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MONOPOLAR AND BIPOLAR ION EXCHANGE MEMBRANES

Mass Transport Limitations

PROEFSCHRIFT

ter verkrijging vande graad van doctor aan de Universiteit Twente,

op gezag van de rector magnificus,prof. dr. F.A. van Vught,

volgens besluit van het College voor Promotiesin het openbaar te verdedigen

op vrijdag 29 augustus te 15.00 uur.

door

John Jacco Krol

geboren op 25 augustus 1969te Grootegast

Dit proefschrift is goedgekeurd door de promotor prof. dr. ing. H. Strathmann ende assistent-promotor dr. ir. M. Wessling.

ISBN 90 365 09866

© J.J. Krol, Enschede, The Netherlands, 1997All rights reserved.

Printed by Print Partners Ipskamp, Enschede, The Netherlands

Contents

1. Monopolar and bipolar ion exchange membranes: an introduction1.1 Ion exchange membranes 11.2 Ion transport and concentration polarisation 71.3 Overlimiting current 131.4 Bipolar membranes 171.5 Water dissociation mechanism 211.6 Structure of this thesis 281.7 List of symbols 301.8 References 31

2. Ion transport through monopolar ion exchange membranes:current - voltage curves and water dissociation2.1 Introduction 372.2 Experimental 39

2.2.1 Current - voltage curves 392.2.2 Water dissociation experiments 44

2.3 Results and discussion 472.3.1 Current - voltage curves 472.3.2 Water dissociation 52

2.4 Conclusions 582.5 List of symbols 592.6 References 60Appendix 2.1: Membrane characterisation

Introduction 62Experimental 62Results and conclusions 64References 65

3. Ion transport through monopolar ion exchange membranes:chronopotentiometry3.1 Introduction 673.2 Mass transport during chronopotentiometric measurements 683.3 Experimental 713.4 Results and discussion 723.5 Conclusions 833.6 List of symbols 843.7 References 85

Appendix 3.1:Ohmic resistance and relation to current - voltage curves

Introduction 87Results and conclusions 87

4. Salt transport in bipolar membranes at low current density4.1 Introduction 914.2 Model to describe the salt transport below the limiting

current density 934.3 Experimental 994.4 Results and discussion 1004.5 Conclusions 1034.6 List of symbols 1044.7 References 104

5. Water dissociation in bipolar membranes5.1 Introduction 1075.2 Concentration and potential profiles 1095.3 Model for the water dissociation in bipolar membranes 1145.4 Experimental 1205.5 Results and discussion 1205.6 Conclusions 1315.7 List of symbols 1325.8 References 134

6. Behaviour of bipolar membranes at high current density:water diffusion limitation6.1 Introduction 1376.2 Experimental 1386.3 Results and discussion 1406.4 Model calculations 1516.5 Conclusions 1556.6 References 157

Summary 159Samenvatting 162Levensloop 165

Voor mijn vader

Chapter

1

Monopolar and Bipolar Ion Exchange

Membranes: an Introduction

1.1 Ion exchange membranes

Principles

A membrane is defined as a permselective barrier separating two phases [1].Under the influence of a driving force certain components can permeate themembrane while others are retained. Thus a membrane is capable of selectivelytransporting components from one phase to the other. Many types of membranesexist which can be classified by various criteria such as their morphology (porous,non-porous, symmetric, asymmetric, neutral or charged) and driving force(pressure difference, concentration difference, electrical potential difference). Themembranes described in this thesis carry fixed positive or negative charges andare generally denoted as ion exchange membranes. Ion exchange membranes canbe subdivided into cation exchange membranes, which contain negativelycharged groups, and anion exchange membranes, which contain positivelycharged groups fixed to the polymer matrix. Ion exchange membranes are used inseparating electrolyte solutions and an electrical potential gradient is used as thedriving force for the material transport.

When placed in an electrolyte solution, the affinity of an ion exchange membranefor the ions in the solution is different. The cations, i.e. the positively charged

2 Chapter 1

ions in the solution, are able to penetrate a cation exchange membrane due to thenegatively charged fixed groups in the membranes. In contrast, the anions aremore or less excluded from the polymer matrix because of their electrical chargewhich is identical to that of the fixed groups. The ion distribution in a cationexchange membrane and the adjacent solution is illustrated in figure 1.1. Themobile ions with opposite charge of the fixed groups are called counter ions, themobile ions with the same charge are called co-ions. The exclusion of co-ions iscalled Donnan exclusion, in honour of his pioneering work [2].

Cation exchangemembrane

Electrolytesolution

polymer matrix with fixednegatively charged ion

counter ion (here: cation)

co-ion (here: anion)

Figure 1.1: Principles of separation achieved by ion exchange membranes: theexclusion of co-ions from the membrane.

Consider a cation exchange membrane in contact with a dilute electrolytesolution. Because of the presence of fixed charges, the cation concentration in themembrane is higher than its concentration in the solution. The concentration ofthe anions, however, is lower in the membrane than in the solution. If the ionsdid not have any charge, diffusion would occur and the concentration differencewould be levelled off. But due to the charge the ions carry, such a process woulddisturb electroneutrality in the membrane and solution. The diffusion of cationsinto the solution and the diffusion of anions into the membrane would create apositive space charge in the solution and a negative space charge in themembrane. Thus an electric field is created that is directed opposite to thediffusional flows. An electrochemical equilibrium (the Donnan equilibrium) willbe reached in which the electric field balances the diffusional driving force of allionic species.

The distribution of ions between membrane and solution can be calculated fromthe electrochemical potential of the ions in the membrane and that in thesolution. The electrochemical potential of a component i, η i, consists of both the

Introduction 3

chemical potential, µi, and the electrical potential according to:

η i = µi + zi F ϕ (1.1)

Here zi is the electrochemical valence, F the Faraday constant and ϕ the electricalpotential. If the pressure difference between solution and membrane is neglected,the chemical potential is given by:

µi = µio + RT lnai (1.2)

where µio is to the chemical potential in the reference state and ai the activity of

component i. In equilibrium the electrochemical potential for component i in thesolution (superscript s) is equal to the electrochemical potential in the membrane(superscript m):

µio,s + RT lnai

s + zi F ϕs = µio,m + RT lnai

m + zi F ϕm (1.3)

With equal reference state for the chemical potential in the solution and in themembrane, equation (1.3) leads to the Donnan potential (ϕDon), i.e the potentialdifference between membrane and solution:

ϕDon = ϕm - ϕs = R Tzi F

ln ai

s

aim (1.4)

Suppose a cation exchange membrane is in contact with a NaCl solution. TheDonnan potential is equal for all components in the solution. Assuming a dilutesolution, activities can be replaced by concentrations and equation (1.4) results in:

ϕDon = R TF

ln CNa

+s

CNa+

m = - R TF

ln CCl

-s

CCl-

m (1.5)

from which it is readily derived that the sodium and chloride ion concentrationsin the membrane and solution are related according to:

CNa+

s

CNa+

m = CCl

-m

CCl-

s (1.6)

4 Chapter 1

In the cation exchange membrane electroneutrality is maintained which meansthat the sodium ion concentration (which is the counter ion concentration)equals the sum of the chloride ion concentration and the fixed charge density X ofthe membrane:

CNa+

m = X + CCl

-m

(1.7)

In the solution the choride and sodium ion concentrations are equal:

CCl-

s = CNa

+s

= Cs

(1.8)

Introducing equation (1.7) and (1.8) into (1.6) gives an expression for the chlorideconcentration in the cation exchange membrane, i.e. the co-ion concentration:

CCl-

m = C

s 2

X + CCl-

m (1.9)

In a first approximation the chloride ion concentration in the membrane is muchsmaller than the fixed charge density and equation (1.9) reduces to:

CCl-

m = C

s 2

X(1.10)

From equation (1.10) it can be seen that the Donnan exclusion, i.e. the exclusion ofco-ions, is most effective when the membrane contains a high concentration offixed charges and when the electrolyte concentration in the solution is low.Concentration distribution between solution and membrane and the Donnanpotential is schematically shown in figure 1.2.

Introduction 5

XCNa+

m

Cl-Cm

Cl-C

sCNa+

s =

solution membrane

ϕDon

ϕs

ϕm

solution membrane

Figure 1.2: Schematic drawing of the concentration distribution of sodium andchloride ions between solution and a cation exchange membrane(left figure) and the Donnan potential (right figure).

Materials

Optimum property criteria which ion exchange membranes have to fulfil are [3,

4]:• a high permselectivity, i.e. an ion exchange membrane should be highly

permeable to counter ions, but should be impermeable to co-ions,• a low electrical resistance, i.e. the permeability of an ion exchange

membrane for the counter ions under the driving force of an electrical potential gradient should be as high as possible,

• a good mechanical and form stability, i.e. the membrane should be mechanically strong and have a low degree of swelling or shrinking in transition from dilute to concentrated ionic solutions,

• a high chemical stability, i.e. depending on the application of the mem-brane, it should be stable over a pH range from 0 to 14 and in the presenceof oxidizing agents (no cleavage of the fixed ionic groups from the polymer backbone).

It is difficult to optimise the properties of ion exchange membranes becauseopposing effects occur. For instance, a good mechanical strength can be achievedby a high degree of crosslinking in the membrane, but this also causes anundesired increase in the electrical resistance. A high concentration of fixedcharges in the membrane matrix leads to a low electrical resistance but, in general,causes a high degree of swelling combined with poor mechanical stability.

6 Chapter 1

The properties of ion exchange membranes are determined by the basic polymermatrix and the type and concentration of the fixed ionic moiety. The basicpolymer matrix determines to a large extent the mechanical, chemical andthermal stability of the membrane. Often the matrices of ion exchangemembranes consist of hydrophobic polymers such as polystyrene, polyethylene orpolysulfone. Although these polymers are insoluble in water and show a lowdegree of swelling, they may become water soluble by the introduction of ionicgroups. Therefore, the polymer matrices are often crosslinked. The degree ofcrosslinking determines to a large extent the swelling and the chemical andthermal stability, but it also has a large effect on the electrical resistance and thepermselectivity of the membrane.

The type and concentration of the fixed ionic charges determine thepermselectivity and the electrical resistance of the membrane, but, as mentionedbefore, they also have a significant effect on the swelling and the mechanicalproperties of the membrane. Most commercially available cation exchangemembranes have sulfonic acid (-SO3-) groups as fixed charges, most anionexchange membranes contain quaternary ammonium (-R3N+) groups (R= alkylor aryl group, e.g. -C2H5, -C4H9). These groups represent strong acids and bases,respectively, and are completely dissociated over the entire pH range. This isimportant as neutralisation of fixed charges will cause the resistance of themembrane to increase and the permselectivity to decrease.

Applications

Ion exchange membranes are used in a variety of different practical applicationssuch as fuel cell technology (conversion of chemical into electrical energy [5]),membrane electrolysis (e.g. the well-known chlor-alkali process for theproduction of chlorine and caustic soda [6, 7]), diffusion dialyis (e.g. the recoveryof acids from salt-acid mixtures [8]) and electrodialysis.

Electrodialysis is an electrical potential driven process to remove ions from anelectrolyte solution or to concentrate this solution. The principles ofelectrodialysis are shown in figure 1.3. An aqueous salt solution is fed to amembrane stack containing an alternating array of cation and anion exchangemembranes between two working electrodes. When an electric field is applied,the anions are transported towards the positively charged anode and the cationstowards the negatively charged cathode. Due to charge interaction, i.e. the

Introduction 7

Donnan exclusion mechanism, cation exchange membranes retain the anionswhile the cations are readily transported through these membranes. In a similarway the cations are retained by the anion exchange membranes while a transportof anions through these membranes can take place. As is illustrated in figure 1.3,the result is the separation of the feed solution into a solution enriched in ions(the concentrate) and a solution depleted of ions (the diluate).

aem cem

cathode anode

cem aem-

-

--

--

++

++

+

+

++

+

++

+

--

--

-

-

--

--

-

-

cem

feed solution

diluate

concentrate

Figure 1.3: Principles of electrodialysis (aem indicates an anion exchangemembrane, cem refers to a cation exchange membrane).

The most important application of electrodialysis is the production of potablewater from brackish water [4, 9]. Furthermore electrodialysis can be used innumerous processes varying from waste water treatment [10] to applications inthe food processing industry (e.g. the desalting of cheese whey or thedeacidification of wine [11]). In Asia electrodialysis is used on a large scale for theproduction of table salt from sea water. In Japan annually over 1.4 million tons oftable salt is produced this way [12, 13].

1.2 Ion transport and concentration polarisation

Ion transport

The total transport of ions through ion exchange membranes can be described bythree contributions, namely a convective part, a diffusive part and a migrationpart:

8 Chapter 1

Ji = v Ci - Di

dCidx

- zi F Ci Di

R T dϕdx

(1.11)

Here Ji is the flux of component i, v the velocity of convective transport, C theconcentration, D the diffusion coefficient, x the direction coordinate, z theelectrochemical valence, F the Faraday constant, R the gas constant, T thetemperature and ϕ the electrical potential. Generally the convective contributioncan be neglected since ion exchange membranes are non-porous and equation(1.11) results in the Nernst-Planck equation in which ion transport is described bya combination of diffusion (concentration gradient as driving force) andmigration (electrical potential gradient as driving force) [14].

The current density, i, passing through a membrane cell is determined by thecombined ionic fluxes according to Faraday’s law:

i = F zi Ji∑i=1

n(1.12)

The transport number of a certain ion, ti, is defined as the current carried by thatspecific ion relative to the total current:

ti = zi Ji

zi Ji∑i=1

n (1.13)

For a 100% permselective membrane all the current in the membrane is carried bythe counter ions which thus have a transport number of 1 in the membrane (andsimultaneously the co-ions have a membrane transport number of 0 in this case).

Concentration polarisation and limiting current density

In electrodialysis it is desirable to operate at the highest practicable current densityin order to get the maximum ion flux per unit membrane area. Operating currentlevels are, however, restricted by concentration polarisation. This polarisationresults from the difference in the transport numbers in the solution, wherecations and anions carry roughly equal amounts of current, and in the highlyselective ion exchange membrane, where virtually all the current is carried by thecounter ions. The difference in transport number leads to a situation in which thesolution close to the membrane surface on the diluate side becomes depleted of

Introduction 9

salt ions. At the same time the concentration near the membrane on theconcentrate side increases [15-17].

To quantify the concentration gradient close to the membrane surface, it iscommon to use the Nernst film model [18]. The convection of the solution byturbulent or laminar flow recedes continuously from the bulk solution in thedirection of the membrane surface. The film concept replaces this situation by azone without any convection and with a sharp boundary separating it from thecompletely agitated bulk solution [14]. Although this is a highly simplifiedpicture, the Nernst model has proved to describe diffusion phenomena at solidinterfaces quite accurately [14]. In practice a concentration profile next to themembrane will show a continuous gradient, as is illustrated in figure 1.4. In theNernst model this is idealised by defining a boundary layer with thickness δ. Thisboundary layer is called the diffusion boundary layer as it refers to the solutionlayer next to the membrane where the concentration gradient occurs with acorresponding diffusional transport. The thickness of this layer is found by theintersection of the two tangents in the concentration profile at the membranesurface and the bulk solution as is shown in figure 1.4.

x

C

δ

ab

Figure 1.4: Schematic of the real (a) and the idealised (b) concentration profilenear the membrane - solution interface, δ is the diffusion boundarylayer thickness.

