Statistical thermodynamics of straight rigid rods with nonadditive 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.

Adsorption of binary mixtures on two-dimensional surfaces: theory and Monte Carlo simulations

“…Thus, even though the BWA has proven to be a simpler way to deal with interactions than the QCA, the last has always proven to be closer to the MC simulation results than the BWA. Even more, in some lattice systems the QCA has yielded results that are indistinguishable from the MC results (Pinto et al 2011;Bulnes et al 2007;Garcı ´a et al 2009).…”

“…Very simple interactions like excluded volume (also called rigid spheres) can also be analytically studied. However for the simplest adsorbate-adsorbate interactions that involve nearest neighbors, complexity grows in such a way that the partition function can only be exactly (and analytically) expressed in very few cases (Ramirez-Pastor et al 2000;Roma ´and Ramirez-Pastor 2004;Pinto et al 2011;Phares and Wunderlich 1985, 1995, 1997, 1999, 2001.…”

The adsorption of a mixture of particles with non-additive interactions: a Monte Carlo study

“…However, the case of repulsive interactions is also of interest mainly because (a) experimental phase diagrams corresponding to many systems in the presence of surface restructuring are explained in terms of those interactions; 45-47 (b) the tendency to dimer formation, which seems to be relevant in several systems mentioned above, can be predicted on the basis of such kind of coupling; and (c) a rich variety of non-symmetrical phase diagrams (around half coverage) can be described. Some efforts in this direction include the study of adsorption of monomers [34][35]48 and linear k-mers 49 with repulsive non-additive lateral interactions on substrates of different connectivity.…”

“…The present paper is a natural extension of previous studies in which non-additive interactions have been included in the context of the lattice theory. [31][32][33][34][35]48,49 The observed occupation by adsorbed particles of preferred sites of a lattice, commensurate with the substrate surface, is a justification for the use of the lattice theory. 33 It is clear that a complete analysis of this field is a quiet difficult subject.…”