i

ALMA MATER STUDIORUM - UNIVERSITÀ DI BOLOGNA

SCUOLA DI INGEGNERIA E ARCHITETTURA

DIPARTIMENTO DI INGEGNERIA CIVILE, CHIMICA, AMBIENTALE E DEI MATERIALI

CORSO DI LAUREA IN

INGEGNERIA CHIMICA E DI PROCESSO

TESI DI LAUREA

in

Bioreactor and downstream processes

Permselectivity and Electrical Resistance of Anion Exchange Membranes:

correlation between process parameters and membrane performance for

phosphate removal

CANDIDATO RELATORE

Prof.ssa. Cristiana Boi

Mohammadreza Jafari Eshlaghi

CORRELATORE

Dott. Louis C. P. M. de Smet

Prof. André de Haan

Anno Accademico 2015/16

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Table of Contents

1 Introduction............................................................................... 1

1.1 Phosphate importance .......................................................................................... 1

1.2 Membranes for phosphate removal ...................................................................... 3

1.3 Aim of Project ...................................................................................................... 4

1.4 Project outline ...................................................................................................... 5

2 Theoretical background ........................................................... 6

2.1 Phosphate ............................................................................................................. 6

2.2 Ion Exchange membrane concept and governing equations ................................ 7

2.2.1 Donnan potential and exclusion .................................................................... 8

2.3 Ion exchange membranes: applications .............................................................. 10

2.3.1 Ion exchange membranes and application in water treatment .................... 11

2.4 Ion exchange membranes: performance parameters evaluation ........................ 14

2.4.1 Ion exchange membrane: permselectivity .................................................. 15

2.4.2 Membrane electrical resistance ................................................................... 20

2.5 Surface chemistry and ion exchange membrane modification ........................... 23

2.5.1 Polyelectrolyte and phosphate attractive group .......................................... 23

2.5.2 Layer by Layer (LBL) approach for surface modification ......................... 24

2.6 Ion transport in ion exchange membrane: mathematical modelling .................. 26

2.6.1 Transport number modelling: ideal solution model .................................... 27

2.6.2 Transport number modelling: Manning theory and number ....................... 29

3 Materials and Methods .......................................................... 32

3.1 Chemicals and materials ..................................................................................... 32

3.2 Layer by layer modification on anion exchange membranes ............................. 32

3.3 Characterization of surface properties ................................................................ 32

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3.3.1 XPS analysis ............................................................................................... 33

3.3.2 SEM-EDX analysis ..................................................................................... 33

3.4 Water uptake ...................................................................................................... 33

3.5 Permselectivity: set-up and method ................................................................... 33

3.5.1 Design of experiments: Taguchi method .................................................... 35

3.6 Electrical resistance: set-up and method ............................................................ 36

4 Result and discussion ............................................................. 39

4.1 Membrane surface modification: LBL techniques ............................................. 39

4.2 Characterization of membrane surface ............................................................... 40

4.2.1 SEM-EDX analysis ..................................................................................... 40

4.2.2 XPS analysis ............................................................................................... 41

4.3 Taguchi results ................................................................................................... 41

4.4 Permselectivity results ........................................................................................ 42

4.4.1 Permselectivity: commercial membrane ..................................................... 43

4.4.2 Permselectivity: LBL modified membrane ................................................. 44

4.4.3 Permselectivity results: water uptake .......................................................... 47

4.5 Electrical resistance results ................................................................................ 48

4.5.1 Electrical resistance results: Commercial membrane ................................. 49

4.5.2 Electrical resistance: limiting current density ............................................. 51

4.6 Ion transport model results ................................................................................. 51

4.6.1 Mathematical modelling: ideal solution model ........................................... 52

4.6.2 Mathematical modelling: real solution model ............................................ 54

5 Conclusion ............................................................................... 57

5.1 Future work ........................................................................................................ 58

6 Appendix .................................................................................. 59

6.1 Appendix A: real Solution model ....................................................................... 59

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6.2 Appendix B: Taguchi approach for design of experiment (DOE) ..................... 61

6.3 Appendix C: membrane surface characterization .............................................. 62

6.4 Appendix D: pH and conductivity results .......................................................... 64

6.5 Appendix E ......................................................................................................... 66

7 References ................................................................................ 73

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Abstract

The excess phosphate in water streams causes eutrophication. Water eutrophication

harms marine species and ecosystem. Ion exchange membranes have demonstrated a high

potential for phosphate removal. In this study, phosphate transport in anion exchange

membranes was investigated by permselectivity and electrical resistance measurements.

Permselectivity and membrane electrical resistance of commercial Fuji anion exchange

membranes were compared with layer by layer (LBL) modified membrane with a phosphate-

attractive receptor. Fuji commercial membranes were modified by LBL techniques by (PAH-

Gu-PSS)5, Guanidinium (Gu) has already showed high phosphate affinity.

Permselectivity measurements on commercial Fuji membranes revealed lower phosphate

permselectivity compared to chloride, due to differences in diffusion coefficients and anions

size. Moreover, the presence of phosphate-attractive groups on the LBL modified membrane

decreased phosphate permselectivity compared to bare Fuji membrane. Membrane electrical

resistance and its dependency on solution concentration were studied for different salts. The

significantly higher membrane resistance for phosphate than chloride was explained by lower

phosphate mobility with respect to chloride. Finally, two mathematical models were proposed

in order to predict the ion transport number in anion exchange membranes. Real solution

model shows a reasonable consistency with experimental results.

Keywords: Anion exchange membranes, Layer by layer (LBL), Phosphate-selective receptor,

Permselectivity, Membrane electrical resistance, Water uptake, Mathematical model.

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پاس عشقی بی کرانه تقدیم به دنیا، ب

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Acknowledgments

I would like to thank everyone who helped me during my thesis to fulfil my project.

First of all, I would like to especially thank my main supervisor, Dr. Louis C. P. M. de Smet

(Delft University of Technology) for giving me the opportunity of working on this great

project. Louis, you taught me a priceless lesson, never underestimate minor stuffs.

I also want to thank to Prof. André de Haan (Delft University of Technology) for his

involvement in the modelling part.

I would like to especially thank MSc. Laura Paltrinieri for her constant presence, our regular

meetings and our academic and non-academic discussions.

I also would like Prof. Ernst J. R. Sudhölter for giving me motivation during the group

meeting. I also, thanks MSc. Anping Cao for the SEM-EDX images.

And finally, I would like to thank Dr. Cristiana Boi (ALMA MATER STUDIORUM -

Università di Bologna) as main supervisor for her supports during this project and also

correcting this report.

Last but not least, I would like to thank my lovely mother for her constant support, regular

motivation and believing in me. Mum, I hope you are proud of me.

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1 Introduction

The present work has been conducted in the department of chemical engineering, Delft

University of Technology, The Netherlands.

1.1 Phosphate importance

The importance of phosphate for human body and industrial applications is undeniable

[1]. Phosphorous is mainly used in the agricultural sector (especially as fertilizer) and in the

production of healthcare products like detergents and cosmetics [2]. In the last decades,

phosphate production have increased in response to high fertilizer demand. Fertilizer

production has grown due to increasing world population and higher food demand.

Figure 1.1. shows the phosphate consumption by different sectors. It is clear that

detergent and food industry are main consumers. The fertilizer industry use less phosphorous

than other sectors, but its indirect role in food industry should be considered as well. The

regions with more developed agricultural industries consume much more phosphate than

others, as illustrated in Figure 1.1.

Figure 1.1 Phosphate consumption distribution by sector (left) and region (right).

The significant increase in phosphate consumption has caused some side effects

especially on water resources. Phosphate excess in water has increased water eutrophication

in rivers, canals and lakes [3, 4]. Water eutrophication is harmful for marine species and water

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quality [3, 4]. Water eutrophication is a common problem in many countries especially in the

USA and China [4].

Several investigations have been performed to estimate the availability of the remaining

phosphate rock reserves and almost the same conclusion has been drawn that with the current

consumption rate, the world will encounter a phosphate shortage within 80-90 years [5]. So,

in order to maintain a sustainable phosphate production, an alternative source should be

considered. Phosphate discharge in wastewater has been increased due to human activities

such as industry, agriculture and household activities [2]. Therefore, phosphate removal and

recovery from wastewater might be the key to solve the water-related problems of excess

phosphate and, at the same time, ensure a sustainable source for the future.

Water eutrophication is highly sensitive to phosphate concentration in water, even very

low amounts of phosphate (0.02 mg/L) can cause a water eutrophication [4]. Therefore,

currently many countries approved series of strict rules about phosphate concentration in

discharge water from industry and agriculture. The Dutch government set a maximum value

of phosphate concentration in municipal wastewater that is lower than 0.15 mg/L [6]. As an

example, Figure 1.2, shows water eutrophication problem in a river in Delft, The Netherlands,

in the summer.

Considering the previous discussion, while phosphate is being one of the most

problematic elements for water resources, phosphate is limited in nature as well. Therefore, it

is highly demanding for the future to find a sustainable source and environmentally-friendly

method to remove and recover phosphate.

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Figure 1.2 An example of water eutrophication of a river (Delftse Schie) in Delft, The

Netherlands.

1.2 Membranes for phosphate removal

As explained in the previous section, the current production/consumption rate of

phosphate resources has stimulated researchers to find a way for phosphate removal and

recovery from wastewater. Wastewater treatments for phosphate removal have been

categorized mainly to two different groups: 1) conventional methods and 2) modern

technologies or alternative methods.

Biological approach and adsorption process are two of the main conventional methods

for phosphate removal from wastewater. Biological wastewater treatment are commonly used

as preliminary water treatment. The low operation cost as well as the high removal efficiency

are the main advantages of biological treatments. But, disposal of concentrated sludge (as a

common residual of biological processes) and highly dependency of phosphate removal

efficiency on stability of phosphate concentration and operation conditions (which are hard to

achieve) are the most important disadvantages of biological treatments [1, 4]. Adsorption

process is an economically attractive method, although not very eco-friendly. Disposal of

absorbents which mainly has been done by landfill discarding have been restricted in most of

first-world countries [7].

Membrane technology is one of the most important alternative technologies for

phosphate removal from wastewater. Membrane technology processes are divided into: 1)

pressure-driven membrane processes and 2) electrical-driven processes. Pressure-driven

processes such as reverse osmosis, RO, and nanofiltration, NF, have been widely used in last

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decades in order to remove phosphate. They have high efficiency at low phosphate

concentration [8] and their efficiency depends mainly on process parameters and membrane

pore size [9]. While, (bio)fouling and scaling are the main problematic issues which have

limited their applications [8]. Although electrical-driven processes and specially

electrodialysis have been used commonly in desalination of seawater, they show high

potential for removal of phosphate. Zhang et al.[8] investigated electrodialysis (ED) to

fractionate multivalent sulphate ions from monovalent chloride ions in aqueous solutions. The

study shows a great potential of electrodialysis for concentrating phosphate due to the high

separation efficiency. Chen et al.[10] investigated phosphate removal using anion exchange

membranes in Donnan dialysis. Although there are some studies on phosphate removal using

ion exchange membranes, applications of ion exchange membranes are limited to heavy metal

removal and seawater desalinations. The lack of comprehensive information on phosphate

removal using ion exchange membranes stimulated us to focus on the removal of phosphate

via anion exchanges membrane in the current study.

1.3 Aim of Project

The goal of this project is to investigate phosphate transport through an anion exchange

membrane (AEM) and find a correlation between membrane performance properties and

external solution parameters. The main aim of the project is to deeply explore the

permselectivity and the electrical resistance of anion exchange membranes and its relation to

external solution concentration and to the type of salts. In addition, a commercial anion

exchange membrane will be compared with a modified membrane containing a phosphate-

selective receptor. The difference in ion transport among the two types of membranes will be

further explored. The obtained experimental results will be related to a mathematical model,

which aims to predict ion transport through the membrane.

In this project, we aim to address the following research questions:

a) To what extent phosphate transport through an anion exchange membrane depends on

the external solution concentration?

b) How membranes performances change when they are in contact with ampholyte

electrolytes (e.g. NaH2PO4 solution) or strong electrolytes (e.g. NaCl solution)?

c) Can phosphate-selective receptors, at the membranes surface, enhance phosphate

transport? How these receptors behave in the presence of different ions?

d) How accurate a model can predict ions (especially phosphate) transport through the

membrane?

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1.4 Project outline

This report consists of five chapters. In Chapter 2, the theoretical background is

presented to give readers a pre-introduction of knowledge required in the following chapters,

such as ion exchange membrane definitions, permselectivity and electrical resistance

definition and their governing equations (Section 2.2), ion exchange membrane application

(Section 2.3), ion exchange membrane performance parameters such as permselectivity and

electrical resistance, polyelectrolyte and Layer by Layer (LBL) approach for surface

modification (Section 2.5) and finally mathematical modelling of ion transport through the

membrane (Section 2.6).

In Chapter 3, materials and experimental methods are described in detail. Chapter 4

covers the results and discussion. Finally, in Chapter 5, the main conclusions are drawn and

some recommendations for future studies are listed.

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2 Theoretical background

2.1 Phosphate

Phosphate speciation in aqueous environment depends highly on pH of the solution [11].

The relation between pH and concentration of salt in aqueous solution is already well-known.

Therefore, phosphate speciation changes with salt concentration in the solution. In a very

acidic condition, monovalent phosphate (𝐻2𝑃𝑂4−) is the main speciation while in neutral

condition both monovalent and divalent (𝐻𝑃𝑂42−) are present in different ratio.

Figure 2.1 Fraction of phosphate speciation as a function of pH [11]

Different phosphate types have different transport behaviour mainly due to their chemical-

physical nature. As ions transport is governed mainly by their size and diffusion coefficients,

these properties have been reported for monovalent ( 𝐻2𝑃𝑂4− ) and divalent phosphate

(𝐻𝑃𝑂42−) in Table 2.1.

Table 2.1 Properties of different phosphate anions [12].

Anion Stoke’s radius

(m)

Diffusion Coefficient (𝑚2 𝑠⁄ )

𝐻2𝑃𝑂4− 0.256 × 10−9 0.96 × 10−9

𝐻𝑃𝑂42− 0.323 × 10−9 0.76 × 10−9

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2.2 Ion Exchange membrane concept and governing

equations

In this section, ion exchange membrane, its concepts and its governing equations will be

discussed. Ion exchange membranes have been categorized to two types: 1) cation exchange

membrane and 2) anion exchange membrane. Cation exchange membranes contain negative

charged ions attached to the surface of membrane (called fixed-ions) while, anion exchange

membranes have positively charged groups attached to the membrane surface. Therefore, due

to electrostatic interactions, anion exchange membranes are more willing to transport anions

(which is called counter-ions) and exclude cations (due to electrostatic repulsion). The

opposite is true for cation exchange membrane, where cations are counter-ions and anions are

co-ions [13].

In other words, the main concepts of an anion exchange membrane are:

a) Counter-ions: ions which pass through the membrane (anions)

b) Co-ions: ions which are excluded from the membrane (cations)

c) Fixed-ions: positive charged groups attached to the membrane surface

The Donnan equilibrium governs a system including electrolyte solutions in contact with

the ion exchange membrane. Donnan well explained the exclusion of co-ions in ion exchange

membranes with his theory [14]. Figure 2.2 illustrated schematically an anion exchange

membrane and its main concepts. It is shown that the amount of co-ions in the membrane are

much lower than the counter-ions.

Figure 2.2 Schematic illustration of an anion exchange membrane

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2.2.1 Donnan potential and exclusion The system consisting an electrolyte solution and an ion exchange membrane is governed

by Donnan equilibrium [13, 14]. The membrane and the electrolyte solution in contact with

each other have both chemical and electrical potentials. The term, 𝜎𝑖, in Equation (2.1) refers

to the “electrochemical potential” which combines both chemical and electrical potentials of

the system. Equation (2.1) shows the electrochemical potential of system as a function of

chemical and electrical potentials.

