2. ii
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
3. iii
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
4. iv
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
5. v
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.
8. 1
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
9. 2
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.
10. 3
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
11. 4
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?
12. 5
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.
13. 6
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 (π»2 ππ4
β
) is the main speciation while in neutral
condition both monovalent and divalent (π»ππ4
2β
) 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 ( π»2 ππ4
β
) and divalent phosphate
(π»ππ4
2β
) in Table 2.1.
Table 2.1 Properties of different phosphate anions [12].
Anion Stokeβs radius
(m)
Diffusion Coefficient
(π2
π β )
π»2 ππ4
β
0.256 Γ 10β9
0.96 Γ 10β9
π»ππ4
2β
0.323 Γ 10β9
0.76 Γ 10β9
14. 7
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
15. 8
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, ππ, in Equation (2.1) refers
to the βelectrochemical potentialβ 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.
ππ = ππ + π§π πΉπ (2.1)
where ππ is the electrochemical potential, ππ is the chemical potential, π§π is the species
valence, πΉ is Faraday constant and π is the electrical potential.
The chemical potential of the system is described by equation (2.2),
ππ = πΒ°π + π π ππππ (2.2)
where ππ is the chemical potential of each species in the system, πΒ°π is the reference potential
in standard conditions, π is the universal gas constant, π is temperature and ππ 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,
ππ
Β°π
+ π π ππππ
π
+ π§π πΉπ π
= ππ
Β°π
+ π π ππππ
π
+ π§π πΉπ π
(2.3)
where superscripts π and π 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]:
π π·ππ = π π β ππ =
π π
π§ π πΉ
ππ
ππ
π
ππ
π (2.4)
here, π π·ππ is Donnan potential, π π is the membrane potential and ππ 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):
16. 9
π π·ππ = π π β ππ =
π π
πΉ
ππ
πΆ ππ
π
πΆ ππ
π =
π π
πΉ
ππ
πΆ πΆπ
π
πΆ πΆπ
π (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.
πΆ ππ
π
πΆ ππ
π =
πΆ πΆπ
π
πΆ πΆπ
π (2.6)
where superscripts π and π 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.
πΆ πΆπ
π
= πΆπππ₯ + πΆ ππ
π
(2.7)
where πΆ πΆπ
π
is the chloride concentration in the membrane, πΆ ππ
π
is the sodium concentration and
πΆπππ₯ 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,
πΆ πΆπ
π
= πΆ ππ
π
= πΆ π
(2.8)
here, πΆ πΆπ
π
is the chloride concentration in solution which is equal to the sodium concentration
in solution πΆ ππ
π
and both are identical to the salt concentration in solution πΆ π
.
Combining equation (2.6) to (2.8), gives equation (2.9) which is able to calculate the co-
ion concentration (πΆ ππ
π
) in the membrane.
πΆ ππ
π
=
(πΆ π )2
πΆ πππ₯+πΆ ππ
π (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 (πΆπππ₯ β« πΆ ππ
π
). The approximation is commonly called Donnan approximation
or Donnan exclusion [13, 14].
πΆ ππ
π
=
(πΆ π )2
πΆ πππ₯
(2.10)
Figure 2.3 illustrates schematically the ion concentration distribution in the membrane. As it
is shown, the sodium concentration in the membrane (πΆ ππ
π
) is lower than the fixed ion
concentration. Donnan potential is illustrated as a potential difference between membrane and
solution [14].
17. 10
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
18. 11
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 βconcentratedβ, while
the other compartments which are depleted from ions are called βdiluteβ [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].
19. 12
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.
20. 13
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].
21. 14
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] :
ο· Permselectivity
ο· Electrical resistance
ο· Mechanical stability
ο· Chemical stability
the above parameters are commonly called βperformance parametersβ. 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
22. 15
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].
23. 16
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:
ο· Transport number approach
ο· 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
24. 17
over system and so-called βelectrochemical potentialβ results as equation (2.11) (as mentioned
earlier in section 2.2.1) [13]:
πππ = πππ + ππ = ππ ππ + π π πππ ππ + π§π πΉππ (2.11)
where πππ is the electrochemical potential which is sum of the chemical potential (πππ) and
the electrical potential (ππ). Here, ππ is the molar volume, π is the pressure, π is universal gas
constant, π is temperature, ππ is the activity, πΉ refers to Faraday constant and π stands for
electrical potential.
