Electrochimica Acta 47 (2002) 1765 – 1775 www.elsevier.com/locate/electacta A Monte-Carlo test of the mean field approximation used for the modeling of the adsorption of organic compounds on electrodes. Evidences for existence of peculiar phase transitions P. Nikitas 1 *, F. Moumtzis Laboratory of Physical Chemistry, Department of Chemistry, Aristotle Uniersity of Thessaloniki, 54006 Thessaloniki, Greece Received 18 October 2001; received in revised form 2 January 2002 Abstract The validity of the simple mean field approximation when it is applied to monolayers adsorbed on electrode surfaces is tested by the Monte-Carlo technique. Using two-, three- and eight-state solvent models it was found that the validity of this approximation depends mainly upon the short-range interaction parameter. If this parameter is close to zero, the mean field approximation gives results that are in excellent agreement with the Monte-Carlo method otherwise the predictions of the mean field approximation exhibit reasonable deviations from those of the Monte-Carlo method over a wide range of molecular parameters. Significant deviations among the results obtained from the mean-field approximation, the quasi-chemical approxima- tion and the Monte-Carlo method may be observed under extreme conditions of very strong electric fields. Under these conditions there are evidences for the existence of a peculiar phase transition appearing below a critical adsorbate concentration and characterized by two or three transition potentials. Another peculiar phase transition exhibiting just one transition potential is also detected and discussed. © 2002 Elsevier Science Ltd. All rights reserved. Keywords: Monte-Carlo method; Adsorption on electrodes; Random mixing approximation 1. Introduction The Bragg – Williams or mean-field or random mixing approximation has been extensively used in the model- ing of the inner layer at charged interfaces in the presence or absence of adsorbed organic molecules [1 – 22]. According to this approximation, the molecules of a system are arranged in space totally randomly. That is, the Bragg – Williams or mean field approxima- tion disregards any local order in the distribution of molecules and for this reason it is also named random mixing approximation. Intuitively we expect that this approximation is ac- ceptable when the mean distance of the molecules of a system is relatively high and/or the molecules interact among themselves with weak short-range forces, for example when they are non-polar molecules. It is evi- dent that these prerequisites are not valid at adsorbed layers on electrode surfaces. The components of such layers are polar or ionic species and, therefore, they interact with strong long-range forces. In addition, unlike the gaseous state, the species of an adsorbed layer on an electrode surface are close to each other. Therefore, we expect local order to play an important role in the properties of such layers. However, any speculation about the distribution of the molecules of a system should be tested and the Monte-Carlo method is the best tool for this purpose. The Monte-Carlo method has been adopted in several studies on the role of the short and long-range inter- molecular interactions in layers formed on electrodes [23–30]. In fact all studies up to now concern the inner layer in the absence of adsorption of organic com- pounds. The majority of this work concerns the simula- tion of the solvent properties in the inner layer and there is just one paper where the Monte-Carlo simula- tions are compared with isotherms based on the mean field approximation [29]. However, this comparison is not general, since it concerns just a certain system—the * Corresponding author. Tel.: +3-310-997773; fax: +3-310- 997709. E-mail address: nikitas@chem.auth.gr (P. Nikitas). 1 ISE member. 0013-4686/02/$ - see front matter © 2002 Elsevier Science Ltd. All rights reserved. PII:S0013-4686(02)00007-5