𝜎𝑖 = 𝜇𝑖 + 𝑧𝑖𝐹𝜑 (2.1)

where 𝜎𝑖 is the electrochemical potential, 𝜇𝑖 is the chemical potential, 𝑧𝑖 is the species

valence, 𝐹 is Faraday constant and 𝜑 is the electrical potential.

The chemical potential of the system is described by equation (2.2),

𝜇𝑖 = 𝜇°𝑖 + 𝑅𝑇 𝑙𝑛𝑎𝑖 (2.2)

where 𝜇𝑖 is the chemical potential of each species in the system, 𝜇°𝑖 is the reference potential

in standard conditions, 𝑅 is the universal gas constant, 𝑇 is temperature and 𝑎𝑖 is the activity

of each species at specific temperature and concertation.

Equation (2.3) describes both chemical and electrical potentials (or so-called

electrochemical potential) of an electrolyte solution and an ion exchange membrane in

equilibrium,

𝜇𝑖°𝑠 + 𝑅𝑇 𝑙𝑛𝑎𝑖

𝑠 + 𝑧𝑖𝐹𝜑𝑠 = 𝜇𝑖°𝑚 + 𝑅𝑇 𝑙𝑛𝑎𝑖

𝑚 + 𝑧𝑖𝐹𝜑𝑚 (2.3)

where superscripts 𝑠 and 𝑚 indicate solution and membrane phases, respectively . Assuming

equal reference chemical potential in membrane and solution phases, Donnan potential is

derived as expressed in equation (2.4) [14]:

𝜑𝐷𝑜𝑛 = 𝜑𝑚 − 𝜑𝑠 =𝑅𝑇

𝑧𝑖𝐹 𝑙𝑛

𝑎𝑖𝑠

𝑎𝑖𝑚 (2.4)

here, 𝜑𝐷𝑜𝑛 is Donnan potential, 𝜑𝑚 is the membrane potential and 𝜑𝑠 is the solution potential.

To simplify the equations understanding and further explanations, ideal solutions are

considered for both solution and membrane phases (activities coefficients are considered to be

equal to unity). In addition, a monovalent electrolyte (e.g. NaCl) and an anion exchange

membrane are considered. Donnan potential for the system mentioned above has been

presented in equation (2.5):

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𝜑𝐷𝑜𝑛 = 𝜑𝑚 − 𝜑𝑠 =𝑅𝑇

𝐹 𝑙𝑛

𝐶𝑁𝑎𝑠

𝐶𝑁𝑎𝑚 =

𝑅𝑇

𝐹 𝑙𝑛

𝐶𝐶𝑙𝑠

𝐶𝐶𝑙𝑚 (2.5)

equation (2.6) is derived from equation (2.5) at constant temperature and correlates

concentration distribution of each ion in the membrane and solution.

𝐶𝑁𝑎𝑠

𝐶𝑁𝑎𝑚 =

𝐶𝐶𝑙𝑠

𝐶𝐶𝑙𝑚 (2.6)

where superscripts 𝑠 and 𝑚 indicate solution and membrane phases, respectively.

To hold the electroneutrality in the anion exchange membrane, equation (2.7) is applied

to ensure that the system is neutral.

𝐶𝐶𝑙𝑚 = 𝐶𝑓𝑖𝑥 + 𝐶𝑁𝑎

𝑚 (2.7)

where 𝐶𝐶𝑙𝑚 is the chloride concentration in the membrane, 𝐶𝑁𝑎

𝑚 is the sodium concentration and

𝐶𝑓𝑖𝑥 is the concentration of positively charged groups attached to the membrane surface. Since

chloride and sodium concentrations are equal in the solution, the equation (2.8) is valid,

𝐶𝐶𝑙𝑠 = 𝐶𝑁𝑎

𝑠 = 𝐶𝑠 (2.8)

here, 𝐶𝐶𝑙𝑠 is the chloride concentration in solution which is equal to the sodium concentration

in solution 𝐶𝑁𝑎𝑠 and both are identical to the salt concentration in solution 𝐶𝑠.

Combining equation (2.6) to (2.8), gives equation (2.9) which is able to calculate the co-

ion concentration (𝐶𝑁𝑎𝑚 ) in the membrane.

𝐶𝑁𝑎𝑚 =

(𝐶𝑠)2

𝐶𝑓𝑖𝑥+𝐶𝑁𝑎𝑚 (2.9)

To simplify the above equation, a rough approximation has been considered to relate the

co-ion concentration to the salt concentration and membrane properties. The approximation

neglects the co-ion concentration in the membrane in comparison with fixed charge

concentration (𝐶𝑓𝑖𝑥 ≫ 𝐶𝑁𝑎𝑚 ). The approximation is commonly called Donnan approximation

or Donnan exclusion [13, 14].

𝐶𝑁𝑎𝑚 =

(𝐶𝑠)2

𝐶𝑓𝑖𝑥 (2.10)

Figure 2.3 illustrates schematically the ion concentration distribution in the membrane. As it

is shown, the sodium concentration in the membrane (𝐶𝑁𝑎𝑚 ) is lower than the fixed ion

concentration. Donnan potential is illustrated as a potential difference between membrane and

solution [14].

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Figure 2.3 Schematic illustration of concentration distribution of a monovalent electrolyte

(here NaCl ) in anion exchange membrane and solution (Left) and Donnan potential as a

potential difference between membrane and solution (right). AEM refers to ion exchange

membrane.

2.3 Ion exchange membranes: applications

Ion exchange membranes mainly have been categorized based on their applications in

two groups: 1) applications in energy production and 2) applications in water treatment; the

former is mainly recognized with fuel cell and reverse electrodialysis [13, 15]. In reverse

electrodialysis energy is produced by sending the solutions with different salinity into a

number of anion and cation exchange membranes [16]. The applications of ion exchange

membranes in water treatment have undergone a rapid improvement in last century.

Especially, potable water shortage triggered researchers to improve efficiency of these

processes [17]. Ion exchange membranes could be used in production of drinking water or

removal of pollutant from industrial and agricultural wastewaters [18, 19]. Processes which

include ion exchange membranes can also be categorized based on type of driving forces that

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are applied in the processes. The driving force for processes containing ion exchange

membrane could be concentration gradient (which are called concentration-driven process) or

electrical field (which are called electrical-driven processes) [13, 14]. In the next sections,

some of the common and popular applications of ion exchange membranes in water treatment

are explained in more detail.

2.3.1 Ion exchange membranes and application in water treatment There are numerous processes which contain ion exchange membranes for water

treatment. Here, electrodialysis, diffusion dialysis and Donnan dialysis as the most applicable

processes in wide range of industries, are discussed. In electrodialysis, an electrical field is the

driving force of the processes while in Donnan and diffusion dialysis, a concentration gradient

is the main driving force.[10, 20, 21].

2.3.1.1 Electrodialysis

Figure 2.4 illustrates simplified electrodialysis (ED) cell. As it is shown, the feed solution

is sent into different compartments and an electrical field is applied as driving force. Anions

tend to go towards anode and cations towards cathode. Anions pass anion exchange

membrane but their passage are limited in cation exchange membrane, similarly, cations pass

cation exchange membrane but they are excluded from anion exchange membrane. Thus, the

ion concentrations in some compartments are higher which are called “concentrated”, while

the other compartments which are depleted from ions are called “dilute” [13, 18, 19, 22]. The

scheme and detailed description of ED with higher number of compartments are discussed in

[13, 14]. Many studies verified ED potential on water treatment. ED is initially introduced for

seawater desalination but then showed a great potential for wastewater treatment especially

removal of heavy metals and multivalent ions [8, 19, 20, 22]. Beside industrial application of

ED in wastewater treatment and waste desalination, ED is also used in food industry such as

diary industry (whey demineralization) and also deacidification of wine and juices [20].

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Figure 2.4 Schematic illustration of simplified electrodialysis cell. AEM refers to anion

exchange membrane and CEM refers to cation exchange membrane [18].

2.3.1.2 Diffusion dialysis

In contrast with electrodialysis, diffusion dialysis is a concentration-driven process [23].

It means that the only driving force in the process is concentration gradient over 2 sides of

membrane. Diffusion dialysis is successfully used to separate and recover acids and bases

from wastewater of metal production industries [24]. Simple operation conditions, low

operating cost and no energy consumption are main advantages of the process. However, its

industrial applications somehow are limited due to its slow kinetics, low efficiency and high

water consumption [23, 24]. Moreover, slow kinetics process, such as diffusion dialysis,

requires higher membrane area which will result a higher capital cost on process. However,

increasing global attentions on environmental issues have made diffusion dialysis an

important process especially due to its environmentally-friendly characteristics [23].

In Figure 2.5 a schematic drawing of a diffusion dialysis is presented. As illustrated in

Figure 2.5.a, diffusion dialysis is used to separate HCl acid using an anion exchange

membrane. The feed side contains desired acid or base and undesired heavy metal (which

should be removed and recovered) while, the other side just contains water [23]. Chloride ions

pass the membrane while heavy metal are excluded. Figure 2.5.b, shows a typical

experimental set-up in diffusion dialysis experiments.

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Figure 2.5 a) Illustration of the diffusion dialysis principle through the HCl separation process

from its feed solution b) a typical experimental set-up for diffusion dialysis [23]

2.3.1.3 Donnan dialysis

Donnan dialysis is a concentration-driven processes, like diffusion dialysis, with its

applications in wastewater treatment [10]. The principle of Donnan dialysis for phosphate

removal is presented schematically in Figure 2.6. In Donnan dialysis, passage of ions to other

side of membrane triggers the transport of other ion in the other compartment in the opposite

direction. In other words, in Figure 2.6, the chloride transport stimulates the phosphate

transport to ensure electroneutrality in both compartments [10, 25]. High potential

applications of Donnan dialysis were reported for heavy metal removal such as arsenic and

nickel [10, 26], valuable compound such as phosphate, nitrate [25] and organic species [26].

Plenty of studies have been conducted on Donnan dialysis due its attractive characteristics

such as no energy consumption, easy operation and low operation cost. Although its industrial

applications are restricted due to its slow kinetics and consequently low effectiveness of

process [13, 26].

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Figure 2.6 Schematic diagram of phosphate removal in Donnan dialysis [10].

With this introduction to the ion exchange membranes and their applications and

limitations, the necessity to optimize ion exchange membranes performance to improve the

process efficiency have been clarified more. To optimize membrane performance, firstly

membrane properties have to be characterized properly to obtain more comprehensive insights

into ion exchange membranes.

2.4 Ion exchange membranes: performance parameters

evaluation

Membrane performance is being evaluated by different factors. The efficiency of

processes which include ion exchange membranes are being evaluated by their extent of

exclusion of undesired ions. The parameters which ion exchange performances depend on are

listed below [14] :

Permselectivity

Electrical resistance

Mechanical stability

Chemical stability

the above parameters are commonly called “performance parameters”. A perfect ion exchange

membrane or ideal membrane should have high permselectivity, low electrical resistance and

high chemical and mechanical stability. There have been a lot of investigations to optimize

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membrane performance parameters [14, 27]. Giese et al [27] found a trade-off between

electrical resistance and permselectivity of ion exchange membranes; Krol et al. [14] reported

that fixed charge concentration and the nature of fixed charge group play the important roles

in membrane performance parameters. To have a better understanding of membrane

performance parameters, some investigators related membrane permselectivity to water

uptake to analyse more deeply the effect of fixed ion concentration (water uptake depends

highly on nature of fixed ion and fixed charge concentration) [27, 28].

Therefore, in the next sections of this chapter, membrane performance will be explained

in more details and their governing equations will be discussed. Among those membrane

performance parameters, permselectivity and electrical resistance are studied in the current

project. In the following paragraphs, membrane permselectivity, its governing equations,

calculation approaches and its relation to membrane water uptake are explained. Finally,

electrical resistance is discussed with its concepts and details

2.4.1 Ion exchange membrane: permselectivity Consider a perfect anion exchange membrane in contact with an electrolyte solution, the

system is governed by Donnan equilibrium and ions transport are determined by Donnan

exclusion. Therefore, a perfect anion exchange membrane allows only the passage of counter-

ion (anions) and does not allow passage of co-ion (cations). Although, in reality there are

always some co-ions which pass the membrane and decrease membrane permselectivity. So,

the membrane permselectivity is being measured based on how the membrane is successful to

transport only counter-ion without allowing passage of co-ion [13, 28, 29]. Membrane

permselectivity varies based on the nature of driving force applied over membrane. In case of

concentration gradient, the ions are transported only by diffusion, while if an electrical field is

applied, the ions transport are accelerated by electrical force [29].

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Figure 2.7 Schematic illustration of a perfect anion exchange membrane (completely

permselective) with 2 possible driving forces namely concentration gradient and electrical

field.

There has been plenty of studies on permselectivity of ion exchange membranes such as

effect of counter-ion on permselectivity [30], permselectivity and membrane potential [29]

and correlation between permselectivity and water content of anion exchange membrane [27].

There are 2 different approaches to calculate permselectivity of ion exchange membrane:

Transport number approach

Membrane potential approach

Before introducing membrane permselectivity and its different calculation approaches, a

brief discussion on physical concepts and governing equations of mass transfer in ion

exchange membrane is necessary since the ion transport in the ion exchange membranes are

always coupled with mass transfer.

2.4.1.1 Mass transport in ion exchange membrane and electrolyte solution

Again, consider an ion exchange membrane in contact with an electrolyte solution, the

ion transport is always accompanied with mass transfer. Mass transfer can occur by counter-

ions, co-ions as well as solvent. If we consider both concentration gradient and electrical field

together in the system as the driving forces, the chemical and electrical potentials are applied

17

over system and so-called “electrochemical potential” results as equation (2.11) (as mentioned

earlier in section 2.2.1) [13]:

𝑑𝜎𝑖 = 𝑑𝜇𝑖 + 𝑑𝜑 = 𝑉𝑖𝑑𝑝 + 𝑅𝑇 𝑑𝑙𝑛 𝑎𝑖 + 𝑧𝑖𝐹𝑑𝜑 (2.11)

where 𝑑𝜎𝑖 is the electrochemical potential which is sum of the chemical potential (𝑑𝜇𝑖) and

the electrical potential (𝑑𝜑). Here, 𝑉𝑖 is the molar volume, 𝑝 is the pressure, 𝑅 is universal gas

constant, 𝑇 is temperature, 𝑎𝑖 is the activity, 𝐹 refers to Faraday constant and 𝜑 stands for

electrical potential.

Considering constant pressure and temperature, the mass flux has been calculated as

equation (2.12),

𝐽𝑖 = ∑ 𝐿𝑖𝑘𝑖𝑑𝛽𝑘

𝑑𝑧= ∑ 𝐿𝑖𝑘𝑖 (𝑅𝑇

𝑑 𝑙𝑛 𝑎𝑖

𝑑𝑧+ 𝑧𝑖𝐹

𝑑𝜑

𝑑𝑧) (2.12)

here, Lik is phenomenological coefficient to related species mass transfer and driving forces.

To simplify the equation (2.12) for further applications and explanations, all the mass

fluxes of different species are considered individual with no interaction with the other fluxes

and a very dilute electrolyte solution is considered. So the activity coefficients are assumed to

be equal to unity and mass flux of individual species are presented as below [13]:

𝐽𝑖 = −𝐷𝑖 (𝑑𝐶𝑖

𝑑𝑧+

𝑧𝑖𝐹𝐶𝑖

𝑅𝑇 𝑑𝜑

𝑑𝑧) (2.13)

where 𝐷𝑖 is the diffusion coefficient, 𝐶𝑖 is the concentration, 𝑑𝐶𝑖

𝑑𝑧 is the concentration gradient

which is causes a chemical potential and 𝑑𝜑

𝑑𝑧 is the electrical potential which is resulted by

applied electricity.

