Critical behavior of long linear molecules on two-dimensional lattices

MATOZ FERNANDEZ, DANIEL ALEJANDRO; D. H. LINARES; A.J RAMIREZ-PASTOR

Natal, Brazil

Otro; Brazilian School on Statistical Mechanics; 2011

International Institute of Physics from the Federal University of Rio Grande do Norte – IIP/UFRN

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior for the isotropic-nematic transition in a system of long rigid rods of length k (k-mers) on 2D lattices. The nematic phase, characterized by a big domain of parallel k-mers, is separated from the isotropic state by a continuous transition occurring at a finite density. The determination of the critical exponents, along with the behavior of Binder cumulants, indicate that the transition belongs to the 2D Ising universality class for square lattices and to the three-state Potts universality class for honeycomb and  triangular lattices. In addition, the configurational entropy of the system is compared with that corresponding to a fully aligned system, whose calculation reduces to the 1D case. The results obtained (1) allow us 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 for the existence of a second transition (from a nematic to a non-nematic state) occurring at a density close to 1; and (3) allow us to test the predictions of the main theoretical models developed to treat the polymer adsorption problem.