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.

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

References in corpus (1)

• Entropy-driven phase transition in a system of long rods on a square lattice

Cited by in corpus (9)

• Percolation of linear $k$-mers on square lattice: from isotropic through partially ordered to completely aligned state
• 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
• The isotropic-nematic transition for hard rods on a three--dimensional (3D) cubic lattice
• 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
• Semi-flexible trimers on the square lattice in the full lattice limit
• Entropy of fully-packed rigid rods on generalized Husimi trees: a route to the square lattice limit