Considering constant pressure and temperature, the mass flux has been calculated as
equation (2.12),
π½π = β πΏπππ
ππ½ π
ππ§
= β πΏπππ (π π
π ππ ππ
ππ§
+ π§π πΉ
ππ
ππ§
) (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]:
π½π = βπ·π (
ππΆ π
ππ§
+
π§ π πΉπΆ π
π π
ππ
ππ§
) (2.13)
where π·π is the diffusion coefficient, πΆπ is the concentration,
ππΆ π
ππ§
is the concentration gradient
which is causes a chemical potential and
ππ
ππ§
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] :
25. 18
ππ =
π§ π π½ π
β π§ π π½ π
π
π
(2.14)
where ππ is te transport number of specie i, π½π is the mass flux of species i and π§π 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),
β ππ = 1π
π (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]:
πΌ (%) =
ππππ’ππ‘ππβπππ
π
βππππ’ππ‘ππβπππ
π
πππβπππ
π Γ 100 (2.16)
where πΌ is the ion exchange membrane permselectivity, π 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 β membrane potentialβ [31]:
ππΊ = βπΉππΈ (2.17)
where ππΊ is the Gibbs free energy produced by the ion transport, πΉ is Faraday constant and
ππΈ is membrane potential.
Gibbs free energy can be written in terms of chemical potential as it is shown in equation
(2.18),
ππΊπ =
π π
π§ π
πππ =
π π
π§ π
π π πππ ππ (2.18)
where ππ is the transport number of species i, π§π is the ion valence, π is the gas constant, π is
temperature and ππ is the activity. Combining equations (2.17) and (2.18) for all the ion
species, the potential is calculated by equation (2.19):
πΈ = β
π π
πΉ
β« β
π π
π§ π
πππ ππ (2.19)
26. 19
integrating over equation (2.19) gives equation (2.20):
πΈ = β(ππππ‘πππ β ππππππ)
π π
ππΉ
ππ
π2
π1
(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):
πΈ πΆππ =
π π
ππΉ
ππ
π2
π1
(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],
πΌ(%) =
πΈ ππππ
πΈ πππ
Γ 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
(ππ’) is calculated using equation (2.23):
ππ’ (g (π»2 π)/gπππ¦ ππππππππ) =
π π€ππ‘βπ πππ¦
π πππ¦
(2.23)
where π π€ππ‘ and π πππ¦ 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]:
27. 20
πΆπππ₯ =
πΌππ ππ₯πβππππ πππππππ‘π¦ (πΌπΈπΆ)
πππ‘ππ π’ππ‘πππ (ππ’)
(2.24)
where πΆπππ₯ is the fixed charge concentration, πΌπΈπΆ is the ion exchange capacity which usually
obtained through the experiment and ππ’ 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):
π π+π =
π
π
( 2.25)
where π π+π is the membrane and solution resistance, π is the potential drop over membrane
and π is the current density. Membrane resistance is obtained by subtracting the solution
resistance (π π) from π π+π. However it should be considered that the membrane resistance
under DC includes diffusion boundary layer resistance and electrical double layer [36]. Tanak
29. 22
Figure 2.8 A classic current-voltage curve and indication of 3 main regions as well as limiting
current density [34].
30. 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
31. 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
32. 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].
33. 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.
34. 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]:
ππ = ππ + π = ππ
Β°
+ ππ π + π π ππ ππ + π§π πΉπ (2.27)
where ππ is the electrochemical potential, ππ
Β°
is the chemical potential in reference state ππ is
the molar species volume, π is the pressure, π is the gas constant, π is temperature, ππ is the
activity, π§π is the ion valence, πΉ is Faraday constant and π 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),
π π = π π
Β°
+ ππ π + π π ππ π π + π§ π πΉπ (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:
ππ
π
= ππ
π
(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:
π πππ
π π
π
π π
π β (π π
β π π )ππ β π§ π πΉ(π π
π
β π π
π ) = 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,
π π·ππ = π π β ππ =
1
π§ π πΉ
(π π πΏπ
ππ
π
ππ
π β πππ) (2.31)
where π is the pressure difference and it is calculated as below:
35. 28
π = π π
β π π
=
π π
π π€
ππ
π π€
π
π π€
π (2.32)
by assuming number of anion and cation moles in the electrolyte solution as πa and πc ,
respectively, and combining the equations (2.31) and (2.32), the Donnan equilibrium is
derived as below for the described system,
ππ [(
πa
π
πa
π)
πa
. (
π π
π
π π
π)
π π
] =
πππ
π π€
ππ (
π π€
π
π π€
π) (2.33)
the equation (2.33) become membrane Donnan equilibrium by replacing π₯ =
πππ
π π€
, [34]
(πa
π) πa(π π
π) π π
(π π€
π) π₯
=
(πa
π ) πa(π π
π ) π π
(π π€
π ) π₯
(2.34)
Applying following assumptions into equation (2.34) will result equation (2.35) which
correlates the ion concentration in the membrane and solution.
