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

TL;DR

This paper develops a statistical thermodynamics model for long rigid rods on triangular lattices, capturing nematic order and adsorption properties, and compares predictions with simulations and experiments.

Contribution

It introduces a generalized lattice-gas model incorporating nematic order for rods on triangular lattices, extending classical approaches.

Findings

The model predicts nematic phase transitions at intermediate densities.

Thermodynamic functions align with Monte Carlo simulation results.

Theoretical predictions match experimental data within certain density ranges.

Abstract

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.