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

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.