Ion selectivity by charged spherical cavities and investigation of intersection point for average cavity density versus electric potential (a DFT study)

Abstract

Ion separation and ion selectivity inside spherical cavities are studied within the framework of the density functional theory. Results show that, at lower electric potentials and depending on cavity size, counter ions accumulate at the wall to form a shell around the co ions that prefer to aggregate in the middle of the cavity. This gives rise to the formation of separated phases of co ions and counter ions inside the spherical cavity. Depending on cavity size, these phases convert to a nearly single phase of counter ions with increasing electric potential. In this situation, small spherical cavities could be exploited as a counter ion selector tool. Our study also shows that counter ion selectivity readily occurs at lower, rather than higher, concentrations of electrolytes. For electrolytes with monovalent co ions, the (+1: −1) electrolytes exhibit a better selectivity than the (+1: −2) ones at low electric potentials. Also the selective counter ion adsorption occurs at lower electric potential when the difference between size of counter ions and co ions becomes larger. The observed selectivity is the result of confinement effect, electrostatic interaction, and excluded volume. Our study of the average cavity density versus electric potential shows an intersection for different plots related to cavities of different sizes. This intersection point reveals two different behaviors of average cavity density with cavity size on the two sides of the intersection point. In other words, average cavity density increases (decreases) with cavity size for those electric potentials which are lower (higher) than that of the intersection point but it becomes independent of cavity size for the electric potential of the intersection point.