Figure 1.5 shows the schematic concentration gradients next to a cation exchangemembrane between two identical electrolyte solutions. To describe concentrationpolarisation, the ion fluxes in the diluate diffusion layer and in the membranewill be considered. The treatment given below is taken from Spiegler [19].Electroneutrality is assumed to be maintained in the system considered.

10 Chapter 1

-------

Cb

Cm

cation exchangemembrane

diffusionboundary layers

J+mig

J+mig

J+diff

J-mig

J-mig

J-diff

anode cathode

Figure 1.5: Schematic diagram illustrating concentration polarisation: concen-tration profiles and ionic fluxes in a cation exchange membrane andits boundary layers (subscript + refers to the positively chargedcounter ion, subscript - to the negatively charged co-ion, migcorresponds to a migrational flux and diff to a diffusional flux, Cb isthe bulk solution concentration, Cm is the concentration at themembrane surface).

In the boundary layer ionic transport occurs both by diffusion and migration. Foran electrolyte solution containing only univalent ions (C+ = C- = C), the Nernst-Planck equation (1.11) applied to the boundary layer gives (neglecting convectivetransport):

J+ = - D+ dCdx

+ F CR T

dϕdx

(1.14)

J- = - D- dCdx

- F CR T

dϕdx

(1.15)

As the solution concentration is taken to be low compared to the fixed chargeconcentration, a diffusional transport due to a concentration gradient in themembrane can be neglected. Therefore it is assumed that ion transport within themembrane is accomplished by migration only. In this case the flux ratio betweenthe positively charged and the negatively charged ion is equal to the ratio betweenthe ion transport number in the membrane:

J+J-

= - t+t-

= - t+

1 - t+

(1.16)

Introduction 11

Here t refers to the transport number in the membrane. The negative sign isintroduced because the fluxes J are vectors. In the membrane J+ and J- haveopposite signs while t+ and t- are always taken positive. In the solution the ratioof ionic diffusion coefficients may be expressed in terms of the solution transportnumbers, t, as:

D+D-

= t+t-

= t+

1 - t+(1.17)

In general it is more convenient to use the diffusion coefficient of the electrolyteD than the ionic diffusion coefficients. The diffusion coefficient for an univalentelectrolyte can be expressed as [20]:

D = 2 D+ D-D+ + D-

= 2 D+ 1 - t+ (1.18)

Since a steady state is considered, the ionic fluxes are independant of position x,i.e. the fluxes in the membrane (represented by equation (1.16)) are equal to thefluxes in the boundary layer (represented by equations (1.14) and (1.15)).Combination of equation (1.14) to (1.18) leads to:

J+ = - D t+

t+ - t+

dCdx

(1.19)

J- = - D t-

t- - t-

dCdx

= D t-

t+ - t+

dCdx

(1.20)

The current density follows from Faraday’s law and is given by:

i = F J+ - J- (1.21)

Substitution of equations (1.19) and (1.20) into (1.21) gives an expression for thecurrent density as a function of the transport numbers and the concentrationgradient in the boundary layer:

i = - F Dt+ - t+

dCdx

= F Dt- - t-

dCdx

(1.22)

12 Chapter 1

If diffusion coefficient and transport numbers are assumed to remain constant,equation (1.22) shows that the concentration gradient in the boundary layer isconstant. Integration of equation (1.22) over the boundary layer thickness δ gives:

i = F Dt+ - t+

Cb - C

m

δ(1.23)

where Cb refers to the bulk solution concentration and Cm to the concentration atthe membrane surface. Increasing the current density causes the concentrationgradient in the boundary layers to become steeper, i.e. the concentration at themembrane surface decreases. At a given current density the concentration at themembrane surface reaches zero and a so-called limiting current density is reached:

ilim = F Dt+ - t+

Cb

δ(1.24)

From equation (1.24) it is seen that the limiting current density increases withincreasing salt diffusion coefficient, increasing bulk concentration, decreasingmembrane transport number and decreasing boundary layer thickness. Theboundary layer thickness is mainly determined by hydrodynamic conditions (e.g.cell geometry, temperature, solution viscosity and flow rate, membrane orien-tation) [21-24].

Severe concentration polarisation is highly undesired in electrodialysis since itdrastically decreases the process efficiency due to the increasing electricalresistance of the solution. Furthermore, as will be explained later, side effects suchas water dissociation can occur which lead to pH changes of the solutions. pHchanges need to be avoided since they can give rise to scaling (deposits such ashydroxides on the membrane). Also the membranes can be degraded if they arenot resistant enough to acidic and alkaline environments [25].

Based on the classical picture of concentration polarisation presented above, nocurrents higher than the limiting current can be expected since the concentrationnear the membrane has reached zero [19]. This is a very common feature inelectrodics. In electrodics, e.g. the metallic reduction at a metal cathode, a truelimiting current is observed (figure 1.6). Higher currents can only be achievedwith increasing voltage when other ions are present and able to react with theelectrode, or, if that is not the case, at high enough electrode potential the

Introduction 13

electrolysis of water will occur. However, when it comes to both cation and anionexchange membranes, it has long been established that currents above thelimiting current density can be reached [26, 27]. The nature of this overlimitingcurrent has been a matter of extensive research and discussion for almost 40 years.In the next section some comments will be made concerning the overlimitingcurrent.

currentdensity

voltage drop

a

b

Figure 1.6: Typical current - voltage curves for an ion exchange membraneshowing an overlimiting current (a) and a metal cathode showing atrue current plateau (b).

1.3 Overlimiting current

This thesis deals with transport limitations occurring with ion exchangemembranes. Therefore a short overview will be presented in this section,focussing on the overlimiting current observed with anion and cation exchangemembranes.

Water dissociation

Frequently the overlimiting current has been related to the occurrence of waterdissociation. In principle this is reasonable since even in deionised water protonsand hydroxyl ions are present in a concentration 10-7 mol/l due to the waterdissociation equilibrium. In section 1.4, where bipolar membranes will bediscussed, attention will be paid to the mechanism of water dissociation. Here,briefly some comments will be made with respect to water dissociation as anexplanation for the overlimiting current.

14 Chapter 1

Since the early studies on concentration polarisation it has been observed thatchanges in the pH values of the solutions can occur when the limiting currentdensity is exceeded [24] . Ever since, much work has been focused on theoccurrence of water dissociation with electrodialysis membranes. The mostimportant observation is that there seems to be a difference in water dissociationbehaviour between cation and anion exchange membranes. Many researchershave found that water dissociation is more pronounced with anion exchangemembranes whereas it seems to be of minor importance with cation exchangemembranes (e.g. [26-35]). The fact that overlimiting currents can be obtained withcation exchange membranes where hardly any water dissociation occurs, indicatesthat it is difficult to accept water dissociation as a general explanation for theoccurrence of an overlimiting current.

Electro-osmosis and permselectivity

Electro-osmosis is the transport of water through the pores of a chargedmembrane caused by the frictional force exerted on the liquid by the migration ofcounter ions through the membrane [14]. This might result in an effectivedecrease in the diffusion layer thickness and thus form a possible explanation forthe overlimiting current. Electrodialysis membranes, however, are dense (non-porous) membranes in which it is difficult to visualise that electro-osmotic flowcan result in current densities many times larger than the limiting value.Furthermore it remains unclear why this electro-osmotic flow would startdiscontinuously, i.e. at the “end” of a current plateau in a current - voltage curve.Hence this phenomenon has generally been rejected as a general mechanism forthe overlimiting current [17, 28, 36].

Another possibility for the occurrence of an overlimiting current would be theloss of permselectivity. This means that an increasing number of co-ions wouldparticipate in the transport across the membrane. Experimental work by severalresearchers has indicated that the transport of co-ions seems to remaininsignificant in the overlimiting region [28, 31, 37].

Hydrodynamic instabilities

Green and co-workers [32, 38, 39] studied ion transport through commercialcation exchange membranes by measuring so-called noise spectra. Spectraobtained below the limiting current density were characteristic of diffusion.

Introduction 15

Specific noise signals were found as soon as the current density applied was largerthan the limiting current density. Measurements were performed at varyingdistance from the membrane surface and the diluate diffusion layer was identifiedas the source for the voltage fluctuations. Two noise sources were concluded to bepresent above the limiting current density, one related to the diffusional transportand one to an instability in the transport processes occurring near the membrane.The nature of this instability remained unclear, but was speculated to be related toa hydrodynamic turbulence at high currents. Reich et al. [40] performed lightscattering experiments in which latex particles were added to the solution next toa cation exchange membrane and they observed a transition from a laminar to aturbulent flow when the potential across the membrane was increased. Usinglight scattering on latex particles the occurrence of a turbulent flow near a cationexchange membrane above the limiting current was also observed by Li et al.

[41].

The above described overview indicates that the overlimiting current ispresumably of convective nature. Gravitational free convection (also callednatural convection) is the convection which occurs due to the force of gravityacting on a liquid film in which a density gradient is present. When concentrationpolarisation occurs, concentration gradients are formed next to the membrane. Onthe diluate side the ion concentration is low compared to that in the bulksolution. This corresponds to a high resistance and may lead to a Joulean heatproduction and the formation of a temperature gradient near the membrane [28,

40, 42]. Due to a concentration and temperature gradient a density gradient will bepresent near the membrane surface when concentration polarisation occurs.Several authors [36, 43, 44] have investigated the effect of natural convection bymounting the membrane in a horizontal position with the diluate compartmentunderneath the membrane. In this case the depleted diffusion layer isgravitationally stabilised, thereby minimising free convection. However, stilloverlimiting currents were measured in this situation.

Electroconvection

Indusekhar and Maeres [45] found a substantial difference between theexperimental limiting current density with a cation exchange membrane when itwas compared with a reversible electrode under identical hydrodynamicalcircumstances. Rubinstein et al. [43] constructed a special membrane cell inwhich the thickness of the diluate diffusion boundary layer was known a priori.

16 Chapter 1

This was achieved by minimising free convection and using a very thin diluatecompartment. Using cation exchange membranes, they were able to compareexperimentally determined limiting current densities with calculated values. Itwas observed that the experimental values were 1.5 to 4 times smaller than thetheoretical prediction (depending on which membrane was used). It wassuggested that the ion conductance through the membrane is not uniform. In theconducting regions the local current would be larger than the measured averagevalue and thus lead to a lower overall limiting current.

In the classical treatment of concentration polarisation the only influence themembranes exert, are through their permselectivity (transport number). Cationexchange membranes with the same permselectivity, however, may exhibitdifferent concentration polarisation behaviour [28, 43]. Rubinstein [46, 47]

developed a new theory to account for the overlimiting current due to cationsthrough a cation exchange membrane, the mechanism of which was calledelectroconvection. Electroconvection was defined as “a non-gravitational freeconvection in macroscopic domains of the electrolyte solutions, caused by theinteractions of a self-consisting electric field with the corresponding space chargewithin the limits of the local electroneutrality approximation”. The theory ofelectroconvection is described by extensive mathematics, the details of which canbe obtained from references [46, 47]. In the next paragraph a qualitative treatmentof the general ideas of this theory will be formulated.

Rather than being of uniform ionic conductance, a membrane should be regardedas an array of conductive and insulating regions yielding a macroscopic hetero-geneity ranging from micrometers to tens of micrometers in size. This wouldreduce the area available for ion transport and thus explain the decrease inexperimentally observed limiting currents compared to calculated values [43].Near the limiting current density the concentration at the membrane surface isvery low and the basic assumption of electroneutrality, which underlies thedescription of polarisation at low currents, does not hold anymore [48, 49]. Theelectric double layer would be drastically distorted and a weak space charge is buildup near the membrane surface. Due to the non-uniform ion conductance throughthe membrane, the electric field at the membrane surface is not uniform; theelectric field lines are concentrated into the spots of higher conductance. Theinteraction of the space charge with the non-uniform electric field at themembrane surface would result in a volume force which grows strong enough toset the fluid in the diffusion layer in motion. As a result an additional driving

Introduction 17

force for ion transport towards the membrane surface is created, leading to thepossibility to obtain an overlimiting current.

It has to be noted that much attention has been paid to cation exchangemembranes when it comes to the overlimiting current. This is due to the fact thatoften it is assumed that the overlimiting current with anion exchangemembranes is a result of water dissociation. However, there is no reason toassume that the mechanism of electroconvection is restricted to cation exchangemembranes only [50].

1.4 Bipolar membranes

Principles

In the previous sections monopolar ion exchange membranes were discussed.Although already known since the mid-fifties [51], a considerable interest hasgrown the last decade in a special type of ion exchange membranes, i.e the so-called bipolar membranes. Bipolar membranes are membranes that contain onone side an anion exchange layer and on the other side a cation exchange layer.

The principles of bipolar membranes is schematically shown in figure 1.7.Suppose a cation and an anion exchange membrane are positioned between twoelectrodes as is shown in figure 1.7A. Under the influence of an electric field, theelectrolyte ions are removed from the compartment between the two membranes(similar to a desalting compartment in electrodialysis). When all salt ions areremoved, the only ions that can carry the current in this compartment are theprotons and hydroxyl ions which are present in deionised water in aconcentration of approximately 10-7 mol/l (figure 1.7B). The conductivity ofdeionised water is very low and to reduce the high electrical resistance of thislayer between the two ion exchange membranes, they have to be placed close toeach other, thus forming a bipolar membrane as illustrated in figure 1.7C. Theprotons and hydroxyl ions migrate out of the bipolar membrane under influenceof the applied electric field in opposite direction. Protons and hydroxyl ionsremoved from the interphase are regenerated according to the water dissociationequilibrium. Water so removed from the interphase is replenished by waterdiffusing from the outer solutions through the ion selective layers into theinterphase region where the two charged layers meet. The interesting feature of

18 Chapter 1

bipolar membranes is, as will be shown in section 1.5, that the water dissociationoccurs much and much faster than can be expected from the ordinary water disso-ciation equilibrium.

H+

Na+ Cl --

-

-

+

+

+

cem aem

Na+ Cl -+

+

+

-

-

-cathode anode

-

-

-

+

+

+

bipolar membrane

A

B

C

H + OH -

H2O

OH -

H2O

H2O

Figure 1.7: The principles of a bipolar membrane (cem refers to a cation ex-change membrane, aem to an anion exchange membrane) [52].

Applications

In combination with anion and cation exchange membranes the waterdissociation feature of bipolar membranes can be used to produce acids and basesfrom the corresponding salt solution. This process is schematically shown infigure 1.8.

