  Diffusion in a two-species 2D system has been simulated using a lattice
approach. Rodlike particles were considered as linear $k$-mers of two mutually
perpendicular orientations ($k_x$- and $k_y$-mers) on a square lattice. These
$k_x$- and $k_y$-mers were treated as species of two kinds. A random sequential
adsorption model was used to produce an initial homogeneous distribution of
$k$-mers. The concentration of $k$-mers, $p$, was varied in the range from 0.1
to the jamming concentration, $p_j$. By means of the Monte Carlo technique,
translational diffusion of the $k$-mers was simulated as a random walk, while
rotational diffusion was ignored. We demonstrated that the diffusion
coefficients are strongly anisotropic and nonlinearly concentration-dependent.
For sufficiently large concentrations (packing densities) and $k \geq 6$, the
system tends toward a well-organized steady state. Boundary conditions (BC)
predetermine the final state of the system. When periodic BCs are applied along
both directions of the square lattice, the system tends to a steady state in
the form of diagonal stripes. The formation of stripe domains takes longer time
the larger the lattice size, and is observed only for concentrations above a
particular critical value. When insulating (zero flux) BCs are applied along
both directions of the square lattice, each kind of $k$-mer tries to completely
occupy a half of the lattice divided by a diagonal, e.g., $k_x$-mers locate in
the upper left corner, while the $k_y$-mers are situated in the lower right
corner ("yin-yang" pattern). From time to time, regions built of $k_x$- and
$k_y$-mers exchange their locations through irregular patterns. When mixed BCs
are used (periodic BCs are applied along one direction whereas insulating BCs
are applied along the other one), the system still tends to form the stripes,
but they are unstable and change their spatial orientation.