ο· Water activity is considered equal in membrane and solution phases (π π€
π
β π π€
π
);
ο· Ideal solution is considered for membrane and bulk solution (activity coefficients are
assumed to be equal to unity in membrane and solution);
ο· MX-type electrolyte is considered to be in contact with membrane (πa = πc = 1);
ο· Homogeneous membrane structure has been considered,
the ideal solution assumptions are the main reason to name the model βIdeal Solution Modelβ.
Equation (2.35) is written for (MX-type electrolyte here NaCl) to simplify further calculations
and decrease number of symbols.
πΆ ππ
π
πΆ πΆπ
π
= πΆ ππ
π
πΆ πΆπ
π
(2.35)
To maintain the electroneutrality condition for an anion exchange membrane and an
electrolyte solution, the equation (2.36) should be valid,
πΆπππ₯ + πΆ ππ
π
= πΆ πΆπ
π
(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
(πΆπππ₯) which is presented below:
πΆ ππ
π
=
1
2
(βπΆπππ₯
2
+ 4πΆ ππ
π
πΆ πΆπ
π
β πΆπππ₯) (2.37)
πΆ πΆπ
π
=
1
2
(βπΆπππ₯
2
+ 4πΆ ππ
π
πΆ πΆπ
π
+ πΆπππ₯) (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],
36. 29
ππΆπ
π
=
π’ πΆπ
π
πΆ πΆπ
π
π’ ππ
π πΆ ππ
π +π’ πΆπ
π
πΆ πΆπ
π (2.39)
π ππ
π
=
π’ ππ
π
πΆ ππ
π
π’ ππ
π πΆ ππ
π +π’ πΆπ
π
πΆ πΆπ
π (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 βIdea solution modelβ 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 βManning parametersβ (π) in order to
define a linear charge density in the polyelectrolytes [48]:
37. 30
π =
π π΅
π
(2.41)
where π π΅ is Bjerrum length and π 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 (π) 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:
πΎπ
π
=
1
π§ π π
π+π§ π π π
π+π§ π π§ π
ππ₯π [β
1
2
π
π+π§ π π§ π π (π π+π π)
] (2.42)
πΎπ
π
= ππ₯π [β
1
2
(
π§ π
π§ π
)
2
π
π+π§ π π§ π π (π π+π π)
] (2.43)
where subscripts π and π refer to counter-ion and co-ion, respectively. Here, π§ is the absolute
charge valance, π£ is the ion numbers in one mole of salt and π is a ratio of fixed charge
concentration over co-ion concentration (π =
πΆ πππ₯
πΆ ππβπππ
π ).
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 (β ) sign are counter-
ion. The equations (2.38) and (2.39) are written based on Donnan equilibrium and
38. 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):
(πΆ+
π
πΆβ
π)(πΎ+
π
πΎβ
π) = (πΎπ
π )2(πΆπ
π )2
(2.44)
πΆβ
π
= πΆπππ₯ + πΆ+
π
(2.45)
where superscripts s and π stand for membrane and solution phases while subscript s refer to
salt, C is concentration, + and β refer to co-ion and counter-ion here and πΎ 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 (π) is chosen as adjustable
parameters.
(πΆπππ₯ + πΆ+
π
)(πΆ+
π) (
πΆ πππ₯
π πΆ+
π+1
πΆ πππ₯
πΆ+
π +1
) ππ₯π [β
πΆ πππ₯
πΆ+
π
πΆ πππ₯
πΆ+
π +2π
] = (πΎπ
π )2(πΆπ
π )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 (πβ
π
) and co-ion (π+
π
) in the membrane are
calculated as below:
πβ
π
=
π’β
π πΆβ
π
π’+
π πΆ+
π+π’β
π πΆβ
π (2.47)
π+
π
=
π’+
π πΆ+
π
π’+
π πΆ+
π+π’β
π πΆβ
π
(2.48)
39. 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, π π€ ~ 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 manufacturersβ 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.
