Statistical thermodynamics of straight rigid rods with non-additive lateral interactions: Theory and Monte Carlo simulations

Abstract

The statistical thermodynamics of straight rigid rods of length k (k-mers) with nonadditive lateral interactions was developed on a generalization in the spirit of the lattice-gas model and the classical Bragg-Williams approximation (BWA) and the quasichemical approximation (QCA). The new theoretical framework is obtained by combining (i) the exact analytical expression for the partition function of noninteracting linear k-mers adsorbed in one dimension and its extension to higher dimensions, and (ii) a generalization of BWA and QCA in which the adsorbate can occupy more than one adsorption site. The traditional assumption of a strictly pairwise additive nearest-neighbors interaction is replaced by a more general one, namely that the bond linking a certain atom with any of its neighbors depends considerably on how many of them are actually present (or absent) on the sites in the first coordination shell of the atom. The coverage and temperature dependence of the Helmholtz free energy, chemical potential, configurational entropy, and differential heat of adsorption are given. The formalism (i) reproduces the classical results for monomers, (ii) leads to the exact statistical thermodynamics of nonadditive interacting k-mers adsorbed in one dimension, and (iii) provides a close approximation for two-dimensional systems, taking into account multisite occupancy and nonadditive lateral interactions. Comparisons with Monte Carlo simulations are performed in order to test the validity of the theoretical model. Significant quantitative differences are shown and discussed. In all cases, the QCA appears to be the more accurate approach.