Theory of Multicomponent Phenomena in Cation-Exchange Membranes: Part I. Thermodynamic Model and Validation

Crothers, Andrew R.; Darling, Robert M.; Kusoglu, Ahmet; Radke, Clayton J.; Weber, Adam Z.

doi:10.1149/1945-7111/ab6723

Title: Theory of Multicomponent Phenomena in Cation-Exchange Membranes: Part I. Thermodynamic Model and Validation

Abstract

We present and validate a mathematical model for multicomponent thermodynamic activity in phase-separated cation-exchange membranes (e.g., perfluorinated sulfonic-acid ionomers). The model consists of an expression for the free energy of the membrane and of the surrounding electrolyte solution. A modified Stokes-Robinson ionic solvation framework treats the solution-like non-idealities resulting from hydration, electrostatics, ion association, and physical interactions in bulk solution and in ionomer hydrophilic domains. Inside the membrane, a mechanics-based composite approach accounts for the swelling of the hydrophobic matrix. Treating the membrane microstructure as a disordered system of domains calculates steric exclusion of ions. Electroneutrality guarantees that the charge of mobile ions in the membrane is equal to the charge on polymer groups. Osmotic coefficients for electrolytes from literature parameterize solution-like interactions while mechanical and X-ray scattering characterization gives most membrane-specific parameters. Model predictions compare favorably to measured membrane thermodynamics (i.e., water and ion uptake) in dilute and concentrated binary and ternary salt electrolytes and in water vapor. Interactions between ions in the membrane are similar to those present in bulk electrolytes. Our results reveal that water and ion uptake is dictated by a balance between solution-like energetics and membrane swelling.

Authors:: Crothers, Andrew R.; Darling, Robert M.; Kusoglu, Ahmet; Radke, Clayton J.; Weber, Adam Z.

Publication Date:: Fri Feb 07 00:00:00 EST 2020

Research Org.:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Advanced Research Projects Agency - Energy (ARPA-E); USDOE Office of Energy Efficiency and Renewable Energy (EERE), Transportation Office. Fuel Cell Technologies Office; USDOE Office of Science (SC), Basic Energy Sciences (BES); US Army Research Office (ARO)

OSTI Identifier:: 1598405

Alternate Identifier(s):: OSTI ID: 1619154

Grant/Contract Number:: AC02-05CH11231; AC02-06CH11357; AR0000149; AWD00004008

Resource Type:: Published Article

Journal Name:: Journal of the Electrochemical Society (Online)

Additional Journal Information:: Journal Name: Journal of the Electrochemical Society (Online) Journal Volume: 167 Journal Issue: 1; Journal ID: ISSN 1945-7111

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats


                    Crothers, Andrew R., Darling, Robert M., Kusoglu, Ahmet, Radke, Clayton J., and Weber, Adam Z. Theory of Multicomponent Phenomena in Cation-Exchange Membranes: Part I. Thermodynamic Model and Validation.  United States: N. p., 2020. 
Web.  doi:10.1149/1945-7111/ab6723.

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                    Crothers, Andrew R., Darling, Robert M., Kusoglu, Ahmet, Radke, Clayton J., & Weber, Adam Z. Theory of Multicomponent Phenomena in Cation-Exchange Membranes: Part I. Thermodynamic Model and Validation.  United States.  https://doi.org/10.1149/1945-7111/ab6723

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                    Crothers, Andrew R., Darling, Robert M., Kusoglu, Ahmet, Radke, Clayton J., and Weber, Adam Z. Fri .  
"Theory of Multicomponent Phenomena in Cation-Exchange Membranes: Part I. Thermodynamic Model and Validation".  United States.  https://doi.org/10.1149/1945-7111/ab6723.

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@article{osti_1598405,

  title        = {Theory of Multicomponent Phenomena in Cation-Exchange Membranes: Part I. Thermodynamic Model and Validation},

  author       = {Crothers, Andrew R. and Darling, Robert M. and Kusoglu, Ahmet and Radke, Clayton J. and Weber, Adam Z.},

  abstractNote = {We present and validate a mathematical model for multicomponent thermodynamic activity in phase-separated cation-exchange membranes (e.g., perfluorinated sulfonic-acid ionomers). The model consists of an expression for the free energy of the membrane and of the surrounding electrolyte solution. A modified Stokes-Robinson ionic solvation framework treats the solution-like non-idealities resulting from hydration, electrostatics, ion association, and physical interactions in bulk solution and in ionomer hydrophilic domains. Inside the membrane, a mechanics-based composite approach accounts for the swelling of the hydrophobic matrix. Treating the membrane microstructure as a disordered system of domains calculates steric exclusion of ions. Electroneutrality guarantees that the charge of mobile ions in the membrane is equal to the charge on polymer groups. Osmotic coefficients for electrolytes from literature parameterize solution-like interactions while mechanical and X-ray scattering characterization gives most membrane-specific parameters. Model predictions compare favorably to measured membrane thermodynamics (i.e., water and ion uptake) in dilute and concentrated binary and ternary salt electrolytes and in water vapor. Interactions between ions in the membrane are similar to those present in bulk electrolytes. Our results reveal that water and ion uptake is dictated by a balance between solution-like energetics and membrane swelling.},

