Study of the adsorption of interacting dimers on square lattices by using a cluster-exact approximation R. Belardinelli, S. Manzi, A.J. Ramirez-Pastor, V.D. Pereyra * Departamento de F  ısica, Laboratorio de Ciencias de Superficie, y Medios Porosos, Universidad Nacional de San Luis, CONICET Chacabuco 917, 5700 San Luis, Argentina Received 19 August 2002; accepted for publication 12 May 2003 Abstract A theoretical approach, based on exact calculation of the partition function on finite rectangular clusters, is in- troduced to study the adsorption of interacting homonuclear dimers on square lattices. An efficient algorithm allows us to calculate the detailed structure of the configuration space for m ¼ðk  lÞ clusters with m varying from 8 to 48. The adsorption process has been monitored by following thermodynamic properties such as coverage versus chemical potential, internal energy and specific heat of the adlayer, etc. The analytical results are compared with those in [Surf. Sci. 411 (1998) 294], which were obtained by using Monte Carlo simulation and finite-size scaling techniques. The theoretical adsorption isotherms and phase diagrams (critical temperature versus coverage) for both attractive and repulsive lateral interactions are in good qualitative agreement with the computational data. This agreement between simulated and theoretical results supports the validity of the cluster-exact approximation proposed in this paper. Ó 2003 Elsevier B.V. All rights reserved. Keywords: Adsorption isotherms; Clusters; Monte Carlo simulations; Surface thermodynamics (including phase transitions) 1. Introduction Adsorption of molecules with multisite occu- pancy has been less developed than the classical monomer problem [1–4]. However, most of the technological applications of adsorption processes involve large molecules. In fact, the experimental evidence has shown that the adsorbed molecules are, in many cases, consisting of a number of single components. Even the simplest gases like nitrogen, carbon monoxide, oxygen, etc., are composed of more than one atom. More complicated molecules like C m H 2ðm1Þ adsorbed on different solid surfaces like zeolite molecular sieves or in activated car- bons, represent a clear example of multisite ad- sorption processes [5,6]. On the other hand, more complex processes like surface reactions, par- ticularly those associated to the heterogeneous catalysis, where large polyatomic molecules are dissociated to obtain different products, are other good examples of adsorbed molecules occupying more than one surface site. The difficult in the analysis of the multisite statistics is mainly asso- ciated with three factors which differentiate the dimers statistic from the usual single particle * Corresponding author. Tel.: +54-65-22-3789; fax: +54-65- 23-0224. E-mail address: vpereyra@unsl.edu.ar (V.D. Pereyra). 0039-6028/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0039-6028(03)00743-X Surface Science 540 (2003) 207–214 www.elsevier.com/locate/susc