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Ion-exchange membranes (IEMs) are widely used in water, energy, and environmental applications, but transport models to accurately simulate ion permeation are currently lacking. This study presents a theoretical framework to predict ionic conductivity of IEMs by introducing an analytical model for condensed counterion mobility to the Donnan-Manning model. Modeling of condensed counterion mobility is enabled by the novel utilization of a scaling relationship to describe screening lengths in the densely charged IEM matrices, which overcame the obstacle of traditional electrolyte chemistry theories breaking down at very high ionic strength environments. Ionic conductivities of commercial IEMs were experimentally characterized in different electrolyte solutions containing a range of mono-, di-, and trivalent counterions. Because the current Donnan-Manning model neglects the mobility of condensed counterions, it is inadequate for modeling ion transport and significantly underestimated membrane conductivities (by up to ≈5× difference between observed and modeled values). Using the new model to account for condensed counterion mobilities substantially improved the accuracy of predicting IEM conductivities in monovalent counterions (to as small as within 7% of experimental values), without any adjustable parameters. Further adjusting the power law exponent of the screen length scaling relationship yielded reasonable precision for membrane conductivities in multivalent counterions. Analysis reveals that counterions are significantly more mobile in the condensed phase than in the uncondensed phase because electrostatic interactions accelerate condensed counterions but retard uncondensed counterions. Condensed counterions still have lower mobilities than ions in bulk solutions due to impedance from spatial effects. The transport framework presented here can model ion migration a priori with adequate accuracy. The findings provide insights into the underlying phenomena governing ion transport in IEMs to facilitate the rational development of more selective membranes.
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A Two‐Step Intermolecular Interaction Of Molecular Macroions With Multivalent Counterions
Abstract Macroion‐counterion interaction is essential for regulating the solution behaviors of hydrophilic macroions, as simple models for polyelectrolytes. Here, we explore the interaction between uranyl peroxide molecular cluster Li68K12(OH)20[UO2(O2)OH]60(U60) and multivalent counterions. Different from interaction with monovalent counterions that shows a simple one‐step process, isothermal titration calorimetry, combined with light/X‐ray scattering measurements and electron microscopy, confirm a two‐step process for their interaction with multivalent counterions: an ion‐pairing betweenU60and the counterion with partial breakage of hydration shells followed by strongU60‐U60attraction, leading to the formation of large nanosheets with severe breakage and reconstruction of hydration shells. The detailed studies on macroion‐counterion interaction can be nicely correlated to the microscopic (self‐assembly) and macroscopic (gelation or phase separation) phase transitions in the diluteU60aqueous solutions induced by multivalent counterions.
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- Award ID(s):
- 2309886
- PAR ID:
- 10642403
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Chemistry – A European Journal
- Volume:
- 30
- Issue:
- 60
- ISSN:
- 0947-6539
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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