2.4.1.2 Permselectivity: transport number approach

In the system including ion exchange membranes and electrolyte solutions, due to driving

force (which could be the concentration gradient or electrical field) an ionic current is

occurred over membrane. This current is made by passage of counter-ion and co-ion. As

explained earlier, the concentration of counter-ion in the ion exchange membrane is always

higher than co-ion concentration, therefore, counter-ion share in the ionic current is much

higher than co-ion. The share of each ion in the ionic current that passes an ion exchange

membrane is called ion transport number. Ion transport number in the system including an ion

exchange membrane and an electrolyte solution is presented in equation (2.14) [13, 14] :

18

𝑇𝑖 =𝑧𝑖𝐽𝑖

∑ 𝑧𝑖𝐽𝑖𝑛𝑖

(2.14)

where 𝑇𝑖 is te transport number of specie i, 𝐽𝑖 is the mass flux of species i and 𝑧𝑖 is the ion

valence. Since all the current is transported by either counter-ions or co-ions, the sum of

transport number for the system should be equal to unity as is presented in equation (2.15),

∑ 𝑇𝑖 = 1𝑛𝑖 (2.15)

To relate membrane permselectivity to ion transport number, the permselectivity and the

transport number definitions are indicative. Membrane permselectivity could somehow

present the counter-ion distribution in the ionic current which passes through the membrane,

therefore, the transport number and membrane permselectivity are related as expressed in

equation (2.16) [29]:

𝛼 (%) =𝑇𝑐𝑜𝑢𝑛𝑡𝑒𝑟−𝑖𝑜𝑛

𝑚 −𝑇𝑐𝑜𝑢𝑛𝑡𝑒𝑟−𝑖𝑜𝑛𝑆

𝑇𝑐𝑜−𝑖𝑜𝑛𝑆 × 100 (2.16)

where 𝛼 is the ion exchange membrane permselectivity, 𝑇 is the ion transport number and

superscripts m and s indicate membrane and solution phases, respectively. When the counter-

ion concentration in the membrane and solution become identical, so, there is no more driving

force for ions transport and consequently, membrane permselectivity approaches to zero [29].

2.4.1.3 Permselectivity: membrane potential approach

Consider a driving force (concentration gradient or electrical field) applied to a system

including an ion exchange membrane and an electrolyte solution, ion passage through the

membrane causes the ionic current as explained earlier. The ion transport through the

membrane causes a difference in charge concentration over two side of the membrane which

results in a potential across the membrane. The potential is called “ membrane potential” [31]:

𝑑𝐺 = −𝐹𝑑𝐸 (2.17)

where 𝑑𝐺 is the Gibbs free energy produced by the ion transport, 𝐹 is Faraday constant and

𝑑𝐸 is membrane potential.

Gibbs free energy can be written in terms of chemical potential as it is shown in equation

(2.18),

𝑑𝐺𝑖 =𝑇𝑖

𝑧𝑖𝑑𝜇𝑖 =

𝑇𝑖

𝑧𝑖 𝑅𝑇 𝑑𝑙𝑛 𝑎𝑖 (2.18)

where 𝑇𝑖 is the transport number of species i, 𝑧𝑖 is the ion valence, 𝑅 is the gas constant, 𝑇 is

temperature and 𝑎𝑖 is the activity. Combining equations (2.17) and (2.18) for all the ion

species, the potential is calculated by equation (2.19):

𝐸 = −𝑅𝑇

𝐹∫ ∑

𝑇𝑖

𝑧𝑖 𝑑𝑙𝑛 𝑎𝑖 (2.19)

19

integrating over equation (2.19) gives equation (2.20):

𝐸 = −(𝑇𝑐𝑎𝑡𝑖𝑜𝑛 − 𝑇𝑎𝑛𝑖𝑜𝑛) 𝑅𝑇

𝑍𝐹 𝑙𝑛

𝑎2

𝑎1 (2.20)

where the subscript cation and anion refers to electrolyte solution. To simplify the above

equation, no co-ion transport is assumed (completely permselective membrane or perfect ion

exchange membrane assumption) which results the equation (2.21):

𝐸𝐶𝑎𝑙 =𝑅𝑇

𝑍𝐹 𝑙𝑛

𝑎2

𝑎1 (2.21)

the equation (2.21) is called simplified Nernst-Planck equation. In the other words, the

Nernst-Planck equation calculates the potential across a perfect permselective ion exchange

membrane in contact with an electrolyte solution.

So, membrane permselectivity is calculated using potential approach with equation (2.22)

that shows to which extent the membrane under investigation deviates from a perfect ion

exchange membrane and correlates it to the membrane permselectivity [29],

𝛼(%) =𝐸𝑚𝑒𝑎𝑠

𝐸𝑐𝑎𝑙× 100 (2.22)

The application of potential approach in permselectivity calculation is limited to

experimental approach due to its limitation for potential value which will be only obtained

through experiment. However, the simplicity of test system and its reasonable accuracy are

advantages of such methods [29].

2.4.1.4 Membrane water uptake and its relation to permselectivity

Membrane water uptake is a membrane characteristic parameter which reflects the

amount of water that has been absorbed by the membrane. Water uptake is an important

parameter in the ion transport in the ion exchange membranes [27]. Membrane water uptake

(𝑊𝑢) is calculated using equation (2.23):

𝑊𝑢 (g (𝐻2𝑂)/g𝑑𝑟𝑦 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒) =𝑚𝑤𝑒𝑡−𝑚𝑑𝑟𝑦

𝑚𝑑𝑟𝑦 (2.23)

where 𝑚𝑤𝑒𝑡 and 𝑚𝑑𝑟𝑦 are the membrane mass after immersing in salt solution and after

drying in the oven, respectively.

Although, water uptake is a crucial membrane property, it is not clearly indicative in the

ion transport through the membrane. It is known based on Donnan exclusion that membrane

permselectivity heavily depends on the fixed charge concentration. However, the fixed charge

concentration in the ion exchange membrane is function of water uptake as is presented below

[27]:

20

𝐶𝑓𝑖𝑥 =𝐼𝑜𝑛 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 (𝐼𝐸𝐶)

𝑊𝑎𝑡𝑒𝑟 𝑢𝑝𝑡𝑎𝑘𝑒 (𝑊𝑢) (2.24)

where 𝐶𝑓𝑖𝑥 is the fixed charge concentration, 𝐼𝐸𝐶 is the ion exchange capacity which usually

obtained through the experiment and 𝑊𝑢 is the membrane water uptake.

Donnan exclusion implies that increasing membrane water uptake will result a decrease

in membrane permselectivity [28]. Since higher water uptake occurs in membranes with lower

fixed charge density and consequently higher co-ion concentration in the membrane.

A considerable decrease in permselectivity value of commercial CEMs by increasing

fixed charge concentration was reported by Tagaki et al.[32] while some other works

observed different trends between permselectivity and water content of membrane (or fixed

charge concentration) and relate such unusual trends to the nature of polymer in the

membrane [27, 29]. Giese et al.[27, 29] studied water uptake on 4 different AEMs and CEMs

for 4 different salts and reported that influence of membrane water uptake on permselectivity

is much lower than co-ion. Also, Amel et al. [33] investigated water uptake of a commercial

AEM for 2 type of salt over temperature range and observed a significant role of salt

dissociation constants in membrane water uptake. While there are some studies that correlated

membrane water uptake and permselectivity, other investigations questioned the ability of

water uptake to fully describe membrane permselectivity, especially due to the fact that water

uptake highly depends on experimental method [27, 28, 34].

2.4.2 Membrane electrical resistance

Membrane resistance illustrates the resistance of ions during their transport through the

membrane. Membrane resistance and its relation to external solution concentration have been

already verified by many studies [27, 34-37]. The challenge in the membrane resistance

determination is its dependency on measurement methods. Galama et al. [35] reported a

highly dependency of membrane resistance on experiment set-up. The most convenient

method to measure membrane resistance is under direct current (DC) [34] which was used in

the current study. Membrane resistance under DC is calculated using equation (2.25):

𝑅𝑀+𝑆 =𝑈

𝑖 ( 2.25)

where 𝑅𝑀+𝑆 is the membrane and solution resistance, 𝑈 is the potential drop over membrane

and 𝑖 is the current density. Membrane resistance is obtained by subtracting the solution

resistance (𝑅𝑆) from 𝑅𝑀+𝑆. However it should be considered that the membrane resistance

under DC includes diffusion boundary layer resistance and electrical double layer [36]. Tanak

21

et al [31] listed electrical resistance of different commercial AEMs and CEMs which mainly

are in the range of 1-10 Ω𝑐𝑚2.

There are also some studies which have investigated membrane conductivity as

membrane performance parameters for the ion transport [11, 38, 39]. Membrane conductivity

is determined as expressed in equation (2.26),

𝐾𝑀 =𝛿

𝑅𝑚𝐴 (2.26)

where 𝐾𝑀 is the membrane conductivity, 𝑅𝑚 is the membrane resistance, 𝛿 is the membrane

thickness and 𝐴 is membrane area.

There have been numerous studies on membrane conductivity and its relation to external

solution [38-40]. Pismenskaya et al.[40] measured membrane conductivity for different ion

exchange membrane over a concentration range and observed an increase in membrane

conductivity with increasing concentration; Amel et al [33] investigated membrane

conductivity over temperature range and observed an increase in conductivity with increasing

temperature.

Together with this brief introduction to membrane resistance and conductivity and its

relation to external solution concentration, more details about membrane resistance concepts

will be discussed in the next section.

2.4.2.1 Current- voltage curve and limiting current density

Current-voltage curve represents a voltage drop across an ion exchange membrane when

a current is applied over the membrane. A classic current-voltage curve with its 3 main

regions is presented in Figure 2.8. Membrane resistance and limiting current density are

obtained by analyzing the first region, which is called Ohmic region [34]. Pismenskaya et

al.[40] reported current-voltage curve for different anion exchange membranes and different

salts. They observed an unusual trend in current-voltage curves especially for phosphate

containing salts. Also, some investigations has been conducted on limiting current density and

its relation to external solution concentration [14, 35]. They observed that the limiting current

density is increased with increasing salt concentration mainly due to increasing concentration

polarization close to the membrane.

22

Figure 2.8 A classic current-voltage curve and indication of 3 main regions as well as limiting

current density [34].

23

2.5 Surface chemistry and ion exchange membrane

modification

2.5.1 Polyelectrolyte and phosphate attractive group Polyelectrolytes as the name is indicative, are polymers with the electrolyte properties.

More precisely, they are polymers which have charged groups and are soluble in aqueous

solutions. Based on their charges, they are classified as polycations and polyanions.

Polyelectrolytes charges are highly dependent on the solution conditions such as pH and

concentration [6, 41]. Polyelectrolytes are also categorized based on their degree of

dissociation in aqueous environment to two groups: 1) strong polyelectrolyte, which are

completely dissociated in aqueous conditions and 2) weak polyelectrolytes which are partially

dissociated in aqueous solutions. The strong polyelectrolytes (PEs) and their charges are not

highly dependent on solution pH, while charge and degree of dissociation of weak PEs are

highly sensitive to the pH and the solution concentration [41]. There are plenty of PEs which

have been used in chemistry and surface modification. But, here only two of them which are

used in the current study are explained in more detail. Polystyrene sulfonate (PSS) and

Polyallylamine hydrochloride (PAH) are the PEs which have been used in this work. Their

properties and schematic structures are presented in Table 2.2 and Figure 2.9, respectively.

Table 2.2 General properties of two polyelectrolytes used in the current study.

Full name Short Name Charge type pKa Type

Polystyrene

sulfonate

PSS

Polyanion

~ 1

Strong

Polyallylamine

hydrochloride

PAH

Polycation

~ 8.5

Weak

24

Figure 2.9 Schematic structure of PSS and PAH polyelectrolytes.

Cao et al. [42] successfully functionalized PAH with Guanidinium (Gu) and synthetized

PAH-Gu polyelectrolytes. PAH-Gu reported a higher phosphate affinity respect to others

anions. In the Figure 2.10.a the synthesized PAH-Gu is illustrated, and in Figure 2.10.b the

phosphate interaction with PAH-Gu is shown. In the following, the layer by layer (LBL)

techniques as one of the promising methods for surface modification of membranes is

discussed.

Figure 2.10 . a) Lab synthesized PAH-Gu polyelectrolyte [42] and b) phosphate affinity with

PAH-Gu and possible hydrogen and electrostatic bonds [6].

2.5.2 Layer by Layer (LBL) approach for surface modification Layer by layer (LBL) techniques as one the important approaches in surface modification

has received a high attention due to its unique characteristics. Since its first introduction in

late 20th century, LBL applications have widely grown in many different fields such as

25

medical science (tissue engineering), sensor production and membrane technology [41]. LBL

approach composes a sequence of charged layers (polycation or polyanion) in order to build a

thin film on the charged surface. Figure 2.11 shows a simplified schematic of LBL approach.

Polycations attached to the substrate with negative surface charge (e.g. an cation exchange

membrane) due to electrostatic attraction. Following, a polyanion is used to build another

layer on top of the polycation (occur due to electrostatic interaction). Rinsing steps are done

to remove weakly adhered groups on the surface [41]. LBL technique enables to build a

stable, ultra-thin film layer on the surface of the membrane which can tune membrane

transport properties [6, 41, 43]. Other promising advantages of LBL are film high thickness

controllability and defect-free film on the membrane which are crucial for separation

efficiency [41, 43]. A comprehensive review has been conducted on LBL preparation

techniques and parameters affecting the modification stability and efficiency [41, 43]. White

et al.[44, 45] observed a significant increase in selectivity of monovalent cation in Nafion

membrane used in ED. They also investigated the effect of number of bilayer on separation

efficiency in ED. Wessling et al.[46] proposed a model to predict selectivity of sodium over

calcium as a function of PE thickness in CEMs.

Figure 2.11 Simplified LBL preparation of polyelectrolyte multilayer on a charged surface.

Polycation and polyanions form the multilayer film on the substrate surface due to

electrostatic interactions [41].

26

2.6 Ion transport in ion exchange membrane: mathematical

modelling

Ion transport through the ion exchange membrane is a complex phenomenon which is

affected by many parameters such external salt concentration, pH, type of counter-ion and co-

ion, nature of fixed ion, fixed ion density, temperature and etc. Therefore, to understand better

the effect of each parameter on the ions transport through the membrane, a mathematical

model is necessary.

There have been a long effort to model the processes consisting ion exchange

membranes. Many investigators proposed models to predict separation efficiency of

monovalent cations and heavy metals in electrodialysis and they reported a good consistency

between model and experimental data [18, 19, 22]. Beck et al. [25] derived a mathematical

model to describe Donnan dialysis and reported a high dependency of anions selectivity on

membrane and solution activity coefficients. Zhang et al.[21] built a model to quantify 1-1

electrolyte solutions concentrations in feed and receiver compartments in diffusion dialysis.

Ion exchange permselectivity and effect of different parameters were theoretically discussed

by [32] in electrodialysis. They reported dependency of membrane permselectivity on

compartments geometry. Femmer et al. [46] numerically modelled monovalent/divalent cation

selectivity in the LBL modified ion exchange membrane. Transport number of NaCl in some

cation and anion exchange membranes were predicted by [34] and they observed a low

compatibility between model and experimental data at low salt concentration. Kamcev et al.

[47] proposed a new approach to predict ion co-ion concentration in the membrane by more

accurate activity coefficients.

