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

Abstract

The isotropic-nematic (I-N) phase transition in a system of long straight rigid rods of length k on square lattices is studied by combining Monte Carlo simulations and theoretical analysis. The process is analyzed by comparing the configurational entropy of the system with the corresponding to a fully aligned system, whose calculation reduces to the 1D case. The results obtained (1) allow to estimate the minimum value of k which leads to the formation of a nematic phase and provide an interesting interpretation of this critical value; (2) provide numerical evidence on the existence of a second phase transition (from a nematic to a non-nematic state) occurring at density close to 1 and (3) allow to test the predictions of the main theoretical models developed to treat the polymers adsorption problem.

14 pages, 6 figures. Accepted for publication in JSTAT

References in corpus (6)

• On the orientational ordering of long rods on a lattice
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• Dimers on two-dimensional lattices
• The Isotropic to Nematic Liquid Crystalline Phase Transition of F-actin Varies from Continuous to First Order
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Cited by in corpus (14)

• The nematic-disordered phase transition in systems of long rigid rods on two dimensional lattices
• Critical behavior of long straight rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations
• 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
• Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations
• Re-entrant Disordered Phase in a System of Repulsive Rods on a Bethe-like Lattice
• High-Activity Expansion for the Columnar Phase of the Hard Rectangle Gas
• Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions
• 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
• The effect of the lateral interactions on the critical behavior of long straight rigid rods on two-dimensional lattices
• Characterisation of diffusion-driven self-organisation of rodlike particles by means of entropy of generalised two-dimensional words
• Entropy of fully-packed rigid rods on generalized Husimi trees: a route to the square lattice limit