# Electrodialysis as a key operating unit in chemical processes: From lab to pilot scale of latest breakthroughs

Guillaume Hopsort, Quentin Cacciuttolo, David Pasquier

► To cite this version:

Guillaume Hopsort, Quentin Cacciuttolo, David Pasquier. Electrodialysis as a key operating unit in chemical processes: From lab to pilot scale of latest breakthroughs. Chemical Engineering Journal, 2024, 494, pp.153111. 10.1016/j.cej.2024.153111. hal-04614216

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# Electrodialysis as a key operating unit in chemical processes: From lab to pilot scale of latest breakthroughs

Guillaume Hopsort, Quentin Cacciuttolo, David Pasquier

► To cite this version:

Guillaume Hopsort, Quentin Cacciuttolo, David Pasquier. Electrodialysis as a key operating unit in chemical processes: From lab to pilot scale of latest breakthroughs. Chemical Engineering Journal, 2024, 494, pp.153111. 10.1016/j.cej.2024.153111. hal-04614216

HAL Id: hal-04614216

https://ifp.hal.science/hal-04614216v1

Submitted on 17 Jun 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

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Distributed under a Creative Commons Attribution 4.0 International License
Review

# Electrodialysis as a key operating unit in chemical processes: From lab to pilot scale of latest breakthroughs

Guillaume Hopsort *, Quentin Cacciuttolo *, David Pasquier

IFP Energies Nouvelles, Rond-point de l'échangeur de Solaize, BP 3, 69360 Solaize, France

<figure><img src="image_2.png" /></figure>

Check for
updates

ARTICLE INFO

Keywords:

Electrodialysis
Ion-exchange membranes
Energy efficiency
Process electrification
Process optimization
Scale-up applications

A B S T R A C T

This review article comprehensively explores the significant advancements in electrodialysis (ED) technology within the field of chemical engineering, presenting a holistic overview that spans fundamental principles, membrane materials and fabrication techniques, operational parameters, and a wide array of applications. Unlike previous studies that often narrow their focus to specific aspects of ED, this work synthesizes global advances, bridging gaps between diverse research themes to offer a coherent understanding of current trends and future directions.

ED, a membrane-based separation process driven by electric potential, is pivotal for its applications in water purification, desalination, resource recovery, and beyond. This review delves into the evolution of ion-exchange membranes, highlighting innovations in materials, alongside advances in fabrication techniques that enhance membrane selectivity and efficiency. It also scrutinizes the impact of operational parameters on the performance of ED systems, addressing challenges like ion leakage, membrane fouling, and the balance between selectivity and conductivity.

Process intensification and system optimization strategies are discussed, revealing how recent developments contribute to energy efficiency, scalability, and sustainability. The review further extends to emerging applications of ED in sectors ranging from environmental management to energy and hydrometallurgy industries, underscored by case studies that demonstrate practical implementations.

Conclusively, this article underlines the multidisciplinary approach required for the advancement of ED technologies, suggesting avenues for future research that prioritize environmental impact, economic feasibility, and technological innovation. Through this global perspective, it aims to catalyze further exploration and application of ED in addressing some of the most pressing challenges.

# 1. Introduction

## 1.1. Purpose and significance of electrodialysis in modern chemical engineering

Electrodialysis (ED) is a membrane technology that employs electric current to transport ions through selective membranes, thereby separating them from a solution and facilitating concentrations of salt and acid/base production. This technology holds a place of significant importance in modern chemical engineering, primarily due to its efficiency in terms of energy [1,2], eco-friendliness [3,4] (solvent-free operation, effluent reduction and/or valorization, etc.), and versatility in separating and purifying ionic compounds [5]. The electrification of processes has attracted even more attention given the possibility of using

an energy vector through the coupling of ED technology and the use of electricity from renewable sources (solar [6–8], wind [9–11], etc. [12,13]). In an era where sustainable practices are paramount, ED offers an energy-efficient alternative to conventional separation processes, such as distillation, which often require high energy inputs [14]. Its ability to operate under mild conditions helps in preserving the integrity of sensitive molecules, making it crucial in industries like pharmaceuticals [15], food processing [16], and biotechnology [17,18]. Additionally, the technology’s adaptability to various scales and its capacity to be fine-tuned for specific ion separation make it a valuable tool in water treatment [19] and desalination [20]. As concerns over water scarcity and the environmental impact of industrial processes grow, ED emerges not just as a technical solution, but as a necessary step towards sustainable chemical engineering practices. The ongoing advancements in membrane technology and system optimization further amplify its

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: hopsort.guillaume@gmail.com (G. Hopsort), quentin.cacciuttolo@ifpen.fr (Q. Cacciuttolo), david.pasquier@ifpen.fr (D. Pasquier).</footnote>
Review

# Electrodialysis as a key operating unit in chemical processes: From lab to pilot scale of latest breakthroughs

Guillaume Hopsort *, Quentin Cacciuttolo *, David Pasquier

IFP Energies Nouvelles, Rond-point de l'échangeur de Solaize, BP 3, 69360 Solaize, France

<figure><img src="image_3.png" /></figure>

Check for
updates

## ARTICLE INFO

Keywords:

- Electrodialysis
- Ion-exchange membranes
- Energy efficiency
- Process electrification
- Process optimization
- Scale-up applications

## ABSTRACT

This review article comprehensively explores the significant advancements in electrodialysis (ED) technology within the field of chemical engineering, presenting a holistic overview that spans fundamental principles, membrane materials and fabrication techniques, operational parameters, and a wide array of applications. Unlike previous studies that often narrow their focus to specific aspects of ED, this work synthesizes global advances, bridging gaps between diverse research themes to offer a coherent understanding of current trends and future directions.

ED, a membrane-based separation process driven by electric potential, is pivotal for its applications in water purification, desalination, resource recovery, and beyond. This review delves into the evolution of ion-exchange membranes, highlighting innovations in materials, alongside advances in fabrication techniques that enhance membrane selectivity and efficiency. It also scrutinizes the impact of operational parameters on the performance of ED systems, addressing challenges like ion leakage, membrane fouling, and the balance between selectivity and conductivity.

Process intensification and system optimization strategies are discussed, revealing how recent developments contribute to energy efficiency, scalability, and sustainability. The review further extends to emerging applications of ED in sectors ranging from environmental management to energy and hydrometallurgy industries, underscored by case studies that demonstrate practical implementations.

Conclusively, this article underlines the multidisciplinary approach required for the advancement of ED technologies, suggesting avenues for future research that prioritize environmental impact, economic feasibility, and technological innovation. Through this global perspective, it aims to catalyze further exploration and application of ED in addressing some of the most pressing challenges.

## 1. Introduction

### 1.1. Purpose and significance of electrodialysis in modern chemical engineering

Electrodialysis (ED) is a membrane technology that employs electric current to transport ions through selective membranes, thereby separating them from a solution and facilitating concentrations of salt and acid/base production. This technology holds a place of significant importance in modern chemical engineering, primarily due to its efficiency in terms of energy [1,2], eco-friendliness [3,4] (solvent-free operation, effluent reduction and/or valorization, etc.), and versatility in separating and purifying ionic compounds [5]. The electrification of processes has attracted even more attention given the possibility of using

an energy vector through the coupling of ED technology and the use of electricity from renewable sources (solar [6–8], wind [9–11], etc. [12,13]). In an era where sustainable practices are paramount, ED offers an energy-efficient alternative to conventional separation processes, such as distillation, which often require high energy inputs [14]. Its ability to operate under mild conditions helps in preserving the integrity of sensitive molecules, making it crucial in industries like pharmaceuticals [15], food processing [16], and biotechnology [17,18]. Additionally, the technology’s adaptability to various scales and its capacity to be fine-tuned for specific ion separation make it a valuable tool in water treatment [19] and desalination [20]. As concerns over water scarcity and the environmental impact of industrial processes grow, ED emerges not just as a technical solution, but as a necessary step towards sustainable chemical engineering practices. The ongoing advancements in membrane technology and system optimization further amplify its

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: hopsort.guillaume@gmail.com (G. Hopsort), quentin.cacciuttolo@ifpen.fr (Q. Cacciuttolo), david.pasquier@ifpen.fr (D. Pasquier).</footnote>
Nomenclature

Acronyms

<table><tr><td>A<sup>+</sup></td><td>Anionic group bonded to the membrane</td></tr><tr><td>AEL</td><td>Anion-Exchange Layer</td></tr><tr><td>AEM</td><td>Anion-Exchange Membrane</td></tr><tr><td>BED</td><td>Bipolar Electrodialysis</td></tr><tr><td>BM</td><td>Bipolar Membrane</td></tr><tr><td>BPPO</td><td>Bromomethylated poly(2,6-dimethyl-1,4-phenylene oxide)</td></tr><tr><td>BTMA</td><td>Benzyl trimethylammonium</td></tr><tr><td>C<sup>+</sup></td><td>Cationic group bonded to the membrane</td></tr><tr><td>CAPEX</td><td>Capital expenditure</td></tr><tr><td>CEL</td><td>Cation-Exchange Layer</td></tr><tr><td>CEM</td><td>Cation-Exchange Membrane</td></tr><tr><td>CFD</td><td>Computational Fluid Dynamics</td></tr><tr><td>COF</td><td>Covalent Organic Framework</td></tr><tr><td>DAC</td><td>Direct Air Capture</td></tr><tr><td>DABCO</td><td>1,4-diazabicyclo-[2,2,2]octane</td></tr><tr><td>DBL</td><td>Diffusion Boundary Layer</td></tr><tr><td>DMA</td><td>Dopamine methacrylamide</td></tr><tr><td>DMAc</td><td>Dimethylacetamide</td></tr><tr><td>DMF</td><td>Dimethylformamide</td></tr><tr><td>DVB</td><td>Divinylbenzene</td></tr><tr><td>EC</td><td>Electrochemical</td></tr><tr><td>ED</td><td>Electrodialysis</td></tr><tr><td>EDTA</td><td>Ethylenediaminetetraacetic acid</td></tr><tr><td>EDI</td><td>Electrodeionization</td></tr><tr><td>EIS</td><td>Electrochemical Impedance Spectroscopy</td></tr><tr><td>ETFE</td><td>Poly(ethene-co-tetrafluoroethene)</td></tr><tr><td>HDPE</td><td>High-density polyethylene</td></tr><tr><td>IEM</td><td>Ion-Exchange Membrane</td></tr><tr><td>IL</td><td>Interfacial Layer</td></tr><tr><td>LCA</td><td>Life Cycle Assessment</td></tr><tr><td>LCCA</td><td>Life-Cycle Costing Analysis</td></tr><tr><td>LDPE</td><td>Low-density polyethylene</td></tr><tr><td>LiB</td><td>Lithium-ion Battery</td></tr><tr><td>M-S</td><td>Maxwell-Stefan</td></tr><tr><td>MMTD</td><td>2-mercapto-5-methyl-1,3,4-thiadiazole</td></tr><tr><td>MOF</td><td>Metal-Organic Framework</td></tr><tr><td>MTPP-(2,4,6-Me)</td><td>Methyl tris(2,4,6-trimethylphenyl)phosphonium</td></tr><tr><td>N</td><td>Nitrogen</td></tr><tr><td>N-P</td><td>Nernst-Plank</td></tr><tr><td>NMC</td><td>Nickel Manganese Cobalt</td></tr><tr><td>NP</td><td>Nanoparticle</td></tr><tr><td>OPEX</td><td>Operational expenditure</td></tr><tr><td>PAES</td><td>Poly(arylene ether sulfone)</td></tr><tr><td>PAMAM</td><td>Polyamidoamine</td></tr><tr><td>PAN</td><td>Polyacrylonitrile</td></tr><tr><td>PANI</td><td>Polyaniline</td></tr><tr><td>PBI</td><td>Polybenzimidazole</td></tr><tr><td>PDDA</td><td>Poly(diallyldimethylammonium chloride)</td></tr><tr><td>PE</td><td>Polyethylene</td></tr><tr><td>PEEK</td><td>Polyether ether ketone</td></tr><tr><td>PEC</td><td>Photoelectrochemical</td></tr><tr><td>PECH</td><td>Polyepichlorohydrin</td></tr><tr><td>PEF</td><td>Pulsed Electric Field</td></tr><tr><td>PES</td><td>Poly(ether)sulfone</td></tr><tr><td>PFSA</td><td>Perfluorosulfonic acid</td></tr><tr><td>PI</td><td>Polyimide</td></tr><tr><td>PMA</td><td>Phosphomolybdic acid</td></tr><tr><td>PNB</td><td>Polynorbornene</td></tr><tr><td>PP</td><td>Polypropylene</td></tr><tr><td>PPO</td><td>Poly(phenylene oxide)</td></tr><tr><td>PSSA-MA</td><td>Poly(styrene sulfonic acid-co-maleic acid)</td></tr></table>

<table><tr><td>PSU</td><td>Polysulfone</td></tr><tr><td>PTFE</td><td>Polytetrafluoroethylene</td></tr><tr><td>PVA</td><td>Poly(vinyl alcohol)</td></tr><tr><td>PVDF</td><td>Polyvinylidene fluoride</td></tr><tr><td>QPVA</td><td>Quaternary ammonium poly(vinyl alcohol)</td></tr><tr><td>RH</td><td>Relative Humidity</td></tr><tr><td>RT</td><td>Room Temperature</td></tr><tr><td>ROMP</td><td>Ring-opening metathesis polymerization</td></tr><tr><td>SPEEK</td><td>Sulfonated poly(ether ether ketone)</td></tr><tr><td>SPPO</td><td>Sulfonated poly (2,6-dimethyl-1,4-phenylene oxide)</td></tr><tr><td>SPPS</td><td>Sulfonated poly(phenylene sulfone)</td></tr><tr><td>ST</td><td>Styrene</td></tr><tr><td>SWOT</td><td>Strengths, Weaknesses, Opportunities, &amp; Threats</td></tr><tr><td>TCA</td><td>Techno-economic assessment</td></tr><tr><td>TMA</td><td>Tetramethylammonium</td></tr><tr><td>TPABr</td><td>Tetrapropylammonium bromide</td></tr><tr><td>TPAOH</td><td>Tetrapropylammonium hydroxide</td></tr><tr><td>TPQPOH</td><td>Tris(2,4,6-trimethoxyphenyl)phosphonium</td></tr></table>

Symbols

<table><tr><td>a</td><td>Activity. [dimensionless]</td></tr><tr><td>A</td><td>Surface area. [m<sup>2</sup>]</td></tr><tr><td>ASR</td><td>Area Specific Resistance. [Ω/m<sup>-2</sup>(-|-)]</td></tr><tr><td>C</td><td>Molar concentration. [mol/m<sup>-3</sup>(-|-)]</td></tr><tr><td>D</td><td>Diffusion coefficient. [m<sup>2</sup>/s]</td></tr><tr><td>e</td><td>Elementary charge. [C]</td></tr><tr><td>E<sup>°</sup></td><td>Standard potential. [V]</td></tr><tr><td>E<sub>th</sub></td><td>Thermoneutral voltage. [V]</td></tr><tr><td>f</td><td>Volume fraction. [dimensionless]</td></tr><tr><td>∫</td><td>Faraday constant. [C/mol]</td></tr><tr><td>g</td><td>Gravitational constant. [m/s<sup>-2</sup>(-|-)]</td></tr><tr><td>I</td><td>Intensity. [A]</td></tr><tr><td>IEC</td><td>Ion Exchange Capacity. [meq g<sup>-1</sup>]</td></tr><tr><td>j</td><td>Current density. [A/m<sup>-2</sup>(-|-)]</td></tr><tr><td>j<sub>0</sub></td><td>Exchange current density. [A/m<sup>-2</sup>(-|-)]</td></tr><tr><td>J</td><td>Flux. [mol m<sup>-2</sup> s<sup>-1</sup>]</td></tr><tr><td>J'</td><td>Volumetric flux. [m<sup>3</sup> m<sup>-2</sup> s<sup>-1</sup>]</td></tr><tr><td>k</td><td>Mass transfer coefficient. [m/s]</td></tr><tr><td>K</td><td>Sorption coefficient. [dimensionless]</td></tr><tr><td>k<sub>b</sub></td><td>Boltzmann constant. [J/K]</td></tr><tr><td>l</td><td>Thickness. [m]</td></tr><tr><td>L<sub>p</sub></td><td>Membrane permeability. [L m<sup>-2</sup> s<sup>-1</sup> bar<sup>-1</sup> or mol m<sup>-2</sup> s<sup>-1</sup> bar<sup>-1</sup>]</td></tr><tr><td>m</td><td>Weight. [g]</td></tr><tr><td>M</td><td>Molar mass. [g/mol]</td></tr><tr><td>n</td><td>Molar amount. [mol]</td></tr><tr><td>n<sub>drag</sub></td><td>Electroosmotic drag coefficient. [dimensionless]</td></tr><tr><td>n<sub>e</sub></td><td>Exchanged electron number. [dimensionless]</td></tr><tr><td>N<sub>cp</sub></td><td>Number of cell pair. [dimensionless]</td></tr><tr><td>p</td><td>Pressure. [Pa]</td></tr><tr><td>P</td><td>Power. [W]</td></tr><tr><td>PS</td><td>Permselectivity. [dimensionless]</td></tr><tr><td>q</td><td>Volumetric flow rate. [m<sup>3</sup>/s]</td></tr><tr><td>r</td><td>Radius. [Å]</td></tr><tr><td>R</td><td>Universal gas constant. [J/K mol<sup>-1</sup>]</td></tr><tr><td>S</td><td>Separation selectivity. [dimensionless]</td></tr><tr><td>Sc</td><td>Schmidt number. [dimensionless]</td></tr><tr><td>SEC</td><td>Specific energy consumption. [Wh/m<sup>-3</sup>(-|-) or Wh kg<sup>-1</sup>]</td></tr><tr><td>t</td><td>Transport number. [dimensionless]</td></tr><tr><td>T</td><td>Absolute temperature. [K]</td></tr><tr><td>u</td><td>Absolute mobility. [m<sup>2</sup> [C V s]<sup>-1</sup>]</td></tr><tr><td>U</td><td>Voltage. [V]</td></tr><tr><td>v</td><td>Velocity. [m/s]</td></tr><tr><td>V</td><td>Volume. [m<sup>3</sup>]</td></tr><tr><td>WC</td><td>Water content. [dimensionless]</td></tr></table>
## Nomenclature

### Acronyms

A Anionic group bonded to the membrane

AEL Anion-Exchange Layer

AEM Anion-Exchange Membrane

BED Bipolar Electrodialysis

BM Bipolar Membrane

BPPO Bromomethylated poly(2,6-dimethyl-1,4-phenylene oxide)

BTMA Benzyl trimethylammonium

C⁺ Cationic group bonded to the membrane

CAPEX Capital expenditure

CEL Cation-Exchange Layer

CEM Cation-Exchange Membrane

CFD Computational Fluid Dynamics

COF Covalent Organic Framework

DAC Direct Air Capture

DABCO 1,4-diazabicyclo-[2,2,2]octane

DBL Diffusion Boundary Layer

DMA Dopamine methacrylamide

DMAc Dimethylacetamide

DMF Dimethylformamide

DVB Divinylbenzene

EC Electrochemical

ED Electrodialysis

EDTA Ethylenediaminetetraacetic acid

EDI Electrodeionization

EIS Electrochemical Impedance Spectroscopy

ETFE Poly(ethene-co-tetrafluoroethene)

HDPE High-density polyethylene

IEM Ion-Exchange Membrane

IL Interfacial Layer

LCA Life Cycle Assessment

LCCA Life-Cycle Costing Analysis

LDPE Low-density polyethylene

LiB Lithium-ion Battery

M-S Maxwell-Stefan

MMTD 2-mercapto-5-methyl-1,3,4-thiadiazole

MOF Metal-Organic Framework

MTPP-(2,4,6-Me) Methyl tris(2,4,6-trimethylphenyl)phosphonium

N Nitrogen

N-P Nernst-Plank

NMC Nickel Manganese Cobalt

NP Nanoparticle

OPEX Operational expenditure

PAES Poly(arylene ether sulfone)

PAMAM Polyamidoamine

PAN Polyacrylonitrile

PANI Polyaniline

PBI Polybenzimidazole

PDDA Poly(diallyldimethylammonium chloride)

PE Polyethylene

PEEK Polyether ether ketone

PEC Photoelectrochemical

PECH Polyepichlorohydrin

PEF Pulsed Electric Field

PES Poly(ether)sulfone

PFSA Perfluorosulfonic acid

PI Polyimide

PMA Phosphomolybdic acid

PNB Polynorbornene

PP Polypropylene

PPO Poly(phenylene oxide)

PSSA-MA Poly(styrene sulfonic acid-co-maleic acid)

PSU Polysulfone

PTFE Polytetrafluoroethylene

PVA Poly(vinyl alcohol)

PVDF Polyvinylidene fluoride

QPVA Quaternary ammonium poly(vinyl alcohol)

RH Relative Humidity

RT Room Temperature

ROMP Ring-opening metathesis polymerization

SPEEK Sulfonated poly(ether ether ketone)

SPPO Sulfonated poly (2,6-dimethyl-1,4-phenylene oxide)

SPPS Sulfonated poly(phenylene sulfone)

ST Styrene

SWOT Strengths, Weaknesses, Opportunities, & Threats

TCA Techno-economic assessment

TMA Tetramethylammonium

TPABr Tetrapropylammonium bromide

TPAOH Tetrapropylammonium hydroxide

TPQPOH Tris(2,4,6-trimethoxyphenyl)phosphonium

### Symbols

a Activity. [dimensionless]

A Surface area. [m²]

ASR Area Specific Resistance. [Ω/m⁻²(⁻|⁻)]

C Molar concentration. [mol/m⁻³(⁻|⁻)]

D Diffusion coefficient. [m²/s]

e Elementary charge. [C]

E° Standard potential. [V]

Eth Thermoneutral voltage. [V]

f Volume fraction. [dimensionless]

