Aqueous ion partitioning in Nafion: Applicability of Manning's counter-ion condensation theory

Sujanani, Rahul; Katz, Lynn E.; Paul, Donald R.; Freeman, Benny D.

doi:10.1016/j.memsci.2021.119687

Aqueous ion partitioning in Nafion: Applicability of Manning's counter-ion condensation theory

Journal Article · Fri Aug 06 00:00:00 EDT 2021 · Journal of Membrane Science

DOI:https://doi.org/10.1016/j.memsci.2021.119687· OSTI ID:1841371

^[1]; Katz, Lynn E. ^[2]; Paul, Donald R. ^[2]; Freeman, Benny D. ^[2]

Univ. of Texas, Austin, TX (United States); The University of Texas at Austin
Univ. of Texas, Austin, TX (United States)

Nafion is a well-studied polymer of significant interest as a fuel cell membrane due to rapid transport of protons, which is often ascribed, at least in part, to its phase-separated morphology. The literature detailing ion sorption and transport in Nafion diverges considerably from that of water purification membranes, with contrasting analyses and models. To help bridge these gaps and facilitate comparisons of membranes with various structures, this study presents measurements of ion activity coefficients and sorption in Nafion 117 equilibrated with aqueous solutions of NaCl, MgCl₂, and Na₂SO₄, which are relevant to water purification. The experimental data are compared to a theoretical framework based on Manning's counter-ion condensation theory and Donnan theory. Good agreement between the model and data is observed for NaCl and MgCl₂, using no adjustable parameters. However, the model significantly underpredicts Na₂SO₄ solubility, which is attributed to ion pairing effects. Furthermore, the results highlight the general applicability of counter-ion condensation theory to highly charged polymers, including those exhibiting nanoscale ordering, while revealing fundamental limitations related to ion pairing.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0019272

OSTI ID:: 1841371

Journal Information:: Journal of Membrane Science, Journal Name: Journal of Membrane Science Vol. 638; ISSN 0376-7388

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (96)