Figure 1.8 shows cation and anion exchange membranes and a bipolar membranearranged in parallel between two electrodes to form individual compartments. If asalt solution is introduced between the anion and cation exchange membrane,cations in the salt solution will migrate towards the cathode, permeate the cationexchange membrane and form a base with hydroxyl ions that are formed withinthe bipolar membrane and are transported towards the anode. On the other sideof the bipolar membrane, which is directed towards the cathode, the protons,which are formed simultaneously with the hydroxyl ions, form an acid with theanions migrating from the salt solution through the anion exchange membrane

Introduction 19

towards the anode. The net result of the process illustrated in figure 1.8 is theproduction of an acid and a base from the corresponding salt solution in anelectrodialysis cell arrangement consisting of three individual compartments. Asin conventional electrodialysis, the three compartment units can be stackedbetween a single pair of electrodes.

saltNaCl

acidHCl

baseNaOH

saltNaCl

bmaem cem

H2O

OH -H+

cathode anode

cem aem

Na+

Cl -Na+

Cl -

-

-

--

--

++

++

+

+

++

+

++

+

+

+

++

++

--

--

-

-

-

-

--

--

H2O

Figure 1.8: Production of acid and base with bipolar membranes (cem refers to acation exchange membrane, aem to an anion exchange membraneand bm to a bipolar membrane) [52].

Bipolar membranes are of considerable interest because their water dissociationcapability is an energy efficient process to produce acids and bases. The theoreticalpotential difference across a 100% permselective bipolar membrane for thegeneration of a one molar acid and base solution at 25 °C can be calculated to be0.83 Volt [53]. The actual potential drop across the bipolar membrane would behigher than this theoretical value because of irreversible effects due to theelectrical resistance of the cation and anion exchange layers and the interphaseregion of the membrane.

An alternative method to produce acids and bases is electrolysis in which water issplit by electrode reactions for obtaining the desired H+ and OH-. Compared toelectrolysis the electrodialytic production of acids and bases with bipolarmembranes has several advantages [53]. The cell unit for electrodialytic waterdissociation is much simpler in construction. A large number of membranes areassembled between one set of electrodes. In contrast, electrolysis needs a set ofelectrodes for each cell unit, resulting in much higher costs of electrodes andelectrical connections. Additionally, electrolysis requires considerably more

20 Chapter 1

energy, because of the co-production of oxygen and hydrogen gas at the electrodes.The theoretical energy requirement for the production of acid and base byelectrolysis depends on the salt being used; for most salts the theoretical potentialto produce one molar acid and base varies between 2.1 and 2.2 Volts at 25 °C [4].The advantage of electrolysis is that usually higher concentrations and higherpurities of the acid and base can be obtained [54].

The production of acid and base solutions with bipolar membranes offers a broadspectrum of possible applications. Aqueous salt streams are generated as wastestreams in many diverse chemical processing operations. Disposal of such wastestreams not only means a loss of resource but has also become very unattractivedue to stringent environmental regulations nowadays. With bipolar membranesthese streams can be regenerated into acids and bases, which usually are theprecursor chemicals for such waste streams. Some other examples of bipolarmembrane applications are the regeneration of ion exchange resins [55, 56], theremoval of sulfur dioxide from flue gases [57, 58], the recovery of acid from pickleliquor in the steel production industry [59] and, based on the decreasing demandfor chlorine, the production of sodium hydroxide as an alternative to the chlor-alkali process [60]. An overview of possible applications in the field of pollutioncontrol, resource recovery and chemical processing can be found in references [61-

64]. Despite the many possibilities that have been identified, electrodialysis withbipolar membranes is still in a development stage.

Bipolar membrane requirements and preparation

Bipolar membranes should meet the following requirements: high waterdissociation capacity, low electrical resistance at high current densities, highpermselectivity as well as good mechanical and chemical stability to provide along useful life under operating conditions [52]. Low electrical resistance of thecation and anion exchange layers of the membrane can be achieved by using ahigh concentration of strong acid and base as fixed charges. A high permselectivityof the two layers is important since it affects the purity of the acid and baseproduced [61, 65, 66]. Co-ion transport through the bipolar membrane results inthe contamination of the acid and base by salt and thus reduces the quality of theproducts. As was illustrated in figure 1.8, an acidic solution is produced in thecompartment adjacent to the cation exchange layer of the bipolar membranewhile simultaneously a basic solution is produced facing the anion exchangelayer. Hence it is clear that the chemical stability of the two layers should be high,

Introduction 21

i.e. the anion exchange layer should be stable in alkaline solutions whereas thecation exchange layer should be stable in acidic solutions.

Bipolar membranes can be divided into two categories, i.e the single film bipolarmembrane and the laminate bipolar membrane. In case of a laminate bipolarmembrane, the membrane is formed by simply laminating (pressing or glueingwith a certain solution) two conventional ion exchange membranes back to back.This procedure was often used in the early studies on bipolar membranes [51, 67,

68]. These membranes, however, were mostly unsatisfactory in that they exhibiteda high electrical resistance. Simons [69] developed a laminate bipolar membranewith low electrical resistance. This membrane consists of two ion exchangemembranes that are treated with a heated alkaline solution containing a heavymetal ion (e.g Cr3+). After this pretreatment the bipolar membrane is formed byplacing the two membranes on top of each other. The membrane, generallydenoted as the WSI bipolar membrane, was commercialised by WSI TechnologiesInc., USA. Single film bipolar membranes can be prepared according to variousprocedures. Starting with a neutral film, the bipolar membrane can be formed byintroducing ionic groups on both sides of the film, e.g by plasma treatment [70] orby chemical treatment with specific solutions [71]. A different method is toproduce one of the layers first and then cast a solution of the second layer on top(e.g. [72-74]). An example of a commercially available single film bipolarmembrane is the BP-1 bipolar membrane produced by Tokuyama Soda Inc., Japan[75].

1.5 Water dissociation mechanism

In ordinary water dissociation protons and hydroxyl ions are in equilibrium withwater. The equilibrium is determined by the dissociation rate constant kd and therecombination rate constant kr:

2H2O H3O+ + OH-kd

kr(1A)

The proton and hydroxyl ion flux from the interphase of the bipolar membranecan not exceed the rate of generation, which means that the maximum flux J ofprotons and hydroxyl ions based on reaction (1A) can be calculated by:

22 Chapter 1

JH+, OH- = kd . CH2O . 2λ (1.25)

in which kd = 2.5 10-5 s-1 at 25 °C [76], CH 2O the water concentration at theinterphase layer (which is estimated to be 6 M [77]) and 2λ the thickness of thislayer. As will be shown in chapter 5, the thickness of the interphase layer is in therange of 1-10 nm. The flux calculated with equation (1.25) corresponds to a currentdensity of about 10-5 mA/cm2. However, from experiments it is known thatbipolar membranes can be operated at current densities in excess of 100 mA/cm2

[52]. This indicates that either the water dissociation rate in the bipolar membraneis much faster than in free solution or the interphase has to be much thicker, inthe range of a few millimeters. The second possibility is ruled out based onscanning electron micrographs which shows that the thickness of the interphaseregion is probably less than 0.1 micron [78] . This means that in bipolarmembranes the water dissociation rate is at least a factor 107 faster than in freesolution. Although much attention has been paid to this enhanced waterdissociation over the past decades, the mechanism of the water dissociation hasremained a controversial topic of discussion.

Na+

Cl -

H2O

H +anode cathode

+

+

+

+

+

-

-

-

-

-

Na+

Cl -anode cathode

+

+

+

+

+

-

-

-

-

-

cation selective layeranion selective layer

bipolar membraneinterphase

A

B

OH-

Figure 1.9: Current rectification with bipolar membranes. A: Reverse current,salt removal from the interphase region and water disscociation(high resistance), B: forward current, salt transport into interphaseregion (low resistance).

Introduction 23

Bipolar membranes behave anisotropically under the influence of an electricfield. This is schematically demonstrated in figure 1.9. Figure 1.9A shows thesame situation as was previously shown in figure 1.7 when discussing theprinciples of bipolar membranes. Under the influence of the electric field, salt isremoved from the bipolar membrane interphase and water dissociation occurs.Since the concentration of charge carriers is very low in the interphase region, themembrane has a relatively high resistance. A different situation arises when thetwo layers are interchanged, i.e. when the cation exchange layer of the membranefaces the anode and the anion exchange layer faces the cathode. As is illustrated infigure 1.9B, in this case the salt ions will be transported into the interphase regionby the electric field. The salt concentration will increase to such an extent that theDonnan exclusion is not effective anymore and the ions are readily transported asco-ions through the second layer [79]. This situation thus corresponds to a lowelectrical resistance. No water dissociation is observed in this case. The featurethat the bipolar membrane passes the current more easily in one direction than inthe reverse direction is called current rectification [67, 80, 81]. The currentdirection shown in figure 1.9A is usually referred to as a reverse current or bias,the situation shown in figure 1.9B as a forward current or bias [79].

Because of its structure, a bipolar membrane can be regarded as being analogous tosolid state semiconductors. Similar to the p-n junction of semiconductor devices,bipolar membranes rectify electric current [68, 82]. This similarity has resulted in aconsiderable “borrowing” of theory developed for semiconductors [82, 83]. Thesimilarities, differences and difficulties of comparing bipolar membranes with thep-n junction were discussed by Bassigna and Reiss [79].

Bipolar membranes are constituted of a polymeric film with a certain fixed chargeconcentration on top of a polymeric film with fixed charges of opposite sign. Thechange of fixed charges at the interphase of the bipolar membrane is usuallyassumed to be abrupt [82, 83]. As will be explained in more detail in chapter 5, athin region at the interphase exists where the fixed charges are almost completelyuncompensated by mobile ions. Electroneutrality does not hold in this region, i.e.a space charge is present in a thin layer where the charged layers of the bipolarmembrane meet.

Because of the lack of mobile carriers in the space charge region, it has a relativelyhigh resistance and a voltage applied to the bipolar membrane appears mainly

24 Chapter 1

across the space charge region [83]. Consequently, the electric field is extremelyhigh in this region (≥ 108 V/m) [52, 77, 84]. Due to the above described features, itis very likely that the enhanced water dissociaton observed in bipolar membranesis located at the interphase region of the membrane where a strong electric field ispresent.

Second Wien effect

At low electric field strengths Ohm’s law is valid for electrolyte solutions, i.e. thecurrent is proportional to the potential gradient. The proportionality factor, theresistance (or its reciprocal value, the conductivity), is independent of the electricfield strength. However, Wien [85, 86] observed that at high electric field strength(above 106 V/m) the conductivity of electrolyte solutions increases. For strongelectrolytes the electric field exerts such a strong force on the ion that it leaves itsionic atmosphere. The high ion velocity prevents rearrangement of the ionicatmosphere during motion. As a result electrophoretic and relaxation effects,which normally slow down the ion, diminish and the conductivity increases. Athigh enough field strength the ionic atmosphere is not formed at all anymore andthe equivalent conductivity reaches a limiting value corresponding to the infinitedilution value [87] . The electric field effect on the conductivity of strongelectrolytes is known as the first Wien effect.

The increase in conductivity with electric field strength was also observed insolutions of weak electrolytes and was found to be much higher than in solu-tions of strong electrolytes. This can therefore not be attributed to the dis-appearance of electrophoretic and relaxation effects. In case of weak electrolytesthe large change in conductivity is a result of collisions of ions, accelerated to ahigh velocity, with non-dissociated molecules [87]. This way the equilibrium:

molecule ⇔ cation + anion

is shifted towards the formation of ions, i.e. the dissociation constant is increased.The influence of the electric field on the dissociation of weak electrolytes isknown as the second Wien effect.

As water is a weak electrolyte, a possible explanation for the enhanced waterdissociation in bipolar membranes might be related to the second Wien effect.According to Onsager’s treatment of the second Wien effect [88] the influence of

Introduction 25

the electric field can be expressed in terms of an increase in the water dissociationrate constant, assuming that the recombination rate constant is uneffected by theelectric field. This effect of the electric field on the dissociation rate constant can becalculated by:

kd(E)kd

= 1 + b + b2

3 + b

3

18 + ...... (1.26)

with

b = 0.09636 Eεr . T

2(1.27)

where E is the electric field strength, εr the dielectric constant and T thetemperature. In equation (1.27) the electric field strength should be introduced inV/m and the temperature in K. For high field strengths (E > 108 V/m) equation(1.26) can be approximated by [88]:

kd(E)kd

= 2π

. (8b)-3/4

. exp 8b (1.28)

In literature some drawbacks of using the second Wien effect as being responsiblefor the enhanced water dissociation reaction are discussed. The theory might notbe valid anymore under the water dissociation circumstances in the bipolarmembrane. The theory has only been verified up to electric field strengths in theorder of 107 V/m [88], while the electric field strength under water dissociationcircumstances in a bipolar membrane is probably higher. Furthermore, additionaleffects such as an accelleration of the rotation of water molecules with aconsequent increase in the mobility of the water ions, are not included [89]. Thetheory considers a homogeneous solution, while it is known that the membranephase can have an important and complex influence on the water molecules,making it difficult to reason that the water dissociation reaction in the bipolarmembrane is of a homogeneous nature [90]. Strathmann et al. [52, 74] calculatedthe increase in dissociation rate constant due to the electric field according to thesecond Wien effect and came to the conclusion that the increase is still at leastthree orders of magnitude too small to explain the experimentally observedcurrent densities.

26 Chapter 1

Perhaps the most serious limitation of the second Wien effect is based onobservations with monopolar ion exchange membranes under severeconcentration polarisation circumstances. As explained in section 1.3, it has beenfound that water dissociaton is usually more pronounced with anion exchangemembranes whereas cation exchange membranes seem to show hardly any waterdissociation. It can be expected that the electric field strength is similar near bothtypes of membranes [89]. The second Wien effect would thus predict a similarwater dissociation behaviour, something which is not in accordance with theexperimental findings.

Proton transfer reactions

A different mechanism of the enhanced water dissociation is based oninvestigations with monopolar membranes. Simons [35] found that waterdissociation hardly occurred with cation exchange membranes. However, for theanion exchange membranes investigated it was found that water dissociationappeared to be an intrinsic property at currents above the limiting current density.The investigated anion exchange membranes showed water dissociation onlyafter prolonged applied current and could almost completely be eliminated bymethylating the membranes with methyliodide. The treated membranes wouldagain manifest water dissociation after prolonged applied current. Experimentswith anion exchange membranes containing tertiary amines showed waterdissociation from the outset, without any prior current flow. The effectdisappeared when the membranes were converted to the quaternary form bymethylation. These results indicated that water dissociation in the anionexchange membranes is due to tertiary amine groups in the surface region of themembrane. In the strongly basic membranes these groups would arise from thedegradation of the quaternary ammonium groups under the influence of theapplied electric field. Further evidence that the water dissociation behaviour isdetermined by the nature of the charged groups was given by Rubinstein et al.

[91]. They prepared an anion exchange membrane containing a crown ethercarrying alkali ions as fixed charges. This membrane, not containing aminogroups, showed very small pH changes above limiting currents in contrast to thesubstantial pH changes by conventional anion exchange membranes containingamino groups.

