Critical behavior of long straight rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

Abstract

The critical behavior of long straight rigid rods of length $k$ ($k$-mers) on square and triangular lattices at intermediate density has been studied. A nematic phase, characterized by a big domain of parallel $k$-mers, was found. This ordered phase is separated from the isotropic state by a continuous transition occurring at a intermediate density ${\theta }_c$. Two analytical techniques were combined with Monte Carlo simulations to predict the dependence of ${\theta }_c$ on $k$, being ${\theta }_c(k)\propto k^{-1}$. The first involves simple geometrical arguments, while the second is based on entropy considerations. Our analysis allowed us also to determine the minimum value of $k$ ($k_{min}=7$), which allows the formation of a nematic phase on a triangular lattice.

arXiv comment23 pages, 5 figures, to appear in The Journal of Chemical Physics

References in corpus (2)

• On the orientational ordering of long rods on a lattice
• Entropy-driven phase transition in a system of long rods on a square lattice

Cited by in corpus (25)

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• The nematic-disordered phase transition in systems of long rigid rods on two dimensional lattices
• Phase transitions in a system of hard rectangles on the square lattice
• Restricted orientation "liquid crystal" in two dimensions: Isotropic-nematic transition or liquid-gas (?)
• Asymptotic Behavior of the Isotropic-Nematic and Nematic-Columnar Phase Boundaries for the System of Hard Rectangles on a Square lattice
• Monolayers of hard rods on planar substrates: I. Equilibrium
• The isotropic-nematic transition for hard rods on a three--dimensional (3D) cubic lattice
• Re-entrant Disordered Phase in a System of Repulsive Rods on a Bethe-like Lattice
• Critical exponents and universality for the isotropic-nematic phase transition in a system of self-assembled rigid rods on a lattice
• Entropy of fully packed hard rigid rods on $d$-dimensional hyper-cubic lattices
• Different phases of a system of hard rods on three dimensional cubic lattice
• High-Activity Expansion for the Columnar Phase of the Hard Rectangle Gas
• The effect of polydispersity on the ordering transition of adsorbed self-assembled rigid rods
• Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions
• The criticality of self-assembled rigid rods on triangular lattices
• The phase transition from nematic to high-density disordered phase in a system of hard rods on a lattice
• Critical behavior of self-assembled rigid rods on triangular and honeycomb lattices
• Polydispersed rods on the square lattice
• Absence of logarithmic divergence of the entanglement entropies at the phase transitions of a 2D classical hard rod model
• Diffusion dynamics and steady states of systems of hard rods on the square lattice
• Nematic and gas-liquid transitions for sticky rods on square and cubic lattices
• Critical behavior of self-assembled rigid rods on two-dimensional lattices: Bethe-Peierls approximation and Monte Carlo simulations
• The effect of the lateral interactions on the critical behavior of long straight rigid rods on two-dimensional lattices
• Entropy of fully-packed rigid rods on generalized Husimi trees: a route to the square lattice limit
• Semi-flexible trimers on the square lattice in the full lattice limit