  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).