Transport numbers in the membrane are one of the most important parameters which

gives a deeper understanding of ion transport in the ion exchange membrane. In the current

study transport number of counter-ion for different salts are modelled in two different

methods. The main challenge on the mathematical modelling is phosphate speciations

dependency on pH and consequently external solution concentration. In the following, 2

mathematical models will be explained and their governing equation are discussed.

27

2.6.1 Transport number modelling: ideal solution model To explain better the ideal solution model and its assumptions, the Donnan equilibrium

and its governing equations are repeated same as section 2.2.1. Consider again an anion

exchange membrane in contact with an electrolyte solution. As explained earlier (see section

2.2.1), the system is determined by Donnan equilibrium which is resulted from the

electrochemical potential. The electrochemical potential of the system is calculated by

equation (2.27) [31]:

𝜎𝑖 = 𝜇𝑖 + 𝜑 = 𝜇𝑖° + 𝑉𝑖𝑝 + 𝑅𝑇 𝑙𝑛 𝑎𝑖 + 𝑧𝑖𝐹𝜑 (2.27)

where 𝜎𝑖 is the electrochemical potential, 𝜇𝑖° is the chemical potential in reference state 𝑉𝑖 is

the molar species volume, 𝑝 is the pressure, 𝑅 is the gas constant, 𝑇 is temperature, 𝑎𝑖 is the

activity, 𝑧𝑖 is the ion valence, 𝐹 is Faraday constant and 𝜑 is the electrical potential. If a salt is

dissociated in the aqueous solution to form an electrolyte solution, cations (c) and anions (a)

water (w) are the main system elements. The electrochemical potential for anions in a

electrolyte solution is presented in equation (2.28),

𝜎𝑎 = 𝜇𝑎° + 𝑉𝑎𝑝 + 𝑅𝑇 𝑙𝑛 𝑎𝑎 + 𝑧𝑎𝐹𝜑 (2.28)

The same equations are valid for cations and water. Since the solution and membrane are

in the electrochemical equilibrium, the equation below for membrane and solution is valid as

well:

𝜎𝑖𝑠 = 𝜎𝑖

𝑚 (2.29)

where superscripts s and m stand for solution and membrane, respectively. Combining

equation (2.28) and (2.29) for anion in the system, the equation (2.30) is resulted:

𝑅𝑇𝑙𝑛 𝑎𝑎

𝑠

𝑎𝑎𝑚 − (𝑃𝑚 − 𝑃𝑠)𝑉𝑎 − 𝑧𝑎𝐹(𝜑𝑎

𝑚 − 𝜑𝑎𝑠) = 0 (2.30)

similarly, the cation and water are determined by same equation. The equation (3.31) is

derived by combining equations (2.30) for anion and cation. The equation (2.31) presents

membrane Donnan potential,

𝜑𝐷𝑜𝑛 = 𝜑𝑚 − 𝜑𝑠 =1

𝑧𝑖𝐹 (𝑅𝑇 𝐿𝑛

𝑎𝑖𝑠

𝑎𝑖𝑚 − 𝜋𝑉𝑖) (2.31)

where 𝜋 is the pressure difference and it is calculated as below:

28

𝜋 = 𝑃𝑚 − 𝑃𝑠 =𝑅𝑇

𝑉𝑤 𝑙𝑛

𝑎𝑤𝑠

𝑎𝑤𝑚 (2.32)

by assuming number of anion and cation moles in the electrolyte solution as 𝜐a and 𝜐c ,

respectively, and combining the equations (2.31) and (2.32), the Donnan equilibrium is

derived as below for the described system,

𝑙𝑛 [(𝑎a

𝑠

𝑎a𝑚)

𝜐a

. (𝑎𝑐

𝑠

𝑎𝑐𝑚)

𝜐𝑐

] =𝑉𝑎𝑐

𝑉𝑤 𝑙𝑛 (

𝑎𝑤𝑠

𝑎𝑤𝑚) (2.33)

the equation (2.33) become membrane Donnan equilibrium by replacing 𝑥 =𝑉𝑎𝑐

𝑉𝑤 , [34]

(𝑎a𝑚)𝜐a(𝑎𝑐

𝑚)𝜐𝑐

(𝑎𝑤𝑚)𝑥

=(𝑎a

𝑠 )𝜐a(𝑎𝑐𝑠)𝜐𝑐

(𝑎𝑤𝑠 )𝑥

(2.34)

Applying following assumptions into equation (2.34) will result equation (2.35) which

correlates the ion concentration in the membrane and solution.

Water activity is considered equal in membrane and solution phases (𝑎𝑤𝑚 ≈ 𝑎𝑤

𝑠 );

Ideal solution is considered for membrane and bulk solution (activity coefficients are

assumed to be equal to unity in membrane and solution);

MX-type electrolyte is considered to be in contact with membrane (𝜐a = 𝜐c = 1);

Homogeneous membrane structure has been considered,

the ideal solution assumptions are the main reason to name the model “Ideal Solution Model”.

Equation (2.35) is written for (MX-type electrolyte here NaCl) to simplify further calculations

and decrease number of symbols.

𝐶𝑁𝑎𝑚 𝐶𝐶𝑙

𝑚 = 𝐶𝑁𝑎𝑠 𝐶𝐶𝑙

𝑠 (2.35)

To maintain the electroneutrality condition for an anion exchange membrane and an

electrolyte solution, the equation (2.36) should be valid,

𝐶𝑓𝑖𝑥 + 𝐶𝑁𝑎𝑚 = 𝐶𝐶𝑙

𝑚 (2.36)

Combining equations (2.35) and (2.36) give the ions concentrations in the anion

exchange membrane as a function of solution concentration and fixed charge concentration

(𝐶𝑓𝑖𝑥) which is presented below:

𝐶𝑁𝑎𝑚 =

1

2 (√𝐶𝑓𝑖𝑥

2 + 4𝐶𝑁𝑎𝑠 𝐶𝐶𝑙

𝑠 − 𝐶𝑓𝑖𝑥) (2.37)

𝐶𝐶𝑙𝑚 =

1

2 (√𝐶𝑓𝑖𝑥

2 + 4𝐶𝑁𝑎𝑠 𝐶𝐶𝑙

𝑠 + 𝐶𝑓𝑖𝑥) (2.38)

The counter-ion and co-ion (here chloride and sodium, respectively) transport numbers in

the anion exchange membrane are calculated as a function of ion concentration membrane and

mobility in the membrane as below [34],

29

𝑇𝐶𝑙𝑚 =

𝑢𝐶𝑙𝑚𝐶𝐶𝑙

𝑚

𝑢𝑁𝑎𝑚 𝐶𝑁𝑎

𝑚 +𝑢𝐶𝑙𝑚𝐶𝐶𝑙

𝑚 (2.39)

𝑇𝑁𝑎𝑚 =

𝑢𝑁𝑎𝑚 𝐶𝑁𝑎

𝑚

𝑢𝑁𝑎𝑚 𝐶𝑁𝑎

𝑚 +𝑢𝐶𝑙𝑚𝐶𝐶𝑙

𝑚 (2.40)

the ion mobility in the membrane has been correlated as its value in aqueous solution by

Tanak et al.[31]. Ion transport numbers are modelled for different salts and the results are

shown in the following sections.

The so-called “Idea solution model” assumed that the activity coefficients in the

membrane and the solution are equal to unity that is a very rough approximation. Kamcev et

al. [47] showed that activity coefficients in the membrane and solution are significantly

different especially at low concentration. This explains the inconsistency observed by [34] in

their simulation with experimental data at low concentration.

2.6.2 Transport number modelling: Manning theory and number Ideal solution model predicts the ion transport number in the membrane based on the

Donnan theory and some simplified assumptions. Donnan equilibrium and consequently ideal

solution model highly depend on ion properties in the membrane. As explained in previous

section, to derive ions transport number through the Donnan equilibrium, ion activity

coefficients in the membrane are assumed to be unity (ideal solution assumption) which is a

rough assumption particularly at low solution concentration. Moreover, activity coefficients in

the membrane are considerably different with the ones in solution mainly due to presence of

polymer [47]. Experimental difficulties and practical limitations are the mains challenge to

measure the ion activity coefficients in the membrane. Therefore, many investigations have

been conducted in order to propose a fundamental model to predict ion activity coefficients in

the membrane [47]. Manning [48] proposed his counter-ion condensation theory to predict ion

activity coefficients for polyelectrolyte dissolved in aqueous solutions. Moreover, the good

compatibility between Manning theory and ion exchange membrane in contact with

electrolyte solution has been reported [47].

In order to assume ion activity coefficients in the membrane, Manning assumes

polyelectrolytes as the long linear chains that charged groups are homogeneously and equally

have distributed through the entire chains [47, 49]. Manning also has neglected the interaction

between the charged groups in the membrane compared to the fixed charged groups and salt

ions [48] Manning proposed a model parameters as “Manning parameters” (𝜉) in order to

define a linear charge density in the polyelectrolytes [48]:

30

𝜉 =𝜆𝐵

𝑏 (2.41)

where 𝜆𝐵 is Bjerrum length and 𝑏 is the distance between fixed charged group in the

membrane. Bjerrum length is the distance that the required energy to separate mobile ion from

fixed charged group are equal to a constant value [47]. Manning proposed to treat Manning

parameters (𝜉) as adjustable factor in case of lack of information about membrane detailed

properties [47]. Activity coefficients as the main limiting factor in the modelling of ion

transport in ion exchange membranes were predicted by Manning theory [47, 48]. In the

followings, ion transport number of different counter-ions are modelled using Donnan

equilibrium coupled with Manning theory.

2.6.2.1 Transport number modelling: real solution model

The ion transport number in the ion exchange membranes are governed by Donnan

equilibrium as explained in previous sections. In the real solution model, Manning theory is

combined with Donnan equilibrium in hope of achieving a more accurate model. The ion

activity coefficients in the membrane are predicted based on Manning and the ones in the

solution extracted from experimental data reported in literature. Donnan membrane

equilibrium (see equation (2.34)) is also valid here. The main assumptions of the real solution

model are membrane homogeneity and water ideality (water activity difference in membrane

and solution is neglected) in membrane and solution (which is not very rough assumption)

[47]. Manning proposed the following equations for counter-ion and co-ion activity

coefficients in the membrane:

𝛾𝑔𝑚 =

1

𝑧𝑔𝜉 𝑋+𝑧𝑔𝜐𝑔

𝑋+𝑧𝑝𝑧𝑔𝑒𝑥𝑝 [−

1

2𝑋

𝑋+𝑧𝑝𝑧𝑔 𝜉 (𝜐𝑝+𝜐𝑔)] (2.42)

𝛾𝑝𝑚 = 𝑒𝑥𝑝 [−

1

2(

𝑧𝑝

𝑧𝑔)

2

𝑋

𝑋+𝑧𝑝𝑧𝑔 𝜉 (𝜐𝑝+𝜐𝑔)] (2.43)

where subscripts 𝑔 and 𝑝 refer to counter-ion and co-ion, respectively. Here, 𝑧 is the absolute

charge valance, 𝑣 is the ion numbers in one mole of salt and 𝑋 is a ratio of fixed charge

concentration over co-ion concentration (𝑋 =𝐶𝑓𝑖𝑥

𝐶𝑐𝑜−𝑖𝑜𝑛𝑚 ).

Again, for the system including a monovalent salt electrolyte in contact with an anion

exchange membrane, cations with (+) sign are co-ions and anions with (– ) sign are counter-

ion. The equations (2.38) and (2.39) are written based on Donnan equilibrium and

31

electroneutrality of system with an anion exchange membrane and a monovalent electrolyte

solution (for more details on other types of salts see Appendix A):

(𝐶+𝑚𝐶−

𝑚)(𝛾+𝑚𝛾−

𝑚) = (𝛾𝑠𝑠)2(𝐶𝑠

𝑠)2 (2.44)

𝐶−𝑚 = 𝐶𝑓𝑖𝑥 + 𝐶+

𝑚 (2.45)

where superscripts s and 𝑚 stand for membrane and solution phases while subscript s refer to

salt, C is concentration, + and – refer to co-ion and counter-ion here and 𝛾 is the activity

coefficient.

Combining equations (2.42) to (2.45) will result equation (2.46) which is enable to

calculate co-ion concentration in the membrane. The equation (2.46) should be solved

numerically by an iteration procedure and Manning parameters (𝜉) is chosen as adjustable

parameters.

(𝐶𝑓𝑖𝑥 + 𝐶+𝑚)(𝐶+

𝑚) (

𝐶𝑓𝑖𝑥

𝜉 𝐶+𝑚+1

𝐶𝑓𝑖𝑥

𝐶+𝑚 +1

) 𝑒𝑥𝑝 [−

𝐶𝑓𝑖𝑥

𝐶+𝑚

𝐶𝑓𝑖𝑥

𝐶+𝑚 +2𝜉

] = (𝛾𝑠𝑠)2(𝐶𝑠

𝑠)2 (2.46)

counter-ion concentration could be derived by the co-ion concentration obtained in (equation

(2.46) and system electroneutrality.

Finally, the transport number of counter-ion (𝑇−𝑚) and co-ion (𝑇+

𝑚) in the membrane are

calculated as below:

𝑇−𝑚 =

𝑢−𝑚𝐶−

𝑚

𝑢+𝑚𝐶+

𝑚+𝑢−𝑚𝐶−

𝑚 (2.47)

𝑇+𝑚 =

𝑢+𝑚𝐶+

𝑚

𝑢+𝑚𝐶+

𝑚+𝑢−𝑚𝐶−

𝑚 (2.48)

32

3 Materials and Methods

3.1 Chemicals and materials

PAH-Gu used in this project was same as the one synthesized previously in our group by

Cao et al. [42] while polystyrene sulfonate (PSS, 𝑀𝑤 ~ 70 000) was purchased from Sigma-

Aldrich and used as received. Sodium chloride (NaCl, p.a., 99.8%, Sigma-Aldrich), sodium

sulfate (Na2SO4, p.a. anhydrous, 99%, Fluka), potassium chloride (KCl, p.a., 99.9%,

J.T.Baker), potassium phosphate monobasic (KH2PO4_H2O, p.a., 99%, Sigma-Aldrich) and

sodium phosphate monobasic monohydrate (NaH2PO4_H2O, p.a., Acros Organics) were used.

Milli-Q water was purified in a Millipore RiOs reverse osmosis system.

3.2 Layer by layer modification on anion exchange

membranes

Commercial Fuji membranes (Fujifilm Manufacturing Europe BV, The Netherlands)

have been used as the bare membranes for surface modification (LBL modification) and the

further characterizations. Commercial Fuji membranes are dense membranes with

polypropylene as the reinforcement. Membranes were cut and stored in the hydrated

conditions according to the manufacturers’ instructions before any experimental

characterization. In order to modify a bare membrane with polyelectrolytes, firstly, 200 mg

PAH-Gu was completely dissolved in 200 mL NaCl 0.5 M. Likewise, PSS-NaCl solution was

made. We performed a layer by layer (LBL) adsorption by sequentially immersing the

commercial membrane in 0.1 M PAH-Gu-0.5 NaCl solution for 10 minutes, immersing in

Milli-Q water to remove weakly adhered polyelectrolytes for 5 minutes, then immersing in

0.1 M PSS-0.5 NaCl solution and again immersing in Milli-Q water for 5 minutes. This

process was repeated 5 times in order to build 5 bilayers (PAH-Gu/PSS)5 [42, 44]. The

modified membranes were stored in 0.5 M NaCl solution prior to experiments.

3.3 Characterization of surface properties

The characterization techniques were used in order to evaluate LBL modification

success. Sulfur as an indicative element was monitored and modification success was

evaluated based on presence of sulfur on the surface (since the bare Fuji membrane does not

contain sulfur) and it is only present in PSS.

