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

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 an 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) proportional to 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.