Critical behavior of repulsive linear k-mers on square lattices at half coverage: Theory and Monte Carlo simulations

Abstract

Monte Carlo (MC) simulations have been used to study the critical behavior of repulsive linear k-mers on square lattices at 50% coverage. A (2k × 2) ordered phase, characterized by a repetition of alternating files of adsorbed k-mers separated by k adjacent empty sites, was found. This ordered phase is separated from the disordered state by a order-disorder phase transition occurring at a critical temperature Tc, which presents an intriguing dependence with the size k of the adsorbed molecules. In addition, two analytical techniques were combined with Monte Carlo simulations to predict the critical temperature of the order-disorder transformation. The first is based on a detailed mean-field approximation (DMFA), considering the exact interactions between the k-mers belonging to a region γ (the cluster) and a mean-field interaction with the rest outside γ. Different sizes for γ (k × 1, k × 2, 2k × 1, 2k × 2) were used in the calculations in order to discuss its influence in the determination of Tc. The second approach is based on a free energy minimization criterion (FEMCA). The dependence on k of the transition temperature Tc(k) observed in MC is in remarkable qualitative agreement with DMFA and FEMCA. Both allow us to interpret the physical meaning of the mechanisms underlying the observed transitions.