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 in 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 such 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 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.

7 pages, 4 figures

References in corpus (6)

• Determination of the Critical Exponents for the Isotropic-Nematic Phase Transition in a System of Long Rods on Two-dimensional Lattices: Universality of the Transition
• Random trimer tilings
• Asymptotic Behavior of the Isotropic-Nematic and Nematic-Columnar Phase Boundaries for the System of Hard Rectangles on a Square lattice
• A fundamental-measure density functional for mixtures of parallel hard cylinders
• Phase transitions in systems of hard rectangles with non-integer aspect ratio
• Polydispersed rods on the square lattice

Cited by in corpus (6)

• Entropy of fully packed hard rigid rods on $d$-dimensional hyper-cubic lattices
• Phase diagram of a system of hard cubes on the cubic lattice
• Demixing and tetratic ordering in some binary mixtures of hard superellipses
• The columnar-disorder phase boundary in a mixture of hard squares and dimers
• Biaxial nematic phase stability and demixing behaviour in monolayers of rod-plate mixtures
• Thermodynamic behavior of binary mixtures of hard spheres: Semianalytical solutions on a Husimi lattice built with cubes