  We investigate by means of continuum percolation theory and Monte Carlo
simulations how spontaneous uniaxial symmetry breaking affects geometric
percolation in dispersions of hard rod-like particles. If the particle aspect
ratio exceeds about twenty, percolation in the nematic phase can be lost upon
adding particles to the dispersion. This contrasts with percolation in the
isotropic phase, where a minimum particle loading is always required to obtain
system-spanning clusters. For sufficiently short rods, percolation in the
uniaxial nematic mimics that of the isotropic phase, where the addition of
particles always aids percolation. For aspect ratios between twenty and
infinity, but not including infinity, we find re-entrance behavior: percolation
in the low-density nematic may be lost upon increasing the amount of
nanofillers but can be re-gained by the addition of even more particles to the
suspension. Our simulation results for aspect ratios of 5, 10, 20, 50 and 100
strongly support our theoretical predictions, with almost quantitative
agreement. We show that a new closure of the connectedness Ornstein-Zernike
equation, inspired by Scaled Particle Theory, is more accurate than the
Lee-Parsons closure that effectively describes the impact of many-body direct
contacts.