F Faraday constant. [C/mol]

g Gravitational constant. [m/s⁻²(⁻|⁻)]

I Intensity. [A]

IEC Ion Exchange Capacity. [meq g⁻¹]

j Current density. [A/m⁻²(⁻|⁻)]

jo Exchange current density. [A/m⁻²(⁻|⁻)]

J Flux. [mol m⁻² s⁻¹]

J' Volumetric flux. [m³ m⁻² s⁻¹]

k Mass transfer coefficient. [m/s]

K Sorption coefficient. [dimensionless]

kb Boltzmann constant. [J/K]

l Thickness. [m]

Lp Membrane permeability. [L m⁻² s⁻¹ bar⁻¹ or mol m⁻² s⁻¹ bar⁻¹]

m Weight. [g]

M Molar mass. [g/mol]

n Molar amount. [mol]

ndrag Electroosmotic drag coefficient. [dimensionless]

ne Exchanged electron number. [dimensionless]

Ncp Number of cell pair. [dimensionless]

p Pressure. [Pa]

P Power. [W]

PS Permselectivity. [dimensionless]

q Volumetric flow rate. [m³/s]

r Radius. [ÅÅ]

R Universal gas constant. [J/K mol⁻¹]

S Separation selectivity. [dimensionless]

Sc Schmidt number. [dimensionless]

SEC Specific energy consumption. [Wh/m⁻³(⁻|⁻) or Wh kg⁻¹]

t Transport number. [dimensionless]

T Absolute temperature. [K]

u Absolute mobility. [m² [C V s]⁻¹]

U Voltage. [V]

v Velocity. [m/s]

V Volume. [m³]

WC Water content. [dimensionless]
<table><tr><td>x</td><td>Distance. [m]</td></tr><tr><td>X</td><td>Fixed-ion concentration. [mol/m<sup>-3</sup>(-|-)]</td></tr><tr><td>z</td><td>Ion valence. [dimensionless]</td></tr></table>

Greeks

α Charge transfer coefficient. [dimensionless]

γ Activity coefficient. [dimensionless]

δ Thickness of diffusion boundary layer. [m]

ΔG Variation in Gibbs free energy. [J]

Δh Loss of hydraulic head across the stack. [m]

ΔH Variation in enthalpy. [J]

ΔS Variation in entropy. [J/K]

ΔV Volume dilatation. [dimensionless]

Δπ Osmotic pressure. [Pa]

Δφ<sub>D</sub> Donnan potential. [V]

ε Porosity. [dimensionless]

ε<sub>r</sub>, ε<sub>0</sub> Relative and free space permittivity. [F/m]

η Overvoltage. [V]

λ Molar ion conductivity. [S m<sup>-1</sup> mol<sup>-1</sup>]

μ Dynamic viscosity. [Pa s]

ξ Current effiency. [dimensionless]

ρ Density. [g/m<sup>-3</sup>(-|-)]

σ Ionic conductivity. [S m<sup>-1</sup>]

φ Electrical potential. [V]

χ Conversion rate. [dimensionless]

ψ Mole fraction. [dimensionless]

Superscripts

ano Anolyte

cat Catholyte

cte Concentrate

dlt Diluate

eo Electro-osmotic

el Electrical

h Hydraulic

j Area j

m Membrane phase

os Osmotic

s Bulk solution phase

* Electrode/membrane surface

Subscripts

a Anodic

act Activation

c Cathodic

conc Concentration

ct Counter-ion

d Dry

D Donnan

f Final

h Hydrated

i Species i

in Inlet

ini Initial

k Species k

lim Limiting

mig Migration

ohm Ohmic

out Outlet

Ox Oxidizing agent

Red Reducing agent

t Time

tot Total

w Water

⊕ Cation

⊗ Anion

significance, promising more efficient, cost-effective, and environmentally benign solutions for a wide range of chemical engineering applications as highlights by the upgoing number of publications extracted from Fig. 1. Since 2000, the research area has been evenly structured between materials engineering (membrane formulation [21], membrane fouling [22], ionic transport [23], etc.) and chemical engineering (process intensification [24], cell's configuration [25], scale-up [26], etc.) illustrating the industrial transfer of this technology [27–29].

<figure><img src="image_3.png" /><figcaption>Fig. 1. Number of research articles when searching for the term 'Electrodialysis' as well as the distribution of search fields by query at Digital Science. (1975–2023) Dimensions available from https://app.dimensions.ai. Accessed on 2024/01/10, under license agreement.</figcaption></figure>

## 1.2. Past research motivations

Tracing the ED's evolution, technologies of electromembrane separation processes have been fundamental. The earliest known use of a non-selective separator in electrochemical (EC) applications dates back to 1889, with an ED process applied to the demineralization of sugar syrup, implemented by Maigrot and Sabates [30]. The term 'electro dialysis' only became widespread about ten years later [31]. The production of ion-exchange materials, first in granular form and then as membranes, did not start until after 1930. This development led to the first use of ion-exchange membranes (IEMs) in 1939 by Manegold and Kalauch, in a three-compartment ED setup [32]. The 1950 s were marked by significant advancements with the work of Juda and McRae at Ionics Inc. [33], Winger et al. at Rohm [34], and Wyllie and Patnode at Gulf Research [35], who developed stable, highly selective, low-resistance membranes. These advancements made ED an essential industrial method for demineralizing and concentrating electrolyte solutions [36]. To assist the reader's understanding, a schematic view of the operation process of the ED procedure is presented for an anion exchange and cation exchange membrane in Fig. 2 – a.

Electrodeionization (EDI), an evolution of ED, was designed for producing ultra-pure water or desalinating low-conductivity media. EDI incorporates an ion-exchange resin bed within the diluate chamber (and occasionally in the concentrate chamber) of an ED setup, enhancing conductivity and creating a more effective three-dimensional phase interface for mass exchange than traditional ED [37]. This method uses an electric field to continuously transport ions from the ion-selective phase to the concentrate stream. Conceptually, EDI combines ED with traditional ion-exchange technology, an idea proposed in the 1970 s
<table><tr><td>x</td><td>Distance. [m]</td></tr><tr><td>X</td><td>Fixed-ion concentration. [mol/m<sup>-3</sup>(-|-)]</td></tr><tr><td>z</td><td>Ion valence. [dimensionless]</td></tr></table>

Greeks

α Charge transfer coefficient. [dimensionless]

γ Activity coefficient. [dimensionless]

δ Thickness of diffusion boundary layer. [m]

ΔG Variation in Gibbs free energy. [J]

Δh Loss of hydraulic head across the stack. [m]

ΔH Variation in enthalpy. [J]

ΔS Variation in entropy. [J/K]

ΔV Volume dilatation. [dimensionless]

Δπ Osmotic pressure. [Pa]

Δφ<sub>D</sub> Donnan potential. [V]

ε Porosity. [dimensionless]

ε<sub>r</sub>, ε<sub>0</sub> Relative and free space permittivity. [F/m]

η Overvoltage. [V]

λ Molar ion conductivity. [S m<sup>-1</sup> mol<sup>-1</sup>]

μ Dynamic viscosity. [Pa s]

ξ Current efficiency. [dimensionless]

ρ Density. [g/m<sup>-3</sup>(-|-)]

σ Ionic conductivity. [S m<sup>-1</sup>]

φ Electrical potential. [V]

χ Conversion rate. [dimensionless]

ψ Mole fraction. [dimensionless]

Superscripts

ano Anolyte

cat Catholyte

cte Concentrate

dlt Diluate

eo Electro-osmotic

el Electrical

h Hydraulic

j Area j

m Membrane phase

os Osmotic

s Bulk solution phase

* Electrode/membrane surface

Subscripts

a Anodic

act Activation

c Cathodic

conc Concentration

ct Counter-ion

d Dry

D Donnan

f Final

h Hydrated

i Species i

in Inlet

ini Initial

k Species k

lim Limiting

mig Migration

ohm Ohmic

out Outlet

Ox Oxidizing agent

Red Reducing agent

t Time

tot Total

w Water

⊕ Cation

Θ Anion

significance, promising more efficient, cost-effective, and environmentally benign solutions for a wide range of chemical engineering applications as highlights by the upgoing number of publications extracted from Fig. 1. Since 2000, the research area has been evenly structured between materials engineering (membrane formulation [21], membrane fouling [22], ionic transport [23], etc.) and chemical engineering (process intensification [24], cell's configuration [25], scale-up [26], etc.) illustrating the industrial transfer of this technology [27–29].

<figure><img src="image_4.png" /><figcaption>Fig. 1. Number of research articles when searching for the term 'Electrodialysis' as well as the distribution of search fields by query at Digital Science. (1975–2023) Dimensions available from https://app.dimensions.ai. Accessed on 2024/01/10, under license agreement.</figcaption></figure>

## 1.2. Past research motivations

Tracing the ED's evolution, technologies of electromembrane separation processes have been fundamental. The earliest known use of a non-selective separator in electrochemical (EC) applications dates back to 1889, with an ED process applied to the demineralization of sugar syrup, implemented by Maigrot and Sabates [30]. The term 'electro dialysis' only became widespread about ten years later [31]. The production of ion-exchange materials, first in granular form and then as membranes, did not start until after 1930. This development led to the first use of ion-exchange membranes (IEMs) in 1939 by Manegold and Kalauch, in a three-compartment ED setup [32]. The 1950 s were marked by significant advancements with the work of Juda and McRae at Ionics Inc. [33], Winger et al. at Rohm [34], and Wyllie and Patnode at Gulf Research [35], who developed stable, highly selective, low-resistance membranes. These advancements made ED an essential industrial method for demineralizing and concentrating electrolyte solutions [36]. To assist the reader's understanding, a schematic view of the operation process of the ED procedure is presented for an anion exchange and cation exchange membrane in Fig. 2 – a.

Electrodeionization (EDI), an evolution of ED, was designed for producing ultra-pure water or desalinating low-conductivity media. EDI incorporates an ion-exchange resin bed within the diluate chamber (and occasionally in the concentrate chamber) of an ED setup, enhancing conductivity and creating a more effective three-dimensional phase interface for mass exchange than traditional ED [37]. This method uses an electric field to continuously transport ions from the ion-selective phase to the concentrate stream. Conceptually, EDI combines ED with traditional ion-exchange technology, an idea proposed in the 1970 s
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Scheme illustrating: (a) the conventional ED principle; (b) cation and/or (b') anion transport through monopolar IEMs; and (c) the bipolar ED principle. Figure (b-b') adapted with permission from [58]. Copyright 2016 American Chemical Society.</figcaption></figure>

[38,39]. The major advantage of EDI is its continuous operation without regenerative agents, reducing environmental impact and saving water needed for treating saturated ion-exchangers. Today, EDI is a commercially established technology [40] and this review will not develop this topic in the rest of this document.

In the field of ED, a notable advancement has been the integration of bipolar membranes (BMs). These specialized membranes are composed of distinct adjacent anion-selective and cation-selective layers [41]. The use of BED, as presented in Fig. 2-c, allows the pH of solutions on either side of the membrane to be modified by dissociating the water within the BM. Depending on the pKa of the various salts present, their acid/base forms will be influenced, resulting in the production of acids and bases [42,43].

Parallel to the development of ED technology, the field of membrane electrolysis has also seen significant advancements. Unlike ED, industrial application of membrane electrolysis requires much higher operational current densities, often exceeding 2000 A/m²(-|-). This approach has played a crucial role in diversifying and expanding the available membrane materials, particularly for cation- and anion-exchange membranes (CEMs and AEMs, respectively). Today, a wide range of such specialized membrane materials is available from various manufacturers [44]. To this end, several recent articles offer insightful reviews on IEMs (local material specifications [45-47]), novelties in fabrication methods [48,49], etc.) or the application of ED in specific field (resource recovery [50,51], reverse ED [52,53], water treatment [54,55], etc.).

### 1.3. Scope and aim of this review

Bolstered by this momentum, research themes related to ED are increasingly leaning towards pilot scale applications today. However, reviews are currently lacking in studies that encompass the field of ED from a chemical engineering perspective. In particular, industrial scaling-up is often neglected. To our knowledge, there is no review available that sheds light on the entirety of this technology as well as highlighting the main advancements in the field. The scope of this article encompasses a comprehensive review of ED as a critical operating unit in chemical processes, focusing primarily on advancements from lab to pilot scale implementations. It aims to provide a detailed analysis of the fundamental principles underlying ED (Section 2). Special emphasis is placed on recent developments in IEM materials and fabrication techniques (Section 3) and exploration of operational parameter process impacts (Section 4), which are pivotal for enhancing the efficiency, selectivity, and sustainability of ED processes. Additionally, the article seeks to address process intensification, system optimization strategies (Section 5), and the challenges associated with scaling up ED systems from lab to pilot scale (Section 6). By integrating diverse applications and case studies (Section 7), this review endeavors to offer a holistic view of the current state and future potential of ED in various industrial sectors. Finally, the main goal is to provide a balanced narrative that not only reflects the current technological advancements but also identifies future research directions and technological frontiers in the field of ED. For this purpose, the authors mainly focused on articles reported in the literature from 2019 to 2024 (year-by-year distribution of cited works in this document illustrated in Supporting Material – SM1).
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Scheme illustrating: (a) the conventional ED principle; (b) cation and/or (b') anion transport through monopolar IEMs; and (c) the bipolar ED principle. Figure (b-b') adapted with permission from [58]. Copyright 2016 American Chemical Society.</figcaption></figure>

[38,39]. The major advantage of EDI is its continuous operation without regenerative agents, reducing environmental impact and saving water needed for treating saturated ion-exchangers. Today, EDI is a commercially established technology [40] and this review will not develop this topic in the rest of this document.

In the field of ED, a notable advancement has been the integration of bipolar membranes (BMs). These specialized membranes are composed of distinct adjacent anion-selective and cation-selective layers [41]. The use of BED, as presented in Fig. 2-c, allows the pH of solutions on either side of the membrane to be modified by dissociating the water within the BM. Depending on the pKa of the various salts present, their acid/base forms will be influenced, resulting in the production of acids and bases [42,43].

Parallel to the development of ED technology, the field of membrane electrolysis has also seen significant advancements. Unlike ED, industrial application of membrane electrolysis requires much higher operational current densities, often exceeding 2000 A/m²(−|−). This approach has played a crucial role in diversifying and expanding the available membrane materials, particularly for cation- and anion-exchange membranes (CEMs and AEMs, respectively). Today, a wide range of such specialized membrane materials is available from various manufacturers [44]. To this end, several recent articles offer insightful reviews on IEMs (local material specifications [45–47]), novelties in fabrication methods [48,49], etc.) or the application of ED in specific field (resource recovery [50,51], reverse ED [52,53], water treatment [54,55], etc.).

### 1.3. *Scope and aim of this review*

Bolstered by this momentum, research themes related to ED are increasingly leaning towards pilot scale applications today. However, reviews are currently lacking in studies that encompass the field of ED from a chemical engineering perspective. In particular, industrial scaling-up is often neglected. To our knowledge, there is no review available that sheds light on the entirety of this technology as well as highlighting the main advancements in the field. The scope of this article encompasses a comprehensive review of ED as a critical operating unit in chemical processes, focusing primarily on advancements from lab to pilot scale implementations. It aims to provide a detailed analysis of the fundamental principles underlying ED (Section 2). Special emphasis is placed on recent developments in IEM materials and fabrication techniques (Section 3) and exploration of operational parameter process impacts (Section 4), which are pivotal for enhancing the efficiency, selectivity, and sustainability of ED processes. Additionally, the article seeks to address process intensification, system optimization strategies (Section 5), and the challenges associated with scaling up ED systems from lab to pilot scale (Section 6). By integrating diverse applications and case studies (Section 7), this review endeavors to offer a holistic view of the current state and future potential of ED in various industrial sectors. Finally, the main goal is to provide a balanced narrative that not only reflects the current technological advancements but also identifies future research directions and technological frontiers in the field of ED. For this purpose, the authors mainly focused on articles reported in the literature from 2019 to 2024 (year-by-year distribution of cited works in this document illustrated in *Supporting Material* – SM1).
The uniqueness of this study lies in its generalist approach to chemical engineering, yet it delves into the scientific nuances of ED technology, marking a contribution to the field. The manuscript is intended to serve not only as an educational resource for those new to ED but also as an update for seasoned researchers and practitioners. The recent literature often provides insufficient comprehensive and holistic guidance for researchers new to the field of ED. Predominantly, reviews focus on specialized applications or functional improvements, engaging in extensive scientific detail yet remaining confined to particular cases. This review endeavors to surmount this deficiency by offering a broader, more accessible, and recent overview of the field.

## 2. Fundamentals of electrodialysis

ED is an ionic purification of a liquid placed between sets of semi-permeable membranes, driven by ion transfers aimed at maintaining electroneutrality between the compartments. These compartments themselves are imbalanced by ED reactions on either side, induced by the application of an electric field. This section delves into the core principles underlying ED, focusing on IEM processes, including monopolar and bipolar configurations, and the mechanisms of ion transport within membranes and solutions. It outlines the basics of ED technology, discussing key aspects such as sorption-migration, ion selectivity, and the balance between membrane permeability and selectivity.

### 2.1. Concepts of ion-exchange membrane processes

#### 2.1.1. Conventional electrodialysis

The core principles of ED are rooted in electrochemistry, ion transport, and membrane science, where a succession of heterogeneous interfaces (i.e., electrode / electrolyte / membrane / electrolyte / ... / electrolyte / membrane / electrolyte / electrode) is implemented, thereby generating reactions and heterogeneous transfer mechanisms. ED systems consist of an anode and a cathode, forming an EC cell as shown in Fig. 2 - a. However, it is important to note that ED process does not involve redox reactions, characteristic of electrolytic processes, except for reactions at the terminal electrodes (judiciously chosen so as not to be the system's critical overvoltage).

At the anode, oxidation reactions occur, while at the cathode, reduction reactions take place. Classically, between these electrodes are a series of IEM, alternating CEM, and AEM. In practical industrial applications, the number of membrane pairs in an ED stack often reaches hundreds. This scaling up is crucial to improving process efficiency and reducing investment costs per unit of production capacity [56]. Cations move towards the cathode and anions towards the anode by migration under the application of an electrical field. The membranes are arranged in a stack, creating alternating compartments of dilute and concentrate solutions. As ions migrate under the influence of the electric potential $\varphi$ (V), they are either captured in concentrate compartments or allowed to pass into dilute compartments, effectively removing them from the solution to be treated [57]. Separation results from the selectivity of membrane ion transport and exclusion by electrostatic repulsion at the membrane surface due to like charges covalently bonded to the membrane material. When an electric field is applied, ions in the solution are driven towards the oppositely charged electrodes through migration and diffusion mechanisms which results in the generation of diffusion boundary layers (DBLs) on either side of each membrane. The diffusion of a species originates from the thermal agitation of molecules, which tends to equalize the concentration. It results in a flux of the species from regions of higher concentration to those of lower concentration. This is true both within the DBLs close to electrode and across the membrane. However, the polarity of the membrane restricts diffusion to ions of the opposite polarity, meaning that concentration cannot be increased indefinitely. At a certain point, Fickian diffusion of ions from the concentrate to the dilute becomes more significant than the flux by

electromigration. Therefore, it would be more prudent to stop ED before this point to maintain its efficiency. It occurs primarily in the vicinity of the electrodes and membranes, in a DBL whose thickness varies from a few micrometers (in the case of agitation) to several centimeters.

#### 2.1.2. Ion-exchange membranes

Alternatively, IEMs are typically categorized into five types, depending on the nature and arrangement of their fixed ionic groups (Fig. 3). These include CEMs [59], AEMs [60], amphoteric IEMs [61], BMs [62], and mosaic IEMs [63]. An IEM is composed of both hydrophilic ionic groups and hydrophobic polymer chains with charged ionic functional groups that allow the transport of oppositely charged species (counter-ions), while retaining like-charged ions (co-ions). Specific focus on the IEM materials will be presented in Section 3.

Bipolar electrodialysis (BED) is an advanced EC process that extends the principles of standard ED by incorporating bipolar membranes (BMs), illustrated in Fig. 3 - c, alongside the traditional CEMs and AEMs. This technique is particularly useful for generating bases and acids from salts. In BED, each BM consists of two layers: a cation-exchange layer and an anion-exchange layer. These layers are fused together, and at their interface, water molecules undergo disproportionation reaction into proton and hydroxide ions without any gas formation. This reaction is sometimes facilitated by catalytic sites within the ion-exchange layers. Upon applying electrical current across a BM, the ionic flow through the membrane is not supported by ions from the surrounding solution because neither cations nor anions can pass through both layers of the BM. Consequently, the transport of ionic current relies on proton and hydroxide ions produced at the membrane's internal interface. This process underlines the critical importance of the BM's orientation relative to the electrodes: to facilitate the migration of $H^+$ and $OH^-$ ions in alignment with the electric field, the Cation Exchange Layer (CEL) must be oriented towards the cathode, while the Anion Exchange Layer (AEL) should face the anode. The resultant movement of $H^+$ and $OH^-$ ions out of the membrane through their respective layers ($H^+$ through the CEL and $OH^-$ through the AEL) leads to the formation of an acid and a base on alternate sides of the membrane, thereby establishing a pH gradient across the BM. This configuration, with the CEL positioned towards the

<figure><img src="image_5.png" /><figcaption>Fig. 3. Diagrammatic representation of various IEM varieties: (a) AEMs, (b) CEMs, (c) BMs, (d) amphoteric IEMs, and (e) mosaic IEMs. In this illustration, the circles represent the counter-ions embedded within the membrane structure, and the distinct background designs illustrate the fixed ionic groups in each type of membrane.</figcaption></figure>
The uniqueness of this study lies in its generalist approach to chemical engineering, yet it delves into the scientific nuances of ED technology, marking a contribution to the field. The manuscript is intended to serve not only as an educational resource for those new to ED but also as an update for seasoned researchers and practitioners. The recent literature often provides insufficient comprehensive and holistic guidance for researchers new to the field of ED. Predominantly, reviews focus on specialized applications or functional improvements, engaging in extensive scientific detail yet remaining confined to particular cases. This review endeavors to surmount this deficiency by offering a broader, more accessible, and recent overview of the field.

