A simple statistical mechanical approach for studying multilayer adsorption of interacting rigid polyatomics

A simple statistical mechanical approach for studying multilayer adsorption of interacting rigid molecular chains of length k (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 ad-molecules hamper the formation of the monolayer and the BET results are not good (even worse than those obtained in the non-interacting case).