Development of a space-charge transport model for ion-exchange membranes Guzmán-Garcia, Angel G.; Pintauro, Peter N.; Verbrugge, Mark W. AIChE Journal, Vol. 36, Issue 7 https://doi.org/10.1002/aic.690360713	journal	July 1990
The critical onset of counterion condensation: A survey of its experimental and theoretical basis Manning, Gerald S. Berichte der Bunsengesellschaft für physikalische Chemie, Vol. 100, Issue 6 https://doi.org/10.1002/bbpc.19961000637	journal	June 1996
Colligative properties of polyelectrolyte solutions. IV. Activity coefficient of sodium ion Nagasawa, Mitsuru; Kagawa, Ikumi Journal of Polymer Science, Vol. 25, Issue 108 https://doi.org/10.1002/pol.1957.1202510806	journal	June 1957
Colligative properties of polyelectrolyte solutions. V. Activity coefficients of counter- and by-ions Nagasawa, Mitsuru; Izumi, Mikio; Kagawa, Ikumi Journal of Polymer Science, Vol. 37, Issue 132 https://doi.org/10.1002/pol.1959.1203713208	journal	June 1959
Water purification by membranes: The role of polymer science Geise, Geoffrey M.; Lee, Hae-Seung; Miller, Daniel J. Journal of Polymer Science Part B: Polymer Physics, Vol. 48, Issue 15 https://doi.org/10.1002/polb.22037	journal	June 2010
Water-mediated transport in ion-containing polymers Hickner, Michael A. Journal of Polymer Science Part B: Polymer Physics, Vol. 50, Issue 1 https://doi.org/10.1002/polb.22381	journal	October 2011
KSO 4 ? , NaSO 4 ? , and MgCl+ ion pairs in aqueous solutions up to 2000 atm Fisher, F. H.; Fox, A. P. Journal of Solution Chemistry, Vol. 6, Issue 10 https://doi.org/10.1007/BF00645881	journal	October 1977
Water orientation and ion solvation effects during multicomponent salt partitioning in a Nafion cation exchange membrane Bontha, J. R.; Pintauro, P. N. Chemical Engineering Science, Vol. 49, Issue 23 https://doi.org/10.1016/0009-2509(94)00205-3	journal	January 1994
Sorption and transport behavior of perfluorinated ionomer membranes in concentrated NaOH solution Chandran, R. R.; Yeo, R. S.; Chin, D. -T. Electrochimica Acta, Vol. 30, Issue 12 https://doi.org/10.1016/0013-4686(85)87003-1	journal	December 1985
Swelling/deswelling of anionic copolymer gels Khare, Atul R.; Peppas, Nikolaos A. Biomaterials, Vol. 16, Issue 7 https://doi.org/10.1016/0142-9612(95)91130-Q	journal	May 1995
Ion association of chloride and sulphate with sodium, potassium, magnesium and calcium in seawater at 25°C Johnson, Kenneth S.; Pytkowicz, Ricardo M. Marine Chemistry, Vol. 8, Issue 1 https://doi.org/10.1016/0304-4203(79)90034-3	journal	August 1979
The calculation of ion pair diffusion coefficients: A comment Johnson, Kenneth S. Marine Chemistry, Vol. 10, Issue 3 https://doi.org/10.1016/0304-4203(81)90041-4	journal	April 1981
Ionic equilibria in ion-exchange membranes: a comparison of pore model predictions with experimental results Cwirko, Eleanor H.; Carbonell, Ruben G. Journal of Membrane Science, Vol. 67, Issue 2-3 https://doi.org/10.1016/0376-7388(92)80026-G	journal	March 1992
The solution-diffusion model: a review Wijmans, J. G.; Baker, R. W. Journal of Membrane Science, Vol. 107, Issue 1-2 https://doi.org/10.1016/0376-7388(95)00102-I	journal	November 1995
Ion and water transport characteristics of Nafion membranes as electrolytes Okada, Tatsuhiro; Xie, Gang; Gorseth, Oddvar Electrochimica Acta, Vol. 43, Issue 24 https://doi.org/10.1016/S0013-4686(98)00132-7	journal	August 1998
Ion transport in Nafion® 117 membrane Lehmani, Albert; Turq, Pierre; Périé, Michelle Journal of Electroanalytical Chemistry, Vol. 428, Issue 1-2 https://doi.org/10.1016/S0022-0728(96)05060-7	journal	May 1997
High frequency dielectric studies of hydrated Nafion® Paddison, Stephen J.; Reagor, David W.; Zawodzinski Jr, Thomas A. Journal of Electroanalytical Chemistry, Vol. 459, Issue 1 https://doi.org/10.1016/S0022-0728(98)00321-0	journal	November 1998