## 2. Fundamentals of electrodialysis

ED is an ionic purification of a liquid placed between sets of semi-permeable membranes, driven by ion transfers aimed at maintaining electroneutrality between the compartments. These compartments themselves are imbalanced by ED reactions on either side, induced by the application of an electric field. This section delves into the core principles underlying ED, focusing on IEM processes, including monopolar and bipolar configurations, and the mechanisms of ion transport within membranes and solutions. It outlines the basics of ED technology, discussing key aspects such as sorption-migration, ion selectivity, and the balance between membrane permeability and selectivity.

### 2.1. Concepts of ion-exchange membrane processes

#### 2.1.1. Conventional electrodialysis

The core principles of ED are rooted in electrochemistry, ion transport, and membrane science, where a succession of heterogeneous interfaces (i.e., electrode / electrolyte / membrane / electrolyte / ... / electrolyte / membrane / electrolyte / electrode) is implemented, thereby generating reactions and heterogeneous transfer mechanisms. ED systems consist of an anode and a cathode, forming an EC cell as shown in Fig. 2 - a. However, it is important to note that ED process does not involve redox reactions, characteristic of electrolytic processes, except for reactions at the terminal electrodes (judiciously chosen so as not to be the system's critical overvoltage).

At the anode, oxidation reactions occur, while at the cathode, reduction reactions take place. Classically, between these electrodes are a series of IEM, alternating CEM, and AEM. In practical industrial applications, the number of membrane pairs in an ED stack often reaches hundreds. This scaling up is crucial to improving process efficiency and reducing investment costs per unit of production capacity [56]. Cations move towards the cathode and anions towards the anode by migration under the application of an electrical field. The membranes are arranged in a stack, creating alternating compartments of dilute and concentrate solutions. As ions migrate under the influence of the electric potential $\varphi$ (V), they are either captured in concentrate compartments or allowed to pass into dilute compartments, effectively removing them from the solution to be treated [57]. Separation results from the selectivity of membrane ion transport and exclusion by electrostatic repulsion at the membrane surface due to like charges covalently bonded to the membrane material. When an electric field is applied, ions in the solution are driven towards the oppositely charged electrodes through migration and diffusion mechanisms which results in the generation of diffusion boundary layers (DBLs) on either side of each membrane. The diffusion of a species originates from the thermal agitation of molecules, which tends to equalize the concentration. It results in a flux of the species from regions of higher concentration to those of lower concentration. This is true both within the DBLs close to electrode and across the membrane. However, the polarity of the membrane restricts diffusion to ions of the opposite polarity, meaning that concentration cannot be increased indefinitely. At a certain point, Fickian diffusion of ions from the concentrate to the dilute becomes more significant than the flux by

electromigration. Therefore, it would be more prudent to stop ED before this point to maintain its efficiency. It occurs primarily in the vicinity of the electrodes and membranes, in a DBL whose thickness varies from a few micrometers (in the case of agitation) to several centimeters.

#### 2.1.2. Ion-exchange membranes

Alternatively, IEMs are typically categorized into five types, depending on the nature and arrangement of their fixed ionic groups (Fig. 3). These include CEMs [59], AEMs [60], amphoteric IEMs [61], BMs [62], and mosaic IEMs [63]. An IEM is composed of both hydrophilic ionic groups and hydrophobic polymer chains with charged ionic functional groups that allow the transport of oppositely charged species (counter-ions), while retaining like-charged ions (co-ions). Specific focus on the IEM materials will be presented in Section 3.

Bipolar electrodialysis (BED) is an advanced EC process that extends the principles of standard ED by incorporating bipolar membranes (BMs), illustrated in Fig. 3 - c, alongside the traditional CEMs and AEMs. This technique is particularly useful for generating bases and acids from salts. In BED, each BM consists of two layers: a cation-exchange layer and an anion-exchange layer. These layers are fused together, and at their interface, water molecules undergo disproportionation reaction into proton and hydroxide ions without any gas formation. This reaction is sometimes facilitated by catalytic sites within the ion-exchange layers. Upon applying electrical current across a BM, the ionic flow through the membrane is not supported by ions from the surrounding solution because neither cations nor anions can pass through both layers of the BM. Consequently, the transport of ionic current relies on proton and hydroxide ions produced at the membrane's internal interface. This process underlines the critical importance of the BM's orientation relative to the electrodes: to facilitate the migration of $H^+$ and $OH^-$ ions in alignment with the electric field, the Cation Exchange Layer (CEL) must be oriented towards the cathode, while the Anion Exchange Layer (AEL) should face the anode. The resultant movement of $H^+$ and $OH^-$ ions out of the membrane through their respective layers ($H^+$ through the CEL and $OH^-$ through the AEL) leads to the formation of an acid and a base on alternate sides of the membrane, thereby establishing a pH gradient across the BM. This configuration, with the CEL positioned towards the

<figure><img src="image_6.png" /><figcaption>Fig. 3. Diagrammatic representation of various IEM varieties: (a) AEMs, (b) CEMs, (c) BMs, (d) amphoteric IEMs, and (e) mosaic IEMs. In this illustration, the circles represent the counter-ions embedded within the membrane structure, and the distinct background designs illustrate the fixed ionic groups in each type of membrane.</figcaption></figure>
cathode, is often termed the ‘reverse bias’ condition (analogous to diode case). Altering the electric field’s direction across the BM—either by switching the electrode’s polarity or by rotating the membrane so that the CEL faces the anode and the AEL the cathode—results in a ‘forward bias’ condition. In the forward bias scenario, H⁺ and OH⁻ ions migrate from the external solutions towards the bipolar junction, recombining into water. This water then diffuses out through the CEL and AEL, leading to the neutralization of the acid and base. BMs with their unique capability to synthesize compounds rather than merely facilitating ion transport, hold a unique place among IEMs [64]. BMs have garnered commercial attention recently, primarily due to their environmental benefits. They offer a chemical-free method for pH modification through direct H⁺ and OH⁻ generation, avoiding the need for external chemical additives. Furthermore, BM technology is pivotal in the chemical industry’s shift towards electrification, significantly contributing to the sustainable production of chemicals. Despite its benefits, the process is energy-intensive, making energy efficiency a crucial factor for its cost-effectiveness. Additionally, the stability and efficiency of BMs are key areas of focus, with ongoing research aimed at developing more durable and efficient membranes, subject to a multitude of recent reviews [65–67].

Amphoteric IEMs are characterized by the inclusion of both weak acidic and weak basic functional groups as shown in Fig. 3 – d. These groups are interspersed throughout the membrane’s structure. This configuration enables the passage of both cations and anions, which can be modulated through pH adjustments. Notably, these membranes have been identified as promising in anti-fouling applications, effectively hindering the adherence of organic compounds and biological macromolecules (proteins) on their surfaces, as highlighted in various works [68,69].

Contrastingly, the structure of mosaic membranes is distinguished by the parallel arrangement of anion and cation exchange sites. These exchange resins are interspersed within a matrix that is either a neutral polymer or facilitates ion exchange, as depicted in Fig. 3 – e. The channels in these membranes that possess a positive charge typically exhibit a higher concentration of negatively charged anions, and the reverse is true for channels with a negative charge. This specific layout creates distinct pathways for the separate movement of anions and cations [36,70]. Mosaic membranes are particularly adept at separating salts from water-soluble organic materials and are valuable in the treatment of waste streams across various industrial sectors, thanks to their negative salt rejection and osmotic pressure capabilities [71]. Mosaic membranes demonstrate efficacy in concentrating dilute electrolytes when subjected to hydrostatic pressure and a gradient in chemical potential, a process known as piezodialysis. The proximity of anion and cation exchange sites within a singular membrane leads to a disproportionately elevated permeability to salts when compared to neutral molecules [72]. This process bears a resemblance to ED. However, a distinguishing feature in this case is the absence of electrodes typically associated with ED. However, the complexity of fabricating mosaic membranes, particularly in achieving a thin, selective layer with controlled domain size and preventing interfacial leakage between domains, presents significant challenges for commercial production [73].

Since most research on ED pilot plant development focuses on conventional IEMs and BMs, this review focuses on the two types of these IEMs.

## 2.2. Overcoming energy losses in ion transport for electrodialyzer

Ion transport in an electrodialyzer occurs under the application of a potential. This transport will generate energy losses within the system that must be overcome to bring the electrodialyzer into nominal operation. Before presenting the transport phenomena within the stack in detail, describing the energy losses in the form of overpotentials will allow for a better understanding of ion transport subsequently.

### 2.2.1. Energetic balance

To better understand the sources of energy loss in the process, it is necessary to establish a rigorous energetic balance on the ED plant. This potential field $\varphi$, illustrated in Fig. 4, gives a better idea of the main electrical overpotential in the process.

The operating voltage itself is composed of various elements, including the thermodynamic cell potential, the overpotential associated with both the cathode and anode reactions (Fig. 4 – b), and the potential losses due to the resistance of the electrolyte and the separator. This energy consumption can be related to the cell’s potential and the system’s overall overvoltage, as shown in Eq. (1).

$$U_{\text{stack}} = U_{\text{Nernst}} + U_{\text{D}} + \eta_{\text{act}} + \eta_{\text{conc}} + \eta_{\text{ohm}} \quad (1)$$

where $U_{\text{stack}}$ is the cell potential of the stack (V); $U_{\text{Nernst}}$ is the redox potential at the electrodes (V); $U_{\text{D}}$ is the Donnan overvoltage of the entire cell (V); $\eta_{\text{act}}$, $\eta_{\text{conc}}$ and $\eta_{\text{ohm}}$ are, respectively, the activation, concentration and ohmic overvoltages (V).

The ion transport in each stage of the ED process necessitates a specific amount of energy consumption/loss, which is described upon in the subsequent sub-sections.

### 2.2.2. Ohmic losses

Ohmic overvoltage represents the primary loss in ED. This overpotential can be broken down into various contributions occurring within the membranes and electrolytes, as outlined in Eq. (2).

$$\eta_{\text{ohm}} = \eta_{\text{ohm}}^{\text{cte}} + \eta_{\text{ohm}}^{\text{dlt}} + \eta_{\text{ohm}}^{\text{CEM}} + \eta_{\text{ohm}}^{\text{AEM}} + \eta_{\text{ohm}}^{\text{ano}} + \eta_{\text{ohm}}^{\text{cat}} \quad (2)$$

In each domain, the ohmic losses follow Ohm’s law, as pointed in Eqs. (3) – (8)

$$\eta_{\text{ohm}}^{\text{cte}} = N_{\text{cp}} \times \frac{1^{\text{cte}}}{A_{\text{cell}} \sigma^{\text{cte}}} \times I \quad (3)$$

$$\eta_{\text{ohm}}^{\text{dlt}} = N_{\text{cp}} \times \frac{1^{\text{dlt}}}{A_{\text{cell}} \sigma^{\text{dlt}}} \times I \quad (4)$$

$$\eta_{\text{ohm}}^{\text{CEM}} = (N_{\text{cp}} + 1) \times \frac{1^{\text{CEM}}}{A_{\text{cell}} \sigma^{\text{CEM}}} \times I \quad (5)$$

$$\eta_{\text{ohm}}^{\text{AEM}} = N_{\text{cp}} \times \frac{1^{\text{AEM}}}{A_{\text{cell}} \sigma^{\text{AEM}}} \times I \quad (6)$$

$$\eta_{\text{ohm}}^{\text{ano}} = \frac{1^{\text{ano}}}{A_{\text{cell}} \sigma^{\text{ano}}} \times I \quad (7)$$

$$\eta_{\text{ohm}}^{\text{cat}} = \frac{1^{\text{cat}}}{A_{\text{cell}} \sigma^{\text{cat}}} \times I \quad (8)$$

where I is the thickness (m); A is the surface area of the cell (m²); σ is the ionic conductivity (S m⁻¹) and I is the current (A).

In dilute electrolytes, ionic conductivity is influenced by both the concentration and the nature of each ion, as described in Eq. (9). In the case of concentrate electrolytes, more complex correlations need to be taken into account [74].

$$\sigma^j = \sum_i \lambda_i^j \times C_i^{j,s} \quad (9)$$

where $\lambda_i$ is the molar ion conductivity (S m⁻¹ mol⁻¹).

Note that the order of magnitude of each of these overvoltages is not identical, and they can be classified according to Eqs. (10) – (11).

$$\eta_{\text{ohm}} > \eta_{\text{act}} > \eta_{\text{conc}} \quad (10)$$

$$\begin{aligned} 10^2 \text{ mV} &\approx \eta_{\text{ohm}}^{\text{CEM}} \approx \eta_{\text{ohm}}^{\text{AEM}} > \eta_{\text{ohm}}^{\text{dlt}} \ge \eta_{\text{ohm}}^{\text{cte}} > \eta_{\text{ohm}}^{\text{ano}} \approx \eta_{\text{ohm}}^{\text{cat}} > \eta_{\text{act}} > \eta_{\text{conc}} \\ &\approx 10^1 \text{ mV} \end{aligned} \quad (11)$$
cathode, is often termed the ‘reverse bias’ condition (analogous to diode case). Altering the electric field’s direction across the BM—either by switching the electrode’s polarity or by rotating the membrane so that the CEL faces the anode and the AEL the cathode—results in a ‘forward bias’ condition. In the forward bias scenario, H⁺ and OH⁻ ions migrate from the external solutions towards the bipolar junction, recombining into water. This water then diffuses out through the CEL and AEL, leading to the neutralization of the acid and base. BMs with their unique capability to synthesize compounds rather than merely facilitating ion transport, hold a unique place among IEMs [64]. BMs have garnered commercial attention recently, primarily due to their environmental benefits. They offer a chemical-free method for pH modification through direct H⁺ and OH⁻ generation, avoiding the need for external chemical additives. Furthermore, BM technology is pivotal in the chemical industry’s shift towards electrification, significantly contributing to the sustainable production of chemicals. Despite its benefits, the process is energy-intensive, making energy efficiency a crucial factor for its cost-effectiveness. Additionally, the stability and efficiency of BMs are key areas of focus, with ongoing research aimed at developing more durable and efficient membranes, subject to a multitude of recent reviews [65–67].

Amphoteric IEMs are characterized by the inclusion of both weak acidic and weak basic functional groups as shown in Fig. 3 – d. These groups are interspersed throughout the membrane’s structure. This configuration enables the passage of both cations and anions, which can be modulated through pH adjustments. Notably, these membranes have been identified as promising in anti-fouling applications, effectively hindering the adherence of organic compounds and biological macromolecules (proteins) on their surfaces, as highlighted in various works [68,69].

Contrastingly, the structure of mosaic membranes is distinguished by the parallel arrangement of anion and cation exchange sites. These exchange resins are interspersed within a matrix that is either a neutral polymer or facilitates ion exchange, as depicted in Fig. 3 – e. The channels in these membranes that possess a positive charge typically exhibit a higher concentration of negatively charged anions, and the reverse is true for channels with a negative charge. This specific layout creates distinct pathways for the separate movement of anions and cations [36,70]. Mosaic membranes are particularly adept at separating salts from water-soluble organic materials and are valuable in the treatment of waste streams across various industrial sectors, thanks to their negative salt rejection and osmotic pressure capabilities [71]. Mosaic membranes demonstrate efficacy in concentrating dilute electrolytes when subjected to hydrostatic pressure and a gradient in chemical potential, a process known as piezodialysis. The proximity of anion and cation exchange sites within a singular membrane leads to a disproportionately elevated permeability to salts when compared to neutral molecules [72]. This process bears a resemblance to ED. However, a distinguishing feature in this case is the absence of electrodes typically associated with ED. However, the complexity of fabricating mosaic membranes, particularly in achieving a thin, selective layer with controlled domain size and preventing interfacial leakage between domains, presents significant challenges for commercial production [73].

Since most research on ED pilot plant development focuses on conventional IEMs and BMs, this review focuses on the two types of these IEMs.

## 2.2. Overcoming energy losses in ion transport for electrodialyzer

Ion transport in an electrodialyzer occurs under the application of a potential. This transport will generate energy losses within the system that must be overcome to bring the electrodialyzer into nominal operation. Before presenting the transport phenomena within the stack in detail, describing the energy losses in the form of overpotentials will allow for a better understanding of ion transport subsequently.

### 2.2.1. Energetic balance

To better understand the sources of energy loss in the process, it is necessary to establish a rigorous energetic balance on the ED plant. This potential field φ, illustrated in Fig. 4, gives a better idea of the main electrical overpotential in the process.

The operating voltage itself is composed of various elements, including the thermodynamic cell potential, the overpotential associated with both the cathode and anode reactions (Fig. 4 – b), and the potential losses due to the resistance of the electrolyte and the separator. This energy consumption can be related to the cell’s potential and the system’s overall overvoltage, as shown in Eq. (1).

$$U_{\text{stack}} = U_{\text{Nernst}} + U_{\text{D}} + \eta_{\text{act}} + \eta_{\text{conc}} + \eta_{\text{ohm}} \quad (1)$$

where $U_{\text{stack}}$ is the cell potential of the stack (V); $U_{\text{Nernst}}$ is the redox potential at the electrodes (V); $U_{\text{D}}$ is the Donnan overvoltage of the entire cell (V); $\eta_{\text{act}}$, $\eta_{\text{conc}}$ and $\eta_{\text{ohm}}$ are, respectively, the activation, concentration and ohmic overvoltages (V).

The ion transport in each stage of the ED process necessitates a specific amount of energy consumption/loss, which is described upon in the subsequent sub-sections.

### 2.2.2. Ohmic losses

Ohmic overvoltage represents the primary loss in ED. This overpotential can be broken down into various contributions occurring within the membranes and electrolytes, as outlined in Eq. (2).

$$\eta_{\text{ohm}} = \eta_{\text{ohm}}^{\text{cte}} + \eta_{\text{ohm}}^{\text{dlt}} + \eta_{\text{ohm}}^{\text{CEM}} + \eta_{\text{ohm}}^{\text{AEM}} + \eta_{\text{ohm}}^{\text{ano}} + \eta_{\text{ohm}}^{\text{cat}} \quad (2)$$

In each domain, the ohmic losses follow Ohm’s law, as pointed in Eqs. (3) – (8)

$$\eta_{\text{ohm}}^{\text{cte}} = N_{\text{cp}} \times \frac{1^{\text{cte}}}{A_{\text{cell}} \sigma^{\text{cte}}} \times I \quad (3)$$

$$\eta_{\text{ohm}}^{\text{dlt}} = N_{\text{cp}} \times \frac{1^{\text{dlt}}}{A_{\text{cell}} \sigma^{\text{dlt}}} \times I \quad (4)$$

$$\eta_{\text{ohm}}^{\text{CEM}} = (N_{\text{cp}} + 1) \times \frac{1^{\text{CEM}}}{A_{\text{cell}} \sigma^{\text{CEM}}} \times I \quad (5)$$

$$\eta_{\text{ohm}}^{\text{AEM}} = N_{\text{cp}} \times \frac{1^{\text{AEM}}}{A_{\text{cell}} \sigma^{\text{AEM}}} \times I \quad (6)$$

$$\eta_{\text{ohm}}^{\text{ano}} = \frac{1^{\text{ano}}}{A_{\text{cell}} \sigma^{\text{ano}}} \times I \quad (7)$$

$$\eta_{\text{ohm}}^{\text{cat}} = \frac{1^{\text{cat}}}{A_{\text{cell}} \sigma^{\text{cat}}} \times I \quad (8)$$

where I is the thickness (m); A is the surface area of the cell (m²); σ is the ionic conductivity (S m⁻¹) and I is the current (A).

In dilute electrolytes, ionic conductivity is influenced by both the concentration and the nature of each ion, as described in Eq. (9). In the case of concentrate electrolytes, more complex correlations need to be taken into account [74].

$$\sigma^j = \sum_i \lambda_i^j \times C_i^{j,s} \quad (9)$$

where λ is the molar ion conductivity (S m⁻¹ mol⁻¹).

Note that the order of magnitude of each of these overvoltages is not identical, and they can be classified according to Eqs. (10) – (11).

$$\eta_{\text{ohm}} > \eta_{\text{act}} > \eta_{\text{conc}} \quad (10)$$

$$\begin{aligned} 10^2 \text{ mV} &\approx \eta_{\text{ohm}}^{\text{CEM}} \approx \eta_{\text{ohm}}^{\text{AEM}} > \eta_{\text{ohm}}^{\text{dlt}} \ge \eta_{\text{ohm}}^{\text{cte}} > \eta_{\text{ohm}}^{\text{ano}} \approx \eta_{\text{ohm}}^{\text{cat}} > \eta_{\text{act}} > \eta_{\text{conc}} \\ &\approx 10^1 \text{ mV} \end{aligned} \quad (11)$$
<figure><img src="image_6.png" /><figcaption>Fig. 4. Potential field $\varphi$ (a) within the complete ED cell, at the interfaces of (b) the cathode, (b') the anode and (c) the monopolar IEM.</figcaption></figure>

### 2.2.3. Losses at the electrode surface

Ion transport at the electrode undergoes three main phenomena: (i) thermodynamic equilibrium through Nernst overvoltage, (ii) kinetics and activation energy barrier through activation overvoltage and (iii) depletion of charge-carriers at the electrode surface generated by diffusion gradient or gas bubbles thorough concentration overvoltage.

Nernst potentials (depicted in Eq. (12)) and activation overvoltages are considered solely for the reactions at the electrodes, which are typically water oxidation and reduction. No other EC reactions occur in ED setup.

$$U_{\text{Nernst}} = \left\{ E_a^\circ - \frac{RT}{z_i F} \ln \frac{a_{\text{Red}}^{\text{ano}}}{a_{\text{Ox}}^{\text{ano}}} \right\} - \left\{ E_c^\circ - \frac{RT}{z_i F} \ln \frac{a_{\text{Red}}^{\text{cat}}}{a_{\text{Ox}}^{\text{cat}}} \right\} \quad (12)$$

where $E_a^\circ$ and $E_c^\circ$ are, respectively, the standard anodic and cathodic potential (V); a is the activity (dimensionless).