33

3.3.1 XPS analysis The elemental analysis of the anion exchange resin was carried out using an X-ray

Photoelectron Spectrometer (Thermo Fisher Scientific Kα model). A monochromatic Al Kα X-

ray source was used with a spot size of 400 μm at a pressure of 10-7 mbar. The flood gun was

turned on during the measurement in order to compensate the potential charging of the

surface. The peak position was adjusted based on the internal standard C 1s peak at 284.8 eV,

with an accuracy of ± 0.05 eV. Avantage processing software was used to analyse all the

spectra.

3.3.2 SEM-EDX analysis Surfaces of membranes were analyzed with FEI Nova NanoSEM™ scanning electron

microscopes (SEM) equipped with Energy-dispersive X-ray spectrometry (EDX) detector

operating at 10 kV. The working distance and magnification were 6.4mm and 150× for the

surface.

3.4 Water uptake

Water uptake was measured after membrane samples (both commercial Fuji and LBL

modified) were equilibrated in 0.5 M aqueous solutions of NaCl, KCl, NaH2PO4 and KH2PO4

at ambient temperature and pressure for 24 h. Wet membrane mass, 𝑚𝑤𝑒𝑡, was measured after

removing surface water of sample membranes by tissues rapidly. Then, the samples were

dried in vacuum oven at 40 °C for 48 h in order to measure dry membrane mass, 𝑚𝑑𝑟𝑦 .

Membrane water uptake 𝑊𝑢 is calculated using equation below [16, 27, 29]

𝑊𝑢 (g (𝐻2𝑂)/g𝑑𝑟𝑦 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒) =𝑚𝑤𝑒𝑡−𝑚𝑑𝑟𝑦

𝑚𝑑𝑟𝑦 (3.1)

Each measurement was repeated 3 times and one standard deviation was considered as

measurement uncertainty.

3.5 Permselectivity: set-up and method

As previously explained in chapter 2, permselectivity is being measured commonly via

membrane potential approach. Membrane potential was determined through a 2 compartments

cell where a sample membrane is placed between solutions with 2 different concentrations (In

this study concentration ratio over two sides of membrane was set at 1-10, in order to ensure

enough driving force for ions transport). The potential difference across the membrane, 𝐸𝑥,

34

was measured using Ag/AgCl double junction reference electrode (Metrohm, The

Netherlands) which were placed in the solution of either side of membrane. Figure 3.1.

schematically shows permselectivity set-up used in this study. Capillary pipes were installed

to measure potential across the membrane. Moreover, in order to determine membrane

potential, 𝐸𝑚𝑒𝑎𝑠 , the electrode offset potential, 𝐸𝑜𝑓𝑓𝑠𝑒𝑡 , which resulted from the reference

electrode potential should be subtracted from 𝐸𝑥.

𝐸𝑚𝑒𝑎𝑠 = 𝐸𝑥 − 𝐸𝑜𝑓𝑓𝑠𝑒𝑡 (3.2)

Permselectivity of the anion exchange membrane was calculated via potential approach

which has been discussed earlier (see section 2.4.1.3).

Figure 3.1 Schematic drawing of permselectivity measurement apparatus.

All the samples equilibrated with the solution of low concentration compartment

(compartment B) overnight prior to the experiments [27, 29]. In addition, permselectivity

apparatus has some side accessories such as sample holder and O-ring (effective area 8.1

cm2). Two channels head pump (Cole-Parmer Co, The Netherlands) were used in order

maintain the solution concentration constant by recirculation of solution at 110 ml/min. A

thermal bath (Thermo Fisher Scientific Inc, USA) was used in order to maintain a constant

temperature of the system. The measurement performed at least 3 times and the results were

averaged. The uncertainty was taken as one standard deviation from the mean. The potential

(𝐸𝑥), mostly was registered after stable value (around 3-5 minutes).

35

3.5.1 Design of experiments: Taguchi method Permselectivity of an anion exchange membrane is mainly governed by Nerst-Planck

equation. The permselectivity practically depends on,

Temperature of solution

Concentration of external solution

Type of ion (salt)

pH of external solution

Flow rate and etc,

It is clear that analysing such number of parameters in order to find the effective

variables is quite complex and time consuming. Number of experiments which give a

comprehensive insight into dependency of the membrane permselectivity on mentioned

parameters have been optimized using design of experiment methods. Design of experiment

has been widely used in study of wastewater treatment. ANOVA and Taguchi methods as

common approaches in design of experiment were used in study of electrodialysis for removal

of various cations [18, 22, 50, 51]. In the current study, Taguchi method has been applied to

optimize the number of experiments needed for the analysis of membrane permselectivity.

Taguchi method gives a robust guideline to optimize and recognize the most important

variables affecting target parameter. Here, a brief introduction on Taguchi approach on design

of experiment is provided (more detail in Appendix B). Figure 3.2. illustrates an overview on

procedure followed by Taguchi to design an experiment.

Figure 3.2 An overview on Taguchi design of experiment procedure [51].

36

The procedure can be grouped as:

Planning a matrix experiment to determine the effects of the control factors;

Conducting matrix of experiment;

Data analysis and results verification;

here are a brief definition of the Taguchi factors:

Quality characteristic: a parameters under investigation ( e.g. permselectivity);

Control factor: the design parameters or the variables which their control is easy (e.g.

Concentration, etc);

Noise factor: the factors which are hard or expensive to control during normal process

(e.g. pH);

In the current project, permselectivity of an anion exchange membrane was chosen as quality

characteristic, 3 factors each with three levels (low, medium and high) were selected as

explained later. Controllable factors and their levels were chosen based on the literature data

as 1) temperature 2) concentration and 3) salt type [22, 50].

Temperature (°C): 15, 20 and 25 °C was considered as levels. Such temperatures were

chosen based on usual wastewater temperature;

Concentration (M): 0.1, 0.2, 0.5 M were considered for concentration levels;

Salt Type: NaH2PO4, NaH2PO4, NaCl. And KCl;

Taguchi proposed a matrix of experiment which include a number of experiments that have to

be performed in order to recognize the effect of variables on quality characteristics.

The obtained data through the experiments were analysed as Taguchi recommended (by

analysing signal-to-noise ratio (SN)) to define the optimum level for the control factors.

Signal-to-noise ratio takes in to account both mean and standard deviation of each experiment

run (more details in Appendix B).

3.6 Electrical resistance: set-up and method

To measure the electrical resistance of anion exchange membrane a six compartment cell

as illustrated in Figure 3.3 was used [37]. The set-up was made of plexiglass by (STT

products B.V., The Netherlands). The central anion exchange membrane is the membrane

under investigation and it is equilibrated overnight in measuring solution prior to experiments.

The membrane under investigation has an effective area of 8.04 cm2, while the area of the

auxiliary membranes are 33.16 cm2. All the AEMs and CEMs used in the experiments were

provided by (Fujifilm Manufacturing Europe BV, The Netherlands). The electrode

37

compartments (compartment 1 and 6) contain 0.5 M Na2SO4 solution. The solutions in

compartments 2 and 5 are kept equal to ensure constant solution concentration in

compartment 3 and 4 (compartments adjacent to the membrane under investigation).

Measurement with various salts in a concentration range has been performed.

Figure 3.3 Schematic diagram of the six-compartment cell used to perform current–voltage

curve and membrane resistance measurements; CEM is a cation exchange membrane, AEM is

an anion exchange membrane, V is the potential difference over the capillaries.

All the solution were pumped by two channels head pump (Cole-Parmer Co, The

Netherlands) with the flow rate of each stream adjusted at 110 ml/min. The anode

compartment contained an anode which was made of titanium. The cathode compartment

contained a cathode which was made from stainless steel. The reactions which occurred in

electrodes are listed below [52]:

Anode: 2𝐻2𝑂 → 𝑂2 ↑ + 4𝐻+ + 4𝑒−

Cathode: 2𝐻2𝑂 + 2𝑒− → 𝐻2 ↑ + 2𝑂𝐻−

Measurement were carried out with a potentiostat/galvanostat apparatus (Metrohm

Autolab B.V, The Netherlands) and using NOVA 10 software in order to register the voltage

drop. Figure 3.4 illustrates the galvanostat apparatus which was used in membrane resistance

measurement.

38

Figure 3.4 The galvanostat apparatus used in membrane electrical resistance measurement

The voltage drop over the membrane under investigation was measured using Haber-

Luggin capillaries which were filled with 3 M KCl . The capillaries were connected to the

reference electrode in order to measure voltage drop. All measurements have been carried out

at constant temperature of 25℃. The final resistance was obtained by slope of current-voltage

curve and equation (2.25). Solution resistance (𝑅𝑠) was measured using same apparatus of

membrane resistance but without presence of the membrane.

39

4 Result and discussion

4.1 Membrane surface modification: LBL techniques

Figure 4.1 shows LBL modified membrane that was made in the current study. Five

bilayers of PSS and PAH-Gu are built on the surface of the commercial Fuji membranes. De

Grooth et al. [53] reported a higher selectivity of LBL modified membranes in the presence of

0.5 M NaCl solution as a solvent. Thus, a salt solution (NaCl 0.5 M) is used to build the

polyelectrolyte multi-layer. The functionalized PAH-Gu is used in order to achieve high

phosphate transport due to the phosphate affinity which has been observed by Cao et al. [42].

The number of bilayers affect ion transport in the membrane and ion selectivity, considerably

[44, 45]. Based on a previous study in our group by Cao et al [42], 5 bilayers showed a good

stability and high phosphate affinity. Therefore, in the current study 5 bilayers of (PAH-

Gu/PSS)5 were used to modified commercial anion exchange membrane. Hereafter, we refer

to surface modified membrane as “LBL modified” which is (PAH-Gu/PSS)5 and the

polyelectrolyte solvent is 0.5 M NaCl solution.

Figure 4.1 Schematic drawing of LBL modified membrane that is conducted in the current

study as (PAH-Gu/PSS)5. Here, AEM refers to anion exchange membrane.

40

4.2 Characterization of membrane surface

4.2.1 SEM-EDX analysis To evaluate modification’s successes, SEM-EDX analysis is performed on LBL modified

membrane surface (Figure 4.2). The location of different elements on the membrane surface

are represented in Figure 4.2. Sulphur atomic percentage (around 2%) shows that the

modification is successful since sulfur indicates presence of PSS. Moreover, membrane bulk

mainly consist of carbon (62%) and oxygen (14%) due to presence of these elements on

membrane matrix and polyelectrolytes.

Carbon is mainly located on the fibers (Figure 4.2.b) while nitrogen and oxygen are in

membrane bulk (Figure 4.2.c,d). For more detail see Appendix C.

Figure 4.2 Element mapping: a) SEM-EDX image of LBL modified Fuji membrane surface,

b) carbon, c) nitrogen, d) oxygen, e) sodium, f) sulphur, g) chloride.

41

4.2.2 XPS analysis XPS analysis was used on different types of LBL modified membranes as well as bare

Fuji membrane to observe sulfur fraction difference on the surface of membrane. Figure 4.3

shows the sulfur fraction on the bare membrane and different type of modifications. As the

number of PSS layer increases, sulfur percentage grows from 0 to 1.4 %. as expected.

Figure 4.3 Sulphur composition of different type of modifications and bare membrane.

XPS analysis is performed also on LBL modified membrane after permselectivity

experiment and sulfur fraction (2.3%) demonstrates that the modification is also stable. The

elemental analysis of the bare and modified membranes are discussed in more detail in

Appendix C.

4.3 Taguchi results

Taguchi method and its procedure to design an experiments are presented in chapter 3 and

Appendix B. In this section, the signal-to- noise ratio (SN ratios) of experimentally obtained

permselectivity data have been analyzed as Taguchi recommended. The analysis was

implemented with the aid of Minitab17 software, Minitab Inc. Figure 4.4 demonstrates the

mean signal-to-noise ratios of permselectivity for a specific matrix of experiment. The highest

42

value for SN ratio is observed at 𝑇 = 20℃ which indicates possibility of minimizing the

effects of temperature on the membrane permselectivity by fixing the temperature constant at

𝑇 = 20℃ . The analysis also ranked temperature as the least important parameters on

permselectivity (see Appendix B). Permselectivity experiments are measured often at constant

temperature at 𝑇 = 20℃ and there have been no explanation for such choice in literature [27,

29, 54]. Here, with the aid of Taguchi method, a reason for our choice for a constant

temperature is proved Moreover, higher dependency are observed for Permselectivity on

concentration at low concentration compared to high concentration (the slope of line between

C(M)=[0.1-0.2] is much higher than C(M)=[0.2-0.5]). Therefore, more investigations and

measurements have performed on low concentration compared to high concentration.

Majority of literature works have measured membrane permselectivity at low external

solution concentration (which is in-line with obtained results by Taguchi analysis) [29, 30,

54].

Figure 4.4 Signal-to-noise ration analysis of permselectivity based on Taguchi analysis

4.4 Permselectivity results

Based on Taguchi analysis, constant temperature 𝑇 = 20℃ was considered and

permselectivity of the anion exchange membranes for 4 different salts (NaCl, KCl, NaH2PO4,

KH2PO4) were measured at different concentration. Permselectivity were measured

experimentally at the concentrations C(M)= [0.1 0.15 0.2 0.25 0.5]. In the following sections,

permselectivity of 4 different salts in LBL modified and commercial Fuji membrane are

discussed.

43

4.4.1 Permselectivity: commercial membrane Membrane permselectivity values are measured for commercial Fuji membrane using

four different electrolytes as shown in Figure 4.5. In general, Fuji membranes’ permselectivity

decreases with increasing external solution concentration for all the given salts, but such

decrease is greater for phosphate-containing salts compared to chloride-containing

electrolytes. A decrease in membrane permselectivity with increasing external solution

concentration was expected based on Donnan exclusion. Donnan exclusion predicts that the

co-ion concentration in the membrane is proportional to external solution concentration as it is

shown in equation (2.10).

(4.1)

Figure 4.5 Permselectivity and its dependency on external solution concentration for 4

different electrolytes in commercial Fuji membrane.

Therefore, as the external solution concentration increases, co-ion concentration

increases which results a decrease in permselectivity values. Additionally, Figure 4.5

demonstrates that chloride-containing solutions have higher permselectivity values than

phosphate-containing salts mainly due to higher values of diffusion coefficient and lower

hydrate radius of chloride ion compared to phosphate ion (see Table 4.1) . The results are in

accordance with works of Geise et al [29] and Cassady et al [28]. They observed the same

trend for other ions in cation exchange membranes and related such lower permselectivity

44

values to the size and the diffusion coefficients of different mobile ions. While Sarapulova et

al.[55] investigated the membrane conductivity for a concentration range and reported that

phosphate-containing electrolytes have lower ion transport due to shift in ion speciation in

phosphate (monovalent phosphate shifts to divalent phosphate) and their explanation was

verified by observing a considerable pH change during experiments. However, such

interpretation could not be valid in the current study, since no pH and conductivity variations

are observed during permselectivity experiments (see Appendix D). So, the lower

permselectivity values for phosphate-containing electrolytes compared to chloride-containing

ones could be explained by the lower diffusion coefficient and higher hydrated radii of

phosphate with respect to chloride. Table 4.1 shows the ions properties, which could affect

permselectivity values and ion transport in the membrane.

Table 4.1 ion properties which affect ion transports in the membrane [12].

ion

Type

Diffusion Coefficient

(10-5 cm2 s-1)

Hydrated radius

(nm)

𝐶𝑙− Anion 2.03 0.195

𝐻2𝑃𝑂4− Anion 0.96 0.302

𝑁𝑎+ Cation 1.05 0.358

𝐾+ Cation 1.08 0.331

The effect of co-ion (cation) in permselectivity is not completely clear in Figure 4.5.