In subsequent articles [89, 92, 93] Simons elucidated these observations. It wasbelieved that the protons and hydroxyl ions originate from chemical reactions

Introduction 27

(protonation and deprotonation reactions) in a very thin (1-10 nm) region at themembrane surface for ion exchange membranes and at the interphase of the fixedcharge regions in the case of bipolar membranes. Experiments were performedwith sulphonic acid cation exchange membranes that did not show any waterdissociation in a NaCl solution. Certain ionizable molecules (e.g. phenol,aminoacids such as taurine, glycine, betaine and proline) were added to thesolution next to the membrane. Except for betaine, pH changes were nowobserved which thus had to be due to the presence of the added molecules. It wasassumed that the H+ and OH- were products of consecutive protonation anddeprotonation reactions involving the ionizable groups. For a basic group B thereaction scheme would be:

B + H2O BH+ + OH

-k1

k-1(1B)

BH+ + H2O B + H3O

+k2

k-2(1C)

If a tertiary amine is taken as the group B, the reactions are:

N

R1

R2

Pol H2O+ N

R1

R2

Pol H+ OH -+

N

R1

R2

Pol H+ H2O+ N

R1

R2

Pol + H3O +

where Pol refers to the polymer matrix and R1 and R2 to an alkyl group.In case of an acid group AH the reaction scheme would be:

A- + H2O AH + OH

-k1

k-1(1D)

AH + H2O A- + H3O

+k2

k-2(1E)

28 Chapter 1

If as an example the sulfonic acid group is taken, reactions (1D) and (1E) become:

H2O+ OH -+Pol SO3 - Pol SO3 H

H2O+ +Pol SO3 -Pol SO3 H H3O +

Betaine contains a quaternary ammonium group which can not undergo anyprotonation or deprotonation reaction and thus its effect is reminiscent to theexperiments described previously with the quaternary ammonium anionexchange membranes in which it was found that the quaternary ammoniumgroups have to be converted to the tertiary form before water dissociation canoccur. The qualitative difference in the measured production of H+ and OH- withthe different molecules was found to be consistent with expectations if the ionswere produced in the above described proton transfer reactions. For a quantativecomparison between experimental and calculated H+ and OH- production, it wasnecessary to assume that the forward rate constants of the reactions were at least 6- 50 times the free solution values [89, 93]. This increase was discussed to possiblybe associated with the presence of a strong electric field.

1.6 Structure of this thesis

The previous paragraphs have shown that there are still a number of openquestions with respect to mass transport occurring with monopolar and bipolarmembranes. The range of currents that can be applied to monopolar membranesis restricted due to concentration polarisation. Currents above the limitingcurrent density can be obtained but the nature of this overlimiting current is stillsubject of extensive studies nowadays. For bipolar membranes the mechanism ofwater dissociation remains a topic of discussions. In rationalising the mechanismof water dissociation, many studies have focussed on the transport processesoccurring at medium current densities, i.e. up to about 150 mA/cm2. Informationabout the ion transport before water dissociation commences is limited.Electrodialysis with bipolar membranes at high current density is attractive as thecurrent efficiency increases with increasing current density [73]. Problems mightbe anticipated with bipolar membranes at very high current densities due todrying of the membrane, resulting from a limitation of water supply into thebipolar membrane. However, experimental data about this process are also very

Introduction 29

limited in literature.

This thesis deals with both monopolar and bipolar ion exchange membranes. Theaim is to investigate and describe the transport limitations occurring with bothtypes of membranes. More specifically, the work in this thesis mainly focusses onthe following questions:

• To what extend does water dissociation contribute to the occurrence of anoverlimiting current with monopolar membranes?

• Does experimental evidence exist supporting the physical picture of a non-uniform ion conductance through monopolar membranes inducingelectroconvection?

• What are the mass transport processes taking place in bipolar membranesover a wide range of driving forces?

Chapter 2 and 3 focus on concentration polarisation occurring with ion transportthrough monopolar ion exchange membranes. Using a commercial cation andanion exchange membrane, concentration polarisation is studied in chapter 2 bydetermining current - voltage curves. General features concerning these curvesare presented, e.g. the occurrence of a limiting and an overlimiting current. Theinfluence of salt kind and concentration as well as the type of membrane on thelimiting current density will be shown. The contribution of water dissociation tothe overlimiting current is studied using two different methods. Firstly pHmeasurements are performed and secondly salt ion transport numbers in themembrane are determined. Although there is a difference in water dissociationbehaviour between the two membranes, it will be shown that water dissociationis of minor importance in the overlimiting region for both membranes.Furthermore the measurements will demonstrate that the membranes remainpermselective at currents above the limiting current density.

In chapter 3 chronopotentiometry is used to characterise the ion transportthrough monopolar ion exchange membranes. In chronopotentiometry dynamicmeasurements are performed in which the transient state of ion transport isinvestigated. The measurements are used to determine fluctuations in voltagedrop observed when currents higher than the limiting current density areapplied. Furthermore this technique is used to establish the picture of aheterogeneous nature of the two membranes. According to the theory postulatingelectroconvection as a mechanism responsible for the overlimiting current, thisheterogeneity is a key parameter. Comparison between measurements and

30 Chapter 1

calculations will indicate that the membranes indeed possess a reduced permeablemembrane area.

Chapter 4, 5 and 6 focus on bipolar membranes. In the consecutive chapterstransport processes in bipolar membranes from very low to very high currentdensity will be described. In chapter 4 current - voltage curves are measured atvery low current densities. The removal of salt ions from the bipolar membranetransition region, before water dissociation commences, is studied. It will beshown that the current - voltage curve is characterised by a limiting currentdensity where all salt has been removed. The influence of the bulk solutionconcentration is determined. Experimental results are compared with a modeldescribing the salt removal from the bipolar membrane.

Chapter 5 treats bipolar membranes in the normal operating range, i.e. up tocurrent densities of 100 mA/cm2. Attention is paid to the water dissociationmechanism. A model originally derived by Rapp [94] will be described which isbased on a combination of proton transfer reaction schemes and the second Wieneffect. Current - voltage curves are measured and compared with this model.Furthermore the influence of several parameters on the water dissociation will bediscussed.

In chapter 6 the behaviour of bipolar membranes is investigated at very highcurrent densities. Again current - voltage curves are used for this study. It will beshown that at high current density the water dissociation is limited by the supplyof water into the bipolar membrane. The measurements will demonstrate thatthis results in a permanent damage of the bipolar membrane. The cause of thisdamage and its relation to the membrane matrix is studied. Furthermore aqualitative comparison between measured and calculated curves will be made,using the water dissociation model described in chapter 5.

1.7 List of symbols

a activity (-)

C concentration (mol m-3)

D diffusion coefficient (m2 s-1)

E electric field strength (V m-1)

F Faraday constant (96485 A s mol-1)

Introduction 31

i current density (A m-2)

J flux (mol m-2 s-1)

k reaction rate constant (s-1)

R gas constant (8.314 J mol-1 K-1)

T temperature (K)

t transport number in solution (-)

t transport number in membrane (-)

v convection velocity (m s-1)

x direction coordinate (m)

X fixed charge concentration (mol m-3)

z electrochemical valence (-)

δ boundary layer thickness (m)

εr dielectric constant (-)

η electrochemical potential (J mol-1)

2λ transition region thickness (m)

µ chemical potential (J mol-1)

ϕ electrical potential (V)

sub- and superscripts

b bulk solution

d dissociation

diff diffusion

Don Donnan

i species i

lim limiting

m membrane

mig migration

r recombination

s solution

1.8 References

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Publishers, Dordrecht (1996).

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32 Chapter 1

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7 D. Bergner, Entwicklungsstand der Alkalichlorid-Elektrolyse, Teil 2: Elektrochemische

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13 M. Hamada, Brackish water desalination by electrodialysis, Desalination & Water Reuse

2/4 (1995) p. 8-15.

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24 D.A. Cowan and J.H. Brown, Effect of turbulence on limiting current in electrodialysis cells,

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25 Y. Oda and T. Yawataya, Neutrality-disturbance phenomenon of membrane-solution

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Introduction 33

28 M. Block and J.A. Kitchener, Polarization phenomena in commercial ion-exchange

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30 T. Yamabe and M. Senô, The concentration polarization effect in ion exchange membrane


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32 Y. Fang, Q. Li and M.E. Green, Noise spectra of sodium and hydrogen ion transport at a cation

membrane - solution interface, J. Coll. Interf. Sci. 88 (1982) p. 214-220.

33 G. Khedr, A. Schmitt and R. Varoqui, Electrochemical membrane properties in relation to

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34 G. Khedr and R. Varoqui, Concentration polarization in electrodialysis with cation

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35 R. Simons, The origin and elimination of water splitting in ion exchange membranes during

water demineralisation by electrodialysis, Desalination 28 (1979) p. 41-42.

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der kritischen Stromdichte, PhD thesis, University of Essen, Germany (1991).

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cation exchange membrane, J. Electroanal. Chem. 336 (1992) p. 171-194.

38 S.H. Stern and M.E. Green, Noise generated during sodium and hydrogen ion transport across

a cation exchange membrane, J. Phys. Chem. 77 (1973) p. 1567-1572.

39 M. Yafuso and M.E. Green, Noise spectra associated with hydrochloric acid transport

through some cation exchange membrane, J. Phys. Chem. 75 (1971) p. 654-662.

40 S. Reich, B. Gavish and S. Lifson, Visualization of hydrodynamic phenomena in the

vicinity of a semipermeable membrane, Desalination 24 (1978) p. 295-296.

41 Q. Li, Y. Fang and M.E. Green, Turbulent light scattering fluctuation spectra near a cation

electrodialysis membrane, J. Coll. Interf. Sci. 91 (1983) p. 412-417.

42 B. Gavish and S. Lifson, Membrane polarisation at high current densities, J. Chem. Soc.,

Far. Trans. I 75 (1979) p. 463-472.

43 I. Rubinstein, E. Staude and O. Kedem, Role of the membrane surface in concentration

polarization at ion-exchange membrane, Desalination 69 (1988) p. 101-114.

44 F. Maletzki, H.-W. Rösler and E. Staude, Ion transfer across electrodialysis membranes in

the overlimiting current range: stationary voltage current characteristics and current noise

spectra under different conditions of free convection, J. Membrane Sci. 71 (1992) p. 105-115.

45 V.K. Indusekhar and P. Meares, The effect of the diffusion layer on the ionic current from a

solution into an ion-exchange membrane, in Physicochemical hydrodynamics II, D.B.

Spalding (Ed.), Advance Publications, London (1977) p. 1031-1043.

46 I. Rubinstein and F. Maletzki, Electroconvection at an electrically inhomogeneous

34 Chapter 1

permselective membrane surface, J. Chem. Soc. Far. Trans. 87 (1991) p. 2079-2087.

47 I. Rubinstein, Electroconvection at an electrically inhomogeneous permselective interface,

Phys. Fluids A3 (1991) p. 2301-2309.

48 I. Rubinstein and L. Shtilman, Voltage against current curves of cation exchange membranes,

J. Chem. Soc., Faraday Trans. II 75 (1979) p. 231-246.

49 I. Rubinstein and L.A. Segel, Breakdown of a stationary solution to the Nernst-Planck-

Poisson equations, J. Chem. Soc., Faraday Trans. II 75 (1979) p. 936-940.

50 H.-W. Rösler, Untersuchungen zum überkritischen Ionentransport durch Elektrodialysemem-

branen mit Hilfe der Chronopotentiometrie, Rauschanalyse und Diffusions-Relaxation, PhD

thesis, University of Essen, Germany (1991).

51 V.J. Frilette, Preparation and characterization of bipolar ion exchange membranes, J. Phys.

Chem. 60 (1956) p. 435-439.

52 H. Strathmann, H.-J. Rapp, B. Bauer and C.M. Bell, Theoretical and practical aspects of

preparing bipolar membranes, Desalination 90 (1993) p. 303-323.

53 K. Nagasubramanian, F.P. Chlanda and K.J. Liu, Use of bipolar membranes for generation of

acid and base - an engineering and economic analysis, J. Membrane Sci. 2 (1977) p. 109-124.

54 D. Raucq, G. Pourcelly and C. Gavach, Production of sulphuric acid and caustic soda from

sodium sulphate by electromembrane processes. Comparison between electro-electrodialysis

and electrodialysis on bipolar membrane, Desalination 91 (1993) p. 163-175.

55 H.R. Bolton, Use of bipolar membranes for ion exchange resin regenerant production, J.

Chem. Tech. Biotechnol. 54 (1992) p. 341-347.

56 F.F. Kuppinger, Experimentelle Untersuchung und mathematische Modellierung von

Elektrodialyseverfahren, PhD thesis, University of Stuttgart, Germany (1996).

57 K.-J. Liu, F.P. Chlanda and K. Nagasubramanian, Application of bipolar membrane

technology: a novel process for control of SO2 from flue fluxes, J. Membrane Sci. 3 (1978) p.

57-70.

58 K.-J. Liu, F.P. Chlanda and K. Nagasubramanian, Membrane electrodialysis process for

recovery of sulfur dioxide from power plant stack gases, J. Membrane Sci. 3 (1978) p. 71-83.

59 J.C. Mc Ardle, J.A. Piccari and G.G. Thornburg, Aquatech Systems' pickle liquor recovery

process - Washington Steel reduces waste disposal costs and liability, Iron Steel Eng. 68

(1991) p. 39-43.

60 M. Paleologou, P.-Y. Wong and R.M. Berry, A solution to caustic/chlorine imbalance: bipolar

membrane electrodialysis, J. Pulp Pap. Sci. 18 (1992) p. 138-145.

61 K.N. Mani, Electrodialysis water splitting technology, J. Membrane Sci. 58 (1991) p. 117-

138.

62 K. Nagasubramanian, F.P. Chlanda and K.-J. Liu, Bipolar membrane technology: an

engineering and economic analysis, AIChE Symp. Ser. 76 (1980) p 97-104.

63 K.N. Mani, F.P. Chlanda and C.H. Byszewski, Aquatech membrane technology for

recovery of acid/base values from salt streams, Desalination 68 (1988) p. 149-166.

64 Y.C. Chiao, F.P. Chlanda and K.N. Mani, Bipolar membranes for purification of acids and

bases, J. Membrane Sci. 61 (1991) p. 239-252.

65 C. Carmen, Bipolar membrane pilot performance in sodium chloride salt splitting,

Desalination & Water Reuse 4/4 (1995) p. 46-50.

Introduction 35

66 J.L. Gineste, Analysis of factors limiting the use of bipolar membranes: a simplified model to

determine trends, J. Membrane Sci. 112 (1996) p. 199-208.

67 M. Seno and T. Yamabe, On the electrolytic rectification effect in ion exchange membranes,

Bull. Chem. Soc. Jpn. 37 (1964) p. 668-671.

68 B. Lovrecek and B. Kunst, Rectifying mechanism of pressed sandwich type membrane

junctions, Electrochim. Acta 12 (1967) p. 687-692.