Kinetics of EC reaction can be typically modelized by a Tafel equation as written in Eq. (13).

$$\eta_{\text{act}} = \frac{RT}{\alpha_a z_i F} \times \log \frac{j}{j_{0,a}} + \frac{RT}{\alpha_c z_i F} \times \log \frac{j}{j_{0,c}} \quad (13)$$

where $\alpha_a$ and $\alpha_c$ are, respectively, the anodic and cathodic charge transfer coefficients (dimensionless); j is the electrode current density (A/m$^{-2}$(−|−)); $j_0$ is the exchange current density (A/m$^{-2}$(−|−)).

The concentration overpotential depends on the hydrodynamics in the electrode compartments and at the interface of each IEM sides (leading to concentration polarization) and thus on the concentration of reactants, as indicated in Eq. (14).

$$\eta_{\text{conc}}^{\text{electrodes}} = \left| \frac{RT}{n_e F} \times \ln \frac{C_{\text{Red},a}^{*}}{C_{\text{Red},s}^{*}} \right| + \left| \frac{RT}{n_e F} \times \ln \frac{C_{\text{Ox},s}^{*}}{C_{\text{Ox},c}^{*}} \right| \quad (14)$$

where $n_e$ is the exchanged electron number (dimensionless) and $C^*$ is the concentration at the electrode surface (mol/m$^{-3}$(−|−)).

### 2.2.4. Losses at the membrane interface

Two main losses of energy are generated at the membrane interface: (i) caused by a concentration polarization and (ii) generated by the thermodynamic equilibrium of ions, called Donnan equilibrium, between solution and membrane interface [75].

The concentration overpotential depends on the hydrodynamics close to IEMs and at the interface of each IEM sides (leading to concentration polarization), as indicated in Eq. (15).

$$\eta_{\text{conc}}^{\text{IEM}} = N_{\text{cp}} \times \left\{ \left| \frac{RT}{z_i F} \ln \frac{C_{\oplus}^{\text{cte},*}}{C_{\oplus}^{\text{cte},s}} \right| + \left| \frac{RT}{z_i F} \ln \frac{C_{\ominus}^{\text{dlt},*}}{C_{\ominus}^{\text{dlt},s}} \right| + \left| \frac{RT}{z_i F} \ln \frac{C_{\ominus}^{\text{cte},*}}{C_{\ominus}^{\text{cte},s}} \right| + \left| \frac{RT}{z_i F} \ln \frac{C_{\oplus}^{\text{dlt},*}}{C_{\oplus}^{\text{dlt},s}} \right| \right\} \quad (15)$$

$$\eta_{\text{conc}} = \eta_{\text{conc}}^{\text{electrodes}} + \eta_{\text{conc}}^{\text{IEM}} \quad (16)$$

where $z_i$ is the ion's valence (dimensionless) and $C^*$ is the concentration at the membrane surface (mol/m$^{-3}$(−|−)).

Donnan formulated the equations for thermodynamic equilibrium in membranes by considering the IEM matrix as a solution containing uniformly distributed fixed charges. It was discovered that an electrical potential at the interface between the membrane and the solution causes the repulsion of co-ions from the membrane matrix as illustrated in Fig. 4 – c by Donnan equilibrium. The phenomenon where co-ions are
<figure><img src="image_7.png" /><figcaption>Fig. 4. Potential field $\varphi$ (a) within the complete ED cell, at the interfaces of (b) the cathode, (b') the anode and (c) the monopolar IEM.</figcaption></figure>

### 2.2.3. Losses at the electrode surface

Ion transport at the electrode undergoes three main phenomena: (i) thermodynamic equilibrium through Nernst overvoltage, (ii) kinetics and activation energy barrier through activation overvoltage and (iii) depletion of charge-carriers at the electrode surface generated by diffusion gradient or gas bubbles thorough concentration overvoltage.

Nernst potentials (depicted in Eq. (12)) and activation overvoltages are considered solely for the reactions at the electrodes, which are typically water oxidation and reduction. No other EC reactions occur in ED setup.

$$U_{\text{Nernst}} = \left\{ E_a^\circ - \frac{RT}{z_i F} \ln \frac{a_{\text{Red}}^{\text{ano}}}{a_{\text{Ox}}^{\text{ano}}} \right\} - \left\{ E_c^\circ - \frac{RT}{z_i F} \ln \frac{a_{\text{Red}}^{\text{cat}}}{a_{\text{Ox}}^{\text{cat}}} \right\} \quad (12)$$

where $E_a^\circ$ and $E_c^\circ$ are, respectively, the standard anodic and cathodic potential (V); a is the activity (dimensionless).

Kinetics of EC reaction can be typically modelized by a Tafel equation as written in Eq. (13).

$$\eta_{\text{act}} = \frac{RT}{\alpha_a z_i F} \times \log \frac{j}{j_{0,a}} + \frac{RT}{\alpha_c z_i F} \times \log \frac{j}{j_{0,c}} \quad (13)$$

where $\alpha_a$ and $\alpha_c$ are, respectively, the anodic and cathodic charge transfer coefficients (dimensionless); j is the electrode current density (A/m$^{-2}$(−|−)); $j_0$ is the exchange current density (A/m$^{-2}$(−|−)).

The concentration overpotential depends on the hydrodynamics in the electrode compartments and at the interface of each IEM sides (leading to concentration polarization) and thus on the concentration of reactants, as indicated in Eq. (14).

$$\eta_{\text{conc}}^{\text{electrodes}} = \left| \frac{RT}{n_e F} \times \ln \frac{C_{\text{Red},a}^{*}}{C_{\text{Red},s}^{*}} \right| + \left| \frac{RT}{n_e F} \times \ln \frac{C_{\text{Ox},s}^{*}}{C_{\text{Ox},c}^{*}} \right| \quad (14)$$

where $n_e$ is the exchanged electron number (dimensionless) and $C^*$ is the concentration at the electrode surface (mol/m$^{-3}$(−|−)).

### 2.2.4. Losses at the membrane interface

Two main losses of energy are generated at the membrane interface: (i) caused by a concentration polarization and (ii) generated by the thermodynamic equilibrium of ions, called Donnan equilibrium, between solution and membrane interface [75].

The concentration overpotential depends on the hydrodynamics close to IEMs and at the interface of each IEM sides (leading to concentration polarization), as indicated in Eq. (15).

$$\eta_{\text{conc}}^{\text{IEM}} = N_{\text{cp}} \times \left\{ \left| \frac{RT}{z_i F} \ln \frac{C_{\oplus}^{\text{cte},*}}{C_{\oplus}^{\text{cte},s}} \right| + \left| \frac{RT}{z_i F} \ln \frac{C_{\ominus}^{\text{dlt},*}}{C_{\ominus}^{\text{dlt},s}} \right| + \left| \frac{RT}{z_i F} \ln \frac{C_{\ominus}^{\text{cte},*}}{C_{\ominus}^{\text{cte},s}} \right| + \left| \frac{RT}{z_i F} \ln \frac{C_{\oplus}^{\text{dlt},*}}{C_{\oplus}^{\text{dlt},s}} \right| \right\} \quad (15)$$

$$\eta_{\text{conc}} = \eta_{\text{conc}}^{\text{electrodes}} + \eta_{\text{conc}}^{\text{IEM}} \quad (16)$$

where $z_i$ is the ion's valence (dimensionless) and $C^*$ is the concentration at the membrane surface (mol/m$^{-3}$(−|−)).

Donnan formulated the equations for thermodynamic equilibrium in membranes by considering the IEM matrix as a solution containing uniformly distributed fixed charges. It was discovered that an electrical potential at the interface between the membrane and the solution causes the repulsion of co-ions from the membrane matrix as illustrated in Fig. 4 – c by Donnan equilibrium. The phenomenon where co-ions are
repelled by IEMs is known as the Donnan effect and the equilibrium leads to a Donnan potential $Δφ_D$ (V). For each membrane, two Donnan potentials occur at each interface. Since the EC potential of ions within the membrane is challenging to estimate, it is assumed to be identical at both interfaces, then we consider a single Donnan potential for the entire membrane. This latter depends on the ion activity on both sides of the membrane and can be expressed as Eq. (17).

$$ \Delta\varphi_D = \varphi^m - \varphi^s = \frac{RT}{z_i F} \times \ln \frac{C_i^e \gamma_i^s}{C_i^m \gamma_i^m} \quad (17) $$

where $Δφ_D$ is the Donnan potential (V) as the potential difference between the membrane $φ^m$ and the solution $φ^s$ potentials (V).

Each membrane in the ED setup possesses a Donnan potential that varies depending on the ion mobility present in the surrounding solutions [76]. Recently, Aydogan Gokturk et al. was the first to determine Donnan potential directly and experimentally by tender ambient pressure X-ray photoelectron spectroscopy [75]. In the scenario depicted in Fig. 4, there are four different membrane configurations. The top membrane is a CEM bordered by the catholyte on one side and the dilute on the other side. The bottom membrane is also a CEM but is bordered by the anolyte and the concentrate. Between the two, there are AEMs and CEMs, present in quantities corresponding to the number of cell pairs ($N_{cp}$) and the number of cell pairs minus two, respectively. All these membranes share a similar configuration, each flanked by a concentrate solution and a dilute solution. However, the mobile ions differ between the membranes: cations move through the CEMs, while anions traverse the AEMs. The Donnan potential in this arrangement is defined by Eq. (18). With a different configuration or in the case of a BM, the equation will vary, and a similar assessment must be conducted.

$$ \begin{aligned} U_D &= \sum_j \Delta\varphi_D^j \\ &= (N_{cp} - 2) \times \left| \frac{RT}{z_i F} \ln \frac{C_{\oplus}^{\text{cte}}}{C_{\oplus}^{\text{dltel}}} \right| + N_{cp} \times \left| \frac{RT}{z_i F} \ln \frac{C_{\ominus}^{\text{dlt}}}{C_{\ominus}^{\text{cte}}} \right| + \frac{RT}{z_i F} \times \ln \frac{C_{\oplus}^{\text{cte}}}{C_{\oplus}^{\text{ano}}} + \left| \frac{RT}{z_i F} \times \ln \frac{C_{\ominus}^{\text{catel}}}{C_{\ominus}^{\text{dlt}}} \right| \end{aligned} \quad (18) $$

where j represent each interface between an electrolyte and the IEM; $N_{cp}$ is the number of cell pair (dimensionless); $C_{\oplus}$ and $C_{\ominus}$ are, respectively, the anion and cation concentration (mol/m$^{-3}$(−|−)).

On the other hand, when using BMs (not illustrated in Fig. 4), the main difference generates a different potential field $Δφ_D$ across the membrane. In the case of these membranes, the Donnan voltage at zero current is presented in Eq. (19).

$$ \Delta\varphi_D = 2.3 \times \frac{RT}{F} \times \Delta\text{pH} \quad (19) $$

where $ΔpH$ is the pH difference across the BM (dimensionless).

In the literature, there are two primary theoretical frameworks utilized for characterizing the structure of the transition region in BMs. These are known as the ‘abrupt junction’ model and the ‘neutral layer’ model, as presented in Fig. 5. The ‘abrupt junction’ model posits that the cation- and anion-exchange layers are directly contiguous, leading to a negligible separation between them. This arrangement results in a pronounced shift in both voltage and concentration profiles at the junction of these layers, as depicted in Fig. 5 – a. The spatial extent of this transition region typically spans a few nanometers [77]. Conversely, the ‘neutral layer’ model, illustrated in Fig. 5 – b, hypothesizes the existence of a slender neutral solution layer interposed between the two ion-exchange layers. A notable observation in BM modelling studies is the prevalent assumption of perfect symmetry, wherein both the AEL and CEL are considered identical in terms of thickness, fixed charge density, and symmetric diffusion coefficients for both counter-ions and co-ions. This symmetric model, while prevalent, constrains the exploration of

<figure><img src="image_7.png" /><figcaption>Fig. 5. Diagram illustrating the profiles of concentration and voltage in a BM, featuring (a) an abrupt junction model, and (b) a model with an intervening neutral solution layer. Adapted from [41], Copyright (2021), with permission from Elsevier.</figcaption></figure>
repelled by IEMs is known as the Donnan effect and the equilibrium leads to a Donnan potential $\Delta\varphi_D$ (V). For each membrane, two Donnan potentials occur at each interface. Since the EC potential of ions within the membrane is challenging to estimate, it is assumed to be identical at both interfaces, then we consider a single Donnan potential for the entire membrane. This latter depends on the ion activity on both sides of the membrane and can be expressed as Eq. (17).

$$ \Delta\varphi_D = \varphi^m - \varphi^s = \frac{RT}{z_i F} \times \ln \frac{C_i^e \gamma_i^s}{C_i^m \gamma_i^m} \quad (17) $$

where $\Delta\varphi_D$ is the Donnan potential (V) as the potential difference between the membrane $\varphi^m$ and the solution $\varphi^s$ potentials (V).

Each membrane in the ED setup possesses a Donnan potential that varies depending on the ion mobility present in the surrounding solutions [76]. Recently, Aydogan Gokturk et al. was the first to determine Donnan potential directly and experimentally by tender ambient pressure X-ray photoelectron spectroscopy [75]. In the scenario depicted in Fig. 4, there are four different membrane configurations. The top membrane is a CEM bordered by the catholyte on one side and the dilute on the other side. The bottom membrane is also a CEM but is bordered by the anolyte and the concentrate. Between the two, there are AEMs and CEMs, present in quantities corresponding to the number of cell pairs ($N_{cp}$) and the number of cell pairs minus two, respectively. All these membranes share a similar configuration, each flanked by a concentrate solution and a dilute solution. However, the mobile ions differ between the membranes: cations move through the CEMs, while anions traverse the AEMs. The Donnan potential in this arrangement is defined by Eq. (18). With a different configuration or in the case of a BM, the equation will vary, and a similar assessment must be conducted.

$$ \begin{aligned} U_D &= \sum_j \Delta\varphi_D^j \\ &= (N_{cp} - 2) \times \left| \frac{RT}{z_i F} \ln \frac{C_{\oplus}^{\text{cte}}}{C_{\ominus}^{\text{dltel}}} \right| + N_{cp} \times \left| \frac{RT}{z_i F} \ln \frac{C_{\oplus}^{\text{dlt}}}{C_{\ominus}^{\text{cte}}} \right| + \frac{RT}{z_i F} \times \ln \frac{C_{\oplus}^{\text{cte}}}{C_{\ominus}^{\text{ano}}} + \left| \frac{RT}{z_i F} \right| \\ & \times \ln \frac{C_{\oplus}^{\text{cat}}}{C_{\ominus}^{\text{dlt}}} \end{aligned} \quad (18) $$

where j represent each interface between an electrolyte and the IEM; $N_{cp}$ is the number of cell pair (dimensionless); $C_{\oplus}$ and $C_{\ominus}$ are, respectively, the anion and cation concentration (mol/m$^{-3}$(-|-) ).

On the other hand, when using BMs (not illustrated in Fig. 4), the main difference generates a different potential field $\Delta\varphi_D$ across the membrane. In the case of these membranes, the Donnan voltage at zero current is presented in Eq. (19).

$$ \Delta\varphi_D = 2.3 \times \frac{RT}{F} \times \Delta\text{pH} \quad (19) $$

where $\Delta\text{pH}$ is the pH difference across the BM (dimensionless).

In the literature, there are two primary theoretical frameworks utilized for characterizing the structure of the transition region in BMs. These are known as the ‘abrupt junction’ model and the ‘neutral layer’ model, as presented in Fig. 5. The ‘abrupt junction’ model posits that the cation- and anion-exchange layers are directly contiguous, leading to a negligible separation between them. This arrangement results in a pronounced shift in both voltage and concentration profiles at the junction of these layers, as depicted in Fig. 5 – a. The spatial extent of this transition region typically spans a few nanometers [77]. Conversely, the ‘neutral layer’ model, illustrated in Fig. 5 – b, hypothesizes the existence of a slender neutral solution layer interposed between the two ion-exchange layers. A notable observation in BM modelling studies is the prevalent assumption of perfect symmetry, wherein both the AEL and CEL are considered identical in terms of thickness, fixed charge density, and symmetric diffusion coefficients for both counter-ions and co-ions. This symmetric model, while prevalent, constrains the exploration of

<figure><img src="image_8.png" /><figcaption>Fig. 5. Diagram illustrating the profiles of concentration and voltage in a BM, featuring (a) an abrupt junction model, and (b) a model with an intervening neutral solution layer. Adapted from [41], Copyright (2021), with permission from Elsevier.</figcaption></figure>
asymmetric BM designs. Such asymmetrical designs hold potential for enhancing water transport across the bipolar junction from the surrounding solutions [41].

The interfacial layer situated between the dual layers of the membrane is often embedded with a catalyst to facilitate the dissociation/association reactions, thereby ensuring a continuous exchange or uptake of ionic charge carriers from each layer of the BM [78,79].

## 2.3. Sorption-migration phenomenon during ion transport in ion-exchange membranes

Ions undergo a two-step process involving initial sorption or partitioning into the membrane, followed by migration across the membrane driven by an electrical potential gradient. The process of ion sorption into the membrane's matrix is dictated by the equilibrium of EC potential between the bulk solution and the membrane matrix. This equilibrium is influenced by the difference in electrostatic potential at the interface between the solution and membrane [80].

The sorption coefficient, denoted as K, quantifies the ratio of the concentration of a specific ion i within the IEM to its concentration in the bulk-phase solution. This relationship is encapsulated in Eq. (20) as follows:

$$K_i = \frac{C_i^m}{C_i^s} = \frac{f^w \gamma_i^z}{\gamma_i^m} \times \exp \left( -\frac{z_i F}{RT} \Delta\varphi_D \right) \quad (20)$$

where C is the concentration (mol/m⁻³(-|·|)); f^w is the water volume fraction in the membrane matrix (dimensionless); γ is the activity coefficient (dimensionless); z is the valence (dimensionless); F is the Faraday constant (C/mol); R is the universal gas constant (J/K mol⁻¹); T is the absolute temperature (K); and superscripts m and s denote membrane and bulk solution phases, respectively.

### 2.3.1. Transport modeling equations

A robust framework for quantitatively analyzing ion transport in IEMs is provided by two different scenarios: (i) Nernst-Planck (N-P) and (ii) Maxwell-Stefan (M-S) equations.

The extended N-P equation [81,82] articulates the ionic flux J (mol m⁻² s⁻¹) as a cumulative function of three distinct components presented in Eq. (21) and quantifies the permeation across the membrane.

$$J_i = v^w \times C_i^m - D_i^m C_i^m \times \frac{d\ln(\gamma_i^m C_i^m)}{dx} - z_i e u_i^m C_i^m \times \frac{d\varphi^m}{dx} \quad (21)$$

$$D_i^m = D_i \times \left( \frac{f_w}{2 - f_w} \right)^2 \quad (22)$$

$$u_i = \frac{D_i}{k_b T} \quad (23)$$

where v^w denotes the water velocity in the membrane (m/s); D^m and u^m are the diffusivity (defined in Eq. (22) [83], m²/s) and absolute mobility (defined in Eq. (23) by the Einstein relation, m² (C V s⁻¹)) of the ion within the IEM; e is the elementary charge (C); x being the spatial coordinate across the membrane (m); k_b is the Boltzmann constant (J/K) and f is the volume fraction of water (dimensionless).

Eq. (21) can apply to all ions under the condition of electro-neutrality. The first term is indicative of ions' convective (advective) transport facilitated by electroosmotic solvent flow. The second term denotes ion diffusion driven by the activity gradient. The third term describes ion electromigration, an outcome of the electric potential gradient [84]. Notably, in the context of ion transport within the membrane, while both diffusion and convection contribute, their influence is minor compared to electromigration [85]. This is particularly true for IEMs, which are characterized by a dense structure, and exhibit an electrolyte diffusion coefficient in the membrane that is significantly lower (by one to three orders of magnitude) than in bulk solutions

[86,87]. The N-P model operates under the presumption of an ideal solution, disregarding the interactions between ions. Its applicability is established for dilute ionic environments. However, in the realm of ED, one often encounters solutions with high ion concentrations. Under these circumstances, the M-S framework offers a more accurate representation, acknowledging the complexities arising from component interactions and deviations from ideal solution behavior. Furthermore, the M-S methodology accounts for the movement of water through its interactions with ions, in contrast to the N-P model which necessitates the addition of a distinct formula (namely the Schlögl equation [88]), to describe water transport. Although the traditional N-P equation (which omits the convective term) has limitations in accurately characterizing ion transport through inhomogeneous media, its extensive applicability and utility have been well-established [89,90].

The M-S theory articulates a balance of forces at the steady state, encapsulating the interplay between the driving forces and the resistive frictional forces encountered by a specific component within a mixture. Eq. (24) delineates the relation between the driving force experienced by a component i within the mixture and the cumulative frictional forces arising from interactions between component i and another component k, expressed in mole fraction terms.

$$\left\{ \begin{array}{l} \text{drivingforceonspeciesi} = \text{frictionforceswithotherspeciesi} \\ C_{\text{tot}}\psi_i \times \left( \text{RT}\frac{d\ln a_i}{dx} + z_i F \frac{d\varphi}{dx} \right) = \sum_{k \neq i} \frac{RT}{D_{i,k}} (\psi_i J_k - \psi_k J_i) \end{array} \right. \quad (24)$$

where ψ is the mole fraction (dimensionless) and a is the activity (dimensionless).

