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We study the percolation of the adsorbed phase of a binary gas mixture in thermodynamic equilibrium. The adsorption process is studied with Monte Carlo simulations carried out following standard Metropolis/Monte Carlo protocol for the study of the monolayer lattice gas model. We explore how the percolation threshold changes as a function of the inter-particle forces and the appearance of ordered phases. The forces considered are repulsive first neighbor forces.

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In this work we study a simple model of multilayer adsorption of noninteracting polyatomic species on homogeneous and heterogeneous surfaces. A new approximate analytic isotherm is obtained and validated by comparing with Monte Carlo simulation in one- and two-dimensional lattices. Then, we use the well-known Brunauer-Emmet-Teller (BET) approach to analyze these isotherms and to estimate the monolayer volume, v(m). In this way, we confirm previous observations that the value of the v(m) obtained by the BET equation depends strongly on adsorbate size and surface heterogeneity. In all cases, we find that the use of the BET equation leads to an underestimate of the true monolayer capacity. Nevertheless, a compensation effect is found for the adsorption on a patchwise bivariate surface, but this is not enough to eliminate the decrease of v(m) caused by the molecular size. In addition, we consider also the possibility to use the model to study the adsorption on nanotube bundles.

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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). .ar 2 Even for simple gases such as oxygen, nitrogen and carbon monoxide, which basically are not altered in their molecular dimensions under physical adsorption, the adsorption energy depends in general on the orientation of the molecule in the adsorbed state.

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