Statistical thermodynamics of long straight rigid rods on triangular lattices: nematic order and adsorption thermodynamic functions

The statistical thermodynamics of straight rigid rods of length $k$ on triangular lattices was developed on a generalization in the spirit of the lattice-gas model and the classical Guggenheim-DiMarzio approximation. In this scheme, the Helmholtz free energy and its derivatives were written in terms of the order parameter $\delta$, which characterizes the nematic phase occurring in the system at intermediate densities. Then, using the principle of minimum free energy with $\delta$ as a parameter, the main adsorption properties were calculated. Comparisons with Monte Carlo simulations and experimental data were performed in order to evaluate the reaches and limitations of the theoretical model.