### 2.3.2. Modes of ion transport

For example, CEM functions by selectively allowing positively charged ions to pass through while blocking negatively charged ions [81]. It is composed of a polymeric matrix, often made from materials like polyethylene or fluoropolymers [91], which is embedded with negatively charged functional groups, such as sulfonic or carboxylic acids. These functional groups bind to cations in the solution as presented in Fig. 2 - b. The ion transport selectivity is largely influenced by electrostatic repulsion between the migrating ions and those fixed within the membrane. Steric hindrance also plays a role in affecting ion transport, which is related to the polymers' topology and the size of migrating ion through the membranes. Polymer chains exhibit both hydrophobic (carbon chains constituting the backbone) and hydrophilic (ionic functionalities) properties. Upon hydration of the polymer membranes, clusters form between water and the hydrophilic segments of the polymers. With sufficient hydration, these clusters evolve into aqueous channels, and the membrane adopts a biphasic structure. Water uptake in the membrane is defined by the ratio of water molecules per functional site. The water content is influenced by factors such as temperature, ion exchange capacity (IEC), membrane pretreatment, water vapor pressure, and the mechanical properties of the membrane, which depend on the ionomer's nature and manufacturing process.

Ion transport through the membrane can occur via two main mechanisms. The first mechanism, known as the Grotthus mechanism, involves mobile ions moving from one ionic site to another via hopping. If the membrane is adequately hydrated, a second mechanism, termed the 'vehicular' mechanism, occurs where ions are directly transported in the aqueous phase, bounded to water molecules [92]. At this point, water is also transported by migration within the membrane. The dominance of one mechanism over the other depends on the polymer's nature, the ionic functionalities (polymer's hydrophobicity and hydrophilicity, acidity of ionic functionalities, cross-linking, chain size, etc.), and operational conditions, particularly the membrane's hydration. For fuel cells, electrolyzers or EDs using a proton exchange membrane, adequate hydration of the membrane is crucial (it can reach up to 20 wt % in Nafion®, for example). Under such conditions, vehicular transport predominantly accounts for the membrane's good ionic conductivity
asymmetric BM designs. Such asymmetrical designs hold potential for enhancing water transport across the bipolar junction from the surrounding solutions [41].

The interfacial layer situated between the dual layers of the membrane is often embedded with a catalyst to facilitate the dissociation/association reactions, thereby ensuring a continuous exchange or uptake of ionic charge carriers from each layer of the BM [78,79].

## 2.3. Sorption-migration phenomenon during ion transport in ion-exchange membranes

Ions undergo a two-step process involving initial sorption or partitioning into the membrane, followed by migration across the membrane driven by an electrical potential gradient. The process of ion sorption into the membrane's matrix is dictated by the equilibrium of EC potential between the bulk solution and the membrane matrix. This equilibrium is influenced by the difference in electrostatic potential at the interface between the solution and membrane [80].

The sorption coefficient, denoted as K, quantifies the ratio of the concentration of a specific ion i within the IEM to its concentration in the bulk-phase solution. This relationship is encapsulated in Eq. (20) as follows:

$$K_i = \frac{C_i^m}{C_i^s} = \frac{f^w \gamma_i^z}{\gamma_i^m} \times \exp\left(-\frac{z_i F}{RT} \Delta\varphi_D\right) \quad (20)$$

where C is the concentration (mol/m⁻³(-|·|)); f^w is the water volume fraction in the membrane matrix (dimensionless); γ is the activity coefficient (dimensionless); z is the valence (dimensionless); F is the Faraday constant (C/mol); R is the universal gas constant (J/K mol⁻¹); T is the absolute temperature (K); and superscripts m and s denote membrane and bulk solution phases, respectively.

### 2.3.1. Transport modeling equations

A robust framework for quantitatively analyzing ion transport in IEMs is provided by two different scenarios: (i) Nernst-Planck (N-P) and (ii) Maxwell-Stefan (M-S) equations.

The extended N-P equation [81,82] articulates the ionic flux J (mol m⁻² s⁻¹) as a cumulative function of three distinct components presented in Eq. (21) and quantifies the permeation across the membrane.

$$J_i = v^w \times C_i^m - D_i^m C_i^m \times \frac{d\ln(\gamma_i^m C_i^m)}{dx} - z_i e u_i^m C_i^m \times \frac{d\varphi^m}{dx} \quad (21)$$

$$D_i^m = D_i \times \left( \frac{f_w}{2 - f_w} \right)^2 \quad (22)$$

$$u_i = \frac{D_i}{k_b T} \quad (23)$$

where v^w denotes the water velocity in the membrane (m/s); D^m and u^m are the diffusivity (defined in Eq. (22) [83], m²/s) and absolute mobility (defined in Eq. (23) by the Einstein relation, m² (C V s⁻¹)) of the ion within the IEM; e is the elementary charge (C); x being the spatial coordinate across the membrane (m); k_b is the Boltzmann constant (J/K) and f is the volume fraction of water (dimensionless).

Eq. (21) can apply to all ions under the condition of electro-neutrality. The first term is indicative of ions' convective (advective) transport facilitated by electroosmotic solvent flow. The second term denotes ion diffusion driven by the activity gradient. The third term describes ion electromigration, an outcome of the electric potential gradient [84]. Notably, in the context of ion transport within the membrane, while both diffusion and convection contribute, their influence is minor compared to electromigration [85]. This is particularly true for IEMs, which are characterized by a dense structure, and exhibit an electrolyte diffusion coefficient in the membrane that is significantly lower (by one to three orders of magnitude) than in bulk solutions

[86,87]. The N-P model operates under the presumption of an ideal solution, disregarding the interactions between ions. Its applicability is established for dilute ionic environments. However, in the realm of ED, one often encounters solutions with high ion concentrations. Under these circumstances, the M-S framework offers a more accurate representation, acknowledging the complexities arising from component interactions and deviations from ideal solution behavior. Furthermore, the M-S methodology accounts for the movement of water through its interactions with ions, in contrast to the N-P model which necessitates the addition of a distinct formula (namely the Schlögl equation [88]), to describe water transport. Although the traditional N-P equation (which omits the convective term) has limitations in accurately characterizing ion transport through inhomogeneous media, its extensive applicability and utility have been well-established [89,90].

The M-S theory articulates a balance of forces at the steady state, encapsulating the interplay between the driving forces and the resistive frictional forces encountered by a specific component within a mixture. Eq. (24) delineates the relation between the driving force experienced by a component i within the mixture and the cumulative frictional forces arising from interactions between component i and another component k, expressed in mole fraction terms.

$$\left\{ \begin{array}{l} \text{drivingforceonspeciesi} = \text{frictionforceswithotherspeciesi} \\ C_{\text{tot}}\psi_i \times \left( RT \frac{d\ln a_i}{dx} + z_i F \frac{d\varphi}{dx} \right) = \sum_{k \neq i} \frac{RT}{D_{i,k}} (\psi_i J_k - \psi_k J_i) \end{array} \right. \quad (24)$$

where ψ is the mole fraction (dimensionless) and a is the activity (dimensionless).

### 2.3.2. Modes of ion transport

For example, CEM functions by selectively allowing positively charged ions to pass through while blocking negatively charged ions [81]. It is composed of a polymeric matrix, often made from materials like polyethylene or fluoropolymers [91], which is embedded with negatively charged functional groups, such as sulfonic or carboxylic acids. These functional groups bind to cations in the solution as presented in Fig. 2 - b. The ion transport selectivity is largely influenced by electrostatic repulsion between the migrating ions and those fixed within the membrane. Steric hindrance also plays a role in affecting ion transport, which is related to the polymers' topology and the size of migrating ion through the membranes. Polymer chains exhibit both hydrophobic (carbon chains constituting the backbone) and hydrophilic (ionic functionalities) properties. Upon hydration of the polymer membranes, clusters form between water and the hydrophilic segments of the polymers. With sufficient hydration, these clusters evolve into aqueous channels, and the membrane adopts a biphasic structure. Water uptake in the membrane is defined by the ratio of water molecules per functional site. The water content is influenced by factors such as temperature, ion exchange capacity (IEC), membrane pretreatment, water vapor pressure, and the mechanical properties of the membrane, which depend on the ionomer's nature and manufacturing process.

Ion transport through the membrane can occur via two main mechanisms. The first mechanism, known as the Grotthus mechanism, involves mobile ions moving from one ionic site to another via hopping. If the membrane is adequately hydrated, a second mechanism, termed the 'vehicular' mechanism, occurs where ions are directly transported in the aqueous phase, bounded to water molecules [92]. At this point, water is also transported by migration within the membrane. The dominance of one mechanism over the other depends on the polymer's nature, the ionic functionalities (polymer's hydrophobicity and hydrophilicity, acidity of ionic functionalities, cross-linking, chain size, etc.), and operational conditions, particularly the membrane's hydration. For fuel cells, electrolyzers or EDs using a proton exchange membrane, adequate hydration of the membrane is crucial (it can reach up to 20 wt % in Nafion®, for example). Under such conditions, vehicular transport predominantly accounts for the membrane's good ionic conductivity
## 2.4. Performance efficiencies

The economic viability of an EC process largely hinges on its consumption of electrical energy [93]. This consumption is intricately linked to several factors: the operating voltage, the electrical charge necessary for the desired separation of the reactant, and the current efficiency of the process. The main criteria for evaluation are presented in this subsection.

### 2.4.1. Limiting current density

Increasing the voltage applied to a module's terminals results in a rise in current density, which in turn boosts the ion flux until the ion concentration at the membrane surface drops to zero. This point represents the peak current density attainable, referred to as the limiting current density, symbolized as $j_{lim}$ and presented in Eq. (25).

$$j_{lim} = \frac{z_i D_i F C_i^s}{\delta \times (t_{i,ct}^m - t_{i,ct}^s)} \quad (25)$$

where $\delta$ is the thickness of the DBL (m) and $t^s$ and $t^m$ represent the transport number in the bulk and in the membrane, respectively (dimensionless); ct stands here for the counter-ion.

Studying the movement of ions from the dilute to the concentrate compartments involves tracking the change in current intensity I relative to the voltage U applied at the module's terminals. The curve generated from this analysis displays three distinct segments and is represented in Fig. 6 – a. The first segment, marked (A), exhibits an almost linear relationship, illustrating the combined resistance effects from the electrolyte, membranes, and the concentration polarization, as indicated by the straight line's slope. In this segment, Ohm's law ($U = R \times I$) holds true. The next segment, denoted as (B), shows a flat plateau indicating complete polarization of the cell. This plateau reveals the limiting current intensity, influenced by ion delivery to the membrane via electric potential-driven flux, diffusion, and convection. Following this, in segment (C), the intensity begins to rise once more. However, this rise is not attributed to resumed solution species transfer but to solvent redox reactions. This process results in excessive energy consumption, pH shifts leading to irreversible damage, and increased resistivity of the medium. Therefore, the procedure's efficiency is adversely affected, underscoring the importance of operating below the threshold of the limiting current density.

In practical terms, when plotting the ratio U/I against 1/I, the inflection point P, termed the polarization point, reveals the limit current intensity, as referred to Fig. 6 – b. This approach is based on the Cowan and Brown methodology [94]. For a more rapid and effective assessment, a potentiostat is commonly employed on a laboratory scale.

Consequently, the limiting current density is a direct measure of the ionic concentration of the solution undergoing demineralization. As the

<figure><img src="image_8.png" /><figcaption>Fig. 6. (a) Evolution of current I as a function of applied voltage U across the stack terminals and (b) experimental determination of the limiting current density.</figcaption></figure>

process of ED progresses and the ion concentration decreases in the dilute, the limiting current similarly reduces. Should this threshold be surpassed, the concentration at the solution-membrane interface approaches zero, and the solution's resistance moves toward infinity. This scenario can cause localized heating, potentially leading to the membrane's irreversible damage, such as burns or pH shifts. It is thus crucial to accurately determine and regulate $j_{lim}$ throughout the ED operation. For optimal control, determining $j_{lim}$ at a steady concentration is advisable, allowing the operational conditions to be adjusted to consistently stay below the $j_{lim}$ threshold.

### 2.4.2. Current efficiency

In the context of electrokinetic separation techniques, the efficiency with which charged particles are separated or migrated is quantitatively evaluated by the metric known as current efficiency ($\xi$, also called Faradaic or Coulombic efficiency). In the case of ED in batch mode, this efficiency is a comparison between the actual amount of target charged species transported and the theoretical amount predicted by the charge delivered. In the case of continuous-mode ED, this efficiency compares a mass flow rate with a corresponding electrical current. For batch and continuous processes, this efficiency is usually represented as a percentage, as depicted in Eqs. (26) – (27).

Batch reactor:

$$\xi = \frac{n_i \times z_i \times F}{\int I \times dt} \quad (26)$$

Continuous reactor:

$$\xi = \frac{\dot{q} \times z_i \times F \times (C_{i,in} - C_{i,out})}{N_{cp} \times I} \quad (27)$$

where n is the transformed molar amount during batch operation (mol); $C_{i,in}$ and $C_{i,out}$ are the concentration of the target species i at the inlet and the outlet of the stack, respectively (mol/m$^{-3}$(–|–)); $\dot{q}$ denotes the stack volumetric flowrate (m$^3$/s); F is the Faraday constant (C/mol).

### 2.4.3. Specific energy consumption

The consumption of electrical energy by the ED stack can be determined through the product of the voltage applied to the stack, and the electric current flowing through it. Additionally, the energy expenditure for operating the hydraulic pumps was derived from the product of flow rate and the pressure differential. Furthermore, the specific energy consumption (SEC), defined in Wh/m$^{-3}$(–|–) (often Wh kg$^{-1}$), represents the energy required by the ED process to produce a specific volume of product solution.

The electrical power ($P^{el}$, W) utilized by the ED stack is computed as follows in Eq. (28)

$$P^{el} = U_{stack} \times I \quad (28)$$

The power required for hydraulic pumping ($P^h$, W) through the ED stack is given by Eq. (29).

$$P^h = \rho \times g \times \dot{q} \times \Delta H \quad (29)$$

where $\rho$ stands for the mass density of the solution, g the gravitational constant (9.81 m s$^{-2}$), $\dot{q}$ the stack flow rate (m$^3$/s), and $\Delta H$ the hydraulic head loss across the stack (m).

The specific energy consumption (SEC) for a batch and a continuous reactors are calculated with Eqs. (30) – (31).

Batch reactor:

$$SEC = \int_{0}^{t} \frac{P^{el} + P^{h}}{V} \times dt \quad (30)$$

Continuous reactor:
## 2.4. Performance efficiencies

The economic viability of an EC process largely hinges on its consumption of electrical energy [93]. This consumption is intricately linked to several factors: the operating voltage, the electrical charge necessary for the desired separation of the reactant, and the current efficiency of the process. The main criteria for evaluation are presented in this subsection.

### 2.4.1. Limiting current density

Increasing the voltage applied to a module's terminals results in a rise in current density, which in turn boosts the ion flux until the ion concentration at the membrane surface drops to zero. This point represents the peak current density attainable, referred to as the limiting current density, symbolized as $j_{lim}$ and presented in Eq. (25).

$$j_{lim} = \frac{z_i D_i F C_i^s}{\delta \times (t_{i,ct}^m - t_{i,ct}^s)} \quad (25)$$

where $\delta$ is the thickness of the DBL (m) and $t^s$ and $t^m$ represent the transport number in the bulk and in the membrane, respectively (dimensionless); ct stands here for the counter-ion.

Studying the movement of ions from the dilute to the concentrate compartments involves tracking the change in current intensity I relative to the voltage U applied at the module's terminals. The curve generated from this analysis displays three distinct segments and is represented in Fig. 6 – a. The first segment, marked (A), exhibits an almost linear relationship, illustrating the combined resistance effects from the electrolyte, membranes, and the concentration polarization, as indicated by the straight line's slope. In this segment, Ohm's law ($U = R \times I$) holds true. The next segment, denoted as (B), shows a flat plateau indicating complete polarization of the cell. This plateau reveals the limiting current intensity, influenced by ion delivery to the membrane via electric potential-driven flux, diffusion, and convection. Following this, in segment (C), the intensity begins to rise once more. However, this rise is not attributed to resumed solution species transfer but to solvent redox reactions. This process results in excessive energy consumption, pH shifts leading to irreversible damage, and increased resistivity of the medium. Therefore, the procedure's efficiency is adversely affected, underscoring the importance of operating below the threshold of the limiting current density.

In practical terms, when plotting the ratio U/I against 1/I, the inflection point P, termed the polarization point, reveals the limit current intensity, as referred to Fig. 6 – b. This approach is based on the Cowan and Brown methodology [94]. For a more rapid and effective assessment, a potentiostat is commonly employed on a laboratory scale.

Consequently, the limiting current density is a direct measure of the ionic concentration of the solution undergoing demineralization. As the

<figure><img src="image_9.png" /><figcaption>Fig. 6. (a) Evolution of current I as a function of applied voltage U across the stack terminals and (b) experimental determination of the limiting current density.</figcaption></figure>

process of ED progresses and the ion concentration decreases in the dilute, the limiting current similarly reduces. Should this threshold be surpassed, the concentration at the solution-membrane interface approaches zero, and the solution's resistance moves toward infinity. This scenario can cause localized heating, potentially leading to the membrane's irreversible damage, such as burns or pH shifts. It is thus crucial to accurately determine and regulate $j_{lim}$ throughout the ED operation. For optimal control, determining $j_{lim}$ at a steady concentration is advisable, allowing the operational conditions to be adjusted to consistently stay below the $j_{lim}$ threshold.

### 2.4.2. Current efficiency

In the context of electrokinetic separation techniques, the efficiency with which charged particles are separated or migrated is quantitatively evaluated by the metric known as current efficiency ($\xi$, also called Faradaic or Coulombic efficiency). In the case of ED in batch mode, this efficiency is a comparison between the actual amount of target charged species transported and the theoretical amount predicted by the charge delivered. In the case of continuous-mode ED, this efficiency compares a mass flow rate with a corresponding electrical current. For batch and continuous processes, this efficiency is usually represented as a percentage, as depicted in Eqs. (26) – (27).

Batch reactor:

$$\xi = \frac{n_i \times z_i \times F}{\int I \times dt} \quad (26)$$

Continuous reactor:

$$\xi = \frac{\dot{q} \times z_i \times F \times (C_{i,in} - C_{i,out})}{N_{cp} \times I} \quad (27)$$

where n is the transformed molar amount during batch operation (mol); $C_{i,in}$ and $C_{i,out}$ are the concentration of the target species i at the inlet and the outlet of the stack, respectively (mol/m$^{-3}$(–|–)); $\dot{q}$ denotes the stack volumetric flowrate (m$^3$/s); F is the Faraday constant (C/mol).

### 2.4.3. Specific energy consumption

The consumption of electrical energy by the ED stack can be determined through the product of the voltage applied to the stack, and the electric current flowing through it. Additionally, the energy expenditure for operating the hydraulic pumps was derived from the product of flow rate and the pressure differential. Furthermore, the specific energy consumption (SEC), defined in Wh/m$^{-3}$(–|–) (often Wh kg$^{-1}$), represents the energy required by the ED process to produce a specific volume of product solution.

The electrical power ($P^{el}$, W) utilized by the ED stack is computed as follows in Eq. (28)

$$P^{el} = U_{stack} \times I \quad (28)$$

The power required for hydraulic pumping ($P^h$, W) through the ED stack is given by Eq. (29).

$$P^h = \rho \times g \times \dot{q} \times \Delta H \quad (29)$$

where $\rho$ stands for the mass density of the solution, g the gravitational constant (9.81 m s$^{-2}$), $\dot{q}$ the stack flow rate (m$^3$/s), and $\Delta H$ the hydraulic head loss across the stack (m).

The specific energy consumption (SEC) for a batch and a continuous reactors are calculated with Eqs. (30) – (31).

Batch reactor:

$$SEC = \int_{0}^{t} \frac{P^{el} + P^{h}}{V} \times dt \quad (30)$$

Continuous reactor:
$$ SEC = \int_{0}^{t} \frac{p^{\text{el}} + p^{\text{h}}}{\dot{q}} \times dt \qquad (31) $$

where $\dot{q}$ the stack flow rate (m³/s).

### 2.4.4. Ion selectivity

In conditions where electromigration is the prevailing mechanism, outstripping the effects of diffusion and convection, the ion flux described in Eq. (21) can be simplified accordingly to $J_i \approx -\frac{z_i D_i^m F C_i^m}{RT} \times \frac{d\phi^m}{dx}$. This simplification is feasible because each ion species is subjected to an identical gradient in the transmembrane electrostatic potential. Consequently, it becomes possible to express the fluxes of different ions, normalized by their concentrations [80], as in Eq. (32).

$$ S_{i,k} = \frac{J_i C_k^s}{J_k C_i^s} \approx \frac{K_i}{K_k} \times \frac{z_i u_i^m}{z_k u_k^m} = \frac{\gamma_i^s \gamma_k^m}{\gamma_k^m \gamma_i^m} \times \exp \left[ - \frac{(z_i - z_k)F}{RT} \times \Delta\phi_D \right] \times \frac{z_i u_i^m}{z_k u_k^m} \qquad (32) $$

Therefore, the ability of IEMs to selectively separate ions arises from disparities in the sorption and migration behaviors of ions i and k. The key determinants influencing the discrimination between ions include the valence (and polarity) of the ions (z), the activity coefficient in the membrane ($y^m$), and the ions' absolute mobility within the membrane ($u^m$).

The ion selectivity capabilities of IEMs can be structured into (i) their charge selectivity (e.g., chlor-alkali process [95]), (ii) valence selectivity (e.g., recovering Li⁺ from Mg²⁺ in lithium-rich brines [96]), and (iii) specific ion selectivity (e.g., separation of Li, Ni, Mn, and Co from LiNi₀.₃₃Mn₀.₃₃Co₀.₃₃O₂ for battery recycling [97]). Selectivity can also be studied between the crossover of uncharged molecule and ions within IEMs and can be systematically divided into two key areas: (iv) ion/solvent selectivity (e.g., solvent crossover [98]) and (v) ion/uncharged solute selectivity (e.g., mixing of dissolved H₂ and O₂(g) creating hazardous situation [99] or vanadium ions cross-over in vanadium redox flow battery [100]). Several detailed reviews focusing on the fundamentals [80,85] or modeling [101] of those aspects are reported in the literature.

