A Simple Statistical Mechanical Approach for Studying Multilayer Adsorption of Interacting Polyatomics

TL;DR

This paper develops a statistical mechanical framework extending the BET isotherm to complex multilayer adsorption of interacting polyatomic molecules, validated by simulations and offering improved thermodynamic descriptions.

Contribution

It introduces a generalized theoretical model for multilayer adsorption of interacting polyatomics, improving upon classical theories and providing accurate predictions for complex systems.

Findings

QCA provides better thermodynamic predictions than BWA.

BET underestimates monolayer volume for non-interacting k-mers.

Attractive interactions improve BET accuracy; repulsive interactions worsen it.

Abstract

A simple statistical mechanical approach for studying multilayer adsorption of interacting polyatomic adsorbates (k-mers) has been presented. The new theoretical framework has been developed on a generalization in the spirit of the lattice-gas model and the classical Bragg-Williams (BWA) and quasi-chemical (QCA) approximations. The derivation of the equilibrium equations allows the extension of the well-known Brunauer-Emmet-Teller (BET) isotherm to more complex systems. The formalism reproduces the classical theory for monomers, leads to the exact statistical thermodynamics of interacting k-mers adsorbed in one dimension, and provides a close approximation for two-dimensional systems accounting multisite occupancy and lateral interactions in the first layer. Comparisons between analytical data and Monte Carlo simulations were performed in order to test the validity of the theoretical model. The study showed that: (i) the resulting thermodynamic description obtained from QCA is significantly better than that obtained from BWA and still mathematically handable; (ii) for non-interacting k-mers, the BET equation leads to an underestimate of the true monolayer volume; (iii) attractive lateral interactions compensate the effect of the multisite occupancy and the monolayer volume predicted by BET equation agrees very well with the corresponding true value; and (iv) repulsive couplings between the admolecules hamper the formation of the monolayer and the BET results are not good (even worse than those obtained in the non-interacting case).