Selective adsorption of ions with different diameter and valence at highly charged interfaces

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 angstrom) 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.