On the development of proton conducting polymer membranes for hydrogen and methanol fuel cells Kreuer, K. D. Journal of Membrane Science, Vol. 185, Issue 1, p. 29-39 https://doi.org/10.1016/S0376-7388(00)00632-3	journal	April 2001
Irreversible thermodynamics of transport across charged membranes Narȩbska, Anna; Koter, Stanisłlaw; Kujawski, Wojciech Journal of Membrane Science, Vol. 25, Issue 2 https://doi.org/10.1016/S0376-7388(00)80248-3	journal	October 1985
The electric-potential profile in ion-exchange membrane pores Pintauro, Peter N.; Verbrugge, Mark W. Journal of Membrane Science, Vol. 44, Issue 2-3 https://doi.org/10.1016/S0376-7388(00)83352-9	journal	June 1989
Effect of conditioning techniques of perfluorinated sulphocationic membranes on their hydrophylic and electrotransport properties Berezina, N. P.; Timofeev, S. V.; Kononenko, N. A. Journal of Membrane Science, Vol. 209, Issue 2 https://doi.org/10.1016/S0376-7388(02)00368-X	journal	November 2002
Divalent/monovalent cation uptake selectivity in a Nafion cation-exchange membrane: Experimental and modeling studies Tandon, R.; Pintauro, P. N. Journal of Membrane Science, Vol. 136, Issue 1-2 https://doi.org/10.1016/S0376-7388(97)00167-1	journal	December 1997
Ion-containing polymers: new energy & clean water Hickner, Michael A. Materials Today, Vol. 13, Issue 5 https://doi.org/10.1016/S1369-7021(10)70082-1	journal	May 2010
Ion mobility in Nafion-117 membranes Stenina, I. A.; Sistat, Ph.; Rebrov, A. I. Desalination, Vol. 170, Issue 1 https://doi.org/10.1016/j.desal.2004.02.092	journal	October 2004
Sorption and permeation of solutions of chloride salts, water and methanol in a Nafion membrane Villaluenga, J. P. G.; Barragán, V. M.; Seoane, B. Electrochimica Acta, Vol. 51, Issue 28 https://doi.org/10.1016/j.electacta.2006.04.011	journal	September 2006
Density Measurements and Partial Molar Volume Analysis of Different Membranes for Polymer Electrolyte Membrane Fuel Cells Bai, Yujia; Schaberg, Mark S.; Hamrock, Steven J. Electrochimica Acta, Vol. 242 https://doi.org/10.1016/j.electacta.2017.04.048	journal	July 2017
Nonrandom two-liquid activity coefficient model for aqueous polyelectrolyte solutions Yu, Yue; Li, Yuan; Hossain, Nazir Fluid Phase Equilibria, Vol. 497 https://doi.org/10.1016/j.fluid.2019.05.009	journal	October 2019
Agreement of electrolyte models with activity coefficient data of sulfuric acid in water Fraenkel, Dan The Journal of Chemical Thermodynamics, Vol. 78 https://doi.org/10.1016/j.jct.2014.06.015	journal	November 2014
Conductivity, permeability, and stability properties of chemically tailored poly(phenylene oxide) membranes for Li+ conductive non-aqueous redox flow battery separators McCormack, Patrick M.; Luo, Hongxi; Geise, Geoffrey M. Journal of Power Sources, Vol. 460 https://doi.org/10.1016/j.jpowsour.2020.228107	journal	June 2020
Reformulation of the solution-diffusion theory of reverse osmosis Paul, D. Journal of Membrane Science, Vol. 241, Issue 2 https://doi.org/10.1016/j.memsci.2004.05.026	journal	October 2004
Role of conditioning on water uptake and hydraulic permeability of Nafion® membranes Evans, Christine E.; Noble, Richard D.; Nazeri-Thompson, Sarah Journal of Membrane Science, Vol. 279, Issue 1-2 https://doi.org/10.1016/j.memsci.2005.12.046	journal	August 2006
Water permeability and water/salt selectivity tradeoff in polymers for desalination Geise, Geoffrey M.; Park, Ho Bum; Sagle, Alyson C. Journal of Membrane Science, Vol. 369, Issue 1-2 https://doi.org/10.1016/j.memsci.2010.11.054	journal	March 2011
Sodium chloride sorption in sulfonated polymers for membrane applications Geise, Geoffrey M.; Falcon, Linda P.; Freeman, Benny D. Journal of Membrane Science, Vol. 423-424 https://doi.org/10.1016/j.memsci.2012.08.014	journal	December 2012
