##
Geometrical Percolation Threshold of Overlapping Ellipsoids.

Geometrical Percolation Threshold of Overlapping
Ellipsoids.
(1042 K)

Garboczi, E. J.; Snyder, K. A.; Douglas, J. F.; Thorpe,
M. F.

Physical Review E, Vol. 52, No. 1, 819-828, July 1995.

### Keywords:

building technology; suspensions

### 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
elliposids) 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.
*