A new model for cation exchange equilibrium considering the electrostatic field of charged particles

Purpose

The aim of this study was to establish a new equilibrium model for cation exchange that quantitatively describe the three important effects: (1) the effect of electrostatic field around soil particles on exchange adsorption; (2) the effect of ionic interaction energy on Boltzmann distribution of cations; and (3) the effect of hydration radius of cation species on cationic distribution between adsorption phase and solution phase.

Materials and methods

In this paper, the Li/Na, Li/K and K/Na exchange were studied theoretically and experimentally. Purified montmorillonite was used as the experimental material and it was H-saturated in advance. In experimental study, approximately 2.5?g of the H-saturated sample was weighed in each experiment, then LiOH/NaOH, LiOH/KOH or KOH/NaOH mixture solution was added. In each experiment, the suspension was allowed to equilibrate for 48?h with continuous shaking at 298?K in an incubator shaker, and then 1?mol/l HCl was used to adjust pH to pH?=?7 when equilibrium was reached. Finally, the suspension was centrifuged and the concentration and of Li⁺, Na⁺ or K⁺ in supernatant was determined.

Results and discussion

In theoretical study, firstly, considering the ionic interaction energy in bulk solution, a modified Poisson?CBoltzmann equation was obtained; secondly, considering the electrostatic field around soil particles, the relationship between the selectivity coefficient and surface potential of particles was established; and thirdly, the modification factors were introduced to modify the effective charge of two cation species that involved in exchange because of the difference in hydration radius. Finally, the new models for describing cation exchange equilibrium were developed. Both theoretical and experimental results showed that the electrostatic field, the ionic interaction energy and the difference in hydration radius of two cation species strongly influenced cation distribution or cation exchange equilibrium. The results indicated that the effective charge could be obtained through either experimental determination or theoretical calculation, and the theoretically predicted values met the experimental results well. Therefore, the ion exchange selectivity series of different cation species with the same valence could be evaluated quantitatively.

Conclusions

New equilibrium models for describing cation exchange were established, for which the three important effects was quantitatively taken into account: the electrostatic field on exchange adsorption, the ionic interaction energy on Boltzmann distribution and the hydration radius of cation species. Both theoretical analyses and experimental results demonstrated that the cation hydration radius and the ionic interaction energy strongly influenced the exchange equilibrium considering the electrostatic field of charged particles.