Influence of acid pretreatment on ionic conductivity of Nafion® membranes Kuwertz, Rafael; Kirstein, Carina; Turek, Thomas Journal of Membrane Science, Vol. 500 https://doi.org/10.1016/j.memsci.2015.11.022	journal	February 2016
Specific ion effects on the permselectivity of sulfonated poly(ether sulfone) cation exchange membranes Cassady, Harrison J.; Cimino, Emily C.; Kumar, Manish Journal of Membrane Science, Vol. 508 https://doi.org/10.1016/j.memsci.2016.02.048	journal	June 2016
Monovalent and divalent ion sorption in a cation exchange membrane based on cross-linked poly (p-styrene sulfonate-co-divinylbenzene) Galizia, Michele; Benedetti, Francesco M.; Paul, Donald R. Journal of Membrane Science, Vol. 535 https://doi.org/10.1016/j.memsci.2017.04.007	journal	August 2017
Monitoring multicomponent transport using in situ ATR FTIR spectroscopy Beckingham, Bryan S.; Lynd, Nathaniel A.; Miller, Daniel J. Journal of Membrane Science, Vol. 550 https://doi.org/10.1016/j.memsci.2017.12.072	journal	March 2018
Specific co-ion sorption and diffusion properties influence membrane permselectivity Ji, Yuanyuan; Luo, Hongxi; Geise, Geoffrey M. Journal of Membrane Science, Vol. 563 https://doi.org/10.1016/j.memsci.2018.06.010	journal	October 2018
Describing ion exchange membrane-electrolyte interactions for high electrolyte concentrations used in electrochemical reactors Peng, Jing; Zawodzinski, Thomas A. Journal of Membrane Science, Vol. 593 https://doi.org/10.1016/j.memsci.2019.117340	journal	January 2020
Combining Manning's theory and the ionic conductivity experimental approach to characterize selectivity of cation exchange membranes Luo, Tao; Zhong, Yanjun; Xu, Dehua Journal of Membrane Science, Vol. 629 https://doi.org/10.1016/j.memsci.2021.119263	journal	July 2021
Characterization of a sulfonated pentablock copolymer for desalination applications Geise, G. M.; Freeman, B. D.; Paul, D. R. Polymer, Vol. 51, Issue 24 https://doi.org/10.1016/j.polymer.2010.09.072	journal	November 2010
Influence of processing history on water and salt transport properties of disulfonated polysulfone random copolymers Xie, Wei; Geise, Geoffrey M.; Freeman, Benny D. Polymer, Vol. 53, Issue 7 https://doi.org/10.1016/j.polymer.2012.01.046	journal	March 2012
Ion partitioning between brines and ion exchange polymers Galizia, Michele; Manning, Gerald S.; Paul, Donald R. Polymer, Vol. 165 https://doi.org/10.1016/j.polymer.2019.01.026	journal	February 2019
Fundamental water and salt transport properties of polymeric materials Geise, Geoffrey M.; Paul, Donald R.; Freeman, Benny D. Progress in Polymer Science, Vol. 39, Issue 1 https://doi.org/10.1016/j.progpolymsci.2013.07.001	journal	January 2014
Single and binary ion sorption equilibria of monovalent and divalent ions in commercial ion exchange membranes Chen, G. Q.; Wei, K.; Hassanvand, A. Water Research, Vol. 175 https://doi.org/10.1016/j.watres.2020.115681	journal	May 2020
Water sorption and cation-exchange selectivity of a perfluorosulfonate ion-exchange polymer Steck, A.; Yeager, H. L. Analytical Chemistry, Vol. 52, Issue 8 https://doi.org/10.1021/ac50058a013	journal	July 1980
Application of Volume Characteristics of Sulfonated Polystyrene Resins as a Tool in Analytical Chemistry Calmon, Calvin Analytical Chemistry, Vol. 25, Issue 3 https://doi.org/10.1021/ac60075a028	journal	March 1953
New Insights into Perfluorinated Sulfonic-Acid Ionomers Kusoglu, Ahmet; Weber, Adam Z. Chemical Reviews, Vol. 117, Issue 3 https://doi.org/10.1021/acs.chemrev.6b00159	journal	January 2017
Dielectric Permittivity Properties of Hydrated Polymers: Measurement and Connection to Ion Transport Properties Chang, Kevin; Geise, Geoffrey M. Industrial & Engineering Chemistry Research, Vol. 59, Issue 12 https://doi.org/10.1021/acs.iecr.9b03950	journal	October 2019
