Phase diagram of a bidispersed hard-rod lattice gas in two dimensions

Abstract

We obtain, using extensive Monte Carlo simulations, virial expansion and a high-density perturbation expansion about the fully packed monodispersed phase, the phase diagram of a system of bidispersed hard rods on a square lattice. We show numerically that when the length of the longer rods is 7, two continuous transitions may exist as the density of the longer rods is increased, keeping the density of shorter rods fixed: first from a low-density isotropic phase to a nematic phase, and second from the nematic to a high-density isotropic phase. The difference between the critical densities of the two transitions decreases to zero at a critical density of the shorter rods so that the fully packed phase is disordered for any composition. When both the rod lengths are larger than 6, we observe the existence of two transitions along the fully packed line as the composition is varied. Low-density virial expansion, truncated at the second virial coefficient, reproduces features of the first transition. By developing a high-density perturbation expansion, we show that when one of the rods is long enough, there will be at least two isotropic-nematic transitions along the fully packed line as the composition is varied.