  We present a numerical study on geometric percolation in liquid dispersions
of hard slender colloidal particles subjected to an external orienting field.
In the formulation and liquid-state processing of nanocomposite materials, the
alignment of particles by external fields such as electric, magnetic or flow
fields is practically inevitable, and often works against the emergence of
large nanoparticle networks. Using continuum percolation theory in conjunction
with Onsager theory, we investigate how the interplay between externally
induced alignment and the spontaneous symmetry breaking of the uniaxial nematic
phase affects cluster formation within nanoparticle dispersions. It is known
that the enhancement of particle alignment by means of a density increase or an
external field may result in the breakdown of an already percolating network.
As a result, percolation can be limited to a small region of the phase diagram
only. Here, we demonstrate that the existence and shape of such a "percolation
island" in the phase diagram crucially depends on the connectivity length -- a
critical distance defining direct connections between neighbouring particles.
Deformations of this percolation island can lead to peculiar re-entrance
effects, in which a system-spanning network forms and breaks down multiple
times with increasing particle density.
