The Variable Capacitance Model: A Strategy for Treating Contrasting Charge-Neutralizing Capabilities of Counterions at the Mineral/Water Interface

Thermodynamic models predicting ion adsorption at mineral/water interfaces can have limitations from the simplifying assumptions that compact plane thicknesses and capacitance values are constant, and that charge densities of electrolyte counterions of different charge-to-size ratios lie at the same planes of adsorption, or split between different planes. To address these limitations a thermodynamic adsorption modeling framework was developed to account for coexisting compact planes for each type of counterion complexes formed on a single mineral surface. This framework was developed to predict charge development at lepidocrocite (gamma-FeOOH) particle surfaces suspended in aqueous solutions of NaCl and NaClO4. The model incorporates properties of Cl-, ClO4-, and Na+ complexes formed at the (001) and (010) faces of this mineral obtained by molecular dynamics (MD) simulations. This concept was incorporated in a thermodynamic adsorption model that predicts an overall variable compact plane capacitance in terms of a linear combination of the capacitances of ion-specific EDL structures scaled for their relative surface loadings. These capacitance values are in turn constrained by compact plane thicknesses of every Cl-, ClO4-, and Na+ complex, based on their MD-derived structures and atomic densities. The model predicts experimental potential-determining (H+, OH-) data for submicrometer-sized synthetic lepidocrocite particles exhibiting both (001) and (010) faces. It also isolates electrostatic contributions from these faces. A computer code solving for this Variable Capacitance Model-VCM-is provided in the Supporting Information section of this article, and can be readily modified to predict molecular-level details of any other mineral/water interface systems using this methodology.