Counterion Mobility in Ion-Exchange Membranes: Spatial Effect and Valency-Dependent Electrostatic Interaction

Abstract

Enhancing the selectivity of ion-exchange membranes (IEMs) is an important need for environmental separations but is hindered by insufficient understanding of the fundamental transport phenomena. Specifically, existing models do not adequately explain the order of magnitude disparity in diffusivities of mono-, di-, and trivalent ions within the membranes. In this study, a transport framework is presented to describe counterion migration mobility using an analytical expression based on firstprinciples. The two governing mechanisms are spatial effect of available fractional volume for ion transport and electrostatic interaction between mobile ions and fixed charges. Mobilities of counterions with different valencies were experimentally characterized and shown to have high R 2 s in regression analyses with the proposed transport model. The influence of membrane swelling caused by different counterions was further accounted for to better model the spatial effect. The frictional effect of electrostatic interaction was quantitatively linked to the membrane structural and electrical properties of fixed charged density and dielectric constant. Additionally, the anion-exchange membrane exhibited a weaker electrostatic effect compared to cation-exchange membranes, which was attributed to steric hindrance caused by hydrocarbon chains of the quaternary amine functional groups. The insights offered in this study can inform the rational development of IEMs and membrane processes for ion-specific separations.

Advancing ion-exchange membranes to ion-selective membranes: principles, status, and opportunities

“…These electrostatic interactions impose friction-like losses on permeating ionic species, retarding their movement across the IEM and resulting in reduction of the effective mobilities. Our previous work showed that u m is related to , where A is an aggregated parameter of , permittivity, temperature, universal constants, and a conversion coefficient (Fan et al, 2022). Critically, u m decays exponentially with z 2 .…”

“…( 4)). Our previous work indicated that absolute ion mobilities are affected by electrostatic interactions, with u m being reciprocally dependent on the exponential of and ε −2 , where ε is permittivity experienced by the permeating ions within the IEM matrix (Fan et al, 2022). Therefore, increasing the membrane fixed charge densities and reducing the dielectric of the local environment in the hydrated nanoscale channels can, in principle, exaggerate the retardation of species with higher |z|, with lower valency counterions impeded to smaller extents.…”

Donnan Dialysis Desalination with a Thermally Recoverable Solute

“…Similar to the uphill mass transfer of Na + in CEM DD, [Cl – ] in the feed surpasses the receiver after ≈2.0 h in the AEM experiments and continues to transport against the concentration gradient. As the electrochemical potential driving ion transport is depleted, a decreasing mass transfer rate is observed: 66% of the change in Cl – concentration is achieved in the initial 2 h and only 8% from 4.0 to 8.0 h. The kinetics of anion exchange is overall slower than that of CEM DD because the Selemion AMV has lower ion conductance compared to the CEM. , Meanwhile, co-ion Na + leaks across the AEM to the receiver chamber and accumulates to 0.731 ± 0.112 mM, which is negligible compared to [Cl – ]. The HCO 3 – exchanged to the feed chamber is 93.8 ± 1.3 mM, and 22.4 ± 1.3 mM NH 4 + permeates across the AEM to the feed chamber (Figure B).…”

Donnan dialysis for phosphate recovery from diverted urine

“…Fig. S3 in the Supplementary Material presents sorption coefficients, X i , for (details on the mechanisms of valence-selectivity can be found in literature) (Fan et al, 2022;Lu et al, 2011;Saracco, 1997;Saracco and Zanetti, 1994). Because the predominant orthophosphate species in fresh urine is H 2 PO 4 − , DD with the ASVN MIPM is expected to improve selectivity for H x PO 4 (3− x)− over SO 4 2− relative to the conventional AMV.…”

“…More generally, both ion fluxes are significantly diminished with the MIPM relative to the conventional AEM (71.3 and 95.8% lower for J P and J S , respectively). The monovalent ion selective coating on the ASVN membrane is composed of highly crosslinked resin, which creates additional steric hindrance for permeating ions (Fan et al, 2022;Lu et al, 2011;Saracco, 1997;Saracco and Zanetti, 1994).…”