Higher permselectivity is observed for sodium in phosphate containing salts while lower

values are registered for sodium in chloride-containing salts. Geise et al. [29] observed an

ambiguous influence of co-ion in permselectivity of cation exchange membrane. While,

Harrison et al. [28] reported a higher value of permselectivity for chloride than sulfate as co-

ions in cation exchange membrane. It is also possible that there is an interaction between co-

ion and counter-ion which affects ion transport and, as a consequence, permselectivity. More

investigations are required to understand better the effects of co-ion and counter-ion on

permselectivity values

4.4.2 Permselectivity: LBL modified membrane Figure 4.6 demonstrates permselectivity values for 4 different electrolytes in the LBL

modified membrane. As mentioned earlier, the modification includes a phosphate–attractive

45

receptor which showed a high affinity to phosphate. Figure 4.6 illustrates that LBL

modifications decreases permselectivity values for all the electrolyte solutions. It is also

observed that permselectivity dependency on external solution concentration decreases with

LBL modification. In other words, the LBL modification has somehow limited validity on

Donnan exclusion for the system under study. Moreover, The effect of co-ion became more

negligible in modified membranes compared to commercial Fuji membranes.

Figure 4.6 Permselectivity values and their dependency on external solution concentration for

4 different electrolytes in LBL modified membrane which contains a phosphate-attractive

group.

Importantly, a drastic decrease in permselectivity values are observed for phosphate-

containing salts compared to chloride-containing salts. The permselectivity values for

phosphate decreased by 10% with the LBL modification respect to commercial AEM, this

could be mainly due to the presence of Guanidinium (Gu) as a phosphate-selective receptor.

White et al [44] reported a significant increase in the selectivity of monovalent-divalent by

LBL modification in cation exchange membranes but they also observed a decrease in ion

fluxes on LBL modified membranes. So, the decrease in flux causes a decrease of ion

transport and consequently lower permselectivity value. Therefore, their observations are in

46

accordance with the results obtained in the current study. Also, Sata et al [56] observed a

decrease in ion permselectivity with the modified cation exchange membranes and relates

such phenomena to sieving effect of ions by dense polyelectrolyte layer. The decrease in the

permselectivity values observed in Figure 4.6 could be explained by high binding affinity of

phosphate to guadinium (Gu), which somehow prevents the passage of phosphate through the

membrane. Figure 4.7 shows the permselectivity values for NaH2PO4 in the commercial Fuji

and LBL modified membrane as a function of concentration. It can be seen that NaH2PO4

permselectivity values (Figure 4.7) decrease significantly with modification, while the values

are almost constant for NaCl (Figure 4.8). A lower phosphate permselectivity in LBL

modified membrane compared to bare Fuji membrane (Figure 4.7) could be explained by

presence of phosphate-attractive receptors. While in Figure 4.8 since the Guanidinium (Gu)

showed a lower affinity to chloride with respect to phosphate, no considerable decrease are

observed for NaCl permselectivity in commercial Fuji and LBL modified membranes.

Figure 4.7 Permselectivity values and their relation to external solution concentration for

NaH2PO4 in commercial Fuji and LBL modified membrane.

Besides phosphate affinity to the charged groups, the electrostatic attraction between

polyanion and cations (co-ions) could also be responsible for a decrease in permselectivity

values. Sata et al. [56] explained permselectivity reduction by electric attraction of anions and

polycation used in their study. So, presence of PSS as polycation in our modification attracts

more cations (𝑁𝑎+, 𝐾+) and therefore co-ion concentration in the membrane increases and

consequently permselectivity decreases.

47

Figure 4.8 Permselectivity values and their relation to external solution concentration for

NaCl in commercial Fuji and LBL modified membrane.

The electrostatic interaction between polyelectrolytes and co-ion may affect

permselectivity for modified membranes, but its effect is not significant in comparison with

affinity of selective group. As it can be seen in Figure 4.8, the electrostatic attraction slightly

decreases the permselectivity for NaCl in LBL as compared to commercial Fuji membrane.

4.4.3 Permselectivity results: water uptake Figure 4.9 shows permselectivity values versus water uptake for Fuji and LBL modified

membrane for the salts under investigation. Immersing a polymeric membrane in solution

decreases the fixed charge concentration of membrane as the fixed charged groups are diluted.

A decline in the fixed charge concentration results the higher co-ion concentration in the

membrane and consequently causes the lower membrane permselectivity values. Figure 4.9

demonstrates that with increasing water uptake, membrane permselectivity declines (based on

Donnan exclusion). So, NaH2PO4 and KH2PO4 which have lower permselectivity values,

show higher water uptake values.

Based on Donnan exclusion, membranes with higher fixed charge concentration should

have lower water uptake, which contrasts the results of Figure 4.9. Membrane fixed charge

48

density is supposed to increase with LBL modification. Therefore, LBL modified membranes

should show lower water uptake values with respect to bare membranes (based on Donnan

exclusion). While, Figure 4.9 shows higher water uptake values for LBL modified membranes

compare to bare Fuji membrane. Many investigators reported water uptake as a poor predictor

for fixed charge concentration [27, 29]

Figure 4.9 Permselectivity versus water uptake for commercial Fuji membrane for 4 testes

salts.

Although water uptake verifies the general trend of permselectivity for tested salts, its

estimation is restricted in the ions transport. Długołecki et al. [34] reported a weak

compatibility between water uptake results and the ions transport number. Also, a high

inconsistency were observed by Geise et al. [27] for water uptake data and membrane

permselectivity and it is related to the high sensitivity of water uptake measurement on the

test system and measurement error.

4.5 Electrical resistance results

The electrical resistance of commercial Fuji membranes was tested for 4 different

electrolyte solutions at constant temperature. All the membranes were equilibrated prior to

experiments in test solution. Concentration range and type of salts were the same that used for

permselectivity measurements for possible future correlation. Most of the literature studies on

membrane resistance focus on membrane resistance and its dependency on NaCl

concentration as the external solution. Lack of literature data for membrane resistance for

Fuji

LBL

FujiLBL

Fuji

LBL

FujiLBL

50

60

70

80

90

0,5 0,55 0,6 0,65 0,7 0,75 0,8

Per

mse

lect

ivit

y (

%)

Water uptake (g water/g dry membrane)

NaCl

KCl

NaH2PO4

KH2PO4

49

other salts and their dependency on the bulk solution concentration triggered us to do the

measurement for different type of salts.

4.5.1 Electrical resistance results: Commercial membrane Figure 4.10 shows the membrane resistance for the commercial Fuji membrane as a

function of concentration for the given salts. Phosphate-containing salts demonstrate much

higher resistance compared to chloride containing ones, indeed their resistance it is almost

seven times higher than the one measured for chloride-containing salts. Figure 4.10 also

shows that co-ions influence (here 𝑁𝑎+𝑎𝑛𝑑 𝐾+) on membrane resistance are greater at low

concentration, while at high concentration similar behavior is observed for both phosphate-

and chloride-containing salts, regardless of their cations. Higher membrane resistance values

are observed for KCl than NaCl at low concentration, which might be referred to the higher

size of potassium than sodium.

Figure 4.10 Membrane resistance values as a function of external solution concentration for

the given salts on commercial Fuji membrane.

Moreover, some fluctuation are observed for the phosphate resistance at lower

concentration, which could mainly be related to the effect of diffusion boundary layer and

double electrical layer. Galama et al [36] reported that the effects of diffusional boundary

layer and the electric boundary layer are higher at low concentration due to the higher

50

concentration polarization effect. Therefore, the higher phosphate resistance for commercial

Fuji membrane can be explained by the higher hydration radius and diffusion coefficients of

chloride compared to phosphate.

Many studies reported an independency between NaCl concentration in external solution

and membrane resistance at high concentration [27, 34-37]. Their results are in accordance

with the obtained results (Figure 4.10) for all the tested salts at concentration higher than 0.3

M.

Figure 4.11 shows a current-voltage curve obtained through the electrical resistance

experiments under direct current (DC) for NaH2PO4 and NaCl at concentration 0.5M. Figure

4.11 indicates ohmic and plateau regions, which have been studied mainly in this work. A

greater slope is observed for NaH2PO4 at ohmic region compared to NaCl, which corresponds

to a higher membrane resistance for phosphate than chloride. Also, limiting current densities

are shown in Figure 4.11 and a lower limiting current density is observed for phosphate than

chloride.

Figure 4.11 Current-voltage curve obtained for NaCl and NaH2PO4 at concentration 0.5 M.

Ohmic and plateau region as well as limiting current density are presented as the main focus

of this study.

51

4.5.2 Electrical resistance: limiting current density Figure 4.12 illustrates the limiting current density values as a function of external

solution concentration in commercial Fuji membranes for the tested electrolytes. For all the

given salts, limiting current density increases with increasing external solution concentration.

As the external solution concentration increases, the concentration polarization effect grows

and therefore, limiting current density increases. The obtained results are consistent with the

data reported in [14, 34]. Moreover, higher current density is observed for chloride containing

salts with respect to phosphate containing salts. The lower limiting current density for

phosphate may be explained by phosphate lower diffusion coefficients and bigger size (see

Table 4.1), which result in a lower mobility for phosphate than chloride. Krol et al [14]

reported a higher value of limiting current density for KCl than NaCl, which is consistent with

the results observed in Figure 4.12.

Figure 4.12 Limiting current density values as function of concentration in a commercial Fuji

membrane for 4 given salts.

4.6 Ion transport model results

Ion transport numbers are modelled for 4 different salts in commercial Fuji membrane.

Mathematical models are conducted to predict ion transport numbers and compare results

52

with experimental values. Experimental values of ion transport number in the membrane are

derived through membrane potential (see Appendix E). Ideal solution model and real solution

model are implemented as described earlier. Table 4.2 shows model parameters and their

values that are used in mathematical models. Monovalent and divalent ion mobility in the

membrane are, respectively, around 1

10 and

1

20−

1

50 of their values in aqueous environment

[31].

Table 4.2 Model parameters and their values which are used in mathematical models.

Model Parameter symbol value unit Reference

Ion exchange

capacity 𝐼𝐸𝐶 1.7 𝑚𝑒𝑞𝑢𝑖𝑣./𝑔 𝑑𝑟𝑦 [16]

Water uptake* 𝑊𝑢 ~ 0.6 g(𝐻2𝑂)/g𝑑𝑟𝑦 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 Experiment

Fixed charge

concentration* 𝐶𝑓𝑖𝑥 ~ 2.8 𝑒𝑞𝑢𝑖𝑣./𝑙 Calculation as

𝐼𝐸𝐶

𝑊𝑢

Sodium ion

mobility in

aqueous

condition

𝑢𝑁𝑎𝑠 7.92 × 10−8 𝑚2 (𝑉𝑠)⁄ [57]

Potassium ion

mobility in

aqueous

condition

𝑢𝐾𝑠 7.62 × 10−8 𝑚2 (𝑉𝑠)⁄ [57]

Chloride ion

mobility in

aqueous

condition

𝑢𝐶𝑙𝑠 5.19 × 10−8 𝑚2 (𝑉𝑠)⁄ [57]

Phosphate

mobility in

aqueous

condition

𝑢𝐻2𝑃𝑂4

𝑠 3.42 × 10−9 𝑚2 (𝑉𝑠)⁄ [58]

Manning

parameter*

𝜉 3.9-4 - chosen

* Value shown may vary for different type of salts.

4.6.1 Mathematical modelling: ideal solution model Figure 4.13 shows ideal solution model calculation of counter-ion transport number for 4

different salts and its dependency on the external solution concentration in a commercial Fuji

membrane. Ions transport numbers decrease with increasing external solution concentration as

Donnan equilibrium is predicted. Figure 4.13 demonstrates that at low solution concentration,

53

the majority of the ionic current are carried out by counter-ions, while with increasing

external solution concentration, the share of co-ions in the ionic current are increased.

Długołecki et al.[34] observed the same values of chloride transport number for NaCl in a

commercial anion exchange membrane. A lower phosphate transport number compared to

chloride ions are explained by lower phosphate mobility in comparison with chloride.

Experimental data of counter-ion transport number (see Appendix E) are in good agreement

with ideal solution model at high concentration ( > 0.3 𝑀 ). An inconsistency with

experimental data and ideal solution model at low concentration was reported by Długołecki

et al.[34] which is in-line with our observations.

Figure 4.13 Ideal solution model calculation of the counter-ion transport number as a function

of external solution concentration in a commercial Fuji anion exchange membrane for 4

different salts.

Ideal solution model is not capable to take in to account the diffusion boundary layer

which affect significantly ion transport at low concentration. The discrepancy between ideal

solution model and experimental data at low concertation might be explained by either

neglecting the effects of diffusion boundary layer or ideal solution assumption in the

membrane. Kamev et al.[47] reported a considerable difference between the ion activity

coefficients in the membrane and solution at low concentration.

54

4.6.2 Mathematical modelling: real solution model The Figure 4.14 illustrates the real solution model calculation for counter-ion transport

numbers in the commercial Fuji membrane for the given salts. The results shows that the

monovalent ions have higher transport number than divalent. Also, monovalent ions show

greater dependency on concentration than divalent. Transport number of monovalent ions in

the membrane decrease with increasing external solution concentration as predicted by

Donnan equilibrium while divalent ions are almost independent of external solution

concentration.

Figure 4.14 Real solution model calculation of the counter-ion transport numbers as a

function of external solution concentration in commercial Fuji anion exchange membrane for

4 different salts.

Lower transport numbers are observed for divalent phosphate than monovalent ion. These

observations are explained by the lower diffusion coefficients and bigger size of divalent

phosphate compared to monovalent phosphate as shown in Table 2.1. Moreover, Figure 4.14

shows the effect of co-ion in ion transport. Potassium-containing salts shows a lower transport

number than sodium-containing salts mainly due to lower mobility of potassium compare to

sodium.

Monovalent

Divalent

55

Figure 4.15 shows the real solution model values for counter-ion transport number of

NaH2PO4 in the commercial Fuji membranes and a comparison with experimental data. The

experimental data are placed between monovalent and divalent transport number that are

predicted by the real solution model. The results are in good agreement with experimental

data as it can be seen from Figure 4.15.

Figure 4.15 Real solution model calculation of counter-ion transport number for NaH2PO4 as

a function of external solution concentration versus experimental data.

Figure 4.16 presents the real solution model for counter-ion transport number for NaCl

and its comparison with experimental data. The data are in good agreements with

experimental data especially at high concentration since Manning predictions for ion activity

coefficients in membrane have higher accuracy at high solution concentration [47].

56

Figure 4.16 Real solution model calculation of counter-ion transport number for NaCl as a

function of external solution concentration versus experimental data.

The real solution model shows good compatibility with experimental data especially for

phosphate containing solutions. The real solution model can predict ion transport in anion

exchange membranes with reasonable accuracy. The lack of information about membrane

molecular properties has limited precise calculation of Manning parameter and consequently

increases the model inaccuracy.

57

5 Conclusion

In this study, commercial Fuji anion exchange membranes were modified with (PAH-

Gu-PSS)5 polyelectrolytes through layer by layer (LBL) approach. PAH-Gu was introduced at

the at membrane surface, because the Guanidinium (Gu) group has already demonstrated a

higher affinity to phosphate than other anions. Phosphate transport through commercial Fuji

anion exchange membrane and LBL modified membrane were compared. Phosphate transport

in the membrane also was compared with other ions to recognize difference between

phosphate transport in anion exchange membrane and other ions (mainly chloride ion).

Permselectivity and electrical resistance of ion exchange membranes were measured with

respect to four types of salt solutions (KCl, NaCl, NaH2PO4 and KH2PO4) as a function of the

external solution concentration.

