platelike particles to the extreme prolate limit of needlelike particles, are used to study the influence of object shape on the value of pc. The reciprocal threshold 1/pc (pc equals the critical volume fraction occupied by the overlapping ellipsoids) is found to scale linearly with the ratio of the larger ellipsoid dimension to the smaller dimension in both the needle and plate limits. Ratios of the estimates of pc are taken with other important functionals of object shape (surface area, mean radius of curvature, radius of gyration, electrostatic capacity, excluded volume, and intrinsic conductivity) in an attempt to obtain a universal description of pc. Unfortunately, none of the possibilities considered proves to be invariant over the entire shape range, so that pc appears to be a rather unique functional of object shape. It is conjectured, based on the numerical evidence, that 1/pc is minimal for a sphere of all objects having a finite volume.

Original language | English (US) |
---|---|

Pages (from-to) | 819-828 |

Number of pages | 10 |

Journal | Physical Review E |

Volume | 52 |

Issue number | 1 |

DOIs | |

State | Published - 1995 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

*Physical Review E*,

*52*(1), 819-828. https://doi.org/10.1103/PhysRevE.52.819

**Geometrical percolation threshold of overlapping ellipsoids.** / Garboczi, E. J.; Snyder, K. A.; Douglas, J. F.; Thorpe, Michael.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 52, no. 1, pp. 819-828. https://doi.org/10.1103/PhysRevE.52.819

}

TY - JOUR

T1 - Geometrical percolation threshold of overlapping ellipsoids

AU - Garboczi, E. J.

AU - Snyder, K. A.

AU - Douglas, J. F.

AU - Thorpe, Michael

PY - 1995

Y1 - 1995

N2 - A recurrent problem in materials science is the prediction of the percolation threshold of suspensions and composites containing complex-shaped constituents. We consider an idealized material built up from freely overlapping objects randomly placed in a matrix, and numerically compute the geometrical percolation threshold pc where the objects first form a continuous phase. Ellipsoids of revolution, ranging from the extreme oblate limit of platelike particles to the extreme prolate limit of needlelike particles, are used to study the influence of object shape on the value of pc. The reciprocal threshold 1/pc (pc equals the critical volume fraction occupied by the overlapping ellipsoids) is found to scale linearly with the ratio of the larger ellipsoid dimension to the smaller dimension in both the needle and plate limits. Ratios of the estimates of pc are taken with other important functionals of object shape (surface area, mean radius of curvature, radius of gyration, electrostatic capacity, excluded volume, and intrinsic conductivity) in an attempt to obtain a universal description of pc. Unfortunately, none of the possibilities considered proves to be invariant over the entire shape range, so that pc appears to be a rather unique functional of object shape. It is conjectured, based on the numerical evidence, that 1/pc is minimal for a sphere of all objects having a finite volume.

AB - A recurrent problem in materials science is the prediction of the percolation threshold of suspensions and composites containing complex-shaped constituents. We consider an idealized material built up from freely overlapping objects randomly placed in a matrix, and numerically compute the geometrical percolation threshold pc where the objects first form a continuous phase. Ellipsoids of revolution, ranging from the extreme oblate limit of platelike particles to the extreme prolate limit of needlelike particles, are used to study the influence of object shape on the value of pc. The reciprocal threshold 1/pc (pc equals the critical volume fraction occupied by the overlapping ellipsoids) is found to scale linearly with the ratio of the larger ellipsoid dimension to the smaller dimension in both the needle and plate limits. Ratios of the estimates of pc are taken with other important functionals of object shape (surface area, mean radius of curvature, radius of gyration, electrostatic capacity, excluded volume, and intrinsic conductivity) in an attempt to obtain a universal description of pc. Unfortunately, none of the possibilities considered proves to be invariant over the entire shape range, so that pc appears to be a rather unique functional of object shape. It is conjectured, based on the numerical evidence, that 1/pc is minimal for a sphere of all objects having a finite volume.

UR - http://www.scopus.com/inward/record.url?scp=0000975565&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000975565&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.52.819

DO - 10.1103/PhysRevE.52.819

M3 - Article

AN - SCOPUS:0000975565

VL - 52

SP - 819

EP - 828

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 1

ER -