Cluster approximation applied to multisite-occupancy adsorption: configurational entropy of the adsorbed phase for dimers and trimers on triangular lattices

Abstract

The adsorption of dimers and trimers on triangular lattices is studied by combining theoretical modeling and Monte Carlo (MC) simulations. The thermodynamic process is analyzed through the behavior of the configurational entropy per site of the adsorbed phase as a function of the coverage. MC calculations, supplemented by the thermodynamic integration method, are performed in the grand canonical ensemble. The theoretical model used in the present study is called Cluster Approximation (CA), and it is based on exact calculation of states on finite cells. An efficient algorithm allows us to determine the detailed structure of the configuration space for m = l₁ × l₂ cells. From there, the thermodynamic properties can be obtained. Five systems are investigated, according to the size and shape of the molecule in the adsorbed state: (i) dimers, (ii) linear trimers, (iii) triangular trimers, (iv) 60°-angular trimers and (v) 120°-angular trimers on triangular lattices. Dimer and trimer are the simplest cases of a polyatomic adsorbate, containing all the properties of the multisite-occupancy adsorption and can be used to model several experimental systems. CA solutions are tested by comparison with MC simulations and previous data in the literature. Special interest is devoted to the calculation of the configurational entropy per site in the limit case of θ → 1 (full coverage), where some exact results are available. The theoretical formalism is also applied to model CH₄ and CO₂ clathrate hydrates. In these systems, a triangular lattice is used to simulate the substrate, and methane(carbon dioxide) molecules can be well represented by triangular(linear) trimers. The good qualitative agreement between simulation and analytical data supports the validity of the CA scheme to predict the behavior of a wide variety of multisite-adsorption models, for which theoretical solutions are very difficult to obtain.