Statistical thermodynamics of aligned rigid rods with attractive lateral interactions: Theory and Monte Carlo simulations

The phase behaviour of aligned rigid rods of length k (k-mers) adsorbed on two-dimensional square lattices has been studied by Monte Carlo (MC) simulations and histogram reweighting technique. The k-mers, containing k identical units (each one occupying a lattice site) were deposited along one of the directions of the lattice. In addition, attractive lateral interactions were considered. The methodology was applied, particularly, to the study of the critical point of the condensation transition occurring in the system. The process was monitored by following the fourth order Binder cumulant as a function of temperature for different lattice sizes. The results, obtained for k ranging from 2 to 7, show that: (i) the transition coverage exhibits a decreasing behaviour when it is plotted as a function of the k-mer size and (ii) the transition temperature, Tc, exhibits a power law dependence on k, Tc∼k0,4, shifting to higher values as k increases. Comparisons with an analytical model based on a generalization of the Bragg-Williams approximation (BWA) were performed in order to support the simulation technique. A significant qualitative agreement was obtained between BWA and MC results.