  doi          = {10.1149/1945-7111/ab6723},

  journal      = {Journal of the Electrochemical Society (Online)},

  number       = 1,

  volume       = 167,

  place        = {United States},

  year         = {Fri Feb 07 00:00:00 EST 2020},

  month        = {Fri Feb 07 00:00:00 EST 2020}

}

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Ion-conducting polymers (ionomers) have been extensively studied in solution, as membranes and substrate-supported thin films for various electrochemical energy-conversion devices, including fuel cells and electrolyzers. Formation of an ionomer film from a solution, however, is not well understood, despite its importance for fabrication of electrodes in energy devices. Here, the evolution of the perfluorinated sulfonic acid morphology upon casting from a solution is observed using in situ grazing-incidence small- and wide-angle X-ray scattering. Aggregate interactions in dispersion directly impact the hydrophilic-domain network of the cast film and the onset of crystallization occurs simultaneously with the solution-to-film transition but continues tomore »« less
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https://doi.org/10.1021/acs.macromol.9b01024

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Subsecond Morphological Changes in Nafion during Water Uptake Detected by Small-Angle X-ray Scattering

Journal Article Kusoglu, Ahmet ; Modestino, Miguel A. ; Hexemer, Alexander ; ... - ACS Macro Letters

The ability of the Nafion membrane to absorb water rapidly and create a network of hydrated interconnected water domains provides this material with an unmatched ability to conduct ions through a chemically and mechanically robust membrane. The morphology and composition of these hydrated membranes significantly affects their transport properties and performance. This research demonstrates that differences in interfacial interactions between the membranes exposed to vapor or liquid water can cause significant changes in kinetics of water uptake. In situ small-angle X-ray scattering (SAXS) experiments captured the rapid swelling of the membrane in liquid water with a nanostructure rearrangement on themore »« less
https://doi.org/10.1021/mz200015c

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Title: Theory of Multicomponent Phenomena in Cation-Exchange Membranes: Part I. Thermodynamic Model and Validation

Abstract

Citation Formats

Commercial perfluorosulfonic acid membranes for vanadium redox flow battery: Effect of ion-exchange capacity and membrane internal structure journal, April 2018

Theory of Multicomponent Phenomena in Cation-Exchange Membranes: Part II. Transport Model and Validation journal, January 2020

Aqueous Solute Partitioning and Mesh Size in HEMA/MAA Hydrogels journal, November 2012

Theory of Multicomponent Phenomena in Cation-Exchange Membranes: Part III. Transport in Vanadium Redox-Flow-Battery Separators journal, January 2020

Counterion Condensation in Nafion journal, November 2011

Potentials of cells with liquid junctions journal, December 1968

Irreversible thermodynamics of transport across charged membranes journal, February 1987

Species Uptake and Mass Transport in Membranes for Vanadium Redox Flow Batteries journal, May 2017

Composition and Conductivity of Membranes Equilibrated with Solutions of Sulfuric Acid and Vanadyl Sulfate journal, January 2013

The Debye-Hückel Theory for Hydrated Ions. II. Osmotic and Activity Coefficients of Ternary Aqueous Solutions of Hydrogen and Alkali Halogenides at 25°C journal, June 1990

Solubility of vanadyl sulfate in concentrated sulfuric acid solutions journal, April 1998

Accounting for frame of reference and thermodynamic non-idealities when calculating salt diffusion coefficients in ion exchange membranes journal, September 2017

The Debye-Hückel Theory for Hydrated Ions. I. Osmotic and Activity Coefficients of Binary Aqueous Solutions of Some 1 : 1 Electrolytes at 25°C journal, June 1990

A Critical Review of Modeling Transport Phenomena in Polymer-Electrolyte Fuel Cells journal, January 2014

Proton Solvation and Transport in Realistic Proton Exchange Membrane Morphologies journal, February 2016

Transport Property Requirements for Flow Battery Separators journal, July 2015

Tuning the Perfluorosulfonic Acid Membrane Morphology for Vanadium Redox-Flow Batteries journal, December 2016

