The phase behavior of interacting rigid rods of length $k$ ($k$-mers) on two-dimensional square and triangular lattices has been studied by theoretical calculations in the framework of the lattice-gas model. The process was analyzed by comparing the dependence on coverage of the free energy per site of an isotropic submonolayer of interacting $k$-mers $f_{\mathrm{iso}}\left(\theta \right)$ with that corresponding to a fully aligned (nematic) system $f_{\mathrm{nem}}\left(\theta \right)$. The existence of an intersection point between the curves $f_{\mathrm{iso}}\left(\theta \right)$ and $f_{\mathrm{nem}}\left(\theta \right)$, which is indicative of the occurrence of an isotropic-nematic phase transition in the adlayer, allowed us to obtain the complete (temperature, coverage, $k$-mer size) phase diagram of the system.

• Received 3 October 2011

DOI:https://doi.org/10.1103/PhysRevE.85.011136