69 R. Simons, Preparation of a high performance bipolar membrane, J. Membrane Sci. 78 (1993)

p. 13-23.

70 Y. Yokoyama, A. Tanioka and K. Miyasaka, Preparation of a single bipolar membrane by

plasma-induced graft polymerization, J. Membrane Sci. 43 (1989) p. 165-175.

71 F. de Körösy and E. Zeigerson, Bipolar membranes made of a single polyolephine sheet, Isr.

J. Chem. 9 (1971) p. 483-497.

72 F.P. Chlanda, L.T.C. Lee and K.-J. Liu, Bipolar membranes and method of making some, US

Patent 4 116 889 (1978).

73 B. Bauer, F.J. Gerner and H. Strathmann, Development of bipolar membranes, Desalination

68 (1988) p. 279-292.

74 H. Strathmann, B. Bauer and H.-J. Rapp, Better bipolar membranes, Chemtech 23 (1993) p.

17-24.

75 F. Hanada, K. Hirayama, N. Ohmura and S. Tanaka, Bipolar membrane and method for its

production, US Patent 5 221 455 (1993).

76 M. Eigen, Disc. Faraday Soc. 17 (1954) p. 194.

77 R. Simons and G. Khanarian, Water dissociation in bipolar membranes: experiments and

theory, J. Membrane Biol. 38 (1978) p. 11-30.

78 H. Strathmann, J.J. Krol, H.-J. Rapp and G. Eigenberger, Limiting current density and water

dissociation in bipolar membranes, J. Membrane Sci. 125 (1997) p. 123-142.

79 I.C. Bassigna and H. Reiss, Ion transport and water dissociation in bipolar ion exchange

membranes, J. Membrane Sci. 15 (1983) p. 27-41.

80 B. Lovrecek, A. Despic and J.O’M. Bockris, Electrolytic junctions with rectifying properties,

J. Phys. Chem. 63 (1959) p. 750-751.

81 P. Läuger, Uber die Gleichrichtereigenschaft bipolarer Ionenaustauschermembranen, Ber.

Bunsenges. Phys. Chem. 68 (1964) p. 534-541.

82 H.G.L. Coster, A quantative analysis of the voltage-current relationships of fixed charge

membranes and the associated property of "punch-through", Bioph. J. 5 (1965) p. 669-686.

83 A. Mauro, Space charge regions in fixed charge membranes and the associated property of

capacitance, Biophys. J. 2 (1962) p. 179-198.

84 P. Ramírez, V.M. Aguilella, J.A. Manzanares and S. Mafé, Effects of temperature and ion

transport on water splitting in bipolar membranes, J. Membrane Sci. 73 (1992) p. 191-201.

85 M. Wien, Über die Gültigkeit des Ohmschen Gesetzes für Elektrolyte bei sehr hohen

Feldstärken, Ann. Physik 73 (1924) p. 161-181.

86 M. Wien, Uber eine Abweichung von Ohmsen Gesetze bei Elektrolyten, Ann. Physik 83

(1927) p. 327-361.

87 T. Erdey-Gruz, Transport phenomena in aqueous solutions, Adam Hilger Ltd., London (1974).

88 L. Onsager, Deviations from Ohm's law in weak electrolytes, J. Chem. Phys. 2 (1934) p. 599-

36 Chapter 1

615.

89 R. Simons, Electric field effects on proton transfer between ionizable groups and water in ion

exchange membranes, Electrochim. Acta 29 (1984) p. 151-158.

90 P. Ramírez, J.A. Manzanares and S. Mafé, Water dissociation effects in ion transport through

anion exchange membranes with thin cationic exchange surface films, Ber. Bunsenges. Phys.

Chem. 95 (1991) p. 499-503.

91 I. Rubinstein, A. Warshawsky, L. Schechtman and O. Kedem, Elimination of acid-base

generation ("water splitting") in electrodialysis, Desalination 51 (1984) p. 55-60.

92 R. Simons, Strong electric field effects on proton transfer between membrane bound amines

and water, Nature 280 (1979) p. 824-826.

93 R. Simons, Water splitting in ion exchange membranes, Electrochim. Acta 30 (1985) p.

275-282.

94 H.-J. Rapp, Die Elektrodialyse mit bipolaren Membranen, Theorie und Anwendung, PhD

thesis, University of Stuttgart, Germany (1996).

Chapter

2

Ion Transport through Monopolar Ion

Exchange Membranes: Current - Voltage

Curves and Water Dissociation

2.1 Introduction

In electrodialysis it is desirable to work at high current density in order to achievea fast desalination process with the lowest possible effective membrane area. Inpractice, however, operating currents are restricted by the occurrence ofconcentration polarisation phenomena. In the bulk solutions roughly an equalamount of the current is carried by both the cations and the anions. Due to theexclusion of co-ions, the current within the membrane is virtually all carried bythe counter ions. As a result concentration gradients are formed in the boundarylayers adjacent to the membranes [1, 2]. On the diluate side the concentrationdecreases with respect to the bulk concentration whereas it increases on theconcentrate side of the membrane. When the current increases, the concentrationnear the membrane surface on the diluate side decreases. At a certain currentdensity this concentration reaches zero and a limiting current density is reached.

An effective method to study the transport of ions through ion exchangemembranes is by determining so-called current - voltage curves [3]. A current -voltage curve shows the relation between the current through a membrane andthe simultaneous voltage drop across membrane and solution boundary layers,

38 Chapter 2

thus giving information about the resistance occurring when ions are transportedfrom the bulk solution through the boundary layers and the membrane. Thischapter focusses on the transport limitations at monopolar ion exchangemembranes. For this purpose current - voltage curves are determined.Characteristic features of these curves are shown. The influence of the nature ofthe membrane (cation or anion exchange membrane) on the limiting currentdensity is investigated, as well as the influence of the type of counter ion to betransported.

Based on the classical treatment of concentration polarisation no currents largerthan the limiting current density can be expected [1]. However, since the earlystudies on concentration polarisation it is known that in practice currents largerthan the limiting current can be obtained [4, 5]. The nature of this overlimitingcurrent is still widely discussed nowadays. One of the possible mechanisms thatcould be responsible for the overlimiting current is the occurrence of waterdissociation [6-8]. Water dissociation takes place at the membrane surface thatfaces the diluate, where the salt concentration decreases during the process ofconcentration polarisation. This is schematically indicated in figure 2.1.

-------

Na+ Na+

anode cathode

H3O+OH -

Cl - Cl -

+++++++

anode cathode

H3O+OH -

Na+ Na+

Cl - Cl -

A

B

Figure 2.1: Occurrence of water dissociation at a cation exchange membrane(A) and at an anion exchange membrane (B) (black dot indicates thelocation of water dissociation).

Figure 2.1 shows that in case of an anion exchange membrane water dissociationoccurs at the surface of the membrane directed towards the cathode whereas itoccurs at the surface facing the anode in case of a cation exchange membrane.

Monopolar membranes: current - voltage curves and water dissociation 39

When water dissociation takes place, hydroxyl ions are transported through theanion exchange membrane while protons are transported through the cationexchange membrane. The result of water dissociation is similar for both types ofmembranes: the solution at the anodic side of the membrane becomes basic(increase in hydroxyl ion concentration) while the solution at the cathodic sidebecomes acidic (increase in proton concentration).

In this chapter also the nature of the overlimiting current will be investigated, inparticular with regard to the contribution of water dissociation, both for a cationand an anion exchange membrane. This is not only interesting with respect to apossible explanation of the overlimiting current but it also contributes to anexplanation of the mechanism of water dissociation [9]. Two complementarymethods will be used. The first one is based on determining the change in pH inthe solutions on both sides of the membrane. The second procedure is based onthe determination of the transport numbers of the salt ions in the membrane. Inthis case the current carried by protons or hydroxyl ions is obtained by subtractingthe current carried by the salt ions from the total current.

2.2 Experimental

2.2.1 Current - voltage curves

Set-up

Current - voltage curves were determined with a set-up schematically shown infigures 2.2 to 2.5. The membrane cell, shown in figures 2.2 and 2.3, is made ofplexiglass and consists of six separate compartments. The two outer compart-ments contain the working electrodes which are used to apply an electric fieldacross the membranes. The anode consists of platinized titanium, the cathode ismade of stainless steel. The membranes are placed between the individual cellcompartments. The complete cell is clamped together by means of four bolts.

The central membrane in the cell is the membrane under investigation, the othermembranes are auxiliary membranes preventing the transport of waterdissociation products formed at the two working electrodes to the centralcompartments. The area of each membrane in the cell is 23.76 cm2.

40 Chapter 2

The voltage drop across the test membrane is measured by Haber-Luggincapillaries. The capillaries are filled with a 2 M KCl solution and each connectedto a small reservoir in which a calomel reference electrode (Schott B2810) isplaced. The calomel reference electrodes are connected to a Knick DC amplifier(type 9000 A1-118) to measure the potential difference. A schematic of this part ofthe set-up is shown in figure 2.4.

AAAAAAAAAAAAAAAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAAAAA




AA

AAAA

outlet

inlet

bolt

Haber-Luggin capillaries

plexiglasshousing

workingelectrode

26 mm 35 mm

Figure 2.2: Drawing of the membrane cell cross-section (front view).

outlet

inlet

Haber-Luggincapillary

plexiglasshousing

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

55 mm

Figure 2.3: Side view of the membrane cell cross-section showing the solution entrance and exit ports.


AAAAAAAA

AAAAA

AAAAAA

AAAAA

Haber-Luggincapillary

siliconetubing

KClreservoir

referenceelectrode

AAAAAA

AAA

V

AAA

voltmeter

Figure 2.4: Schematic drawing of the system measuring the voltage drop across the membrane.

Depending on the experimental requirements one of the following powersupplies was used to establish a current through the membrane cell: a Delta SM300-10D (maximum 300 V, 10 A) or a Delta ES 30-5D (maximum 30 V, 5A) powersupply (Delta Elektronika). The power supply is connected to a PC through anIEEE interface enabling to control all experiments by computer.

Figure 2.5 shows the complete experimental set-up. Since the membrane cellconsists of six compartments, six reservoirs were present in the set-up from whichthe solutions were pumped through the cell. Double-headed peristaltic pumps(Watson Marlow, type 504 S/50) were used for the four outer compartments.Verder 2036 gear pumps were used for the two central compartments. Gearpumps were used in this case because they show considerable less pulsations thanperistaltic pumps. The flowcycles through each compartment also containedflowmeters (Porter Instrument 150AV-B250-4RVS for the four outer flowcyclesand Cole Parmer G-03217-90 for the two central streams) as well as sensors formeasuring the pH (Ingold 405 S7/120 electrodes, WTW KI/PH and pH 219amplifying system), the temperature (WTW TFK 530/1.5 electrodes, WTW TE 219amplifying system) and the conductivity (WTW TetraCon DU/TH electrodes,WTW KI/LF and LF 219/4 amplifying system). A DAS 1601 board (Keithley)extended with an EXPG16 card (Keithley) was used for the data acquisition of allthe variables to the PC in the set-up. The measurements could be followed real-time on the computer monitor while simultaneously the experimental data were

42 Chapter 2

written to file.

The volume of the solutions flowing through the two central compartments was800 ml, the volume of the solutions in the other four compartments was 1600 ml.The flowrate of each stream was adjusted to 475 ml/min.

AAAAAA

AA

1

AAAA AAAAAAAAA2

3

4 44 4 4 4

5 55555

67

••

Figure 2.5: Experimental set-up consisting of six flowstreams through themembrane cell (1: membrane cell, as illustrated in figures 2.2 and2.3, 2: measurement of the membrane voltage drop, as illustratedin figure 2.4, 3: power supply, 4: pH, conductivity and temperaturesensors, 5: solution reservoirs, 6: data acquisition board, 7: PC).

Membrane arrangement

Figure 2.6 shows the membrane sequence in the six-compartment cell along withthe ideal (i.e. assuming 100 % permselective membranes) transport direction ofthe different ionic species. The central membrane, which is the membrane underinvestigation, was either a cation or an anion exchange membrane. In betweenthe anode and the test membrane two cation exchange membranes were present.A cation exchange membrane was positioned next to the anode compartment toprevent chloride transport to the anode thereby avoiding the production ofchlorine gas at this electrode.

In the electrode compartments a 0.5 M Na2SO4 solution was used. The electrodereactions are:


cathode: 2 H2O + 2 e- ⇒ H2 ↑ + 2 OH- (2A)

anode: 2 H2O ⇒ O2 ↑ + 4 H+ + 4 e- (2B)

In the other four compartments a different salt solution was used. Theconcentration in the second and fifth compartment was 0.5 M, the concentrationin the third and fourth compartment (adjacent to the test membrane) was alwayslower and varied between 0.05 M and 0.15 M. This was done to ensure that, whenstudying the ion transport through the test membrane, no interference occurredby concentration polarisation at any of the other membranes.

O2

H+

Na+

SO42- X -

H2

M+

X -M+

X -M+

X -M+

SO42-

M+

OH -Na+

cemcem cemaem

0.5 M 0.5 Mvar0.5 M 0.5 M

anode cathode

var

cem

O2

H+

Na+

SO42- X -

H2

M+

X -M+

X -M+

X -M+

SO42-

M+

OH -

aem

Na+

cemcem cemaem

0.5 M 0.5 Mvar0.5 M 0.5 M

anode cathode

var

A

B

Figure 2.6: Schematic drawings showing the membrane arrangement and idealionic transport in the six-compartment cell when a cation (topfigure) or when an anion exchange membrane (bottom figure) wasstudied (cem refers to a cation exchange membrane, aem to ananion exchange membrane, var to a varying solution concen-tration).

Chemicals

For the preparation of the electrode rinsing solutions Na2SO4 (Merck, analyticalgrade) was used. The solutions in the other four compartments were preparedwith either NaCl, KCl or LiCl (all Merck, analytical grade). Deionised water (18.2

44 Chapter 2

MΩcm) was obtained from a Milli-Q ultra pure water installation (Millipore).

Membranes

The membranes used in the experiments were kindly supplied by TokuyamaSoda Inc., Japan. As the cation exchange membrane the Neosepta CMX membranecontaining sulfonic acid groups as fixed charges and as the anion exchangemembrane the Neosepta AMX membrane containing quaternary ammoniumgroups as fixed charges were used. These are reinforced, standard grademembranes for general concentration or desalination purposes [10] . Theproperties of these membranes are described in appendix 2.1.

Experimental procedure to determine current - voltage curves

Current - voltage curves were determined by a stepwise increase of the currentdensity through the cell (steps of typically 0.5 mA/cm2 were used). After a currentincrease the system was allowed to reach steady state for some time (typically 30seconds) after which the voltage drop across the membrane was measured,followed by the next current increase. The obtained combinations of currentdensity and membrane voltage drop gave the experimental current - voltagecurve.