40. 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 KΞ± model). A monochromatic Al KΞ± X-
ray source was used with a spot size of 400 ΞΌm 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 Β± 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 NanoSEMβ’ 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 150Γ 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, π π€ππ‘, was measured after
removing surface water of sample membranes by tissues rapidly. Then, the samples were
dried in vacuum oven at 40 Β°C for 48 h in order to measure dry membrane mass, π πππ¦.
Membrane water uptake ππ’ is calculated using equation below [16, 27, 29]
ππ’ (g (π»2 π)/gπππ¦ ππππππππ) =
π π€ππ‘βπ πππ¦
π πππ¦
(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, πΈ π₯,
41. 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, πΈ ππππ , the electrode offset potential, πΈ ππππ ππ‘ , which resulted from the reference
electrode potential should be subtracted from πΈ π₯.
πΈ ππππ = πΈ π₯ β πΈ ππππ ππ‘ (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
(πΈ π₯), mostly was registered after stable value (around 3-5 minutes).
42. 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,
ο· Temperature of solution
ο· Concentration of external solution
ο· Type of ion (salt)
ο· pH of external solution
ο· 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].
43. 36
The procedure can be grouped as:
ο· Planning a matrix experiment to determine the effects of the control factors;
ο· Conducting matrix of experiment;
ο· Data analysis and results verification;
here are a brief definition of the Taguchi factors:
ο· Quality characteristic: a parameters under investigation ( e.g. permselectivity);
ο· Control factor: the design parameters or the variables which their control is easy (e.g.
Concentration, etc);
ο· 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].
ο· Temperature (Β°C): 15, 20 and 25 Β°C was considered as levels. Such temperatures were
chosen based on usual wastewater temperature;
ο· Concentration (M): 0.1, 0.2, 0.5 M were considered for concentration levels;
ο· 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
44. 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 currentβvoltage
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: 2π»2 π β π2 β + 4π»+
+ 4πβ
Cathode: 2π»2 π + 2πβ
β π»2 β + 2ππ»β
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.
45. 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 25β. The final resistance was obtained by slope of current-voltage
curve and equation (2.25). Solution resistance (π π ) was measured using same apparatus of
membrane resistance but without presence of the membrane.
46. 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 βLBL modifiedβ 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.
47. 40
4.2 Characterization of membrane surface
4.2.1 SEM-EDX analysis
To evaluate modificationβs 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.
48. 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
49. 42
value for SN ratio is observed at π = 20β which indicates possibility of minimizing the
effects of temperature on the membrane permselectivity by fixing the temperature constant at
π = 20β . The analysis also ranked temperature as the least important parameters on
permselectivity (see Appendix B). Permselectivity experiments are measured often at constant
temperature at π = 20β 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 π = 20β 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.
50. 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 membranesβ 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
51. 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)
πΆπβ Anion 2.03 0.195
π»2 ππ4
β Anion 0.96 0.302
ππ+ Cation 1.05 0.358
πΎ+ 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 phosphateβattractive
52. 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
53. 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 (ππ+
, πΎ+
) and therefore co-ion concentration in the membrane increases and
consequently permselectivity decreases.
54. 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
55. 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. DΕugoΕecki 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
Fuji
LBL
Fuji
LBL
Fuji
LBL
50
60
70
80
90
0,5 0,55 0,6 0,65 0,7 0,75 0,8
Permselectivity(%)
Water uptake (g water/g dry membrane)
NaCl
KCl
NaH2PO4
KH2PO4
56. 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 ππ+
πππ πΎ+
) 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
57. 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.
58. 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
59. 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
β
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
πΌπΈπΆ 1.7 ππππ’ππ£./π πππ¦ [16]
Water uptake*
ππ’ ~ 0.6 g(π»2 π)/gπππ¦ ππππππππ Experiment
Fixed charge
concentration*
πΆπππ₯ ~ 2.8 πππ’ππ£./π Calculation as
πΌπΈπΆ
ππ’
Sodium ion
mobility in
aqueous
condition
π’ ππ
π
7.92 Γ 10β8
π2
(ππ )β [57]
Potassium ion
mobility in
aqueous
condition
π’ πΎ
π
7.62 Γ 10β8
π2
(ππ )β [57]
Chloride ion
mobility in
aqueous
condition
π’ πΆπ
π
5.19 Γ 10β8
π2
(ππ )β [57]
Phosphate
mobility in
aqueous
condition
π’ π»2 ππ4
π
3.42 Γ 10β9
π2
(ππ )β [58]
Manning
parameter*
π 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,
60. 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.
DΕugoΕecki 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 π ). An inconsistency with
experimental data and ideal solution model at low concentration was reported by DΕugoΕecki
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.