Transport of Neutral and Charged Solutes in Imidazolium-Functionalized Poly(phenylene oxide) Membranes for Artificial Photosynthesis Dischinger, Sarah M.; Gupta, Shubham; Carter, Blaine M. Industrial & Engineering Chemistry Research, Vol. 59, Issue 12 https://doi.org/10.1021/acs.iecr.9b05628	journal	December 2019
Cation Hydration and Ion Pairing in Aqueous Solutions of MgCl ₂ and CaCl ₂ Friesen, Sergej; Hefter, Glenn; Buchner, Richard The Journal of Physical Chemistry B, Vol. 123, Issue 4 https://doi.org/10.1021/acs.jpcb.8b11131	journal	January 2019
Ion Activity Coefficients in Ion Exchange Polymers: Applicability of Manning’s Counterion Condensation Theory Kamcev, Jovan; Paul, Donald R.; Freeman, Benny D. Macromolecules, Vol. 48, Issue 21 https://doi.org/10.1021/acs.macromol.5b01654	journal	October 2015
Insights into the Impact of the Nafion Membrane Pretreatment Process on Vanadium Flow Battery Performance Jiang, Bo; Yu, Lihong; Wu, Lantao ACS Applied Materials & Interfaces, Vol. 8, Issue 19 https://doi.org/10.1021/acsami.6b03529	journal	May 2016
Predicting Salt Permeability Coefficients in Highly Swollen, Highly Charged Ion Exchange Membranes Kamcev, Jovan; Paul, Donald R.; Manning, Gerald S. ACS Applied Materials & Interfaces, Vol. 9, Issue 4 https://doi.org/10.1021/acsami.6b14902	journal	January 2017
Microstructure Determines Water and Salt Permeation in Commercial Ion-Exchange Membranes Kingsbury, R. S.; Zhu, S.; Flotron, S. ACS Applied Materials & Interfaces, Vol. 10, Issue 46 https://doi.org/10.1021/acsami.8b14494	journal	October 2018
State of Understanding of Nafion Mauritz, Kenneth A.; Moore, Robert B. Chemical Reviews, Vol. 104, Issue 10 https://doi.org/10.1021/cr0207123	journal	October 2004
Electrostriction in Electrolyte Solutions Marcus, Yizhak Chemical Reviews, Vol. 111, Issue 4 https://doi.org/10.1021/cr100130d	journal	February 2011
Mass transport of electrolytes in membranes. 1. Development of mathematical transport model Pintauro, Peter N.; Bennion, Douglas N. Industrial & Engineering Chemistry Fundamentals, Vol. 23, Issue 2 https://doi.org/10.1021/i100014a016	journal	May 1984
Mass transport of electrolytes in membranes. 2. Determination of sodium chloride equilibrium and transport parameters for Nafion Pintauro, Peter N.; Bennion, Douglas N. Industrial & Engineering Chemistry Fundamentals, Vol. 23, Issue 2 https://doi.org/10.1021/i100014a017	journal	May 1984
Equilibrium Partitioning of Monovalent/Divalent Cation-Salt Mixtures in Nafion Cation-Exchange Membranes Pintauro, P. N.; Tandon, R.; Chao, L. The Journal of Physical Chemistry, Vol. 99, Issue 34 https://doi.org/10.1021/j100034a034	journal	August 1995
Determination of water diffusion coefficients in perfluorosulfonate ionomeric membranes Zawodzinski, Thomas A.; Neeman, Michal; Sillerud, Laurel O. The Journal of Physical Chemistry, Vol. 95, Issue 15 https://doi.org/10.1021/j100168a060	journal	July 1991
Prediction of ion solvation free energies in a polarizable dielectric continuum Bontha, J. R.; Pintauro, P. N. The Journal of Physical Chemistry, Vol. 96, Issue 19 https://doi.org/10.1021/j100198a051	journal	September 1992
Experimental and theoretical investigation of perfluorosulfonic acid membranes equilibrated with aqueous sulfuric acid solutions Verbrugge, Mark W.; Hill, Robert F. The Journal of Physical Chemistry, Vol. 92, Issue 23 https://doi.org/10.1021/j100334a056	journal	November 1988
Thermodynamics of electrolytes. I. Theoretical basis and general equations Pitzer, Kenneth S. The Journal of Physical Chemistry, Vol. 77, Issue 2 https://doi.org/10.1021/j100621a026	journal	January 1973
Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent Pitzer, Kenneth S.; Mayorga, Guillermo The Journal of Physical Chemistry, Vol. 77, Issue 19 https://doi.org/10.1021/j100638a009	journal	September 1973
Sodium and magnesium sulfate ion pairing. Evidence from Raman spectroscopy Daly, Francis P.; Brown, Chris W.; Kester, Dana R. The Journal of Physical Chemistry, Vol. 76, Issue 24 https://doi.org/10.1021/j100668a027	journal	November 1972
Donnan Equilibria in Cross-Linked Polymethacrylic Acid-Sodium Chloride Systems Gustafson, Richard L. The Journal of Physical Chemistry, Vol. 67, Issue 12 https://doi.org/10.1021/j100806a012	journal	December 1963
Mean activity coefficient of polyelectrolytes. VIII. Osmotic and activity coefficients of poly(styrenesulfonates) of various gegenions Ise, Norio; Okubo, Tsuneo The Journal of Physical Chemistry, Vol. 72, Issue 4 https://doi.org/10.1021/j100850a051	journal	April 1968
Electrolyte Uptake Equilibria with Low Cross-Linked Ion-Exchange Resins Freeman, David H.; Patel, Vithal C.; Buchanan, Thomas M. The Journal of Physical Chemistry, Vol. 69, Issue 5 https://doi.org/10.1021/j100889a007	journal	May 1965
A Selectivity Scale for Some Divalent Cations on Dowex 50 Bonner, O. D.; Smith, Linda Lou The Journal of Physical Chemistry, Vol. 61, Issue 3 https://doi.org/10.1021/j150549a011	journal	March 1957
Thermodynamics of electrolytes. 7. Sulfuric acid Pitzer, Kenneth S.; Roy, Rabindra N.; Silvester, Leonard F. Journal of the American Chemical Society, Vol. 99, Issue 15 https://doi.org/10.1021/ja00457a008	journal	June 1977
The Donnan Equilibrium in Cross-Linked Polystyrene Cation and Anion Exchangers Boyd, G. E.; Bunzl, K. Journal of the American Chemical Society, Vol. 89, Issue 8 https://doi.org/10.1021/ja00984a003	journal	April 1967
Study of Self-Diffusion of Monovalent and Divalent Cations in Nafion-117 Ion-Exchange Membrane Goswami, A.; Acharya, Anjali; Pandey, A. K. The Journal of Physical Chemistry B, Vol. 105, Issue 38 https://doi.org/10.1021/jp010529y	journal	September 2001
Ion and Water Transport Characteristics of Perfluorosulfonated Ionomer Membranes with H ⁺ and Alkali Metal Cations Okada, Tatsuhiro; Satou, Hiroyuki; Okuno, Mitsuhiro The Journal of Physical Chemistry B, Vol. 106, Issue 6 https://doi.org/10.1021/jp013195l	journal	February 2002
Complexity in “Simple” Electrolyte Solutions: Ion Pairing in MgSO ₄ (aq) Buchner, Richard; Chen, Ting; Hefter, Glenn The Journal of Physical Chemistry B, Vol. 108, Issue 7 https://doi.org/10.1021/jp034870p	journal	February 2004
Electrical Conductances of Aqueous Na ₂ SO ₄ , H ₂ SO ₄ , and Their Mixtures: Limiting Equivalent Ion Conductances, Dissociation Constants, and Speciation to 673 K and 28 MPa Hnedkovsky, Lubomir; Wood, Robert H.; Balashov, Victor N. The Journal of Physical Chemistry B, Vol. 109, Issue 18 https://doi.org/10.1021/jp045707c	journal	May 2005
Diffusion and Interfacial Transport of Water in Nafion Zhao, Qiao; Majsztrik, Paul; Benziger, Jay The Journal of Physical Chemistry B, Vol. 115, Issue 12 https://doi.org/10.1021/jp1112125	journal	March 2011
Ion-Pair and Solvent Relaxation Processes in Aqueous Na ₂ SO ₄ Solutions Buchner, Richard; Capewell, Stephen G.; Hefter, Glenn The Journal of Physical Chemistry B, Vol. 103, Issue 7 https://doi.org/10.1021/jp983706c	journal	February 1999
Proton tunneling within the hydration structure of hydroxyl-containing perfluorosulfonate ionomer membranes Mauritz, Kenneth A.; Gray, C. L. Macromolecules, Vol. 16, Issue 8 https://doi.org/10.1021/ma00242a006	journal	August 1983
Glass Transition Temperature of Perfluorosulfonic Acid Ionomers Osborn, Shawn J.; Hassan, Mohammad K.; Divoux, Gilles M. Macromolecules, Vol. 40, Issue 10 https://doi.org/10.1021/ma062029e	journal	May 2007
Counterion Condensation in Nafion Beers, Keith M.; Hallinan, Daniel T.; Wang, Xin Macromolecules, Vol. 44, Issue 22 https://doi.org/10.1021/ma2015084	journal	November 2011
