14 May 2001 Physics Letters A 283 (2001) 257–269 www.elsevier.nl/locate/pla Fermi-like description of the adsorption phenomenon G. Barbero a,∗ , F. Batalioto b , L.R. Evangelista a,b a Dipartimento di Fisica del Politecnico and INFM, Corso Duca degli Abruzzi, 24-10129 Torino, Italy b Departamento de Física, Universidade Estadual de Maringá, Av. Colombo 5790, 87020-900 Maringá, PR, Brazil Received 7 March 2001; accepted 21 March 2001 Communicated by V.M. Agranovich Abstract A Fermi-like description for the adsorption of particles at a surface is proposed. It is shown that this theory accounts, in a natural way, for the saturation phenomenon found in real samples. Furthermore, it is shown also that this approach removes some limitations of the classical one, based on a Maxwell–Boltzmann description. As an application, we consider the steady- state distribution of ionic impurities in a sample of an isotropic fluid, whose limiting surfaces are supposed to adsorb positive charged particles. The fundamental equations of the problem are numerically solved, thus permitting the determination of the electrical potential distribution in the sample, and the full thickness dependence of the surface density of adsorbed charges.  2001 Elsevier Science B.V. All rights reserved. PACS: 61.30.-v; 61.30.Cz; 61.30.Gd 1. Introduction The surface of real systems, even if cleaned and polished, are usually covered with adsorption sites, at which particles of the fluid may attach themselves [1]. This phenomenon is due to interatomic forces acting between the particles of the system and the surface particles, and can be present in a broad variety of phys- ical and chemical systems [2]. Among the examples we mention, in particular, the general problem of a per- fect gas in equilibrium with an adsorbing surface [3]; the selective adsorption of charged particles in a weak electrolyte due to some electrochemical forces at the surface [4]; the adsorption of ferrofluid particles (mag- netic grains) by the surface in a doped lyotropic ne- * Corresponding author. E-mail address: barbero@polito.it (G. Barbero). matic sample even in the absence of external field [5,6]. The phenomenon is also relevant in liquid crys- talline systems with variable molecular shape, where reversible transformations between different molecu- lar structures can be induced by temperature variation [7,8] as well as by absorption of light [9,10]. These examples illustrate the necessity to take into account the adsorption phenomenon in order to correctly inter- pret the experimental measurements performed on a variety of different samples. Several theoretical mod- els have been proposed to treat the problem where the particle distribution were assumed to be given by the Maxwell–Boltzmann (MB) statistics [11–13]. In this framework, if the interactions between neighboring particles are significant, the adsorption tends to a satu- ration controlled by the interactions themselves. How- ever, the case in which the interaction among the par- ticles cannot be neglected is very difficult to be solved analytically. The problem is usually approached in the 0375-9601/01/$ – see front matter  2001 Elsevier Science B.V. All rights reserved. PII:S0375-9601(01)00244-4