### 2.4.5. Permeability-selectivity balance

The permeability of an IEM towards a specific ion is foundational to the efficiency of most IEM processes. Membrane permeance is defined as the ion flux per unit driving force, and when this value is multiplied by the membrane's thickness, it yields the membrane's permeability $L_p$ (L m⁻² s⁻¹ bar⁻¹).

Ionic conductivity $\sigma_i$ (S m⁻¹) emerges as a significant parameter. This measure is not an intrinsic membrane property but is influenced by operational conditions such as the concentrations of solutions involved [102]. A higher $\sigma_i$ suggests more efficient ion transport, implying that a membrane with higher ionic conductivity for a particular ion would require less surface area to achieve a specific separation yield, potentially reducing both capital and operational costs [103]. However, the pursuit of increased ionic conductivity often leads to a decrease in selectivity, particularly in the discrimination between counter-ions and co-ions. The compromise between conductivity and selectivity is attributed to the alteration in the membrane's water content, steric effects and the density of fixed charges within the membrane which affects the ion transport pathways [104,105].

Within ED apparatuses, it has been noted that the membrane's thickness significantly influences the overall performance of the cell. Thicker membranes tend to elevate the cell's resistance. On the contrary, thinner membranes decrease the area-specific resistance but concurrently cause an increase in the crossover flux of reactants, which is proportionally related to selectivity [106]. This not only leads to diminished power efficiency but also accelerates the rate of degradation, affecting the system's longevity adversely. Employing thinner

membranes can also serve to lower the costs associated with materials, presenting an advantageous aspect for the commercial viability. Consequently, there is a discernible compromise among cost reduction, enhanced performance, and longevity [107]. A recent examination conducted by researchers at General Motors [108] on fuel cell membranes revealed that the interplay between conductivity and permeability due to varying membrane thickness has a direct correlation with both the durability and the total cost of ownership. Enhancements in conductivity are beneficial for increasing power density and diminishing the cost of the stack, whereas an increase in gas crossover (i.e., permeability) elevates fuel expenses and detracts from the membrane's and the system's operational lifespan.

This trade-off is analyzed through the lens of sorption-migration transport equation (Eq. (32)). The flux of ion i, and thus its conductivity $\sigma_i$, can be enhanced by either increasing (i) the ion's concentration within the membrane or (ii) its mobility. The sorption of ion i is governed by its activity coefficient ($C_i^m \propto 1/\gamma_i^m$), which dictates how readily the ion is absorbed into the membrane. For improved conductivity, conditions that lower the activity coefficient and increase the ion's mobility ($u^m$) are preferred. Conversely, enhancing selectivity ($S_{i,k}$) involves optimizing the relative sorption and mobility ratios of ions i and k, aiming for conditions where the activity coefficient ratio is low ($\gamma_i^m/\gamma_k^m$) and the mobility ratio is high ($u_i^m/u_k^m$).

This nuanced understanding of the conductivity-selectivity trade-off in IEMs underscores the challenges in optimizing membrane performance for specific applications. It highlights the need for a balanced approach in membrane design, where enhancements in selectivity or conductivity are achieved without significantly compromising the other metric [109].

## 3. Advances in membrane materials and fabrication techniques

In the context of ED, the development of new electrode materials is not an active area of research, as it is not a limiting factor in the process. However, concerning membrane technology and selectivity optimization, significant advancements have been made in the development of innovative membrane materials, each addressing specific challenges and applications in the field of separation processes. The recent advancements in both robust and efficient AEM and BPM have enabled the industrial-scale development of ED. The following sections will concisely present the state of the art concerning (i) membrane materials, (ii) advances in fabrication and finally (iii) IEM performance characterization methods.

### 3.1. AEM materials

AEMs must operate effectively within alkaline environments to fulfill their roles. To position AEM technologies as viable alternatives to current CEM and Nafion® solutions, ongoing research is intensively directed towards enhancing both the conductivity and longevity of these membranes under such challenging conditions [110]. The European Union's Horizon2020 initiative, through its FCG-02-4-2019 call for projects (ANIONE [111], CHANNEL [112] and NEWELY [113]), has established specific targets (stability of 2000 h, hydroxide conductivity of 50 mS cm⁻¹, etc. [114]). Among these, durability emerges as a paramount objective, pursued through a variety of strategies focusing on the selection of ionic functionalities and the structural composition of the polymer backbone.

#### 3.1.1. Functional carriers

In AEMs, ionic functionalities comprise cationic groups containing heteroatoms such as nitrogen, phosphorus, sulfur, or metallic cations.

##### 3.1.1.1. Quaternary ammoniums
Quaternary ammoniums are characterized by a N atom substituted by four groups, forming a cation, and are
$$ SEC = \int_{0}^{t} \frac{p^{\text{d}} + p^{\text{h}}}{\dot{q}} \times dt \qquad (31) $$

where $\dot{q}$ the stack flow rate (m³/s).

### 2.4.4. Ion selectivity

In conditions where electromigration is the prevailing mechanism, outstripping the effects of diffusion and convection, the ion flux described in Eq. (21) can be simplified accordingly to $J_i \approx -\frac{z_i D_i^m F C_i^m}{RT} \times \frac{d\phi^m}{dx}$. This simplification is feasible because each ion species is subjected to an identical gradient in the transmembrane electrostatic potential. Consequently, it becomes possible to express the fluxes of different ions, normalized by their concentrations [80], as in Eq. (32).

$$ S_{i,k} = \frac{J_i C_k^s}{J_k C_i^s} \approx \frac{K_i}{K_k} \times \frac{z_i u_i^m}{z_k u_k^m} = \frac{\gamma_i^s \gamma_k^m}{\gamma_k^m \gamma_i^m} \times \exp \left[ - \frac{(z_i - z_k)F}{RT} \times \Delta\phi_D \right] \times \frac{z_i u_i^m}{z_k u_k^m} \qquad (32) $$

Therefore, the ability of IEMs to selectively separate ions arises from disparities in the sorption and migration behaviors of ions i and k. The key determinants influencing the discrimination between ions include the valence (and polarity) of the ions (z), the activity coefficient in the membrane ($y^m$), and the ions' absolute mobility within the membrane ($u^m$).

The ion selectivity capabilities of IEMs can be structured into (i) their charge selectivity (e.g., chlor-alkali process [95]), (ii) valence selectivity (e.g., recovering Li⁺ from Mg²⁺ in lithium-rich brines [96]), and (iii) specific ion selectivity (e.g., separation of Li, Ni, Mn, and Co from LiNi₀.₃₃Mn₀.₃₃Co₀.₃₃O₂ for battery recycling [97]). Selectivity can also be studied between the crossover of uncharged molecule and ions within IEMs and can be systematically divided into two key areas: (iv) ion/solvent selectivity (e.g., solvent crossover [98]) and (v) ion/uncharged solute selectivity (e.g., mixing of dissolved H₂ and O₂(g) creating hazardous situation [99] or vanadium ions cross-over in vanadium redox flow battery [100]). Several detailed reviews focusing on the fundamentals [80,85] or modeling [101] of those aspects are reported in the literature.

### 2.4.5. Permeability-selectivity balance

The permeability of an IEM towards a specific ion is foundational to the efficiency of most IEM processes. Membrane permeance is defined as the ion flux per unit driving force, and when this value is multiplied by the membrane's thickness, it yields the membrane's permeability $L_p$ (L m⁻² s⁻¹ bar⁻¹).

Ionic conductivity $\sigma_i$ (S m⁻¹) emerges as a significant parameter. This measure is not an intrinsic membrane property but is influenced by operational conditions such as the concentrations of solutions involved [102]. A higher $\sigma_i$ suggests more efficient ion transport, implying that a membrane with higher ionic conductivity for a particular ion would require less surface area to achieve a specific separation yield, potentially reducing both capital and operational costs [103]. However, the pursuit of increased ionic conductivity often leads to a decrease in selectivity, particularly in the discrimination between counter-ions and co-ions. The compromise between conductivity and selectivity is attributed to the alteration in the membrane's water content, steric effects and the density of fixed charges within the membrane which affects the ion transport pathways [104,105].

Within ED apparatuses, it has been noted that the membrane's thickness significantly influences the overall performance of the cell. Thicker membranes tend to elevate the cell's resistance. On the contrary, thinner membranes decrease the area-specific resistance but concurrently cause an increase in the crossover flux of reactants, which is proportionally related to selectivity [106]. This not only leads to diminished power efficiency but also accelerates the rate of degradation, affecting the system's longevity adversely. Employing thinner

membranes can also serve to lower the costs associated with materials, presenting an advantageous aspect for the commercial viability. Consequently, there is a discernible compromise among cost reduction, enhanced performance, and longevity [107]. A recent examination conducted by researchers at General Motors [108] on fuel cell membranes revealed that the interplay between conductivity and permeability due to varying membrane thickness has a direct correlation with both the durability and the total cost of ownership. Enhancements in conductivity are beneficial for increasing power density and diminishing the cost of the stack, whereas an increase in gas crossover (i.e., permeability) elevates fuel expenses and detracts from the membrane's and the system's operational lifespan.

This trade-off is analyzed through the lens of sorption-migration transport equation (Eq. (32)). The flux of ion i, and thus its conductivity $\sigma_i$, can be enhanced by either increasing (i) the ion's concentration within the membrane or (ii) its mobility. The sorption of ion i is governed by its activity coefficient ($C_i^m \propto 1/\gamma_i^m$), which dictates how readily the ion is absorbed into the membrane. For improved conductivity, conditions that lower the activity coefficient and increase the ion's mobility ($u^m$) are preferred. Conversely, enhancing selectivity ($S_{i,k}$) involves optimizing the relative sorption and mobility ratios of ions i and k, aiming for conditions where the activity coefficient ratio is low ($\gamma_i^m/\gamma_k^m$) and the mobility ratio is high ($u_i^m/u_k^m$).

This nuanced understanding of the conductivity-selectivity trade-off in IEMs underscores the challenges in optimizing membrane performance for specific applications. It highlights the need for a balanced approach in membrane design, where enhancements in selectivity or conductivity are achieved without significantly compromising the other metric [109].

## 3. Advances in membrane materials and fabrication techniques

In the context of ED, the development of new electrode materials is not an active area of research, as it is not a limiting factor in the process. However, concerning membrane technology and selectivity optimization, significant advancements have been made in the development of innovative membrane materials, each addressing specific challenges and applications in the field of separation processes. The recent advancements in both robust and efficient AEM and BPM have enabled the industrial-scale development of ED. The following sections will concisely present the state of the art concerning (i) membrane materials, (ii) advances in fabrication and finally (iii) IEM performance characterization methods.

### 3.1. AEM materials

AEMs must operate effectively within alkaline environments to fulfill their roles. To position AEM technologies as viable alternatives to current CEM and Nafion® solutions, ongoing research is intensively directed towards enhancing both the conductivity and longevity of these membranes under such challenging conditions [110]. The European Union's Horizon2020 initiative, through its FCG-02-4-2019 call for projects (ANIONE [111], CHANNEL [112] and NEWELY [113]), has established specific targets (stability of 2000 h, hydroxide conductivity of 50 mS cm⁻¹, etc. [114]). Among these, durability emerges as a paramount objective, pursued through a variety of strategies focusing on the selection of ionic functionalities and the structural composition of the polymer backbone.

#### 3.1.1. Functional carriers

In AEMs, ionic functionalities comprise cationic groups containing heteroatoms such as nitrogen, phosphorus, sulfur, or metallic cations.

##### 3.1.1.1. Quaternary ammoniums
Quaternary ammoniums are characterized by a N atom substituted by four groups, forming a cation, and are
widely studied for AEM development due to their straightforward and cost-effective synthesis. However, their lifespan in alkaline conditions is limited by various degradation mechanisms, with propyl-trimethyl amine exhibiting a half-life of only 33.2 h in strong alkaline conditions (6 mol/L NaOH), including nucleophilic substitution ($S_N2$ reaction), Hofmann elimination, Stevens rearrangement, Sommelet-Hauser rearrangement, and 1,4-elimination [115]. The most concerning are nucleophilic substitution and elimination reactions, involving carbons adjacent and next to the N atom, respectively.

To improve longevity, tetramethylammonium (TMA) [116] and benzyl trimethylammonium (BTMA) [117] derivatives have been studied, showing enhanced resistance to degradation, though challenges persist in integrating them into membranes. Innovations in membrane design, including the use of side chains and multi-cation chains, aim to counteract these issues but often face trade-offs between ionic conductivity and stability [118]. Notably, cyclic and spirocyclic ammonium structures have emerged as highly promising for their remarkable stability in harsh alkaline environments, attributed to their unique geometric configurations that resist common degradation reactions [119,120].

### 3.1.1.2. Imidazoles.
Imidazoles are aromatic heterocyclic compounds with a 5-atom ring, including two N atoms. When both N atoms are substituted, imidazole forms a cation with charge delocalization across the ring. Imidazoles are readily synthesized and converted into cations through alkylation [121]. The stability of imidazole derivatives in alkaline conditions varies significantly with the substitution pattern on the ring. Unsubstituted imidazoles are particularly prone to degradation, including ring-opening and deprotonation reactions. However, strategic substitutions at specific positions on the imidazole ring can enhance stability. For instance, substituents at the carbon between the N atoms (C2) or on the N itself can prevent degradation, with aryl groups providing better protection than benzyl groups. Additionally, substitutions at the outer carbons (C4 and C5) effectively inhibit degradation, likely due to steric hindrance and electronic effects, including resonance stabilization [116,122]. Hugar et al. demonstrated that certain imidazole derivatives, especially those with mesityl groups or bis-substituted with aryl groups, exhibit remarkable resistance to alkaline degradation, showing less than 1 % degradation after extensive exposure to harsh conditions [122].

### 3.1.1.3. Guanidiums.
Guanidiniums, derivatives of guanidine where nitrogen bounded by a double bond to a carbon is quaternary, feature a charge delocalized across the nitrogen and carbon. This characteristic can enhance the catalytic properties of platinum and other metals supported on carbon in oxygen oxidation and reduction reactions [121]. However, the guanidinium group is susceptible to addition reactions in alkaline environments, risking the elimination of the quaternary nitrogen. To counteract this, the introduction of sterically hindering groups, such as ethyl substituents on the N atoms, has been shown to limit degradation, with compounds exhibiting less than 10 % degradation after 312 h in a 1 mol/L KOH solution at 60 °C [123].

### 3.1.1.4. Quaternary phosphoniums.
Beyond N, phosphorus atoms can also bear cationic charges as in quaternary phosphonium ions. These ions, susceptible to nucleophilic attacks and α- and β-eliminations like ammonium ions, face additional vulnerability to direct OH⁻ attacks on the phosphorus, leading to phosphonium group detachment due to phosphorus's oxophilic nature [121].

Enhancing the stability of these cations can be achieved through phenolic substitutions, which donate electrons to the phosphorus, thus conjugating and stabilizing it against degradation. For instance, the MTPP-(2,4,6-Me) degrades only 10 % after 2000 h in 1 mol/L KOH at 80 °C [124].

The tetra(dialkylamino)phosphonium family showcases a different

stabilization strategy, where alkyl or cyclohexyl substituents mitigate degradation through structural reinforcement, reducing susceptibility to nucleophilic and elimination reactions [125,126]. This approach is exemplified by membranes such as TPQPOH, which exhibit low anionic conductivity (27 mS cm⁻¹) but high resistance to degradation (less than 1 % degradation over 720 h), underscoring the potential of tailored substituents in enhancing the durability of phosphonium-based materials in harsh environments [127].

#### 3.1.1.5. Organometallic cations.
Multivalent metal cations can coordinate with multiple anions, enhancing IEC, evident in ruthenium, nickel, and cobalt cations. Ru-based cations show good alkaline stability, but AEMs incorporating them have relatively low conductivities comparable to quaternary ammoniums and, due to their cost, remain of limited interest. Conversely, nickel serves both as an ionic conductor and a cross-linker to form ionic clusters, yet membranes containing it suffer from mechanical properties unsuitable for ED applications [121]. In addition, tetra-tert-butyl cobaltocene undergoes only 8.2 % degradation after 1000 h in 5 mol/L KOH at 80 °C [128], and octamethyl cobaltocene 8.5 % degradation after 1000 h in 1 mol/L NaOH at 140 °C [129].

### 3.1.2. Backbones

In the exploration of polymer backbones for enhanced stability in alkaline environments, the focus has shifted towards developing polymers beyond traditional aryl ether-based polymers like PEEK, PSU, and PPO. These conventional polymers are vulnerable to nucleophilic attacks, prompting the search for more resistant skeletal structures without ethers [130].

Radiative grafting has emerged as a promising method to modify commercial polyolefins and fluoropolymers, such as ETFE, HDPE, and LDPE, with BTMA [110]. This technique allows for the direct attachment of BTMA onto these polymers, yielding membranes with high conductivity and variable stability against alkaline degradation.

Polynorbornene (PNB) synthesized via ring-opening metathesis polymerization (ROMP) offer another avenue, leveraging the ROMP method's ability to create polymers with complex architectures. These polymers can achieve high conductivity and low degradation rates in alkaline solutions, with enhanced performance through strategic modifications such as side chains and cross-linking [110,130].

Synthesized through Diels-Alder polymerization, polyfluorenes and polyphenylenes via metal-catalyzed coupling reactions (Suzuki-Miyaura and Yamamoto couplings), represent advanced approaches to polymer backbone development [110,130]. These methods provide pathways to easily incorporate functional groups like quaternary ammoniums into the polymer structure, although they differ in synthesis complexities and polymer properties [131,132].

Acid-catalyzed polycondensation offers a route to synthesize ether-free, metal-free polyaromatics with high molecular weight, demonstrating significant potential [130,133].

### 3.2. CEM materials

CEMs are currently prevalent in a variety of industrial applications, including fuel cells, electrolysis, ED, and vanadium flow batteries. Predominantly, these membranes are based on perfluorosulfonic acid (PFSA, -CF₂SO₃H) materials. Originating from Dupont's innovation in the 1960s, marketed under the brand name Nafion®, this copolymer foundation is similarly employed in the development of Solvay's Aquilion®, Flemion®, Hyflon®, Dow®, Aciplex® or BAM3G® and Gore-Select® membranes [134]. The key benefits of using this polymer include its notable ionic conductivity, excellent chemical resistance, especially against oxidation, and its satisfactory mechanical durability. However, its production is relatively expensive, and the degradation process releases environmentally harmful perfluorosulfonic and perfluorocarboxylic acids due to the presence of perfluorinated groups
widely studied for AEM development due to their straightforward and cost-effective synthesis. However, their lifespan in alkaline conditions is limited by various degradation mechanisms, with propyl-trimethyl amine exhibiting a half-life of only 33.2 h in strong alkaline conditions (6 mol/L NaOH), including nucleophilic substitution ($S_N2$ reaction), Hofmann elimination, Stevens rearrangement, Sommelet-Hauser rearrangement, and 1,4-elimination [115]. The most concerning are nucleophilic substitution and elimination reactions, involving carbons adjacent and next to the N atom, respectively.

To improve longevity, tetramethylammonium (TMA) [116] and benzyl trimethylammonium (BTMA) [117] derivatives have been studied, showing enhanced resistance to degradation, though challenges persist in integrating them into membranes. Innovations in membrane design, including the use of side chains and multi-cation chains, aim to counteract these issues but often face trade-offs between ionic conductivity and stability [118]. Notably, cyclic and spirocyclic ammonium structures have emerged as highly promising for their remarkable stability in harsh alkaline environments, attributed to their unique geometric configurations that resist common degradation reactions [119,120].

### 3.1.1.2. Imidazoles.
Imidazoles are aromatic heterocyclic compounds with a 5-atom ring, including two N atoms. When both N atoms are substituted, imidazole forms a cation with charge delocalization across the ring. Imidazoles are readily synthesized and converted into cations through alkylation [121]. The stability of imidazole derivatives in alkaline conditions varies significantly with the substitution pattern on the ring. Unsubstituted imidazoles are particularly prone to degradation, including ring-opening and deprotonation reactions. However, strategic substitutions at specific positions on the imidazole ring can enhance stability. For instance, substituents at the carbon between the N atoms (C2) or on the N itself can prevent degradation, with aryl groups providing better protection than benzyl groups. Additionally, substitutions at the outer carbons (C4 and C5) effectively inhibit degradation, likely due to steric hindrance and electronic effects, including resonance stabilization [116,122]. Hugar et al. demonstrated that certain imidazole derivatives, especially those with mesityl groups or bis-substituted with aryl groups, exhibit remarkable resistance to alkaline degradation, showing less than 1 % degradation after extensive exposure to harsh conditions [122].

### 3.1.1.3. Guanidiums.
Guanidiniums, derivatives of guanidine where nitrogen bounded by a double bond to a carbon is quaternary, feature a charge delocalized across the nitrogen and carbon. This characteristic can enhance the catalytic properties of platinum and other metals supported on carbon in oxygen oxidation and reduction reactions [121]. However, the guanidinium group is susceptible to addition reactions in alkaline environments, risking the elimination of the quaternary nitrogen. To counteract this, the introduction of sterically hindering groups, such as ethyl substituents on the N atoms, has been shown to limit degradation, with compounds exhibiting less than 10 % degradation after 312 h in a 1 mol/L KOH solution at 60 °C [123].

### 3.1.1.4. Quaternary phosphoniums.
Beyond N, phosphorus atoms can also bear cationic charges as in quaternary phosphonium ions. These ions, susceptible to nucleophilic attacks and α- and β-eliminations like ammonium ions, face additional vulnerability to direct OH⁻ attacks on the phosphorus, leading to phosphonium group detachment due to phosphorus's oxophilic nature [121].

Enhancing the stability of these cations can be achieved through phenolic substitutions, which donate electrons to the phosphorus, thus conjugating and stabilizing it against degradation. For instance, the MTPP-(2,4,6-Me) degrades only 10 % after 2000 h in 1 mol/L KOH at 80 °C [124].