2.2.2 Water dissociation experiments

To determine the contribution of water dissociation products to the total iontransport through the membranes two different procedures were followed. Thefirst one is based on pH measurements of the solutions next to the testmembrane. The second procedure is based on determination of the transportnumbers of the salt co- and counter ions.

pH measurements

pH measurements were performed using the six-compartment membrane celland the experimental set-up described earlier. A constant current density wasapplied through the membrane cell and the pH of the solutions flowing throughthe compartments next to the membrane was measured as a function of time.


Initially an 0.1 M NaCl solution was present in the compartments adjacent to thetest membrane. Measurements were performed both with an AMX anionexchange membrane and a CMX cation exchange membrane. Membranes werebrought into the salt form prior to each experiment. At higher current densitiesthe area of the membrane under investigation was reduced by means of two glassplates with a circular hole with area 4.75 cm2. This way it was ensured that noconcentration polarisation and water dissociation occurred at any of the othermembranes in the cell.

The current carried by the products of water dissociation can be calculated fromthe change in proton or hydroxyl ion concentration in the solution on thecathodic or anodic side of the test membrane, respectively:

IH+ = F V dCH+

dtor: IOH- = F V

dCOH-

dt(2.1)

Here I refers to the current, F is the Faraday constant, V the volume of thesolution, C the concentration and t the time. The transport number of a certainion in a membrane, t, is defined as the ratio between the current carried by thision and the total current, I. The transport numbers of the water dissociationproducts can thus be calculated according to:

tH+ = F V

dCH+

dtI

= F V

dCH+

dti A

or: tOH- = F V

dCOH-

dtI

= F V

dCOH-

dti A

(2.2)

where i is the current density and A is the membrane area.

Salt co- and counter ion transport numbers

The six-compartment cell is not very suitable for determining the transportnumber of the co- and counterions in the test membrane since eitherassumptions have to be made about the permselectivity of the membranes next tothe test membrane or a complete mass balance has to be made based on allcompartments. Hence a different membrane cell, consisting of just twocompartments, was used for these measurements. For this purpose the twoelectrode compartments of the previously described six-compartment cell weretaken. To avoid water dissociation reactions at the working electrodes, Ag/AgClelectrodes were used. The electrodes were prepared [11] from spiral wound silver

46 Chapter 2

wire (Aldrich, 99.99 %, 1 mm diameter). To form the cathode, AgCl was depositedon the wire in a 0.10 M KCl solution by applying a small current (5-10 mA) for 90minutes using the wire as the anode and a platinated titanium electrode ascounter electrode. The electrodes were allowed to age for at least one day prior toan experiment. The experimental set-up is depicted in figure 2.7.

The electrode reactions during an experiment using Ag/AgCl working electrodesare:

cathode: AgCl + e- ⇒ Ag + Cl- (2C)

anode: Ag + Cl- ⇒ AgCl + e- (2D)

Cl -

Na+++++++++

Cl -

Na+

• H+OH - cathode anode

Cl -

Na+

Cl -

Na+

• H+OH - cathode anode

--------

A

B

Figure 2.7: Two-compartment cell arrangement with Ag/AgCl working elec-trodes and ionic fluxes when an anion exchange membrane(A) or a cation exchange membrane (B) was investigated (electrodereactions are given by reactions (2C) and (2D).

Experiments were performed with an 0.10 M NaCl solution flowing on both sidesof the test membrane (flowrate: 475 ml/min, total solution volume 150 ml). Afixed current density was applied to the two-compartment cell and solutionsamples were taken at different times. Sodium ion concentrations weredetermined from analysis of the samples by atomic adsorption (Varian SpectrAA-10), chloride ion concentrations were determined by HPLC (Waters). Transportnumbers of the sodium and chloride ions were calculated from the change in thecorresponding concentrations with time. Since the sum of transport numbersequals one, the transport number of the water dissociation product can be


calculated from the relation:

tH+or OH- = 1 - tNa+ - tCl- (2.3)

2.3 Results and discussion

2.3.1 Current - voltage curves

General features

Figure 2.8 shows a typical example of a measured current - voltage curve. Threedistinct regions can be distinguished. In the first region, at low current densities, alinear relationship is obtained between current and voltage drop. This region isgenerally called the ohmic region. As the current density increases concentrationpolarisation becomes more pronounced, the concentration in the diluateboundary layer decreases and hence the resistance increases. As a result adeviation of the linear behaviour occurs. When the limiting current density isreached a current plateau is observed (region II). From figure 2.8 it is clear thatafter the current plateau the current density is increasing again. This part of thecurrent - voltage curve is called the overlimiting region (region III).

0

5

10

15

20

0 0.5 1 1.5 2

current density(mA/cm2 )

voltage drop (V)

I II III

ilim

Figure 2.8: Current - voltage curve measured with a CMX membrane in a 0.05M NaCl solution showing the occurrence of a limiting currentdensity (il im) and the presence of the three distinct regions. Thelimiting current density is determined by the intersection of thetwo slopes belonging to the ohmic and the plateau region.

48 Chapter 2

Figure 2.8 also shows that the first two regions are smooth while the region of theoverlimiting current is characterised by a considerable scatter. This feature hasbeen found to be present both for the CMX and the AMX membrane. It stemsfrom the fact that the voltage drop across the membrane and adjacent solution isnot averaged over a certain time period but is measured at a fixed time afterincreasing the current density. The scatter in the overlimiting region might be anindication that certain instabilities occur in this region. In chapter 3 wherechronopotentiometry is used to study the ion transport through the membranes,the instabilities will be investigated in more detail.

Limiting current density

The influence of the NaCl concentration on the current - voltage curve wasstudied, the results of which are shown in figure 2.9 for the CMX and in figure2.10 for the AMX membrane.

0

5

10

15

20

25

30

0 0.5 1 1.5 2 2.5

current density

(mA/cm2)

voltage drop (V)

0.15 M 0.10 M 0.05 M

Figure 2.9: Influence of bulk NaCl concentration on the current - voltage curveof a CMX membrane.


0

10

20

30

40

50

0 0.5 1 1.5 2 2.5

current density

(mA/cm2)

voltage drop (V)

0.15 M0.10 M

0.05 M

Figure 2.10: Influence of bulk NaCl concentration on the current - voltage curveof an AMX membrane.

Figures 2.9 and 2.10 show that the current - voltage curves are very similar for thetwo membranes. It is also observed that the value of the limiting current densityincreases with increasing bulk solution concentration. In chapter 1 an equationfor the limiting current density was derived, which was given by:

ilim = F Cb D

δ ti - ti

(2.4)

Here ilim is the limiting current density, F the Faraday constant, Cb the bulksolution concentration, D the salt diffusion coefficient, δ the boundary layerthickness, ti the counter ion transport number in the membrane and ti thetransport number in the solution. If it is assumed that D, δ, ti and ti remainconstant, equation (2.4) predicts a linear relationship between the limiting currentdensity and the bulk solution concentration. Figure 2.11 shows the determinedlimiting current densities as a function of the bulk NaCl concentration for the twomembranes. This figure indicates that, within experimental error, the limitingcurrent density indeed increases linearly with bulk solution concentration.

50 Chapter 2

0

5

10

15

20

25

0 0.05 0.1 0.15 0.2

limiting current

density (mA/cm2)

NaCl concentration (mol/l)

CMX

A M X

Figure 2.11: Limiting current density as a function of bulk NaCl concentration for the AMX and CMX membrane.

Comparing the AMX and CMX membrane in figure 2.11, it is seen that at givenNaCl concentration, the limiting current density is higher for the anion exchangemembrane. This is due to the difference in solution transport number of thecounter ion. The chloride ion is the counter ion for the AMX membrane, thesodium ion for the CMX membrane. The chloride ion transport number in thesolution (which equals 0.61 [12]) is higher than the solution sodium ion transportnumber (which equals 0.39 [12]). Equation (2.4) shows that this results in a higherlimiting current density for the AMX anion exchange membrane in NaCl. Inappendix 2.1 to this chapter it will be shown that the permselectivity of the twomembranes is about 95 %. Taking 0.95 for the counter ion transport number andassuming equal boundary layer thickness δ for the AMX and the CMX membrane,the ratio in limiting current density between these two membranes can becalculated from equation (2.4) by:

ilim, AMX

ilim, CMX =

tNa+ - tNa+CMX

tCl- - tCl-AMX

= 1.6 (2.5)

The ratio of limiting current densities determined from the slopes in figure 2.11 is1.5 and is in good agreement with the calculated ratio.

The solution transport number of a certain ion is related to the ionic diffusioncoefficient and for a 1:1 electrolyte it can be calculated according to [13]:


t+ = D+

D+ + D-or: t- =

D-D+ + D-

(2.6)

in which D+ and D- are the ionic diffusion coefficients of the positively andnegatively charged ion, respectively. This means that in principle the differencein limiting current density found between the cation and anion exchangemembrane is based on a difference in ionic diffusivities of the counter ions.

From the previous described measurements it is clear that the nature of thecounter ion has a large influence on the limiting current density. This was furtherinvestigated by measuring current - voltage curves for a CMX cation exchangemembrane in different salt solutions, varying the type of counter ion. The resultsare shown in figure 2.12.

0

5

10

15

20

25

30

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

KClNaClLiCl

current density

(mA/cm2 )

voltage drop (V)

Figure 2.12: Current - voltage curves measured with a CMX membrane in different salt solutions (concentration 0.10 M).

Figure 2.12 shows that the limiting current density decreases in the sequence KCl(ilim= 13.5 mA/cm2) > NaCl (ilim = 9.5 mA/cm2) > LiCl (ilim = 7.0 mA/cm2). Againthis can be rationalised considering equation (2.4), showing that the limitingcurrent density is determined by the salt diffusion coefficient and the counter iontransport number in the solution. Assuming a constant boundary layer thickness,the ratio of the limiting current density of a salt A to B differing in counter ioncan be calculated according to:

52 Chapter 2

ilim, A

ilim, B =

DADB

. ti, B - ti, B

ti, A - ti, A

(2.7)

Table 2.1 shows the transport numbers and salt diffusion coefficients for the saltsused. Table 2.2 shows that, using the values in table 2.1, there is good agreementbetween the calculated and experimentally observed ratios of the limiting currentdensities when different counter ions are used in the experiments with the CMXcation exchange membrane.

Table 2.1: Counter ion transport number in the solution and salt diffusion coefficients (data obtained from Robinson and Stokes [12]).

counterion

counter iontransport number

salt diffusioncoefficient (10-5 cm2/s)

K+ 0.49 1.84

Na+ 0.39 1.48

Li+ 0.32 1.26

Table 2.2: Comparison between calculated (equation (2.7)) and experimentallimiting current density ratios for a CMX membrane when thetype of counter ion is varied.

ratio limiting current density

calculated experimental

KCl / LiCl 2.0 1.9

NaCl / LiCl 1.3 1.4

2.3.2 Water dissociation

The previous section showed that current densities larger than the limitingcurrent density can be obtained, both for the CMX cation exchange membrane andthe AMX anion exchange membrane. Experiments were performed to investigatewhether the overlimiting current can be explained by the occurrence of waterdissociation.


pH measurements

The pH of the solutions next to the test membrane was measured as a function oftime at different fixed current densities. The results are shown in figure 2.13.

3

4

5

6

7

8

9

10

11

0 20 40 60 80 100 120

pH

time (min)

146(b)

72(b)

25(b)

15(b)

146( a )72( a )25( a )

15( a )

A M X

4.5

5

5.5

6

6.5

7

7.5

0 20 40 60 80 100 120

pH

time (min)

150(b)

19(b)

99(b)

9(b)

9( a )

19( a )

99( a )

150( a )

CMX

Figure 2.13: Change in solution pH adjacent to the membrane as a function oftime for the AMX membrane (top figure) and the CMX membrane(bottom figure). Values in the figures indicate the applied currentdensity in mA/cm2, superscript a refers to the solution in the acidcompartment (cathodic side of the membrane), superscript b to thesolution in the base compartment (anodic side of the membrane).

The limiting current density for the CMX membrane in 0.1 M NaCl is 9.5mA/cm2, for the AMX membrane it is 14.5 mA/cm2. Figure 2.13 shows that thepH of the solutions remains constant when a current density smaller or equal tothe limiting current density is applied. With increasing applied current density

54 Chapter 2

the changes in pH of the solutions become more prominent. Comparing the pHvariations between the CMX and the AMX membrane, it is observed that the pHchanges are much more pronounced in case of the anion exchange membrane.

In order to calculate the transport number of the water dissociation products inthe membrane (equation (2.2)), it is necessary to convert the pH values into H+ orOH- concentrations. Figure 2.14 shows two examples of the concentration increaseas a function of time.

0

2

4

6

8

0 20 40 60 80 100 120

[H+]

(10 - 4 mol/l)

time (min)

146 mA/cm2

72 mA/cm2

AMX

0

1

2

3

4

5

0 20 40 60 80 100 120

[OH -]

(10 - 4 mol/l)

time (min)

146 mA/cm2

72 mA/cm2

AMX

Figure 2.14: Increase in proton concentration in the acid compartment (topfigure) and the simultaneous hydroxyl ion concentration in the basecompartment (bottom figure) as a function of time for an AMXmembrane. Values in the figures refer to the applied currentdensity.

Paying attention to the y-axis in figure 2.14, it is seen that the increase in protonconcentration in the acid compartment is much higher than the increase inhydroxyl ion concentration in the base compartment. Similar features were


observed in the experiments with the CMX membrane. The difference in protonand hydroxyl ion concentration is probably due to the generation of protons at theanode (see figure 2.6). Protons have a much higher mobility than sodium ionsand are transported easily through the two cation exchange membranes betweenthe anode and the test membrane, recombining with some of the hydroxyl ionswhich are transported into the base compartment as a result of the waterdissociation. This can also be observed in figure 2.13 for the CMX membrane. Hereit is seen that at high applied current densities the pH in the base compartmentstarts to decrease again after some time. This can only be due to a flux of protonsinto this compartment, the source of which must be the electrode reaction at theanode.

To calculate the contribution of water dissociation to the total current through theanion exchange membrane, the flux of hydroxyl ions through this membrane hasto be determined, i.e. the increase of the hydroxyl ion concentration in the basecompartment should be regarded. Due to the above described feature that theincrease in hydroxyl ion concentration is always much smaller in this compart-ment than the increase in proton concentration in the other compartment, thiscalculation would result in a too low value for the hydroxyl ion transport numberin the AMX membrane. Since an equal production in H+ and OH- can be expected[14], the increase in proton concentration in the acid compartment was usedwhen calculating the hydroxyl ion transport number in equation (2.2). The resultsof the thus determined transport numbers are shown in figure 2.15.

0

0.01

0.02

0.03

0 40 80 120 160

A M XCMX

transportnumber

current density (mA/cm2)

Figure 2.15: Proton and hydroxyl ion transport number in the CMX and AMX membrane, respectively, as a function of applied current density.

