Partitioning of mobile ions between ion exchange polymers and aqueous salt solutions: importance of counter-ion condensation

Abstract

Equilibrium partitioning of ions between a membrane and a contiguous external solution strongly influences transport properties of polymeric membranes used for water purification and energy generation applications. This study presents a theoretical framework to quantitatively predict ion sorption from aqueous electrolytes (e.g., NaCl, MgCl2) into charged (i.e., ion exchange) polymers. The model was compared with experimental NaCl, MgCl2, and CaCl2 sorption data in commercial cation and anion exchange membranes. Ion sorption in charged polymers was modeled using a thermodynamic approach based on Donnan theory coupled with Manning's counter-ion condensation theory to describe non-ideal behavior of ions in the membrane. Ion activity coefficients in solution were calculated using the Pitzer model. The resulting model, with no adjustable parameters, provides remarkably good agreement with experimental values of membrane mobile salt concentration. The generality of the model was further demonstrated using literature data for ion sorption of various electrolytes in charged polymers, including HCl sorption in Nafion.

Modelling of Ion Transport in Electromembrane Systems: Impacts of Membrane Bulk and Surface Heterogeneity

“…Kamcev et al [47][48][49] propose to use the Bjerrum length as the distance from the fixed ions, which determines the boundary dividing the electrolyte solution in membrane pores into two parts whose properties are different. The Bjerrum length, λ B , is the distance at which the electrostatic potential energy between two charges equals the thermal energy scale [50].…”

“…The Bjerrum length, λ B , is the distance at which the electrostatic potential energy between two charges equals the thermal energy scale [50]. According to Bjerrum, if a counter-ion is closer to the fixed charge than λ B , it is regarded as "associated": its electrostatic interaction with the fixed ion is so great that it cannot diffuse away from the fixed charge [48]. If the distance between two ions is less than λ B , the energy of electrostatic interaction exceeds the kinetic energy of thermal motion, which reduces the mobility of ions.…”

“…Manning [51,52] proposed a model for polyelectrolyte known as the Manning condensation theory [53]. Kamcev et al [47][48][49] have applied recently this theory to ion-exchangers. According to [49], if the distance between two fixed charges (b) is less than λ B , counterions condense (or localize) on the polymer chain, which is a result of strong electrostatic interaction between the fixed ions and mobile counterions.…”

“…In strongly charged IEMs, K s is essentially less than 1 due to Donnan exclusion of co-ions. With increasing external concentration, the Donnan exclusion gets less strong and K s increases [46,48,93,94].…”

The plastics revolution: how chemists are pushing polymers to new limits

“…Earlier this year, Freeman and his colleagues published 8 what he believes is the first model to do just that, which could enable chemists to build particular properties into a membrane by tailoring its chemical substituents and cross-linking the molecules. "I'm on a mission to get people to ask these kinds of questions about structure-property relations, which could really guide synthesis, " he says.…”