The tetra(dialkylamino)phosphonium family showcases a different

stabilization strategy, where alkyl or cyclohexyl substituents mitigate degradation through structural reinforcement, reducing susceptibility to nucleophilic and elimination reactions [125,126]. This approach is exemplified by membranes such as TPQPOH, which exhibit low anionic conductivity (27 mS cm⁻¹) but high resistance to degradation (less than 1 % degradation over 720 h), underscoring the potential of tailored substituents in enhancing the durability of phosphonium-based materials in harsh environments [127].

#### 3.1.1.5. Organometallic cations.
Multivalent metal cations can coordinate with multiple anions, enhancing IEC, evident in ruthenium, nickel, and cobalt cations. Ru-based cations show good alkaline stability, but AEMs incorporating them have relatively low conductivities comparable to quaternary ammoniums and, due to their cost, remain of limited interest. Conversely, nickel serves both as an ionic conductor and a cross-linker to form ionic clusters, yet membranes containing it suffer from mechanical properties unsuitable for ED applications [121]. In addition, tetra-tert-butyl cobaltocene undergoes only 8.2 % degradation after 1000 h in 5 mol/L KOH at 80 °C [128], and octamethyl cobaltocene 8.5 % degradation after 1000 h in 1 mol/L NaOH at 140 °C [129].

### 3.1.2. Backbones

In the exploration of polymer backbones for enhanced stability in alkaline environments, the focus has shifted towards developing polymers beyond traditional aryl ether-based polymers like PEEK, PSU, and PPO. These conventional polymers are vulnerable to nucleophilic attacks, prompting the search for more resistant skeletal structures without ethers [130].

Radiative grafting has emerged as a promising method to modify commercial polyolefins and fluoropolymers, such as ETFE, HDPE, and LDPE, with BTMA [110]. This technique allows for the direct attachment of BTMA onto these polymers, yielding membranes with high conductivity and variable stability against alkaline degradation.

Polynorbornene (PNB) synthesized via ring-opening metathesis polymerization (ROMP) offer another avenue, leveraging the ROMP method's ability to create polymers with complex architectures. These polymers can achieve high conductivity and low degradation rates in alkaline solutions, with enhanced performance through strategic modifications such as side chains and cross-linking [110,130].

Synthesized through Diels-Alder polymerization, polyfluorenes and polyphenylenes via metal-catalyzed coupling reactions (Suzuki-Miyaura and Yamamoto couplings), represent advanced approaches to polymer backbone development [110,130]. These methods provide pathways to easily incorporate functional groups like quaternary ammoniums into the polymer structure, although they differ in synthesis complexities and polymer properties [131,132].

Acid-catalyzed polycondensation offers a route to synthesize ether-free, metal-free polyaromatics with high molecular weight, demonstrating significant potential [130,133].

### 3.2. CEM materials

CEMs are currently prevalent in a variety of industrial applications, including fuel cells, electrolysis, ED, and vanadium flow batteries. Predominantly, these membranes are based on perfluorosulfonic acid (PFSA, -CF₂SO₃H) materials. Originating from Dupont's innovation in the 1960s, marketed under the brand name Nafion®, this copolymer foundation is similarly employed in the development of Solvay's Aquilion®, Flemion®, Hyflon®, Dow®, Aciplex® or BAM3G® and Gore-Select® membranes [134]. The key benefits of using this polymer include its notable ionic conductivity, excellent chemical resistance, especially against oxidation, and its satisfactory mechanical durability. However, its production is relatively expensive, and the degradation process releases environmentally harmful perfluorosulfonic and perfluorocarboxylic acids due to the presence of perfluorinated groups
[135]. Additionally, its application at temperatures exceeding 100 °C poses challenges due to a decrease in mechanical strength and the necessity for hydration to maintain conductivity. Altering the polymer structure to introduce new functional groups or to create a copolymer tailored for specific applications presents significant difficulties [136].

In this section, two strategies are presented for the creation of advanced generations of CEM. The first strategy involves subjecting PFSA to various treatments or engaging in its hybridization. The second strategy concentrates on the development of innovative polymers.

### 3.2.1. Enhancements to polymer properties

Modifying the PFSA polymer's electrical conductivity, resistance, water retention, and mechanical properties through alterations in its chemical structure presents considerable challenges. Nonetheless, advancements in treatment methodologies, preparation protocols, and hybridization approaches have shown potential to induce these changes effectively, as cataloged comprehensively by Karimi et al. [137]. Thermal treatments influence the crystalline architecture of PFSA membranes, with the effects varying substantially based on the temperature and method of the treatment. These processes, which include annealing in controlled environments such as ovens or through wet methods involving boiling solutions, modify the crystalline state towards equilibrium, thus affecting the membrane's water uptake and conductivity. High temperatures, however, might increase crystallinity, thereby hindering the polymer's flexibility and functional performance [138–141]. Employed primarily to prepare PFSA membranes for applications in fuel cells and electrochemical devices, acid and peroxide treatments target the removal of organic residues and enhance proton conductivity by protonation at the anionic sites of PFSA. The choice of acid is critical, requiring a dissociation capability superior to the PFSA's acidic groups to achieve effective protonation, as demonstrated by the distinct protonation levels achieved with different acids [142]. These treatments not only refine the IEC but also modulate the membrane's water absorption and electrical resistance, tailoring it for specific ion exchange applications. Alternative strategies, such as exposure to supercritical CO₂ or subjecting PFSA membranes to electric fields, have been utilized to manipulate the membrane properties further. These treatments aim to enhance crystallinity and align the copolymer blocks and ionic clusters within the membrane, thereby facilitating improved pathway formation for proton conduction and achieving significant increases in conductivity [143,144]. Hybridization of PFSA membranes with polymers like PTFE [137], or inorganic NPs like titanium dioxide (TiO₂) and silicon dioxide (SiO₂) introduces additional properties into the base material [145]. These composites enhance mechanical strength and water uptake through the formation of new ionic clusters around the NPs. Moreover, the size and surface functionalization of these nanoparticles are critical; smaller, functionalized nanoparticles significantly enhance conductivity by forming efficient conduction paths and promoting mechanisms beneficial under varying humidity conditions [146–148]. Such modifications also protect the membrane from radical-induced degradation, crucial for maintaining long-term stability and performance in electrochemical applications.

It should be noted that the primary objective must be to do without PFSA groups, which are now recognized worldwide as an eternal pollutant harmful to our environment.

### 3.2.2. Advancements in the field of new ionic groups and backbones

Despite the advantageous attributes of PFSA membranes, innovative polymer families have been introduced as alternatives for CEMs. These advancements aim to identify membranes that offer similar conductivity and degradation resistance as PFSA membranes during operational use, while being more cost-effective to produce and fluorine-free, thereby lessening their environmental footprint. Similar to the case with AEMs, the characteristics of these membranes are influenced by both their functional groups and structural frameworks. The frameworks designed for CEMs are similar to those for AEMs, and as such, will not be

extensively elaborated on in this section.

#### 3.2.2.1. Ionic groups.
CEMs can incorporate various functional groups that are easily deprotonatable acids, such as the sulfonic group $-SO_3H$ in PFSA membranes. These groups' pKa values influence membrane conductivity; higher pKa correlates with higher conductivity, yet selection also considers stability and resistance to degradation [110]. For instance, sulfonimide groups offer superior proton conductivity but are oxidation-prone, limiting their application. Conversely, carboxylic acid groups, despite their moderate high pKa value (4–5) and resulting low conductivity, can enhance membrane chemical and thermal stability, especially when combined with sulfonic acid and used in high-temperature applications through cross-linking methods like terephthalic dihydrazide [149,150].

#### 3.2.2.2. Backbones.
Backbones containing heteroatoms, such as SPEEK or SPPS, are easily synthesized through polycondensation and require a higher IEC than PFSA due to their less hydrophobic nature, affecting phase separation and mechanical properties [110]. Strategies to enhance phase separation include (i) separating the functional group from the backbone with a flexible chain [151], (ii) utilizing copolymer architectures [152], (iii) adding side chains [153], and (iv) increasing sulfonation density [154]. Despite these strategies, the presence of heteroatoms makes the polymers prone to oxidation and radical attacks. Various works developing novel polymers such as fluorinated polystyrenes [110], organized sulfonated polyethylene [155] or polyphenylenes [156,157], have been published over the years.

## 3.3. Bipolar membrane materials

BMs bear resemblance to p-n junction semiconductors, with the junction at the BM's interfacial layer (IL) acting as a depletion zone. The fabrication of BMs traditionally involves the layer-by-layer deposition of CEL and AEL materials, or by physically bonding CEL and AEL through the application of external heat and pressure or employing adhesives. Through these fabrication techniques, a thin, modified IL emerges between the CEL and AEL, facilitating the production of protons and hydroxide ions. At the CEL interface, a higher pKa value for a functional group enhances the dissociation kinetics. Hence, the sulfonic group, with a pKa of 1–2, is less suitable compared to carboxylic and phosphonic groups, which have pKa values of 4–6 and 3–7, respectively [158]. On the AEL side, primary, secondary, or tertiary amines [159], tertiary ammoniums, pyridyls, or imidazole are preferred. It is crucial that the materials employed in both CEL and AEL facilitate efficient ion transport to achieve optimal ionic conductivity in membranes. To this end, strong ionic groups such as sulfonic acid for CELs and quaternary ammonium or pyridinium for AELS are essential. A promising approach involves the encapsulation of catalysts within the IL to introduce alternative pathways for the dissociation reaction. This necessitates incorporating a specific catalytic layer at the ion exchange layers' interface, which can be a polymer containing weak acid functions like pyridyl, amino, carboxylic, sulfonic, and ammonium groups, showing promise. Alternatively, the polymer may be designed as a dendrimer, such as PAMAM [160] or Boltorn® series [161], whose branched structure enables a high concentration of catalytic groups. The recent use of metal–organic framework (MOF on the metal or ligand site) [162] or graphene catalyst [163] has also been reported in the literature.

The above solutions are starting to be developed on an industrial scale. Recent literature [41,44,164–167] provides a wealth of tabulated information on the characteristics (e.g., manufacturer, functional groups, composition, performance, etc.) of various commercial membranes, including AEM, CEM and BM, available on the market.
[135]. Additionally, its application at temperatures exceeding 100 °C poses challenges due to a decrease in mechanical strength and the necessity for hydration to maintain conductivity. Altering the polymer structure to introduce new functional groups or to create a copolymer tailored for specific applications presents significant difficulties [136].

In this section, two strategies are presented for the creation of advanced generations of CEM. The first strategy involves subjecting PFSA to various treatments or engaging in its hybridization. The second strategy concentrates on the development of innovative polymers.

### 3.2.1. Enhancements to polymer properties

Modifying the PFSA polymer's electrical conductivity, resistance, water retention, and mechanical properties through alterations in its chemical structure presents considerable challenges. Nonetheless, advancements in treatment methodologies, preparation protocols, and hybridization approaches have shown potential to induce these changes effectively, as cataloged comprehensively by Karimi et al. [137]. Thermal treatments influence the crystalline architecture of PFSA membranes, with the effects varying substantially based on the temperature and method of the treatment. These processes, which include annealing in controlled environments such as ovens or through wet methods involving boiling solutions, modify the crystalline state towards equilibrium, thus affecting the membrane's water uptake and conductivity. High temperatures, however, might increase crystallinity, thereby hindering the polymer's flexibility and functional performance [138–141]. Employed primarily to prepare PFSA membranes for applications in fuel cells and electrochemical devices, acid and peroxide treatments target the removal of organic residues and enhance proton conductivity by protonation at the anionic sites of PFSA. The choice of acid is critical, requiring a dissociation capability superior to the PFSA's acidic groups to achieve effective protonation, as demonstrated by the distinct protonation levels achieved with different acids [142]. These treatments not only refine the IEC but also modulate the membrane's water absorption and electrical resistance, tailoring it for specific ion exchange applications. Alternative strategies, such as exposure to supercritical CO₂ or subjecting PFSA membranes to electric fields, have been utilized to manipulate the membrane properties further. These treatments aim to enhance crystallinity and align the copolymer blocks and ionic clusters within the membrane, thereby facilitating improved pathway formation for proton conduction and achieving significant increases in conductivity [143,144]. Hybridization of PFSA membranes with polymers like PTFE [137], or inorganic NPs like titanium dioxide (TiO₂) and silicon dioxide (SiO₂) introduces additional properties into the base material [145]. These composites enhance mechanical strength and water uptake through the formation of new ionic clusters around the NPs. Moreover, the size and surface functionalization of these nanoparticles are critical; smaller, functionalized nanoparticles significantly enhance conductivity by forming efficient conduction paths and promoting mechanisms beneficial under varying humidity conditions [146–148]. Such modifications also protect the membrane from radical-induced degradation, crucial for maintaining long-term stability and performance in electrochemical applications.

It should be noted that the primary objective must be to do without PFSA groups, which are now recognized worldwide as an eternal pollutant harmful to our environment.

### 3.2.2. Advancements in the field of new ionic groups and backbones

Despite the advantageous attributes of PFSA membranes, innovative polymer families have been introduced as alternatives for CEMs. These advancements aim to identify membranes that offer similar conductivity and degradation resistance as PFSA membranes during operational use, while being more cost-effective to produce and fluorine-free, thereby lessening their environmental footprint. Similar to the case with AEMs, the characteristics of these membranes are influenced by both their functional groups and structural frameworks. The frameworks designed for CEMs are similar to those for AEMs, and as such, will not be

extensively elaborated on in this section.

#### 3.2.2.1. Ionic groups.
CEMs can incorporate various functional groups that are easily deprotonatable acids, such as the sulfonic group $-SO_3H$ in PFSA membranes. These groups' pKa values influence membrane conductivity; higher pKa correlates with higher conductivity, yet selection also considers stability and resistance to degradation [110]. For instance, sulfonimide groups offer superior proton conductivity but are oxidation-prone, limiting their application. Conversely, carboxylic acid groups, despite their moderate high pKa value (4–5) and resulting low conductivity, can enhance membrane chemical and thermal stability, especially when combined with sulfonic acid and used in high-temperature applications through cross-linking methods like terephthalic dihydrazide [149,150].

#### 3.2.2.2. Backbones.
Backbones containing heteroatoms, such as SPEEK or SPPS, are easily synthesized through polycondensation and require a higher IEC than PFSA due to their less hydrophobic nature, affecting phase separation and mechanical properties [110]. Strategies to enhance phase separation include (i) separating the functional group from the backbone with a flexible chain [151], (ii) utilizing copolymer architectures [152], (iii) adding side chains [153], and (iv) increasing sulfonation density [154]. Despite these strategies, the presence of heteroatoms makes the polymers prone to oxidation and radical attacks. Various works developing novel polymers such as fluorinated polystyrenes [110], organized sulfonated polyethylene [155] or polyphenylenes [156,157], have been published over the years.

## 3.3. Bipolar membrane materials

BMs bear resemblance to p-n junction semiconductors, with the junction at the BM's interfacial layer (IL) acting as a depletion zone. The fabrication of BMs traditionally involves the layer-by-layer deposition of CEL and AEL materials, or by physically bonding CEL and AEL through the application of external heat and pressure or employing adhesives. Through these fabrication techniques, a thin, modified IL emerges between the CEL and AEL, facilitating the production of protons and hydroxide ions. At the CEL interface, a higher pKa value for a functional group enhances the dissociation kinetics. Hence, the sulfonic group, with a pKa of 1–2, is less suitable compared to carboxylic and phosphonic groups, which have pKa values of 4–6 and 3–7, respectively [158]. On the AEL side, primary, secondary, or tertiary amines [159], tertiary ammoniums, pyridyls, or imidazole are preferred. It is crucial that the materials employed in both CEL and AEL facilitate efficient ion transport to achieve optimal ionic conductivity in membranes. To this end, strong ionic groups such as sulfonic acid for CELs and quaternary ammonium or pyridinium for AELS are essential. A promising approach involves the encapsulation of catalysts within the IL to introduce alternative pathways for the dissociation reaction. This necessitates incorporating a specific catalytic layer at the ion exchange layers' interface, which can be a polymer containing weak acid functions like pyridyl, amino, carboxylic, sulfonic, and ammonium groups, showing promise. Alternatively, the polymer may be designed as a dendrimer, such as PAMAM [160] or Boltorn® series [161], whose branched structure enables a high concentration of catalytic groups. The recent use of metal-organic framework (MOF on the metal or ligand site) [162] or graphene catalyst [163] has also been reported in the literature.

The above solutions are starting to be developed on an industrial scale. Recent literature [41,44,164–167] provides a wealth of tabulated information on the characteristics (e.g., manufacturer, functional groups, composition, performance, etc.) of various commercial membranes, including AEM, CEM and BM, available on the market.
### 3.4. IEM specification for electrodialysis

The integration of ion exchange membranes into the ED process differs from other types of membrane (e.g., ultrafiltration, nano-filtration, etc.) in 2 ways: (i) the use of BMs to vary the pH of adjacent solutions, and (ii) the use of AEM and CEM to selectively separate anions (OH⁻ and other negative ions) and cations (H⁺ and other positively charged ions). ED remains the technology of choice for BM. For IEMs of the AEM/CEM type, the use of these membranes in electrolyzers or energy storage systems needs to be distinguished with their use in ED. In the first case, the membrane is preferentially used for transporting protons or hydroxides. In the case of ED, membrane selectivity needs to be optimized to allow the passage of specific ions (other than protons and hydroxides).

Unlike conventional membranes, IEMs are distinguished not only by their material composition or pore size but by their interactions with charged molecules and the specific nature of their functional groups. Ion transport through an IEM can be broken down into five steps: (i) ions move from the dilute compartment to the membrane surface across a solution boundary layer, (ii) ions partition into the membrane at the surface, (iii) ions traverse through the bulk of the membrane, (iv) ions exit on the opposite side of the membrane surface, and (v) ions move across a solution boundary layer to the concentrate. The selectivity of counter-ions is predominantly determined during the partitioning phase and their migration through the membrane matrix and boundary layer in the electrolyte solution [59].

Consequently, charge density is a crucial factor influencing ion transport to maintain electroneutrality. Enhancing ion removal efficiency involves adjusting the charge density and incorporating specific functional groups that form hydrophilic or hydrophobic domains, thereby improving selectivity for ions of varying valences [168,169]. The selectivity of IEMs for ions with different valences arises directly from how these ions interact with the hydrophilic domains. High-valence ions exhibit higher charge densities, leading to stronger electrostatic interactions with the fixed charged groups in the hydrophilic regions. This interaction creates a greater energy barrier for their passage compared to monovalent ions. As a result, the hydrated channels within these hydrophilic domains are more conducive to the transport of monovalent ions, as they require less energy to move through the membrane [170].

The morphology of the membrane also plays a significant role in ion removal. For example, perfluorosulfonic membranes like Nafion® 117 have a homogeneous structure with uniformly sized pores and evenly distributed functional groups [171]. In contrast, the heterogeneous HDX 100 membrane shows irregular ion depletion due to a broader distribution of pore sizes and functional groups, resulting in surface concentration polarization [172]. The literature frequently documents the reduced $j_{lim}$ values observed in heterogeneous IEMs [173]. This reduction is ascribed to the existence of surface regions with varying conductance. The underlying mechanism involves the deflection of current paths as they near ion-impermeable zones, such as those associated with the reinforcing fabric or polymer binder-rich areas [174]. These deviations, from a direct trajectory observed in the case of homogeneous IEM, lead to the observed decrease in $j_{lim}$ values.

Ionic selectivity during the separation of multiple counter-ions is governed by other mechanisms. One such mechanism is the electrostatic barrier effect, which results from the varying degrees of electrostatic interaction between counter-ions and the membrane surface [175]. Counter-ions with higher valency, larger size within the same valency, or lower hydration energy tend to have stronger electrostatic affinities [176].

Another influential mechanism is the ion's affinity for water (i.e., solvation shell [177]), as described by Gibbs hydration energy, and the hydrophobicity of the membrane surface. Ions with lower hydration energy shed their water molecules more easily, facilitating their transport through the hydrophobic membrane [178].

Steric hindrance also affects ionic selectivity by restricting the partitioning of larger ions within the dense structures of IEMs. Smaller ions, typically less than a nanometer in size, can penetrate the hydrophilic pores of the membrane more rapidly. Therefore, the ease of counter-ion partitioning depends on factors such as ion size, valency, hydration energy, as well as the membrane's fixed-charge concentration and water uptake capacity [179,180]. For example, the fabrication and characterization of AEMs (fabricated with ion-exchange resins with different alkyl groups and a polymeric binder with charged functional groups) demonstrated enhanced selectivity for $NO_3^-$ over $Cl^-$.

This investigation focused on how varying the length of alkyl substituents in quaternary ammonium groups influenced membrane properties, particularly water content. The increased selectivity for $NO_3^-$ was linked to a reduction in water content, resulting in greater membrane hydrophobicity as the alkyl chain length increased. This rise in hydrophobicity, coupled with enhanced steric hindrance from larger alkyl groups, likely caused a partial loss of water molecules from the hydration shells of the counterions [170].

Moreover, other solutions studied on a lab scale are still under development, such as (i) monovalent ion perm-selective membranes (permeation of mono-valent ions, while blocking passage of multi-valent ions) [181] and (ii) mixed matrix membranes (inorganics embedded into organic polymers) [182].

### 3.5. Advances in fabrication

Crafting new materials with advantageous features for IEMs is as critical as adopting appropriate fabrication techniques to assure the membranes' quality. The conventional fabrication process, called phase inversion, involves dissolving these innovative materials in solvents, spreading the solutions on a smooth surface to form films, followed by solvent evaporation and sometimes subsequent modifications (like sulfonation or amination) to enhance the membranes' properties [36,183]. At the same time, innovative methods for preparing IEMs are being developed to enhance their structural integrity and functional characteristics.

