Surface charge regulation using classical density functional theory: the effect of divalent potential determining ions

Abstract

The charge regulation approach has been used to describe the charge of surfaces susceptible to the presence of protons and other ions. Conventionally, this model is used with the Poisson–Boltzmann equation, which generally neglects the finite size of the ions and the electrostatic correlations. Recently, progress has been made by coupling charge regulation with classical density functional theory (DFT), which explicitly includes these correlations. However, little is known about charge regulation at surfaces with both acid-base equilibria and complexation with multivalent ions. The main purpose of this work is to investigate the role divalent ions play in charge regulation. Using DFT, we show that the size of the divalent ion has significant consequences on the surface charge density and it should not be neglected. For the surface reactions investigated, the larger the size of the divalent cation, the greater the charge on the surface due to higher divalent concentration there. At low divalent concentration, the ion correlations play a second-order but non-negligible role; using Poisson–Boltzmann theory with point ions cannot recover the DFT surface charge. At high concentrations, ion correlations play a dominant role by creating charge inversion.