  We investigate percolation in mixtures of nanorods in the presence of
external fields that align or disalign the particles with the field axis. Such
conditions are found in the formulation and processing of nanocomposites, where
the field may be electric, magnetic, or due to elongational flow. Our focus is
on the effect of length polydispersity, which -- in the absence of a field --
is known to produce a percolation threshold that scales with the inverse weight
average of the particle length. Using a model of non-interacting
spherocylinders in conjunction with connectedness percolation theory, we show
that a quadrupolar field always increases the percolation threshold and that
the universal scaling with the inverse weight average no longer holds if the
field couples to the particle length. Instead, the percolation threshold
becomes a function of higher moments of the length distribution, where the
order of the relevant moments crucially depends on the strength and type of
field applied. The theoretical predictions compare well with the results of our
Monte Carlo simulations, which eliminate finite size effects by exploiting the
fact that the universal scaling of the wrapping probability function holds even
in anisotropic systems. Theory and simulation demonstrate that the percolation
threshold of a polydisperse mixture can be lower than that of the individual
components, confirming recent work based on a mapping onto a Bethe lattice as
well as earlier computer simulations involving dipole fields. Our work shows
how the formulation of nanocomposites may be used to compensate for the adverse
effects of aligning fields that are inevitable under practical manufacturing
conditions.