Morphology of Hydrated As-Cast Nafion Revealed through Cryo Electron Tomography Allen, Frances I.; Comolli, Luis R.; Kusoglu, Ahmet ACS Macro Letters, Vol. 4, Issue 1, p. 1-5 https://doi.org/10.1021/mz500606h	journal	December 2014
Partitioning of mobile ions between ion exchange polymers and aqueous salt solutions: importance of counter-ion condensation Kamcev, Jovan; Galizia, Michele; Benedetti, Francesco M. Physical Chemistry Chemical Physics, Vol. 18, Issue 8 https://doi.org/10.1039/C5CP06747B	journal	January 2016
Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I. Colligative Properties Manning, Gerald S. The Journal of Chemical Physics, Vol. 51, Issue 3 https://doi.org/10.1063/1.1672157	journal	August 1969
Activity and osmotic coefficients of aqueous sulfuric acid at 298.15 K Staples, Bert R. Journal of Physical and Chemical Reference Data, Vol. 10, Issue 3 https://doi.org/10.1063/1.555648	journal	July 1981
Charged Polymer Membranes for Environmental/Energy Applications Kamcev, Jovan; Freeman, Benny D. Annual Review of Chemical and Biomolecular Engineering, Vol. 7, Issue 1 https://doi.org/10.1146/annurev-chembioeng-080615-033533	journal	June 2016
Water Treatment: Are Membranes the Panacea? Landsman, Matthew R.; Sujanani, Rahul; Brodfuehrer, Samuel H. Annual Review of Chemical and Biomolecular Engineering, Vol. 11, Issue 1 https://doi.org/10.1146/annurev-chembioeng-111919-091940	journal	June 2020
Diffusion Coefficients of Alkali Metal Cations in Nafion® from Ion‐Exchange Measurements: An Advanced Kinetic Model Samec, Z.; Trojánek, A.; Langmaier, J. Journal of The Electrochemical Society, Vol. 144, Issue 12 https://doi.org/10.1149/1.1838172	journal	December 1997
Thermodynamics and Proton Transport in Nafion Choi, Pyoungho; Jalani, Nikhil H.; Datta, Ravindra Journal of The Electrochemical Society, Vol. 152, Issue 3 https://doi.org/10.1149/1.1855872	journal	January 2005
Thermodynamics and Proton Transport in Nafion Choi, Pyoungho; Jalani, Nikhil H.; Datta, Ravindra Journal of The Electrochemical Society, Vol. 152, Issue 3 https://doi.org/10.1149/1.1859814	journal	January 2005
Halide and Sulfate Ion Diffusion in Nafion Membranes Herrera, A. Journal of The Electrochemical Society, Vol. 134, Issue 10 https://doi.org/10.1149/1.2100219	journal	January 1987
Water Absorption and Donnan Equilibria of Perfluoro Ionomer Membranes for the Chlor‐Alkali Process Kimoto, K. Journal of The Electrochemical Society, Vol. 130, Issue 2 https://doi.org/10.1149/1.2119707	journal	February 1983
Ion Clustering and Proton Transport in Nafion Membranes and Its Applications as Solid Polymer Electrolyte Yeo, Richard S. Journal of The Electrochemical Society, Vol. 130, Issue 3 https://doi.org/10.1149/1.2119746	journal	March 1983
A Hydrogen-Bromine Cell for Energy Storage Applications Yeo, R. S. Journal of The Electrochemical Society, Vol. 127, Issue 3 https://doi.org/10.1149/1.2129710	journal	January 1980
Composition and Conductivity of Membranes Equilibrated with Solutions of Sulfuric Acid and Vanadyl Sulfate Tang, Zhijiang; Svoboda, Rachel; Lawton, Jamie S. Journal of The Electrochemical Society, Vol. 160, Issue 9 https://doi.org/10.1149/2.083309jes	journal	January 2013
Sodium, Magnesium, and Calcium Sulfate Ion-Pairs in Seawater at 25c1: Ion-Pairs in Seawater Kester, Dana R.; Pytkowicx, Ricardo M. Limnology and Oceanography, Vol. 14, Issue 5 https://doi.org/10.4319/lo.1969.14.5.0686	journal	September 1969

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36 MATERIALS SCIENCE
Counter-ion condensation
Ion exchange membranes
Ion pairing
Ion sorption
Nafion

Aqueous ion partitioning in Nafion: Applicability of Manning's counter-ion condensation theory

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