Geometrical percolation threshold of overlapping ellipsoids

E. J. Garboczi, K. A. Snyder, J. F. Douglas, Michael Thorpe

Research output: Contribution to journalArticle

608 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)819-828
Number of pages10
JournalPhysical Review E
Volume52
Issue number1
DOIs
StatePublished - 1995
Externally publishedYes

Fingerprint

Percolation Threshold
Ellipsoid
ellipsoids
Overlapping
thresholds
radii
gyration
Extremes
materials science
Ellipsoid of revolution
functionals
needles
Radius of curvature
Materials Science
curvature
electrostatics
Surface area
Finite Volume
Volume Fraction
Electrostatics

ASJC Scopus subject areas

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

Cite this

Garboczi, E. J., Snyder, K. A., Douglas, J. F., & Thorpe, M. (1995). Geometrical percolation threshold of overlapping ellipsoids. 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.

In: Physical Review E, Vol. 52, No. 1, 1995, p. 819-828.

Research output: Contribution to journalArticle

Garboczi, EJ, Snyder, KA, Douglas, JF & Thorpe, M 1995, 'Geometrical percolation threshold of overlapping ellipsoids', Physical Review E, vol. 52, no. 1, pp. 819-828. https://doi.org/10.1103/PhysRevE.52.819
Garboczi, E. J. ; Snyder, K. A. ; Douglas, J. F. ; Thorpe, Michael. / Geometrical percolation threshold of overlapping ellipsoids. In: Physical Review E. 1995 ; Vol. 52, No. 1. pp. 819-828.
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