  The percolation behavior of aligned rigid rods of length $k$ ($k$-mers) on
two-dimensional triangular lattices has been studied by numerical simulations
and finite-size scaling analysis. The $k$-mers, containing $k$ identical units
(each one occupying a lattice site), were irreversibly deposited along one of
the directions of the lattice. The connectivity analysis was carried out by
following the probability $R_{L,k}(p)$ that a lattice composed of $L \times L$
sites percolates at a concentration $p$ of sites occupied by particles of size
$k$. The results, obtained for $k$ ranging from 2 to 80, showed that the
percolation threshold $p_c(k)$ exhibits a increasing function when it is
plotted as a function of the $k$-mer size. The dependence of $p_c(k)$ was
determined, being $p_c(k)=A+B/(C+\sqrt{k})$, where $A = p_c(k \rightarrow
\infty)= 0.582(9)$ is the value of the percolation threshold by infinitely long
$k$-mers, $B =-0.47(0.21)$ and $C = 5.79(2.18)$. This behavior is completely
different to that observed for square lattices, where the percolation threshold
decreases with $k$. In addition, the effect of the anisotropy on the properties
of the percolating phase was investigated. The results revealed that, while for
finite systems the anisotropy of the deposited layer favors the percolation
along the parallel direction to the nematic axis, in the thermodynamic limit,
the value of the percolation threshold is the same in both parallel and
transversal directions. Finally, an exhaustive study of critical exponents and
universality was carried out, showing that the phase transition occurring in
the system belongs to the standard random percolation universality class
regardless of the value of $k$ considered.