Thermodynamics of phase equilibria in aqueous-organic systems with salt journal, April 1994

Equilibrium water and solute uptake in silicone hydrogels journal, May 2015

Simple Hofmeister series journal, January 2009

The Influence of Electric Field on Crossover in Redox-Flow Batteries journal, July 2015

Ionic Hydration and Activity in Electrolyte Solutions journal, May 1948

Review of material research and development for vanadium redox flow battery applications journal, July 2013

Equilibrium ion partitioning between aqueous salt solutions and inhomogeneous ion exchange membranes journal, November 2018

Cluster Theory of Polyelectrolyte Solutions. I. Activity Coefficients of the Mobile Ions journal, December 1965

Ion and Water Transport Characteristics of Perfluorosulfonated Ionomer Membranes with H + and Alkali Metal Cations journal, February 2002

Structural and transport properties of Nafion in hydrobromic-acid solutions journal, December 2013

Proton Exchange Membrane Performance Characterization in VRFB conference, January 2012

Irreversible thermodynamics of transport across charged membranes journal, October 1985

Design of an Electrochemical Cell Making Syngas (CO + H2) from CO2 and H2O Reduction at Room Temperature journal, January 2008

Mass transport of electrolytes in membranes. 1. Development of mathematical transport model journal, May 1984

Ion and Water Transport Characteristics in Membranes for Polymer Electrolyte Fuel Cells Containing H[sup +] and Ca[sup 2+] Cations journal, January 1997

Ion Effects on Vanadium Transport in Nafion Membranes for Vanadium Redox Flow Batteries journal, January 2017

New Insights into Perfluorinated Sulfonic-Acid Ionomers journal, January 2017

Ion partitioning between brines and ion exchange polymers journal, February 2019

Hydration of Ionomers and Schroeder’s Paradox in Nafion journal, January 2009

A Hydrogen-Bromine Cell for Energy Storage Applications journal, January 1980

Concentrated Solution Model of Transport in All Vanadium Redox Flow Battery Membrane Separator journal, September 2014

Mechanisms of Ion and Water Transport in Perfluorosulfonated Ionomer Membranes for Fuel Cells journal, October 2004

Hydration of Nafion and Dowex in liquid and vapor environment: Schroeder's paradox and microstructure journal, January 2008

Maximizing the right stuff: The trade-off between membrane permeability and selectivity journal, June 2017

The Debye-Hückel theory and its importance in modeling electrolyte solutions journal, April 2018

Mechanics-based model for non-affine swelling in perfluorosulfonic acid (PFSA) membranes journal, May 2009

The role of internal pressure for the hydration and transport properties of ionomers and polyelectrolytes journal, December 2013

Water orientation and ion solvation effects during multicomponent salt partitioning in a Nafion cation exchange membrane journal, January 1994

Elastic energy in microscopically phase-separated swollen polymer networks journal, January 2002

Vanadium Electrolyte Studies for the Vanadium Redox Battery-A Review journal, June 2016

Mathematical Modeling of a Cation-Exchange Membrane Containing Two Cations journal, January 2008

Concentration Dependence of VO 2+ Crossover of Nafion for Vanadium Redox Flow Batteries journal, January 2013

Numerical Optimization book, January 2006

Micromechanics model based on the nanostructure of PFSA membranes journal, November 2008

Ion Diffusion Coefficients in Ion Exchange Membranes: Significance of Counterion Condensation journal, July 2018

Multicomponent Space-Charge Transport Model for Ion-Exchange Membranes with Variable Pore Properties journal, June 2004

Mathematical Modelling of Cation Contamination in a Proton-exchange Membrane journal, December 2008

Statistical theory for the equilibrium distribution of rigid molecules in inert porous networks. Exclusion chromatography journal, December 1968

The Effect of Impurity Cations on the Transport Characteristics of Perfluorosulfonated Ionomer Membranes journal, April 1999

Structure-Transport Relationship of Perfluorosulfonic-Acid Membranes in Different Cationic Forms journal, December 2016

Water-soluble drug partitioning and adsorption in HEMA/MAA hydrogels journal, January 2014

Impact of hygrothermal aging on structure/function relationship of perfluorosulfonic-acid membrane journal, October 2015

Processing and Pretreatment Effects on Vanadium Transport in Nafion Membranes journal, October 2015

Coupled Membrane Transport Parameters for Ionic Species in All-Vanadium Redox Flow Batteries journal, November 2016

A Molecular Dynamics Study of the Effects of V 2+ and V 3+ on the Local Structure of Hydrated Nafion journal, June 2015

Membrane transport characteristics of binary cation systems with Li+ and alkali metal cations in perfluorosulfonated ionomer journal, May 2005