Based on the obtained results, phosphate-containing solution demonstrates lower

permselectivity than chloride-containing salt, this is mainly due to phosphate lower diffusion

coefficients and bigger size. Also, LBL modified membranes with phosphate-selective

receptor show a considerably lower phosphate permselectivity than bare Fuji membrane

probably due to high phosphate affinity to the receptor. Water uptake correlation to

permselectivity shows a higher value of permselectivity at lower water uptake.

Electrical resistance measurements were performed on commercial Fuji membrane for

given salts and considerably higher resistances were observed for phosphate compared to

chloride due to higher size and lower diffusion coefficient of phosphate. Also, at high

concentration, the membrane resistance shows an independency on external solution

concentration.

Finally, two mathematical models were built to predict ions transport in the membrane

and the results were compared to experimental data. the proposed mathematical models

enable to predict ions transport numbers in the membrane. The so-called real solution model

uses Manning approach to predict activity coefficients in the membrane and its results show a

reasonable consistency with experimental data.

58

5.1 Future work

Further efforts are required to have a better understanding of the ion transport in the

membrane. Here, some recommendation are listed which could be helpful for future work:

Membrane electrical resistance and permselectivity measurements should be

implemented on other commercial membranes;

Membrane permselectivity and membrane electrical resistance should be

measured in a wider concentration range and, particularly, at concentration lower

than 0.1 M (since concentration polarization has a significant effect at low

concentration);

Electrical resistance should be done for LBL modified membrane and the results

should be compared with commercial Fuji membrane. Surface characterization

techniques (such as XPS analysis and SEM-EDX) should be performed to

evaluate modification stability in the presence of electrical field;

A more comprehensive model could be obtained by correlating a structural

parameters which takes into account the membrane structure in the ions transport

through the membrane. Such parameter can be modeled by Monte Carlo random

method due to complexity of membrane structure.

59

6 Appendix

6.1 Appendix A: real Solution model

Consider an anion exchange membrane in contact with MX2-type electrolyte. Number of

cations moles are half of the number of anions mole in solution, so, equation (A.1) shows the

cations and anions distribution in solution,

𝐶+𝑠 =

1

2𝐶−

𝑠 = 𝐶𝑠𝑠 (A.1)

Membrane and solution are in chemical equilibrium and so, Donnan equilibrium implies

equation (A.2) as below:

(𝐶+𝑚 𝛾+

𝑚)(𝐶−𝑚 𝛾−

𝑚)2 = (𝐶−𝑠𝛾−

𝑠)2(𝐶+𝑠 𝛾+

𝑠) (A.2)

To maintain electroneutrality in the membrane, equation (A.3) should be held to keep

system neutral,

𝐶−𝑚 = 𝐶𝑓𝑖𝑥 + 2𝐶+

𝑚 (A.3)

Manning proposed equations (A.4) and (A.5) to predict ion activity coefficients in an

anion exchange membrane in contact with MX2-type electrolyte.

𝛾−𝑚 = (

𝐶𝑓𝑖𝑥

𝜉𝐶+𝑚+2

𝐶𝑓𝑖𝑥

𝐶+𝑚 +2

) 𝑒𝑥𝑝 [−

1

2 𝐶𝑓𝑖𝑥

𝐶+𝑚

𝐶𝑓𝑖𝑥

𝐶+𝑚 +6𝜉

] (A.4)

𝛾+𝑚 = 𝑒𝑥𝑝 [−

2 𝐶𝑓𝑖𝑥

𝐶+𝑚

𝐶𝑓𝑖𝑥

𝐶+𝑚 +6𝜉

] (A.5)

Co-ion concentration in an anion exchange membrane for MX2 electrolyte membrane is

calculated by combining equations (A.2)-(A.5) and is presented below,

(𝐶𝑓𝑖𝑥 + 2 𝐶+𝑚)(𝐶+

𝑚) (

𝐶𝑓𝑖𝑥

𝜉 𝐶+𝑚+1

𝐶𝑓𝑖𝑥

𝐶+𝑚 +1

)

2

𝑒𝑥𝑝 [−3

𝐶𝑓𝑖𝑥

𝐶+𝑚

𝐶𝑓𝑖𝑥

𝐶+𝑚 +6𝜉

] = 4 (𝛾𝑠𝑠)3(𝐶𝑠

𝑠)3 (A.6)

Counter-ion transport number will be calculated as explained earlier by equation below:

𝑇−𝑚 =

𝑢−𝑚𝐶−

𝑚

𝑢+𝑚𝐶+

𝑚+𝑢−𝑚𝐶−

𝑚 (A.8)

60

Now, suppose an anion exchange membrane in contact with M2X-type electrolyte.

number of cations are double of number of anions mole in solution, so, equation (A.9) shows

the cations and anions distribution in solution,

1

2𝐶+

𝑠 = 𝐶−𝑠 = 𝐶𝑠

𝑠 (A.9)

Membrane and solution are in chemical equilibrium and Donnan equilibrium implies

equation (A.10) as below:

( 𝐶−𝑚 𝛾−

𝑚)(𝐶+𝑚 𝛾+

𝑚)2 = (𝐶+𝑠 𝛾+

𝑠)2( 𝐶−𝑠𝛾−

𝑠) (A.10)

To maintain electroneutrality in the membrane, equation (A.11) should be held to keep

system neutral,

𝐶−𝑚 =

1

2𝐶𝑓𝑖𝑥 + 𝐶+

𝑚 (A.11)

Manning proposed equations (A.12) and (A.13) to predict ion activity coefficients in an

anion exchange membrane in contact with M2X-type electrolyte.

𝛾−𝑚 = (

𝐶𝑓𝑖𝑥

2𝜉𝐶+𝑚+2

𝐶𝑓𝑖𝑥

𝐶+𝑚 +2

) 𝑒𝑥𝑝 [−

1

2 𝐶𝑓𝑖𝑥

𝐶+𝑚

𝐶𝑓𝑖𝑥

𝐶+𝑚 +6𝜉

] (A.12)

𝛾+𝑚 = 𝑒𝑥𝑝 [−

1

8 𝐶𝑓𝑖𝑥

𝐶+𝑚

𝐶𝑓𝑖𝑥

𝐶+𝑚 +6𝜉

] (A.13)

Co-ion concentration in an anion exchange membrane for M2X electrolyte membrane is

calculated by combining equations (A.9)-(A.13) and is presented below,

(1

2𝐶𝑓𝑖𝑥 + 𝐶+

𝑚) (𝐶+𝑚)2 (

𝐶𝑓𝑖𝑥

2𝜉 𝐶+𝑚+2

𝐶𝑓𝑖𝑥

𝐶+𝑚 +2

) 𝑒𝑥𝑝 [−

3

4 𝐶𝑓𝑖𝑥

𝐶+𝑚

𝐶𝑓𝑖𝑥

𝐶+𝑚 +6𝜉

] = (𝛾𝑠𝑠)3(𝐶𝑠

𝑠)3 (A.14)

61

6.2 Appendix B: Taguchi approach for design of

experiment (DOE)

Taguchi method was used to design permselectivity experiment. Taguchi is a method to

quantitatively identifying the right inputs and parameters levels for making a product. As

explained earlier, Taguchi uses signal-to-noise ratio to determine the optimal parameters for

design of an experiment. Although Taguchi proposed wide range of signal-to-noise ratios,

three of them are the most important ones, which are listed below:

Nominal is best: 𝑆𝑁𝑖 = 10 𝑙𝑜𝑔(𝑦�̅�)2

𝑠𝑖2

Larger is better: 𝑆𝑁𝑖 = −10 𝑙𝑜𝑔 (∑ 1

𝑦𝑖2⁄

𝑛𝑖

𝑛)

Smaller is better: 𝑆𝑁𝑖 = −10 𝑙𝑜𝑔 (∑ 𝑦𝑖

2𝑛𝑖

𝑛)

Taguchi proposed a number of orthogonal arrays to aid in the design of experiment.

Taguchi uses 2 array matrices for design of experiment. The inner array is used to investigate

the effect of control factor while the outer is used to model noise factor. In the current study,

for experiments design of permselectivity, 3 control factors in mix level was considered.

Taguchi proposed a L16 matrix of experiments. The ranking of parameter for their effects on

permselectivity based on different approach are listed below:

Ranking of parameters effect on signal-to-noise ratio:

1. Salt type

2. Concentration

3. Temperature

Ranking of parameters effect on mean value of permselectivity:

1. Concentration

2. Salt type

3. Temperature

62

6.3 Appendix C: membrane surface characterization

SEM-EDX analysis

The details information of SEM-EDX analysis in LBL modified membrane surface are

presented in Figure 6.1. Sample and related peaks are analyzed using ZAF to identify surface

elements.

Figure 6.1 Peak identification using ZAF with SEM-EDX apparatus.

To improve peaks identification results, a statistical analysis has been done. Smart quants

shows weight percentages of each elements on the membrane surface. The smart quant results

are presented in Table 6.2.

Table 6.1 Smart quant results for LBL modified Fuji membrane surface.

element Weight

%

Atomic

%

Net Int. Error % K ratio Z R A F

C 51.84 59.69 631.00 6.96 0.2630 1.0353 0.9875 0.4900 1.0000

N 19.24 19.00 66.50 10.18 0.0375 1.0039 0.9970 0.1940 1.0000

O 2.82 18.00 181.60 9.25 0.0559 0.9770 1.0053 0.2747 1.0000

Na 0.6 0.36 12.00 6.46 0.0037 0.8742 1.0255 0.7034 1.0026

S 0.77 0.33 15.00 3.92 0.0067 0.8415 1.0476 0.9973 1.0337

Cl 6.73 2.63 105.20 2.74 0.0546 0.7979 1.0504 1.0040 1.0133

63

XPS analysis

XPS analysis is performed to recognize the elements, which are presents on the

membrane surface. The table shows that with increasing PSS layer the amount of sulfur are

increasing which indicates modification successes. The amount of sulfur after permselectivity

experiments is still high, therefore, the modification is stable. The higher sulfur percentage

after permselectivity could be explained by inhomogeneity of modification.

Table 6.2 XPS analysis results for different membrane samples.

C

(%)

O

(%)

N

(%)

S

(%)

P

(%)

Cl

(%)

Si

(%)

Bare Fuji

71.7

19.8

5.7

0

0

0

2.7

Fuji -PSS

64.1

22.2

7.9

0.6

1.5

0

3.8

Fuji

(PAH-Gu-

PSS)5

64.1

21.6

7.6

1.4

1.5

0.4

3.7

Fuji

(PAH-Gu-

PSS)5- After

Permselectivity

68

19

6.1

2.3

0.4

0.5

3.7

64

6.4 Appendix D: pH and conductivity results

To investigate the possibility of H+ ion transport phenomena during permselectivity

experiment on commercial Fuji membrane, pH and conductivity of solutions in both

concentrated compartment (compartment A) and dilute compartment (compartment B) are

measured before and after permselectivity experiment. Figure 2.6 shows conductivity

measurement for NaH2PO4 electrolyte over a concentration range in concentered and dilute

compartments before and after permselectivity. It can be seen that the conductivity of each

compartments at each specific concentration does not vary, therefore, deprotonation of

phosphate could not be the reason for lower permselectivity of phosphate containing

electrolytes with respect to chloride containing electrolytes.

Figure 6.2 Conductivity measurement in concentrated compartment (compartment A) and

dilute compartment (compartment B) in permselectivity experiment for NaH2PO4. Empty dots

are after permselectivity experiments and filled dots are before permselectivity experiment.

Moreover, in order to verify the above explanation, pH measurements are done in the

same experiments and compartments. Figure 6.3 presents pH measurement in 2 compartments

consisting NaH2PO4 solution. It can be seen that pH does not vary for each compartment at a

specific concentration before and after experiments. Thus, deprotonation of phosphate could

not be responsible of lower phosphate permselectivity.

0

5

10

15

20

25

0 0,1 0,2 0,3 0,4 0,5 0,6

Co

nd

uct

ivit

y (m

s/s)

Concentration (M)

Compartent A(initial)Compsrtment B(initial)Compartment A(final)Compartment B(final)

65

Figure 6.3 pH measurement in concentrated compartment (compartment A) and dilute

compartment (compartment B) in permselectivity experiment for NaH2PO4. Empty dots are

after permselectivity experiments and filled dots are before permselectivity experiment.

Therefore, the results that are shown above have verified that the deprotonation of

monovalent phosphate to divalent phosphate could not be a reason for lower phosphate

permselectivity since in that case, pH of solution in receiving compartment (compartment B)

should be considerably decreased.

4

4,1

4,2

4,3

4,4

4,5

4,6

4,7

4,8

4,9

0 0,2 0,4 0,6

PH

Concentration (M)

Compartment A(initial)

Compartment B(initial)

Compsrtment A(final)

Compartment B(Finall)

66

6.5 Appendix E

Counter-ion transport number were derived from experimental values of membrane

potential. The equation (E.1) shows a relation with counter-ion transport number, membrane

potential and external solution concentration [31].

𝑇𝑐𝑜𝑢𝑛𝑡𝑒𝑟−𝑖𝑜𝑛𝑚 =

1

2[1 +

𝐸𝑚𝑅𝑇

𝐹 𝑙𝑛

𝐶𝐴 𝛾𝐴𝐶𝐵 𝛾𝐵

] (E.1)

the counter-ion transport number are presented for different electrolytes in a commercial Fuji

membrane. Higher transport number were observed for chloride containing than phosphate

containing which is in accordance to real solution model.

Figure 6.4 Experimental values of counter-ion transport numbers in commercial Fuji membrane as a

function of external solution concentration.

67

Nomenclature

Abbreviation

Abbreviation Description

AEM Anion Exchange Membrane

CEM Cation Exchange Membrane

ED Electro-Dialysis

LBL Layer-by-Layer

PE Polyelectrolyte

PSS Polystyrene sulfonate

PAH Polyallylamine hydrochloride

Gu Guanidinium

DC Direct Current

SN Signal-to-Noise

XPS X-ray Photoelectron Spectrometer

SEM-EDX Scanning Electron Microscope/Energy Dispersive Using X-Ray

IEC Ion Exchange Capacity

68

Symbols

Symbol Description Symbol Description

𝜎 Electrochemical

potential 𝐴

Membrane effective

area

𝜇 Chemical potential 𝜁 Manning Parameter

𝑧 Ion valance 𝑢 Ion mobility

𝐹 Faraday constant Superscripts

𝜑 Electrical potential 𝑠 Solution phase

𝛿 Membrane thickness 𝑚 Membrane phase

𝑎 Activity Subscripts

𝐶 Concentration 𝑓𝑖𝑥 Fixed charge group

𝐿𝑖𝐾 Phenomenological

coefficient 𝑚𝑒𝑎𝑠 Measured value

𝑇 Transport number 𝑐𝑎𝑙 Calculated Value

𝐸 Potential 𝑚 + 𝑠 Solution and

membrane

𝑊𝑢 Water uptake 𝑚 Membrane

𝛼 Permselectivity 𝑠 Solution

𝑅𝑖 Resistance g Counter-ion

𝐾𝑚 Membrane

conductivity p Co-ion

69

List of Figures

Figure 1.1 Phosphate consumption distribution by sector (left) and region (right). .................. 1

Figure 1.2 An example of water eutrophication of a river (Delftse Schie) in Delft, The

Netherlands. ................................................................................................................................ 3

Figure 2.1 Fraction of phosphate speciation as a function of pH [11] ....................................... 6

Figure 2.2 Schematic illustration of an anion exchange membrane .......................................... 7

Figure 2.3 Schematic illustration of concentration distribution of a monovalent electrolyte

(here NaCl ) in anion exchange membrane and solution (Left) and Donnan potential as a

potential difference between membrane and solution (right). AEM refers to ion exchange

membrane. ................................................................................................................................ 10

Figure 2.4 Schematic illustration of simplified electrodialysis cell. AEM refers to anion

exchange membrane and CEM refers to cation exchange membrane [18]. ............................. 12

Figure 2.5 a) Illustration of the diffusion dialysis principle through the HCl separation process

from its feed solution b) a typical experimental set-up for diffusion dialysis [23] .................. 13

Figure 2.6 Schematic diagram of phosphate removal in Donnan dialysis [10]. ...................... 14

Figure 2.7 Schematic illustration of a perfect anion exchange membrane (completely

permselective) with 2 possible driving forces namely concentration gradient and electrical

field. .......................................................................................................................................... 16

Figure 2.8 A classic current-voltage curve and indication of 3 main regions as well as limiting

current density [34]. ................................................................................................................. 22

Figure 2.9 Schematic structure of PSS and PAH polyelectrolytes. ......................................... 24

Figure 2.10 . a) Lab synthesized PAH-Gu polyelectrolyte [42] and b) phosphate affinity with

PAH-Gu and possible hydrogen and electrostatic bonds [6]. .................................................. 24

70

Figure 2.11 Simplified LBL preparation of polyelectrolyte multilayer on a charged surface.