56 Chapter 2

Despite the scatter, figure 2.15 shows that the contribution of water dissociation islarger for the anion exchange membrane than for the cation exchange membrane.According to this figure the proton transport number in the CMX membraneremains negligible. Also for the AMX membrane the determined transportnumber is very low, smaller than 0.03 even when a current density is applied thatis ten times larger than the limiting current density. This means that in theoverlimiting region more than 97 % of the current must still be carried by saltions. In other words, from the pH measurements it can be concluded that thecontribution of water dissociation to the occurrence of an overlimiting current forthe two membranes investigated is only minor. Especially when figure 2.13 isregarded, it is clear that water dissociation is much more pronounced in case ofthe AMX anion exchange membrane than for the CMX cation exchangemembrane. Thus the experiments are in agreement with the work of Simons [9,

15] who based the concept of proton transfer reactions as a mechanism for waterdissociation on the observation that anion exchange membranes generally showmore water dissociation than cation exchange membranes.

Salt co- and counter ion transport numbers

A two-compartment cell with Ag/AgCl working electrodes was used to determinethe transport numbers of Na+ and Cl- ions in the membrane. The intention ofthese measurements was twofold. Firstly they were performed to confirm theresults of the pH measurements that the overlimiting current is still mainlycarried by the salt ions. Secondly they were used to determine whether a loss inmembrane selectivity is the reason for the overlimiting current. The results ofthese experiments are shown in table 2.3.

Table 2.3 shows that the relative error in the determined transport numbers islarge, especially for the co-ion. This is due to the small concentration changes thatoccur and the accuracy of the analysis equipment used. Furthermore it was foundthat it is not easy to work with Ag/AgCl working electrodes. The cathode has aAgCl layer at the start of an experiment and this layer is removed when applyinga current (see electrode reaction (2C)). This limits the duration of eachexperiment. As soon as the AgCl layer is removed at a certain position of thecathode, water reacts, which is highly unwanted in this type of measurement. Theanode, where chloride ions from the solution react to form silver chloride,determines the range of current densities which can be applied in this cell. Athigher current density concentration polarisation occurs at the anode which


means that the chloride concentration near the electrode reaches zero and also inthis case the reaction of water at the electrode commences.

Table 2.3: Sodium and chloride transport numbers in an AMX and CMX membrane determined as a function of applied current density.

membrane current density(mA/cm2)

chloride iontransport number

sodium iontransport number

AMX 11 0.91 ± 0.06 0.06 ± 0.04

19 0.91 ± 0.08 0.05 ± 0.05

41 0.99 ± 0.05 0.08 ± 0.05

60 0.89 ± 0.08 0.05 ± 0.04

65 0.95 ± 0.09 0.05 ± 0.04

CMX 10 0.04 ± 0.03 0.93 ± 0.06

21 0.06 ± 0.03 0.90 ± 0.08

45 0.06 ± 0.05 0.91 ± 0.06

Calculation of the proton or hydroxyl ion transport number (equation (2.3)) basedon the transport numbers in table 2.3 is not very meaningful due to the errorsinvolved. In contrast to the pH measurements described earlier, it is difficult todraw conclusions about any difference in water dissociation behaviour betweenthe CMX and AMX membrane based on the results shown in table 2.3. However,if attention is paid to the co-ion transport numbers it is clear that these valuesremain low when currents larger than the limiting current density are applied.This indicates, as was found by other authors [14, 16, 17], that a loss inpermselectivity can not be the mechanism responsible for the occurrence of anoverlimiting current. More important, the values of the counter ion transportnumber are larger than 0.9 for the current densities below and above the limitingcurrent density. This is in agreement with the pH measurements indicating thatsalt transport is the major contribution to overlimiting transport, also stating thatwater dissociation is only a side-effect that can not account for the overlimitingcurrent.

58 Chapter 2

2.4 Conclusions

Current - voltage curves were determined both for a Neosepta CMX cationexchange membrane and a Neosepta AMX anion exchange membrane. All curveshave similar distinct features. At low current density there is a linear relationbetween current density and voltage drop (ohmic region). As the current densityincreases, concentration polarisation becomes more pronounced and the saltconcentration in the diluate boundary layer decreases. This results in an increasein resistance and a deviation from the ohmic behaviour occurs. A second regionin the current - voltage curve starts as the limiting current density is reached anda current plateau is observed. Furthermore a third region is present in whichcurrents larger than the limiting value are measured. This is the region ofoverlimiting current.

It was observed that the first two regions of the measured current - voltage curveswere smooth whereas the third region was characterised by a considerable scatter.The scatter might be an indication that instabilities in ion transport occur in thisregion and will be treated in more detail in chapter 3.

The equation for the limiting current density (equation (2.4)) based on the classicaltreatment of concentration polarisation was found to explain satisfactorily theinfluence of several parameters. The limiting current density increases linearlywith increasing bulk solution concentration. Comparing the anion and the cationexchange membrane, it was found that the limiting current density measured inNaCl was higher for the anion exchange membrane. This is due to a difference incounter ion diffusivity in the solution. A similar effect was measured when thetype of counter ion was varied when investigating the CMX membrane.

The occurrence of water dissociation was studied. It was found that the pHremained constant both for the CMX and the AMX membrane when currentssmaller than the limiting current density were applied. From the pH measure-ments it was evident that water dissociation occurred for both types ofmembranes when currents larger than the limiting current density was applied.However, the change in pH was much more pronounced in case of the anionexchange membrane. This is in agreement with the work of Simons who basedthe concept of proton transfer reactions as a mechanism for water dissociation onthe observation that anion exchange membranes generally show more waterdissociation than cation exchange membranes.


From the change in solution pH the transport number of protons in the CMXmembrane and of hydroxyl ions in the AMX membrane was determined. Thecontribution of water dissociation appeared to be negligible for the cationexchange membrane. Although this contribution was more substantial in case ofthe anion exchange membrane, the determined transport number remainedsmaller than 0.03 even when current densities about ten times the limitingcurrent density was applied. This means that in the overlimiting region morethan 97 % of the current is still carried by the salt ions. Thus it can be concludedthat water dissociation can not be responsible as the mechanism for obtaining anoverlimiting current with the two investigated membranes.

With a two-compartment cell the co- and counter ion transport numbers throughan AMX and CMX membrane were determined. This was done as a secondmethod to establish the contribution of water dissociation. Due to the large errorsinvolved no difference in water dissociation behaviour between the two types ofmembranes could be established. However, it seems that the co-ion transportnumber did not significantly change over the current range investigated. Thisindicates that also a loss in permselectivity can not be responsible for theoverlimiting current which means that in the overlimiting region virtually allthe current is carried by the counter ions for the two membranes investigated.

2.5 List of symbols

A membrane area (m2)





I current (A)


t time (s)

ti transport number in solution (-)

ti transport number in membrane (-)

T temperature (K)

V volume (m3)

W weight (kg)



α permselectivity (-)

γ activity coefficient (-)

60 Chapter 2

δ boundary layer thickness (m)

∆ V voltage drop (V)

τ transition time (s)

Sub- and superscripts

b bulk solution

calc calculated value for an ideally permselective membrane

lim limiting

meas measured

2.6 References

1 K.S. Spiegler, Polarization at ion exchange membrane-solution interfaces, Desalination 9

(1971) p. 367-385.

2 C. Forgacs, N. Ishibashi and J. Leibovitz, Polarization at ion exchange membranes in


3 M. Mulder, Basic principles of membrane technology, 2nd Edition, Kluwer Academic

Publishers, Dordrecht (1996).

4 B.A. Cooke, Concentration polarization in electrodialysis-I. The electrometric measurement

of interfacial concentration, Electrochim. Acta 3 (1961) p. 307-317.




(1957) p. 780-784.

7 D.A. Cowan and J.H. Brown, Effect of turbulence on limiting current in electrodialysis cells,

Ind. Eng. Chem. 51 (1959) p. 1445-1448.

8 T.R.E. Kressman and F.L. Tye, pH changes at the anion selective membranes under realistic

flow conditions, J. Electrochem. Soc. 116 (1969) p. 25-31.


275-282.

10 Neosepta® ion exchange membranes, Product brochure Tokuyama Soda Inc.

11 D.T. Sawyer and J.L. Roberts, Experimental electrochemistry for chemists, John Wiley &

Sons, New York (1974).

12 R.A. Robinson and R.H. Stokes, Electrolyte solutions, 2nd Edition, Butterworths, London

(1959).

13 E.L. Cussler, Diffusion, mass transfer in fluid systems, Cambridge University Press, New

York (1984).





Appendix 2.1

Membrane Characterisation

Introduction

The measurements described in chapter 2 and 3 are performed with theTokuyama Soda AMX anion and CMX cation exchange membrane. In thisappendix the characterisation of these two membranes will be described. Themembranes are characterised with respect to swelling, permselectivity, electricalresistance and ion exchange capacity. The determined values are compared withdata which are supplied by the manufacturer of the membranes.

Experimental

Swelling

The degree of swelling was determined according to a weighing procedure [1]. Themembrane was equilibrated overnight in a 0.5 M NaCl solution to bring themembrane into the Na+ or Cl- form. Then the membrane was placed for 2 days indeionised water at 25 °C and after removing the surface water from the samplewith a tissue, the weight of the wet membrane was determined (Wwet). Thesample was dried in a vacuum oven at 80 °C until constant weight (Wdry) and thedegree of swelling was calculated according to:

swelling = Wwet - Wdry

Wdry . 100 % (A2.1)

Electrical resistance

The electrical resistance of the membranes was measured under direct current ina 0.5 M KCl solution at 25 oC. A four-compartment cell was used in theexperiments (similar to the six-compartment cell described in the experimental

Appendix 2.1: membrane characterisation 63

section of chapter 2). Apart from the test membrane, two cation exchangemembranes were present in the cell in order to avoid gas bubbles, originatingfrom the working electrodes, to disturb the measurement with the capillaries. Thevoltage drop across the membrane was measured as a function of applied currentdensity (currents much smaller than the limiting current density were applied,i.e. measurements were performed in the lower part of the ohmic region). Firstthe area resistance (voltage drop divided by current density) was determined withthe membrane in the cell. As this resistance also contains a contribution of thesolution in between the tips of the voltage measuring capillaries, a secondmeasurement was performed without the membrane in the cell. The membranearea resistance was calculated by subtracting the resistance of the system withoutmembrane from the resistance with membrane.

Permselectivity

The permselectivity was determined by the static membrane potential measure-ment [1]. The test system consisted of two cells separated by the membrane sample(similar cell compartments were used as was described in the experimentalsection of chapter 2). Two calomel reference electrodes (Schott B2810) were placedinto the solutions on either side of the membrane and were used to measure thepotential difference across the membrane. On one side of the membrane a 0.1 MKCl solution flowed through the cell, on the other side a 0.5 M KCl solution (25°C). The permselectivity of the membrane (α ) is given by the ratio of themeasured potential difference (∆Vmeas) and the potential difference calculated fora 100% permselective membrane (∆Vcalc):

α = ∆Vmeas

∆Vcalc

. 100 % (A2.2)

In case of a 0.1 and 0.5 M KCl solution, the calculated potential difference is 36.9mV. It is calculated using the Nernst equation:

∆Vcalc = R.Tz.F

ln C2.γ2C1.γ1

(A2.3)

in which R is the gas constant, T the temperature, z the electrochemical valence, Fthe Faraday constant, C1 and C2 the concentrations of the solutions and γ1 and γ2

64 Chapter 2

the respective activity coefficients. Prior to an experiment the membrane wasequilibrated in a 0.1 M KCl solution for 24 hours. The potential difference usuallytook 10-20 minutes to reach a steady state value.

Ion exchange capacity

Ion exchange capacity of the membranes was determined by titration [1, 2]. In caseof the cation exchange membrane a sample was brought into the H+ form byimmersion into a 1 M HCl solution for 24 hours. The sample was soaked indeionised water to remove sorbed acid, after which the sample was placed in a 2M NaCl solution to exchange the protons with sodium ions. To ensure completeexchange the NaCl solution was renewed two more times. The NaCl solutionswhich now contained the released protons were combined and titrated withNaOH.

A similar procedure was used for the anion exchange membrane. In this case thesample was initially brought into the OH- form by equilibration in a 1M NaOHsolution for 24 hours. The sample was rinsed with deionised water. The hydroxylions were exchanged with chloride ions by placing the sample in a 2 M NaCl solu-tion which was renewed two times. The amount of released hydroxyl ions wasdetermined by titration with HCl. The membrane samples were dried and the ionexchange capacity was calculated per gram dry membrane.

Results and conclusions

The results of the determined CMX and AMX characteristics are shown in tableA2.1. This table shows that for most properties the measured values agree wellwith data supplied by the manufacturer. The ion exchange capacity of the AMXwas found to be somewhat lower.

Appendix 2.1: membrane characterisation 65

Table A2.1: Measured membrane properties and data supplied by the manu-facturer [3] . ((1): measured in 0.5M NaCl, (2): measured by electro-dialysis with sea water, current density 20 mA/cm2).

membrane property measured manufacturerdata

CMX swelling (%) 30 ± 3 0.25 - 0.30

exchange capacity (mmol/g dry) 1.6 ± 0.3 1.5 - 1.8

electrical resistance (Ω cm2) 2.6 ± 0.3 2.5 - 3.5 (1)

permselectivity (%) 95 ± 2 > 96 (2)

AMX swelling (%) 31 ± 3 0.25 - 0.30

exchange capacity (mmol/g dry) 1.0 ± 0.3 1.4 - 1.7

electrical resistance (Ω cm2) 3.0 ± 0.5 2.5 - 3.5 (1)

permselectivity (%) 93 ± 2 > 96 (2)

References

1 H. Strathmann, Electrodialysis, in Membrane Handbook, W.S. Winston Ho and K.K. Sirkar

(Eds), Van Nostrand Reinhold, New York (1992) p 218-262.


3 Neosepta® ion exchange membranes, Product brochure Tokuyama Soda Inc.

Chapter

3

Ion Transport through Monopolar Ion

Exchange Membranes:

Chronopotentiometry

3.1 Introduction

In the previous chapter ion transport through monopolar membranes wasstudied by measuring current - voltage curves. It was observed that currents abovethe limiting current density can be obtained. While the measured curvesappeared to be smooth at lower current densities, the region of the overlimitingcurrent was characterised by a considerable scatter. This indicates that fluctuationsin membrane voltage drop occur at a given current density in this region.

In chapter 2 it was also established that the overlimiting current could not beexplained by the occurrence of water dissociation or a loss in permselectivity, i.e.most of the current in this region is still carried by the salt counter ions. Themechanism for this counter ion transport above the limiting current density hasbeen a matter of discussion for a number of years. A possible explanation for theoverlimiting current was given by Rubinstein who developed a theory referred toas electroconvection [1, 2]. Basis of this theory, which was described in more detailin chapter 1, is the presence of heterogeneities in ion exchange membranes. Themembranes should be regarded more as an alternating array of insulating and

68 Chapter 3

conductive domains than as a truly homogeneous barrier. As a result a non-uniform electric field is present at the membrane surface. Its interaction with aweak space charge creates a bulk force which sets the fluid in the depletedboundary layer in motion. The resulting mixing up of the boundary layer createsan additional salt transport to the membrane surface and thus allows for anoverlimiting current. The key to this mechanism seems to be the presence ofheterogeneities in ion exchange membranes. Rösler et al. [3] performedexperiments on ion exchange membranes and indicated the presence of a reducedpermeable membrane area. This was achieved by studying the non-steady stateion transport using chronopotentiometric measurements.