Fundamental water and salt transport properties of polymeric materials journal, January 2014

Role of Mechanical Factors in Controlling the Structure–Function Relationship of PFSA Ionomers journal, September 2012

Divalent/monovalent cation uptake selectivity in a Nafion cation-exchange membrane: Experimental and modeling studies journal, December 1997

Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I. Colligative Properties journal, August 1969

Selectivity of ion exchange membranes: A review journal, June 2018

Ion Activity Coefficients in Ion Exchange Polymers: Applicability of Manning’s Counterion Condensation Theory journal, October 2015

Concentrated Solutions of Strong Electrolytes. journal, December 1936

Density Measurements and Partial Molar Volume Analysis of Different Membranes for Polymer Electrolyte Membrane Fuel Cells journal, July 2017

Study of methanesulfonates and trifluoromethanesulfonates. Evidence for hydrogen bonding to the trifluoro group journal, June 1981

The Donnan Equilibrium journal, January 1956

Water−Nafion Equilibria. Absence of Schroeder's Paradox journal, August 2007

Modeling of vanadium ion diffusion across the ion exchange membrane in the vanadium redox battery journal, May 2012

Commercial perfluorosulfonic acid membranes for vanadium redox flow battery: Effect of ion-exchange capacity and membrane internal structure
journal, April 2018

Theory of Multicomponent Phenomena in Cation-Exchange Membranes: Part II. Transport Model and Validation
journal, January 2020

Aqueous Solute Partitioning and Mesh Size in HEMA/MAA Hydrogels
journal, November 2012

Theory of Multicomponent Phenomena in Cation-Exchange Membranes: Part III. Transport in Vanadium Redox-Flow-Battery Separators
journal, January 2020

Counterion Condensation in Nafion
journal, November 2011

Potentials of cells with liquid junctions
journal, December 1968

Irreversible thermodynamics of transport across charged membranes
journal, February 1987

Species Uptake and Mass Transport in Membranes for Vanadium Redox Flow Batteries
journal, May 2017

Composition and Conductivity of Membranes Equilibrated with Solutions of Sulfuric Acid and Vanadyl Sulfate
journal, January 2013

The Debye-Hückel Theory for Hydrated Ions. II. Osmotic and Activity Coefficients of Ternary Aqueous Solutions of Hydrogen and Alkali Halogenides at 25°C
journal, June 1990

Solubility of vanadyl sulfate in concentrated sulfuric acid solutions
journal, April 1998

Accounting for frame of reference and thermodynamic non-idealities when calculating salt diffusion coefficients in ion exchange membranes
journal, September 2017

The Debye-Hückel Theory for Hydrated Ions. I. Osmotic and Activity Coefficients of Binary Aqueous Solutions of Some 1 : 1 Electrolytes at 25°C
journal, June 1990

A Critical Review of Modeling Transport Phenomena in Polymer-Electrolyte Fuel Cells
journal, January 2014

Proton Solvation and Transport in Realistic Proton Exchange Membrane Morphologies
journal, February 2016

Transport Property Requirements for Flow Battery Separators
journal, July 2015

Tuning the Perfluorosulfonic Acid Membrane Morphology for Vanadium Redox-Flow Batteries
journal, December 2016

Thermodynamics of phase equilibria in aqueous-organic systems with salt
journal, April 1994

Equilibrium water and solute uptake in silicone hydrogels
journal, May 2015

Simple Hofmeister series
journal, January 2009

The Influence of Electric Field on Crossover in Redox-Flow Batteries
journal, July 2015

Ionic Hydration and Activity in Electrolyte Solutions
journal, May 1948

Review of material research and development for vanadium redox flow battery applications
journal, July 2013

Equilibrium ion partitioning between aqueous salt solutions and inhomogeneous ion exchange membranes
journal, November 2018

Cluster Theory of Polyelectrolyte Solutions. I. Activity Coefficients of the Mobile Ions
journal, December 1965

Ion and Water Transport Characteristics of Perfluorosulfonated Ionomer Membranes with H ⁺ and Alkali Metal Cations
journal, February 2002

Structural and transport properties of Nafion in hydrobromic-acid solutions
journal, December 2013

Proton Exchange Membrane Performance Characterization in VRFB
conference, January 2012

Irreversible thermodynamics of transport across charged membranes
journal, October 1985

Design of an Electrochemical Cell Making Syngas (CO + H₂) from CO₂ and H₂O Reduction at Room Temperature
journal, January 2008

Mass transport of electrolytes in membranes. 1. Development of mathematical transport model
journal, May 1984