Polycation and polyanions form the multilayer film on the substrate surface due to

electrostatic interactions [41]. .................................................................................................. 25

Figure 3.1 Schematic drawing of permselectivity measurement apparatus. ............................ 34

Figure 3.2 An overview on Taguchi design of experiment procedure [51]. ............................ 35

Figure 3.3 Schematic diagram of the six-compartment cell used to perform current–voltage

curve and membrane resistance measurements; CEM is a cation exchange membrane, AEM is

an anion exchange membrane, V is the potential difference over the capillaries. ................... 37

Figure 3.4 The galvanostat apparatus used in membrane electrical resistance measurement .. 38

Figure 4.1 Schematic drawing of LBL modified membrane that is conducted in the current

study as (PAH-Gu/PSS)5. Here, AEM refers to anion exchange membrane. .......................... 39

Figure 4.2 Element mapping: a) SEM-EDX image of LBL modified Fuji membrane surface,

b) carbon, c) nitrogen, d) oxygen, e) sodium, f) sulphur, g) chloride. ..................................... 40

Figure 4.3 Sulphur composition of different type of modifications and bare membrane. ....... 41

Figure 4.4 Signal-to-noise ration analysis of permselectivity based on Taguchi analysis ....... 42

Figure 4.5 Permselectivity and its dependency on external solution concentration for 4

different electrolytes in commercial Fuji membrane. .............................................................. 43

Figure 4.6 Permselectivity values and their dependency on external solution concentration for

4 different electrolytes in LBL modified membrane which contains a phosphate-attractive

group. ........................................................................................................................................ 45

Figure 4.7 Permselectivity values and their relation to external solution concentration for

NaH2PO4 in commercial Fuji and LBL modified membrane. ................................................. 46

71

Figure 4.8 Permselectivity values and their relation to external solution concentration for

NaCl in commercial Fuji and LBL modified membrane. ........................................................ 47

Figure 4.9 Permselectivity versus water uptake for commercial Fuji membrane for 4 testes

salts. .......................................................................................................................................... 48

Figure 4.10 Membrane resistance values as a function of external solution concentration for

the given salts on commercial Fuji membrane. ........................................................................ 49

Figure 4.11 Current-voltage curve obtained for NaCl and NaH2PO4 at concentration 0.5 M.

Ohmic and plateau region as well as limiting current density are presented as the main focus

of this study. ............................................................................................................................. 50

Figure 4.12 Limiting current density values as function of concentration in a commercial Fuji

membrane for 4 given salts. ..................................................................................................... 51

Figure 4.13 Ideal solution model calculation of the counter-ion transport number as a function

of external solution concentration in a commercial Fuji anion exchange membrane for 4

different salts. ........................................................................................................................... 53

Figure 4.14 Real solution model calculation of the counter-ion transport numbers as a

function of external solution concentration in commercial Fuji anion exchange membrane for

4 different salts. ........................................................................................................................ 54

Figure 4.15 Real solution model calculation of counter-ion transport number for NaH2PO4 as

a function of external solution concentration versus experimental data. ................................. 55

Figure 4.16 Real solution model calculation of counter-ion transport number for NaCl as a

function of external solution concentration versus experimental data. .................................... 56

Figure 6.1 Peak identification using ZAF with SEM-EDX apparatus. .................................... 62

Figure 6.2 Conductivity measurement in concentrated compartment (compartment A) and

dilute compartment (compartment B) in permselectivity experiment for NaH2PO4. Empty dots

are after permselectivity experiments and filled dots are before permselectivity experiment. 64

72

Figure 6.3 pH measurement in concentrated compartment (compartment A) and dilute

compartment (compartment B) in permselectivity experiment for NaH2PO4. Empty dots are

after permselectivity experiments and filled dots are before permselectivity experiment. ...... 65

Figure 6.4 Experimental values of counter-ion transport numbers in commercial Fuji

membrane as a function of external solution concentration. .................................................... 66

73

7 References

1. Ye, Y., et al., Insight into biological phosphate recovery from sewage. Bioresource

Technology, 2016. 218: p. 874-881.

2. Das, J., et al., Adsorption of phosphate by layered double hydroxides in aqueous

solutions. Applied Clay Science, 2006. 32(3-4): p. 252-260.

3. Levlin, E., RECOVERY OF PHOSPHATE FROM SEWAGE SLUDGE AND

SEPARATION OF METALS BY ION EXCHANGE. 2003.

4. Li, R., et al., Recovery of phosphate from aqueous solution by magnesium oxide

decorated magnetic biochar and its potential as phosphate-based fertilizer substitute.

Bioresour Technol, 2016. 215: p. 209-14.

5. Cordell, D., Sustainability implications of global phosphorus scarcity for food

security. 2010, University of Technology of Sydney, Sydeny.

6. Wang, M., Functionalized Fe3O4 Nanoparticles for Phosphate Adsorption. 2016.

7. Arsand, D. and A. Moura Bernardes, Electrodialysis Treatment of Phosphate

Solutions. 2014: p. 101-109.

8. Zhang, Y., et al., Phosphate Separation and Recovery from Wastewater by Novel

Electrodialysis. Environmental Science & Technology, 2013. 47(11): p. 5888-5895.

9. Zeng, Z., Phosphorus removal by ceramic tight ultra-filtration (CTUF) membranes for

RO pre-treatment. 2012, Delft university of Technology.

10. Chen, S.y., et al., Phosphate removal from aqueous solution by Donnan dialysis with

anion-exchange membrane. Journal of Central South University, 2014. 21(5): p. 1968-

1973.

11. Pismenskaya, N., Dependence of composition of anion-exchange membranes and their

electrical conductivity on concentration of sodium salts of carbonic and phosphoric

acids. Journal of Membrane Science, 2001. 181: p. 185-197.

12. Lide, D.R., Handbook of Chemistry and Physics. 2003: CRC Press.

13. Strathmann, H., Chapter 6 Ion-Exchange Membrane Processes in Water Treatment.

2010. 2: p. 141-199.

14. Krol, J.J., Monopolar and Bopolar ion exchange membrane: transport limitation. 1997,

University of Twente.

15. Schmidt, S.A., Mathematical models of ion transport through nafion membranes in

modified electrodes and fuel cells without electroneutrality. 2010, University of

IOWA.

16. Güler, E., et al., Monovalent-ion-selective membranes for reverse electrodialysis.

Journal of Membrane Science, 2014. 455: p. 254-270.

17. Vaselbehagh, M., et al., Surface modification of an anion exchange membrane to

improve the selectivity for monovalent anions in electrodialysis – experimental

74

verification of theoretical predictions. Journal of Membrane Science, 2015. 490: p.

301-310.

18. Sadrzadeh, M., A. Kaviani, and T. Mohammadi, Mathematical modeling of

desalination by electrodialysis. Desalination, 2007. 206(1-3): p. 538-546.

19. Sadrzadeh, M., et al., Neural network modeling of Pb2+ removal from wastewater

using electrodialysis. Chemical Engineering and Processing: Process Intensification,

2009. 48(8): p. 1371-1381.

20. Mohammadi, T., A. Razmi, and M. Sadrzadeh, Effect of operating parameters on Pb2+

separation from wastewater using electrodialysis. Desalination, 2004. 167: p. 379-385.

21. Zhang, X., et al., A quantification of diffusion dialysis process: Single electrolyte

system (hydrochloric acid solution). Chemical Engineering Science, 2015. 135: p.

547-552.

22. Mohammadi, T., et al., Modeling of metal ion removal from wastewater by

electrodialysis. Separation and Purification Technology, 2005. 41(1): p. 73-82.

23. Luo, J., et al., Diffusion dialysis-concept, principle and applications. Journal of

Membrane Science, 2011. 366(1-2): p. 1-16.

24. Zhang, X., et al., A preliminary study on electrically assisted diffusion dialysis.

Separation and Purification Technology, 2014. 122: p. 331-340.

25. Beck, A. and M. Ernst, Kinetic modeling and selectivity of anion exchange in Donnan

dialysis. Journal of Membrane Science, 2015. 479: p. 132-140.

26. Agarwal, C. and A. Goswami, Nernst Planck approach based on non-steady state flux

for transport in a Donnan dialysis process. Journal of Membrane Science, 2016. 507:

p. 119-125.

27. Geise, G.M., M.A. Hickner, and B.E. Logan, Ionic resistance and permselectivity

tradeoffs in anion exchange membranes. ACS Appl Mater Interfaces, 2013. 5(20): p.

10294-301.

28. Harrison J. cassady, m.A.H., Emily C. Cimino, Spesific ion effects on permselectivity

of sulfonated polycation exchange membranes. journal of Membrane Science, 2016.

508: p. 146-152.

29. Geise, G.M., et al., Specific ion effects on membrane potential and the permselectivity

of ion exchange membranes. Phys Chem Chem Phys, 2014. 16(39): p. 21673-81.

30. Xu, T. and K. Hu, A simple determination of counter-ionic permselectivity in an ion

exchange membrane from bi-ionic membrane potential measurements: permselectivity

of anionic species in a novel anion exchange membrane. Separation and Purification

Technology, 2004. 40(3): p. 231-236.

31. Tanak, Y., Chapter 3 Membrane Characteristics and Transport Phenomena. 2007. 12:

p. 37-57.

75

32. Takagi, R., M. Vaselbehagh, and H. Matsuyama, Theoretical study of the

permselectivity of an anion exchange membrane in electrodialysis. Journal of

Membrane Science, 2014. 470: p. 486-493.

33. Amel, A., et al., Bicarbonate and chloride anion transport in anion exchange

membranes. Journal of Membrane Science, 2016. 514: p. 125-134.

34. Piotr Długołęcki, A., Benoît, et al., Transport limitations in ion exchange membranes

at low salt concentrations. Journal of Membrane Science, 2010. 346(1): p. 163-171.

35. A.H. Galama, N.A.H., D.R. Yntema, Method for determining ion exchange membrane

resistance for electrodialysis systems. Desalination 2016. 380: p. 1-11.

36. A.H.Galama, D.A.V., J.Veerman , M.Saakes , H.H.M.Rijnaarts , J.W.Post , and K.

Nijmeijer, Membrane resistance:The effect of salinity gradients over a cation

exchange membrane. Journal of Membrane Science 2014. 467: p. 279-291.

37. Piotr Dlugolecki, P.O., Litty Nijmeijr, Matthias Wessling, On the resistance of

membrane, diffusion boundary layer and double layer in ion exchange membrane

transport. journal of membrane science, 2010. 349: p. 369-379.

38. al., N.P.e., Dependence of composition of anion-exchange membranes and their

electrical conductivity on concentration of sodium salts of carbonic and phosphoric

acids. Journal of Membrane Science, 2001. 181: p. 185.

39. Youcef Sedkaoui , A.S., Hakim Lounici , Omar Arous A new lateral method fo

rcharacterizing the electrical conductivity of ion exchange membranes. Journal of

Membrane Science, 2016. 507: p. 34-42.

40. Natalia Pismenskaya, G.P., Tranport of weak-electrolyte anion through anion

exchange membranes: Current-voltage characteristics. Journal of Membrane Science,

2001. 189: p. 129-140.

41. Joseph, N., et al., Layer-by-layer preparation of polyelectrolyte multilayer membranes

for separation. Polymer Chemistry, 2014. 5(6): p. 1817-1831.

42. Cao, Z., et al., The effect of guanidinium functionalization on the structural properties

and anion affinity of polyelectrolyte multilayers. Soft Matter, 2016. 12(5): p. 1496-

1505.

43. Cheng, C., A. Yaroshchuk, and M.L. Bruening, Fundamentals of Selective Ion

Transport through Multilayer Polyelectrolyte Membranes. Langmuir, 2013. 29(6): p.

1885-1892.

44. White, N., et al., Highly selective separations of multivalent and monovalent cations in

electrodialysis through Nafion membranes coated with polyelectrolyte multilayers.

Polymer, 2015.

45. White, N., et al., Coating of Nafion Membranes with Polyelectrolyte Multilayers to

Achieve High Monovalent/Divalent Cation Electrodialysis Selectivities. ACS Applied

Materials & Interfaces, 2015. 7(12): p. 6620-6628.

46. Femmer, R., A. Mani, and M. Wessling, Ion transport through

electrolyte/polyelectrolyte multi-layers. Scientific Reports, 2015. 5: p. 11583.

76

47. Kamcev, J., et al., Partitioning of mobile ions between ion exchange polymers and

aqueous salt solutions: importance of counter-ion condensation. Phys Chem Chem

Phys, 2016. 18(8): p. 6021-31.

48. MANNING, G.S., Limiting Laws and Counterion Condensation in Polyelectrolyte

Solutions: Colligative Properties. The Journal of Physical Chemistry, 1969. 51.

49. Manning, G.S. and J. Ray, Counterion Condensation Revisited. Journal of

Biomolecular Structure and Dynamics, 1998. 16(2): p. 461-476.

50. Mohammadi, T., Separation of copper ions by electrodialysis using Taguchi

experimental design. Desalination 2004. 169: p. 20-31.

51. Sadrzadeh, M., A. Razmi, and T. Mohammadi, Separation of monovalent, divalent and

trivalent ions from wastewater at various operating conditions using electrodialysis.

Desalination, 2007. 205(1-3): p. 53-61.

52. Dlugolecki, P., et al., Current status of ion exchange membranes for power generation

from salinity gradients. Journal of Membrane Science, 2008. 319(1-2): p. 214-222.

53. de Grooth, J., et al., The role of ionic strength and odd–even effects on the properties

of polyelectrolyte multilayer nanofiltration membranes. Journal of Membrane Science,

2015. 475: p. 311-319.

54. Sata, T., Studies on anion exchange membranes having permselectivity for specific

anions in electrodialysis—effect of hydrophilicity of anion exchange membranes on

permselectivity of anions. Journal of Membrane Science 2000. 167: p. 1-31.

55. Sarapulova, V., et al., Unusual concentration dependence of ion-exchange membrane

conductivity in ampholyte-containing solutions: Effect of ampholyte nature. Journal of

Membrane Science, 2015. 479: p. 28-38.

56. Toshikatsu Sata, T.S., Wongkang Yang, Studies on cation-exchange membranes

having permselectivity between cations in electrodialysis. Journal of Membrane

Science 2002. 206: p. 31-60.

57. Solvent Structure, Dynamics, and Ion Mobility in Aqueous Solutions at 25 °C. J. Phys.

Chem, 1998. 102(214193-4204).

58. Lynch, B. Ion mobility in water condition. 2003; Available from:

http://web.med.unsw.edu.au/phbsoft/mobility_listings.htm.