Estimating Hofmeister energy in ion-clay mineral interactions from the Gouy-Chapman theory

Hofmeister effects are of scientific importance in cation-clay mineral interactions. In this study, we present a kinetics-based approach to estimate the Hofmeister energy of such interactions from the Gouy-Chapman theory. Montmorillonite was employed as the experimental material; the Hofmeister energies of Cs+ and Na+ were estimated. A mathematical relationship between the Hofmeister energy (as well as the classical Coulomb energy and the total energy) of a cation and its equilibrium adsorption amount was first established based on the modified Gouy-Chapman theory; the miscible displacement technique was then employed to estimate the amount of the cation adsorbed at equilibrium. The Hofmeister energy was calculated by introducing the equilibrium adsorption amount into the established mathematical relationship. The validity of the suggested approach was further corroborated. Our study indicated that the observed Hofmeister energy in cation-clay mineral interactions cannot be explained by cationic size, hydration, or dispersion forces. The observed Hofmeister energy bears two important characteristics: it increased with an increase of electric field strength, and it was much larger for the softer Cs+ cation than for the harder Na+ cation. These characteristics implied that Hofmeister effects in cation-clay mineral interactions are closely related to the changes of cationic energy in the strong electric field near the clay mineral surface. Because of the strong Hofmeister energy from the Gouy-Chapman theory, the apparent charge of Cs+ increased from the normal/typical value of + 1 to an effective charge of + 2.354; in contrast, the apparent charge of Na+ merely increased from the normal/typical + 1 to an effective charge of + 1.112 in this clay mineral system.