#### 3.5.1. Polymer blending

Within the realm of IEMs, polymer blending is a pivotal technique [184], distinguished by two principal approaches: the mixing of fluorinated with non-fluorinated polymers and the combination of functional with non-functional polymers. The strategic amalgamation of these polymers aims to harness their respective strengths, enhancing IEM performance by improving ion conductivity through the introduction of water channels by ion-functionalized polymers, while mitigating water swelling and bolstering stability through the incorporation of hydrophobic polymers. This blend not only promises to refine the physical and chemical properties of IEMs but also faces the challenge of maintaining mechanical integrity amidst the diversity of materials employed, such as PVDF/SPPO [185], PAES/PPO [186] or PVA/PSSA-MA [187] for example. Yet, achieving harmony among diverse materials poses a significant hurdle, potentially leading to compromised mechanical strength in blended IEMs due to the proliferation of interfaces [164].

#### 3.5.2. Pore filling

Numerous researchers have recently developed IEMs characterized by minimal swelling and enhanced selectivity through pore-filling techniques, involving the infiltration of electrolytes into porous substrates (PAN [188], high density PE [189], PP [190], PES [191], PI [192]) as illustrated in Fig. 7. This method leverages the chemical and mechanical robustness of these substrates to effectively limit the expansion of electrolyte polymers, using either polymeric or monomeric electrolytes.

#### 3.5.3. In-situ polymerization

The conventional methods for producing IEMs often involve
### 3.4. IEM specification for electrodialysis

The integration of ion exchange membranes into the ED process differs from other types of membrane (e.g., ultrafiltration, nano-filtration, etc.) in 2 ways: (i) the use of BMs to vary the pH of adjacent solutions, and (ii) the use of AEM and CEM to selectively separate anions (OH⁻ and other negative ions) and cations (H⁺ and other positively charged ions). ED remains the technology of choice for BM. For IEMs of the AEM/CEM type, the use of these membranes in electrolyzers or energy storage systems needs to be distinguished with their use in ED. In the first case, the membrane is preferentially used for transporting protons or hydroxides. In the case of ED, membrane selectivity needs to be optimized to allow the passage of specific ions (other than protons and hydroxides).

Unlike conventional membranes, IEMs are distinguished not only by their material composition or pore size but by their interactions with charged molecules and the specific nature of their functional groups. Ion transport through an IEM can be broken down into five steps: (i) ions move from the dilute compartment to the membrane surface across a solution boundary layer, (ii) ions partition into the membrane at the surface, (iii) ions traverse through the bulk of the membrane, (iv) ions exit on the opposite side of the membrane surface, and (v) ions move across a solution boundary layer to the concentrate. The selectivity of counter-ions is predominantly determined during the partitioning phase and their migration through the membrane matrix and boundary layer in the electrolyte solution [59].

Consequently, charge density is a crucial factor influencing ion transport to maintain electroneutrality. Enhancing ion removal efficiency involves adjusting the charge density and incorporating specific functional groups that form hydrophilic or hydrophobic domains, thereby improving selectivity for ions of varying valences [168,169]. The selectivity of IEMs for ions with different valences arises directly from how these ions interact with the hydrophilic domains. High-valence ions exhibit higher charge densities, leading to stronger electrostatic interactions with the fixed charged groups in the hydrophilic regions. This interaction creates a greater energy barrier for their passage compared to monovalent ions. As a result, the hydrated channels within these hydrophilic domains are more conducive to the transport of monovalent ions, as they require less energy to move through the membrane [170].

The morphology of the membrane also plays a significant role in ion removal. For example, perfluorosulfonic membranes like Nafion® 117 have a homogeneous structure with uniformly sized pores and evenly distributed functional groups [171]. In contrast, the heterogeneous HDX 100 membrane shows irregular ion depletion due to a broader distribution of pore sizes and functional groups, resulting in surface concentration polarization [172]. The literature frequently documents the reduced $j_{lim}$ values observed in heterogeneous IEMs [173]. This reduction is ascribed to the existence of surface regions with varying conductance. The underlying mechanism involves the deflection of current paths as they near ion-impermeable zones, such as those associated with the reinforcing fabric or polymer binder-rich areas [174]. These deviations, from a direct trajectory observed in the case of homogeneous IEM, lead to the observed decrease in $j_{lim}$ values.

Ionic selectivity during the separation of multiple counter-ions is governed by other mechanisms. One such mechanism is the electrostatic barrier effect, which results from the varying degrees of electrostatic interaction between counter-ions and the membrane surface [175]. Counter-ions with higher valency, larger size within the same valency, or lower hydration energy tend to have stronger electrostatic affinities [176].

Another influential mechanism is the ion's affinity for water (i.e., solvation shell [177]), as described by Gibbs hydration energy, and the hydrophobicity of the membrane surface. Ions with lower hydration energy shed their water molecules more easily, facilitating their transport through the hydrophobic membrane [178].

Steric hindrance also affects ionic selectivity by restricting the partitioning of larger ions within the dense structures of IEMs. Smaller ions, typically less than a nanometer in size, can penetrate the hydrophilic pores of the membrane more rapidly. Therefore, the ease of counter-ion partitioning depends on factors such as ion size, valency, hydration energy, as well as the membrane's fixed-charge concentration and water uptake capacity [179,180]. For example, the fabrication and characterization of AEMs (fabricated with ion-exchange resins with different alkyl groups and a polymeric binder with charged functional groups) demonstrated enhanced selectivity for $NO_3^-$ over $Cl^-$.

This investigation focused on how varying the length of alkyl substituents in quaternary ammonium groups influenced membrane properties, particularly water content. The increased selectivity for $NO_3^-$ was linked to a reduction in water content, resulting in greater membrane hydrophobicity as the alkyl chain length increased. This rise in hydrophobicity, coupled with enhanced steric hindrance from larger alkyl groups, likely caused a partial loss of water molecules from the hydration shells of the counterions [170].

Moreover, other solutions studied on a lab scale are still under development, such as (i) monovalent ion perm-selective membranes (permeation of mono-valent ions, while blocking passage of multi-valent ions) [181] and (ii) mixed matrix membranes (inorganics embedded into organic polymers) [182].

### 3.5. Advances in fabrication

Crafting new materials with advantageous features for IEMs is as critical as adopting appropriate fabrication techniques to assure the membranes' quality. The conventional fabrication process, called phase inversion, involves dissolving these innovative materials in solvents, spreading the solutions on a smooth surface to form films, followed by solvent evaporation and sometimes subsequent modifications (like sulfonation or amination) to enhance the membranes' properties [36,183]. At the same time, innovative methods for preparing IEMs are being developed to enhance their structural integrity and functional characteristics.

#### 3.5.1. Polymer blending

Within the realm of IEMs, polymer blending is a pivotal technique [184], distinguished by two principal approaches: the mixing of fluorinated with non-fluorinated polymers and the combination of functional with non-functional polymers. The strategic amalgamation of these polymers aims to harness their respective strengths, enhancing IEM performance by improving ion conductivity through the introduction of water channels by ion-functionalized polymers, while mitigating water swelling and bolstering stability through the incorporation of hydrophobic polymers. This blend not only promises to refine the physical and chemical properties of IEMs but also faces the challenge of maintaining mechanical integrity amidst the diversity of materials employed, such as PVDF/SPPO [185], PAES/PPO [186] or PVA/PSSA-MA [187] for example. Yet, achieving harmony among diverse materials poses a significant hurdle, potentially leading to compromised mechanical strength in blended IEMs due to the proliferation of interfaces [164].

#### 3.5.2. Pore filling

Numerous researchers have recently developed IEMs characterized by minimal swelling and enhanced selectivity through pore-filling techniques, involving the infiltration of electrolytes into porous substrates (PAN [188], high density PE [189], PP [190], PES [191], PI [192]) as illustrated in Fig. 7. This method leverages the chemical and mechanical robustness of these substrates to effectively limit the expansion of electrolyte polymers, using either polymeric or monomeric electrolytes.

#### 3.5.3. In-situ polymerization

The conventional methods for producing IEMs often involve
<figure><img src="image_9.png" /><figcaption>Fig. 7. Schematic structure of the pore-filling membrane preparation based on the reaction between DMA and DABCO motifs. Adapted with permission from [193]. Copyright 2024 American Chemical Society.</figcaption></figure>

modifying pure polymers or synthesizing monomers with specific functions, processes that typically require significant amounts of harmful organic solvents (e.g., DMF, DMAc, etc. [194]). To facilitate the production of IEMs on an industrial scale in an environmentally friendly manner, the development of straightforward, quick, and green fabrication techniques is crucial. A novel solvent-free in-situ polymerization approach has been introduced to address the environmental and practical challenges posed by traditional solvent-reliant methods. This innovative technique, already investigated with different systems (BPPO/ST/DVB [195], SPEEK/PMA/PANI [196]), distinguishes itself by using liquid monomers that become an integral part of the finished membrane, thereby eliminating the need for organic solvents.

### 3.5.4. Electro-spinning

This technic, illustrated in Fig. 8 – a, has emerged as a popular method for creating continuous nanofibers, offering key benefits like a high specific surface area, increased chemical reactivity, and a cost-effective production approach [197]. The solvent electrospinning process leverages electrostatic repulsion from surface charges in the polymer solution to extend a viscoelastic jet uniaxially. This method involves a high-voltage power supply, a spinneret equipped with a needle for the polymer solution, and a grounded collector. The polymer solution, fed through the needle by a syringe pump at a controlled rate, becomes charged under high voltage. This induces electrostatic repulsion among surface charges and Coulombic forces from the external field, forming a Taylor cone. Overcoming surface tension, the jet stretches, thins, and solidifies into nanofibers as the solvent evaporates, collected as a nonwoven membrane [198]. This technique, already developed at commercial stage (Elmarco s.r.o., Liberec, Czechia and Inovenso Ltd., Istanbul, Turkey for example), allows for precise control over the nanofibers' structure (average fiber diameter often approaching 200 nm) and morphology by adjusting variables such as polymer type, solution concentration, solvent characteristics, and spinning conditions [199]. Several studies have explored the impact of size on ion-exchange nanofibers, finding that smaller diameters generally lead to improvements in IEC and ionic conductivity. For instance, research by Dong et al. [200] demonstrated in Fig. 8 – b; that Nafion® nanofibers with a diameter of 400 nm achieved a conductivity of 1.5 S cm⁻¹ (measured by electrochemical impedance spectroscopy (EIS)), highlighting the potential of nanofibers for enhancing EC separation processes. The reduction in fiber size contributes to lower internal resistance (nI<sub>ohm</sub>) and higher efficiency in these applications. The versatility of electrospinning has led to the development of numerous polymers and composite materials (PECH/PAN/DABCO [201], QPVA/PDDA [202], PBI [203] nanofibers), finding applications across various domains.

### 3.6. Basic specifications and characterization of ion-exchange membranes

Once manufactured, membrane performance can be evaluated according to several criteria, for example to optimize manufacturing conditions. Fine-tuning the properties of IEMs is a complex task due to the conflicting effects of certain parameters. For example, enhancing mechanical strength through increased cross-linking can lead to higher electrical resistance due to a lower mobility of polymer chains. The core polymer matrix is fundamental in establishing the membrane's mechanical, chemical, and thermal properties, whereas the type and concentration of ionic groups within the matrix are key to its permselectivity and electrical characteristics, yet they also influence its mechanical integrity [183].

#### 3.6.1. Basic characteristics

##### 3.6.1.1. Ion exchange capacity.
IEC quantifies the membrane's total active or functional groups facilitating ion exchange. It is typically measured via a standard acid-base titration, where the IEC value, expressed in meq g⁻¹ or mol/g, is calculated based on the volume of titrant utilized in titration, the membrane's dry weight, and the titrant solution's concentration, as depicted in Eq. (33). This metric is crucial for evaluating the membrane's ion exchange efficiency [205,206].

$$IEC = \frac{\text{molar amount of ion carriers}}{\text{m}^{\text{m}}_{\text{d}}} \qquad (33)$$

where IEC is expressed in mol/g and m<sub>d</sub><sup>m</sup> is the dry membrane weight (g).

Additionally, the IEC aids in calculating the membrane's fixed-ion concentration X<sup>m</sup> in terms of moles of sites per unit volume of the wet membrane, employing Eq. (34). This calculation is essential for assessing the density of active ion-exchange sites within the membrane's structure.

$$X^{\text{m}} = \frac{\epsilon \times \text{IEC} \times \rho_{\text{d}}}{\Delta V} \qquad (34)$$

where ε is the porosity (i.e., volume of free water within the membrane per unit of volume of wet membrane, dimensionless); IEC is expressed in equivalent per gram of dry membrane; ΔV is the volume dilatation of the membrane upon absorption of water per unit of volume of dry membrane (m³); ρ<sub>d</sub> is the density of the dry membrane (g/m⁻³(−|−|)).

##### 3.6.1.2. Water content.
The degree to which IEMs expand in presence of water can vary based on the solution's salinity and chemical makeup they come into contact with. This expansion, or water content WC (also known as water uptake), measured in grams of water per gram of dry
<figure><img src="image_10.png" /><figcaption>Fig. 7. Schematic structure of the pore-filling membrane preparation based on the reaction between DMA and DABCO motifs. Adapted with permission from [193]. Copyright 2024 American Chemical Society.</figcaption></figure>

modifying pure polymers or synthesizing monomers with specific functions, processes that typically require significant amounts of harmful organic solvents (e.g., DMF, DMAc, etc. [194]). To facilitate the production of IEMs on an industrial scale in an environmentally friendly manner, the development of straightforward, quick, and green fabrication techniques is crucial. A novel solvent-free in-situ polymerization approach has been introduced to address the environmental and practical challenges posed by traditional solvent-reliant methods. This innovative technique, already investigated with different systems (BPPO/ST/DVB [195], SPEEK/PMA/PANI [196]), distinguishes itself by using liquid monomers that become an integral part of the finished membrane, thereby eliminating the need for organic solvents.

### 3.5.4. Electro-spinning

This technic, illustrated in Fig. 8 – a, has emerged as a popular method for creating continuous nanofibers, offering key benefits like a high specific surface area, increased chemical reactivity, and a cost-effective production approach [197]. The solvent electrospinning process leverages electrostatic repulsion from surface charges in the polymer solution to extend a viscoelastic jet uniaxially. This method involves a high-voltage power supply, a spinneret equipped with a needle for the polymer solution, and a grounded collector. The polymer solution, fed through the needle by a syringe pump at a controlled rate, becomes charged under high voltage. This induces electrostatic repulsion among surface charges and Coulombic forces from the external field, forming a Taylor cone. Overcoming surface tension, the jet stretches, thins, and solidifies into nanofibers as the solvent evaporates, collected as a nonwoven membrane [198]. This technique, already developed at commercial stage (Elmarco s.r.o., Liberec, Czechia and Inovenso Ltd., Istanbul, Turkey for example), allows for precise control over the nanofibers' structure (average fiber diameter often approaching 200 nm) and morphology by adjusting variables such as polymer type, solution concentration, solvent characteristics, and spinning conditions [199]. Several studies have explored the impact of size on ion-exchange nanofibers, finding that smaller diameters generally lead to improvements in IEC and ionic conductivity. For instance, research by Dong et al. [200] demonstrated in Fig. 8 – b; that Nafion® nanofibers with a diameter of 400 nm achieved a conductivity of 1.5 S cm⁻¹ (measured by electrochemical impedance spectroscopy (EIS)), highlighting the potential of nanofibers for enhancing EC separation processes. The reduction in fiber size contributes to lower internal resistance (nI<sub>ohm</sub>) and higher efficiency in these applications. The versatility of electrospinning has led to the development of numerous polymers and composite materials (PECH/PAN/DABCO [201], QPVA/PDDA [202], PBI [203] nanofibers), finding applications across various domains.

### 3.6. Basic specifications and characterization of ion-exchange membranes

Once manufactured, membrane performance can be evaluated according to several criteria, for example to optimize manufacturing conditions. Fine-tuning the properties of IEMs is a complex task due to the conflicting effects of certain parameters. For example, enhancing mechanical strength through increased cross-linking can lead to higher electrical resistance due to a lower mobility of polymer chains. The core polymer matrix is fundamental in establishing the membrane's mechanical, chemical, and thermal properties, whereas the type and concentration of ionic groups within the matrix are key to its permselectivity and electrical characteristics, yet they also influence its mechanical integrity [183].

#### 3.6.1. Basic characteristics

##### 3.6.1.1. Ion exchange capacity.
IEC quantifies the membrane's total active or functional groups facilitating ion exchange. It is typically measured via a standard acid-base titration, where the IEC value, expressed in meq g⁻¹ or mol/g, is calculated based on the volume of titrant utilized in titration, the membrane's dry weight, and the titrant solution's concentration, as depicted in Eq. (33). This metric is crucial for evaluating the membrane's ion exchange efficiency [205,206].

$$IEC = \frac{\text{molar amount of ion carriers}}{\text{m}^{\text{m}}_{\text{d}}} \qquad (33)$$

where IEC is expressed in mol/g and m<sub>d</sub><sup>m</sup> is the dry membrane weight (g).

Additionally, the IEC aids in calculating the membrane's fixed-ion concentration X<sup>m</sup> in terms of moles of sites per unit volume of the wet membrane, employing Eq. (34). This calculation is essential for assessing the density of active ion-exchange sites within the membrane's structure.

$$X^{\text{m}} = \frac{\epsilon \times \text{IEC} \times \rho_{\text{d}}}{\Delta V} \qquad (34)$$

where ε is the porosity (i.e., volume of free water within the membrane per unit of volume of wet membrane, dimensionless); IEC is expressed in equivalent per gram of dry membrane; ΔV is the volume dilatation of the membrane upon absorption of water per unit of volume of dry membrane (m³); ρ<sub>d</sub> is the density of the dry membrane (g/m⁻³(−|−|)).

##### 3.6.1.2. Water content.
The degree to which IEMs expand in presence of water can vary based on the solution's salinity and chemical makeup they come into contact with. This expansion, or water content WC (also known as water uptake), measured in grams of water per gram of dry
<figure><img src="image_10.png" /><figcaption>Fig. 8. (a) The electrospinning device and (b) proton conductivity (at 30 °C, 90 % RH) vs. fiber diameter for high-purity Nafion® nanofibers measured on individual nanofibers. Figure (a) reprinted with permission from [204] (CC-BY MDPI). Figure (b) reprinted with permission from [200]. Copyright 2010 American Chemical Society.</figcaption></figure>

polymer, plays a critical role on ion mobility through the membrane. The water content of the membrane is determined, as illustrated in Eq. (35), by comparing its mass when dry and when swollen, a process done through gravimetric measurements.

$$WC = \frac{m_{\text{wet}}^{m} - m_{\text{dry}}^{m}}{m_{\text{dry}}^{m}} \qquad (35)$$

where $m^m$ is the mass of the membrane sample (g).

Note that the ionic strength (and therefore the osmotic pressure) of the medium in contact with the membrane has an impact on its swelling. In addition, it is possible to observe water in the membrane by simple equilibrium with a gaseous phase having a certain relative humidity.

### 3.6.1.3. Mechanical properties.
Evaluating the mechanical properties of IEMs encompasses assessments of not only thickness and swelling but also dimensional stability, tensile strength, and hydraulic permeability,

requiring membranes that have been pre-treated and equilibrated. The study of water permeability illuminates the movement of water through membranes influenced by hydrostatic pressure. Notably, the occurrence of pinholes and high porosity can heighten permeability (Eq. (36)) [207,208].

$$\epsilon = \frac{\Delta V}{(1 + \Delta V)} \qquad (36)$$

$$\Delta V = \frac{(m_h - m_d) \times \rho_d}{\rho_w \times m_d} \qquad (37)$$

where $\epsilon$ is the porosity (i.e., volume of free water within the membrane per unit of volume of wet membrane, dimensionless); $\Delta V$ is the volume dilatation of the membrane upon absorption of water per unit of volume of dry membrane (dimensionless); $m$ and $\rho$ are, respectively, the weight (g) and density (g/m$^{-3}$(−|−)); h and d stands, respectively, for hydrated
<figure><img src="image_11.png" /><figcaption>Fig. 8. (a) The electrospinning device and (b) proton conductivity (at 30 °C, 90 % RH) vs. fiber diameter for high-purity Nafion® nanofibers measured on individual nanofibers. Figure (a) reprinted with permission from [204] (CC-BY MDPI). Figure (b) reprinted with permission from [200]. Copyright 2010 American Chemical Society.</figcaption></figure>

polymer, plays a critical role on ion mobility through the membrane. The water content of the membrane is determined, as illustrated in Eq. (35), by comparing its mass when dry and when swollen, a process done through gravimetric measurements.

$$WC = \frac{m_{\text{wet}}^{m} - m_{\text{dry}}^{m}}{m_{\text{dry}}^{m}} \qquad (35)$$

where $m^m$ is the mass of the membrane sample (g).

Note that the ionic strength (and therefore the osmotic pressure) of the medium in contact with the membrane has an impact on its swelling. In addition, it is possible to observe water in the membrane by simple equilibrium with a gaseous phase having a certain relative humidity.

### 3.6.1.3. Mechanical properties.
Evaluating the mechanical properties of IEMs encompasses assessments of not only thickness and swelling but also dimensional stability, tensile strength, and hydraulic permeability,

requiring membranes that have been pre-treated and equilibrated. The study of water permeability illuminates the movement of water through membranes influenced by hydrostatic pressure. Notably, the occurrence of pinholes and high porosity can heighten permeability (Eq. (36)) [207,208].

$$\epsilon = \frac{\Delta V}{(1 + \Delta V)} \qquad (36)$$

$$\Delta V = \frac{(m_h - m_d) \times \rho_d}{\rho_w \times m_d} \qquad (37)$$

where $\epsilon$ is the porosity (i.e., volume of free water within the membrane per unit of volume of wet membrane, dimensionless); $\Delta V$ is the volume dilatation of the membrane upon absorption of water per unit of volume of dry membrane (dimensionless); $m$ and $\rho$ are, respectively, the weight (g) and density (g/m$^{-3}$(–|–)); h and d stands, respectively, for hydrated