particles onto a plane
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Rods of length $l$ and zero thickness, $d=0$, (i.e., with an infinite aspect ratio, $a=l/d=\infty$) were deposited onto a plane substrate with a desired number density, $n$. Newly-deposited particles were allowed to overlap previously deposited ones. Periodic boundary conditions were assumed, i.e., the rods were deposited onto a torus.

The rods were aligned with respect to a selected direction, $x$. To characterize the anisotropy, we used the mean order parameter defined as (see, e.g, [@Frenkel1985]) $$\label{eq:S}
s  = 2\langle \cos^2\theta \rangle - 1.$$

Two distinct possibilities were taken into account for the anisotropic deposition of particles. Model I was equivalent to that considered in [@Balberg1983; @Balberg1983a; @Balberg1984]; the rods being randomly distributed within the interval $-\theta_m < \theta < \theta_m$, i.e., only some angles were allowed with equal probabilities [@Balberg1983a]. In this case, $$\label{eq:stheta1}
   s  = \frac{2}{\theta_m}\int_{0}^{\theta_m} \cos^2 \theta \, d\theta -1 = \frac{\sin 2\theta_m} {2\theta_m}.$$

The order parameter, $s$, defined as , and the degree of anisotropy, $A$, defined as , are related to each other as $$\label{eq:svsPP}
  s = \frac{2 A\left(A^2-1\right)}{\left(A^2+1\right)^2\arctan\left(2 A/\left(A^2-1\right)\right)}.$$

In Model II, the orientations of the rods were distributed according to a normal distribution, i.e., all angles, $\theta$, were allowed, 