Theorization on ion-exchange equilibria: activity of species in 2-D phases

Ion-exchange reactions are naturally occurring at soil and sediment/water interphases, determining soil fertility and water quality. These ion-exchange reactions with inorganic and organic exchangers are applied to chemical analysis, recovery of useful ions from low-grade ores (potentially from sea water), water purification including the preparation of "ultrapure" water, production of foods and medicines, therapy, and other uses. It is important to theorize about or to model ion-exchange reactions for quantitative explanations of ion-exchange phenomena and for efficient operation of ion-exchange processes. This paper describes the modeling of ion-exchange equilibria for hydroxyl sites on metal oxides and carboxyl sites in resins with monovalent cations (alkali metal ions), a monovalent anion (nitrate ion), and divalent heavy metal ions. The procedure of modeling is as follows: the stoichiometry and material balance equations of the respective ion-exchange reactions were established based on findings here and by others. The equilibrium conditions were given by the Frumkin equation, where the mass-action relation is modified with lateral interactions between species at the interphase. The model equations were fitted to the measured data and model parameter values were determined by nonlinear regression analysis. The formation of bonds between ions and exchanger sites was evaluated by the equilibrium constant and the suppression of bond formation by electrostatic, geometric, and other lateral interactions was evaluated by the interaction constant. It was established that the properties of ions are determined by the valence, size, and hydration state of the ions. Monovalent ions (anions and cations) react with oxide surface hydroxyl and resin carboxyl sites as hydrated ions and form loose ion-site pairs by a weak electrostatic bond (nonspecific adsorption). However, the lateral interactions are large because of a large polarization of the ion-site pairs. When the monovalent cations are dehydrated to react with carboxyl sites in narrow resin nanopores, the bond formation is difficult because energy for dehydration is necessary. The suppressive lateral interactions here are small because of a small polarization of the dehydrated ion-site pairs that are in direct contact. Divalent heavy metal ions react with oxide hydroxyl sites by replacing their hydrated water molecules and form ion-site pairs in direct strong contact (specific adsorption). The bond formation becomes easier with increasing charge density of the ions evaluated by the charge/radius ratio, agreeing with the order of these ions to form hydroxo complexes in solution. The suppressive lateral interaction is, however, small for ions with large charge densities, because a strong contact bond reduces the polarization of ion-site pairs by neutralization. The properties of exchangers are functions of the molecular and pore environments around the functional groups. The acid-base nature of oxide surface-hydroxyl groups is determined by the electronegativity of surrounding lattice metal ions, and that of resin carboxyl groups by the electron-repelling effect of adjacent methyl groups. Pores in oxides have diameters sufficient to accommodate hydrated ions, and the suppression is large because of repulsion from ions adsorbed on opposite pore walls (across-pore interaction). Pores in resins differentiate ions that can access or not access sites on the internal surfaces of the pores. Narrow nanopores with diameters less than those of the hydrated ions require ions to dehydrate before they can enter. The ion-exchange reactivity here is small, as described above for dehydrated monovalent ions. In wide nanopores where hydrated ions can enter, bond formation is easier, but suppression is greater because of a larger polarization of hydrated ion-site pairs and also of the across-pore interaction. Macropores have diameters much larger than those of the hydrated ions and the bond formation is the same as that in wide nanopores, but the suppression is smaller because of the absence oe of the absence of the across-pore interaction. Finally, this paper attempts a formulation of activity coefficients of exchanging sites and adsorbed ion-site pairs and compares the proposed activity coefficients of interphase species with that of solution species given by the Debye-Hückel equation.