Selective Adsorption of Ions with Different Diameter and Valence at Highly Charged Interfaces † Mo ´ nika Valisko ´ Department of Physical Chemistry, UniVersity of Pannonia, H-8201 Veszpre ´ m, P.O. Box 158, Hungary Dezso _ Boda* Department of Molecular Biophysics and Physiology, Rush UniVersity Medical Center, Chicago, Illinois 60612, and Department of Physical Chemistry, UniVersity of Pannonia, H-8201 Veszpre ´ m, P.O. Box 158, Hungary Dirk Gillespie Department of Molecular Biophysics and Physiology, Rush UniVersity Medical Center, Chicago, Illinois 60612 ReceiVed: May 14, 2007; In Final Form: August 8, 2007 Monte Carlo simulation and density functional theoretical (DFT) results are reported for the selective adsorption of two competing cationic species at a highly charged planar interface. The two cations differ in both their diameter (2 and 4.25 Å) and valence (mono- and divalent). Our results show that in general the smaller or the divalent cation is preferentially adsorbed at the electrode. In the case when the divalent ion is larger and the monovalent ion is smaller, we find a competitive situation: at lower surface charges the electrostatic advantage of the divalent ions dominates, whereas at higher surface charges the entropic advantage of the small ions dominates. We show results for the excess adsorption, density profiles, and mean electrical potential in various situations where charge inversion occurs when divalent ions are present. Using the DFT decomposition of the chemical potential into various terms (e.g., ideal, electrostatic, hard sphere), we demonstrate that the competition between ionic species of different sizes and valences originates in the balance of excluded volume and electrostatic terms. 1. Introduction The selective adsorption of ions of different diameters and valences at highly charged interfaces is studied using Monte Carlo (MC) simulations and density functional theory (DFT). Ion selectivity has a fundamental technological importance involving ion selective electrodes, ion exchange equipments, filters, and sensors. 1 Membranes that selectively allow the permeation of specific ions have an important roles in these techniques. One of the most obvious examples of such a membrane is the biological plasma membrane of cells. Because the lipid bilayer is impermeable to ions, the selective transport of ions through the membrane is facilitated by membrane proteins that have a huge diversity in their structure, working mechanism, and physiological role. Ion channels, for example, allow the passive transport of specific ions down their electro- chemical gradients whenever they get a proper signal to open. 2 Other important biological examples are calcium binding proteins like calsequestrin that selectively bind ions from a solution where that specific ion might be present only at nanomolar concentrations. The mechanism by which all of these systems discriminate between ions might be very different. Adsorption on a surface, for example, can be physical in nature when the molecules are bound by weak van der Waals forces, whereas chemical adsorption occurs when stronger bonds (hydrogen or covalent) are formed between the adsorbed molecules and the surface. In this work, we consider another kind of force that adsorbs ions near a charged surface: the electrostatic force. Specifically, we are interested in the case when the interface is highly charged so that the ions accumulate in the double layer (DL) at a high ionic density. In such a case, the size of the ions is very important and a competition between the two counter-ion species that might have different charges and different sizes occurs. The electrical DL appears whenever an ionic solution is in contact with a surface of an electrode, a membrane, or a macromolecule, and so forth. The diffuse layer formed by counter-ions and co-ions extends into the electrolyte and plays a crucial role in the dynamics of electrochemical reactions and ion transport. Considerable effort has been employed to explain the structure of this region. The first attempt to describe the diffuse layer was that of Gouy, 3 Chapman, 4 and Stern 5 using the Poisson-Boltzmann (PB) treatment of point ions embedded in a continuum solvent. Because of its simplicity, this theory is widely used in many fields such as biophysics, solution chemistry (where it is known as Debye-Hu ¨ckel theory 6 ), and colloid chemistry (where it is known as Derjaguin-Landau- Verwey-Overbeek theory 7,8 ). The limitations of the PB theory are well-known; 9 most importantly, because the ions have finite size, it is applicable only in dilute solutions. The analytical form of the PB theory, nevertheless, still makes it a popular method for describing experimental phenomena, for example when the treatment of the DL structure is coupled to equations of electrochemical hydrodynamics. 10-12 Steric effects were taken into account in many works 13-16 by adding † Part of the “Keith E. Gubbins Festschrift”. * Author to whom correspondence should be addressed. E-mail address: dezso_boda@rush.edu. 15575 J. Phys. Chem. C 2007, 111, 15575-15585 10.1021/jp073703c CCC: $37.00 © 2007 American Chemical Society Published on Web 10/06/2007