Ion and Water Transport Characteristics in Membranes for Polymer Electrolyte Fuel Cells Containing H[sup +] and Ca[sup 2+] Cations
journal, January 1997

Ion Effects on Vanadium Transport in Nafion Membranes for Vanadium Redox Flow Batteries
journal, January 2017

New Insights into Perfluorinated Sulfonic-Acid Ionomers
journal, January 2017

Ion partitioning between brines and ion exchange polymers
journal, February 2019

Hydration of Ionomers and Schroeder’s Paradox in Nafion
journal, January 2009

A Hydrogen-Bromine Cell for Energy Storage Applications
journal, January 1980

Concentrated Solution Model of Transport in All Vanadium Redox Flow Battery Membrane Separator
journal, September 2014

Mechanisms of Ion and Water Transport in Perfluorosulfonated Ionomer Membranes for Fuel Cells
journal, October 2004

Hydration of Nafion and Dowex in liquid and vapor environment: Schroeder's paradox and microstructure
journal, January 2008

Maximizing the right stuff: The trade-off between membrane permeability and selectivity
journal, June 2017

The Debye-Hückel theory and its importance in modeling electrolyte solutions
journal, April 2018

Mechanics-based model for non-affine swelling in perfluorosulfonic acid (PFSA) membranes
journal, May 2009

The role of internal pressure for the hydration and transport properties of ionomers and polyelectrolytes
journal, December 2013

Water orientation and ion solvation effects during multicomponent salt partitioning in a Nafion cation exchange membrane
journal, January 1994

Elastic energy in microscopically phase-separated swollen polymer networks
journal, January 2002

Vanadium Electrolyte Studies for the Vanadium Redox Battery-A Review
journal, June 2016

Mathematical Modeling of a Cation-Exchange Membrane Containing Two Cations
journal, January 2008

Concentration Dependence of VO ²⁺ Crossover of Nafion for Vanadium Redox Flow Batteries
journal, January 2013

Numerical Optimization
book, January 2006

Micromechanics model based on the nanostructure of PFSA membranes
journal, November 2008

Ion Diffusion Coefficients in Ion Exchange Membranes: Significance of Counterion Condensation
journal, July 2018

Multicomponent Space-Charge Transport Model for Ion-Exchange Membranes with Variable Pore Properties
journal, June 2004

Mathematical Modelling of Cation Contamination in a Proton-exchange Membrane
journal, December 2008

Statistical theory for the equilibrium distribution of rigid molecules in inert porous networks. Exclusion chromatography
journal, December 1968

The Effect of Impurity Cations on the Transport Characteristics of Perfluorosulfonated Ionomer Membranes
journal, April 1999

Structure-Transport Relationship of Perfluorosulfonic-Acid Membranes in Different Cationic Forms
journal, December 2016

Water-soluble drug partitioning and adsorption in HEMA/MAA hydrogels
journal, January 2014

Impact of hygrothermal aging on structure/function relationship of perfluorosulfonic-acid membrane
journal, October 2015

Processing and Pretreatment Effects on Vanadium Transport in Nafion Membranes
journal, October 2015

Coupled Membrane Transport Parameters for Ionic Species in All-Vanadium Redox Flow Batteries
journal, November 2016

A Molecular Dynamics Study of the Effects of V ²⁺ and V ³⁺ on the Local Structure of Hydrated Nafion
journal, June 2015

Membrane transport characteristics of binary cation systems with Li+ and alkali metal cations in perfluorosulfonated ionomer
journal, May 2005

Fundamental water and salt transport properties of polymeric materials
journal, January 2014

Role of Mechanical Factors in Controlling the Structure–Function Relationship of PFSA Ionomers
journal, September 2012

Divalent/monovalent cation uptake selectivity in a Nafion cation-exchange membrane: Experimental and modeling studies
journal, December 1997

Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I. Colligative Properties
journal, August 1969

Selectivity of ion exchange membranes: A review
journal, June 2018

Ion Activity Coefficients in Ion Exchange Polymers: Applicability of Manning’s Counterion Condensation Theory
journal, October 2015

Concentrated Solutions of Strong Electrolytes.
journal, December 1936

Density Measurements and Partial Molar Volume Analysis of Different Membranes for Polymer Electrolyte Membrane Fuel Cells
journal, July 2017

Study of methanesulfonates and trifluoromethanesulfonates. Evidence for hydrogen bonding to the trifluoro group
journal, June 1981

The Donnan Equilibrium
journal, January 1956

Water−Nafion Equilibria. Absence of Schroeder's Paradox
journal, August 2007

Modeling of vanadium ion diffusion across the ion exchange membrane in the vanadium redox battery
journal, May 2012