Chronopotentiometry is a technique which has been used frequently toinvestigate kinetic effects, adsorption and transport phenomena near electrodesurfaces [4-6] . Chronopotentiometric measurements are performed in agalvanostatic mode (i.e. a constant current density is applied) in which the voltagedrop between the electrode and a reference electrode is measured as a function oftime. Apart from their permselectivity, ion exchange membranes behaveanalogue to electrodes and thus the method can also be used to study membraneproperties [3, 7-10].

In this chapter chronopotentiometry is used to study the transport of ions across acation and an anion exchange membrane. The aim of these investigations isfirstly to further characterise the fluctuations in membrane voltage dropoccurring in the overlimiting region. Secondly this technique is used to establishthe picture of a heterogeneous nature of the two membranes, similar to the workby Rösler et al. [3, 11]. As mentioned before, according to the theory postulatingelectroconvection as a mechanism responsible for the overlimiting current, thisheterogeneity is a key parameter.

3.2 Mass transport during chronopotentiometric measurements

When an electric current is applied to a system containing an ion exchangemembrane concentration polarisation occurs, i.e. concentration gradients aredeveloped in the vicinity of the membrane. The transient process occurring nearthe membrane until a steady state is reached, can be followed by measuring thevoltage drop across the membrane as a function of time. To describe the non-steady ion transport a homogeneous ion selective interface is assumed in contact

Monopolar membranes: chronopotentiometry 69

with a univalent electrolyte solution without convection. The latter indicates anunlimited growth of the diffusion layer adjacent to the membrane. Theconcentration change of the electrolyte as a function of distance and time isrepresented by Fick’s second law:

∂C(x,t)

∂t = D

∂2C(x,t)

∂x2(3.1)

Here C is the electrolyte concentration, x the distance coordinate, t the time and Dthe electrolyte diffusion coefficient. At time zero the concentrations throughoutthe system are equal: C(x,0)= Co. Furthermore, since a semi-infinite diffusionproblem is considered, the concentration remains constant at all times forpositions sufficiently far from the membrane: C(x→ ∞, t)= Co. The counter ionflux in the membrane, Ji

m, is due to migration and is equal to the counter ion fluxin the solution, Ji

s, where both migration and diffusion occurs [8]:

Jim =

i tiz F

(3.2)

Jis =

i tiz F

- D ∂C

∂x x=0

(3.3)

In these equations i is the current density, ti the counter ion transport number inthe membrane, ti the counter ion transport number in the solution, z theelectrochemical valence and F the Faraday constant. Combining equation (3.2) and(3.3) gives a boundary condition for the concentration at the membrane surface(x=0) at t>0:

∂C

∂x x=0

= - iz F D

ti - ti (3.4)

Equation (3.1) can now be solved using Laplace transformation [12]:

C(x,t) = Co - i ti - tiz F D

2 D tπ

exp - x2

4Dt - x.erfc x

2 D t(3.5)

The concentration at the membrane surface as a function of time can thus beexpressed as:

70 Chapter 3

C(0,t) = Co - iz F D

ti - ti 2 D tπ

(3.6)

From equation (3.6) it is clear that the concentration at the membrane surfacedecreases in time. At a certain time τ, called the transition time, this concentrationreaches zero. The transition time as a function of applied current density is readilyderived from equation (3.6) and is given by:

τ = πD4

Co z F

ti - ti

2 1

i2(3.7)

Equation (3.7) shows that the transition time is proportional to the inverse of thecurrent density squared. It also shows that the transition time increases when themembrane transport number decreases, i.e. when the membrane is lesspermselective. Equation (3.7) is equivalent to the Sand equation frequently usedin studies of electrode systems [13].

Chronopotentiometry can also be used to determine the permselectivity of an ionexchange membrane [8]. The permselectivity P can be calculated from thetransport number in the membrane, ti, and the transport number in the solution,ti:

P = ti - ti1 - ti

(3.8)

The transition time measured with the membrane under investigation is givenby equation (3.7) while the transition time for an ideally permselective membraneis given by the same equation in which ti is substituted by 1. Thus thepermselectivity can be determined by comparing the measured transition time,τmeas, with the transition time calculated for an ideally permselective membrane,τideal, according to:

P = τidealτmeas

(3.9)

From equation (3.9) it is clear that in order to obtain realistic values for thetransport number or permselectivity (i.e. a value smaller than or equal to 1), theexperimentally determined transition time should be larger than or equal to the


one calculated for an ideally permselective membrane.

3.3 Experimental

Chronopotentiometry

Chronopotentiometric curves were determined with the six-compartmentmembrane cell and the experimental set-up described in chapter 2. The voltagedrop across the membrane under investigation was measured by means of twoHaber-Luggin capillaries connected to two calomel reference electrodes (Schott B2810). At given time a fixed value of the current density was applied to themembrane cell and the voltage drop across the membrane was measured as afunction of time with a frequency of 600 times per minute. Conductivity and pHwere monitored continuously to ensure constant solution composition during aset of experiments.

The membranes used in the investigations were the Neosepta AMX anion andCMX cation exchange membrane, supplied by Tokuyama Soda Inc. (Japan). Themembrane area was 23.76 cm2. All measurements were performed with a 0.10 MNaCl solution on either side of the test membrane. Prior to the experiments themembranes were equilibrated in 0.10 M NaCl for at least 12 hours. The membranearrangement in the membrane cell when the transport through the anion or thecation exchange membrane was studied, was shown in the experimental sectionof chapter 2.

To study the influence of hydrodynamics, chronopotentiometric measurementswere performed with two different test configurations. The first configurationequals the set-up which was used in chapter 2 to measure current - voltage curves.In this case the membrane cell is placed in such a way that the membranes are in avertical position. The electrolyte solutions are pumped through the membranecell with a flowrate of 475 ml/min. In the second configuration the membranecell is rotated 90 degrees. Thus the membranes are placed in a horizontal position.In this case no solution flow is applied during a chronopotentiometricmeasurement, the solutions in the cell compartments are stagnant. The twoconfigurations are shown in figure 3.1.

72 Chapter 3

AAAAAA

NaCl solution

testmembrane

no solution flow

A B

counter ionflux

counter ionflux

Figure 3.1: Schematic drawing of the membrane cell positions used in thechronopotentiometric experiments. A: test membrane in a verticalposition, with solution flow through the membrane cell. B: testmembrane in horizontal position, no solution flow through themembrane cell. Arrow through the membrane indicates thedirection of the counter ion flux.


In this section the results of different chronopotentiometric investigations arediscussed. The first part deals with chronopotentiometry using the experimentalset-up as shown in figure 3.1A, i.e. test membrane in a vertical position and asolution flowing through the membrane cell. The second part is focussed onchronopotentiometric curves obtained with the configuration as shown in figure3.1B (test membrane in a horizontal position, counter ion flux upwards withoutsolution flow in the membrane cell). In the third part transition timesdetermined from the different chronopotentiometric measurements arecompared with those calculated from theory.

Vertically positioned membrane with solution flow

Figure 3.2 shows a typical example of a chronopotentiometric curve, measuredwith a CMX membrane in a 0.10 M NaCl solution when applying a currentdensity above the limiting current density of this system. The curve consists offour parts. At time zero the experiment is started but no current is applied yet andsince the solutions on either side of the membrane are equal, the voltage dropremains zero. At point A a fixed current density is applied. At this point aninstantaneous increase in voltage drop occurs which is part 1 of the curve shown


in figure 3.2. This increase in voltage drop is due to the initial ohmic resistance ofthe system composed of solution and membrane between the tips of the voltagemeasuring capillaries (see appendix 3.1 to this chapter). After the increase involtage due to the ohmic resistance, part 2 commences which is a very slowincrease in voltage drop in time. At a certain time this is followed by a strongincrease in voltage drop (part 3). The point at which this increase occurs is thetransition time which can be determined by the intersection of the tangents topart 2 and 3 of the curve [11]. Finally the fourth part of the curve is reached wherethe voltage drop levels off.

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8

voltage drop(V)

time (min)A

τ1

2

3

4

Figure 3.2: Example of a chronopotentiometric curve measured for a CMXcation exchange membrane in a 0.10 M NaCl solution. Point Adenotes the time at which a fixed current density of 15 mA/cm2 isapplied, τ is the transition time. The numbers in the graph refer tothe different stages explained in the text.

Figure 3.3 shows a characteristic set of chronopotentiometric curves measured atdifferent applied current densities with a CMX membrane in 0.10 M NaCl. Thelimiting current density for this system is 9.5 ± 0.5 mA/cm2. Firstly it is observedthat the curve measured at a current density below the limiting current does notshow the sharp increase in voltage drop which is measured when applying acurrent density above the limiting value. This curve is not characterised by atransition time because the concentration near the membrane surface does notreach zero. Furthermore figure 3.3 shows that a more or less steady state voltagedrop is reached for the curves measured below the limiting current density.However, this is not the case when current densities larger than the limitingcurrent are applied; for these curves only a quasi steady state is reachedcharacterised by large fluctuations in voltage drop. This is in agreement with the

74 Chapter 3

findings in chapter 2 where current - voltage curves were measured whichshowed a smooth pattern below and a considerable scatter near and above thelimiting current density. Figure 3.3 shows that the amplitude of these fluctuationsclearly increase with increasing applied current density. Experiments performedwith an AMX anion exchange membrane showed similar results as shown infigure 3.3 for the CMX cation exchange membrane. The strong fluctuations involtage drop in the overlimiting region is also observed by other researchers andindicate the presence of hydrodynamic instabilities in the depleted diffusion layeroccurring in this region [14, 15].

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5

voltage drop(V)

time (min)

23

mA/cm2

15

11

97

Figure 3.3: Chronopotentiometric curves at different applied current densitiesmeasured with a CMX membrane in 0.10 M NaCl (set-up: verticallyplaced membrane, with solution flow). Numbers next to the curvesrefer to the applied current density.

Prior to the chronopotentiometric measurements shown in figure 3.3 a current -voltage curve was determined using the exact same set-up configuration. Whendetermining a current - voltage curve it is assumed that the values in the curvecorrespond to steady state situations. The (quasi) steady state values of thechronopotentiometric measurements were compared with the determinedcurrent - voltage curve. The results are given in figure 3.4 showing that thevalues from the chronopotentiometric curves coincide with the current - voltagecurve. Hence the data points obtained in the current - voltage curve indeed referto the (quasi) steady state and not to the transient trajectory before this stage isreached (in other words, the data points in the current - voltage curve correspondto region 4 and not to region 2 or 3 in figure 3.2).


0 0.5 1 1.5 2 2.50

5

10

15

20

25

30current-voltage curvechronopotentiometric

current density

(mA/cm2)

voltage drop (V)

Figure 3.4: Comparison between current - voltage curve and the (quasi) steadystate voltage drops determined from chronopotentiometric mea-surements at different applied current densities as shown in figure3.3. Error bars refer to the maximum amplitude of the voltagefluctuations in the chronopotentiometric curves.

Horizontally positioned membrane without solution flow

Figure 3.5 shows a set of chronopotentiometric curves measured with zerosolution flowrate, the membrane placed in a horizontal position and the counterion flux upwards. This way the concentration gradients underneath themembrane are stabilised by gravitation and the occurrence of natural convectionis minimised [3, 14] (A “lighter” salt depleted layer on top of a “heavier” solutionwhere no concentration gradients have developed yet). Since the solution in thiscompartment is stagnant (zero flowrate), the thickness of the boundary layerincreases in time, i.e no fixed boundary layer thickness is obtained. This is inagreement with the results shown in figure 3.5: after applying a fixed currentdensity a similar pattern as shown in figure 3.3 is seen with an inflection at thetransition time. However, since there is an unlimited growth of the thickness ofthe depleted boundary layer, no steady state voltage drop is obtained but thevoltage drop remains increasing in time.

76 Chapter 3

0

1

2

3

4

0 0.5 1 1.5 2 2.5 3

voltage drop(V)

time (min)

22 mA/cm2 14

9

7

Figure 3.5: Chronopotentiometric curves at different applied current densitiesmeasured with the CMX membrane, horizontally positioned,counter ion flux upwards and without solution flow (“gravitatio-nally stabilised position”).

The curves measured with the depleted membrane boundary layer in thegravitationally stabilised position also show the presence of instabilities; withincreasing voltage drop and time, fluctuations in voltage drop become evident,the magnitude of which is increasing in time. A clear example of this feature isshown in figure 3.6. Since there is no flow through the membrane cell, thesemeasurements demonstrate that the fluctuations are not a result of forcedconvection.

0

2

4

6

8

10

0 0.2 0.4 0.6 0.8 1 1.2 1.4

voltage drop(V)

time (min)

Figure 3.6: The occurrence of fluctuations in voltage drop with the membranein the horizontally, gravitationally stabilised position (CMX mem-brane, applied current density is 35 mA/cm2).


The experiments were repeated with the AMX anion exchange membrane usingthe same set-up configuration. The results, shown in figure 3.7, are very similar tothe results obtained with the CMX membrane.

0

1

2

3

4

0 1 2 3 4

voltage drop(V)

time (min)

35 mA/cm2 22 15

11

Figure 3.7: Chronopotentiometric curves at different applied current densitiesmeasured with the AMX membrane, placed horizontally andwithout solution flow (“gravitationally stabilised position”).

Transition times

Rösler [3, 11] used chronopotentiometric experiments to establish the presence ofheterogeneities, i.e. a reduced permeable membrane area, in ion exchangemembranes to support the hypothesis of electroconvection as a reason for theoverlimiting current. The experimentally determined transition times werecompared with the transition times calculated with equation (3.7) which wasgiven by:

τ = πD4

Co z F

ti - ti

2 1

i2(3.7)

Figures 3.3, 3.5 and 3.7 show that the transition time decreases with increasingapplied current density. Equation (3.7) predicts the transition time beingproportional to the inverse of the current density squared. Transition times weredetermined for the CMX membrane as a function of applied current density. Thiswas done for the two set-up configurations described earlier. The results, shown

78 Chapter 3

in figure 3.8 show that indeed a linear relationship is observed between thetransition time and the inverse current density squared.

0

5

10

15

0 0.002 0.004 0.006

horizontal, no flowvertical, with flow

transitiontime (s)

i -2 (cm4/mA2)

Figure 3.8: Comparison of transition time as a function of the inverse currentdensity squared between the two different membrane set-ups,i.e. horizontally positioned membrane, counter ion flux upwardsand no solution flow versus vertically placed membrane withsolution flow (CMX membrane).

From figure 3.8 it is clear that the experimentally determined transition timescoincide for the two different membrane set-ups although the hydrodynamics arecompletely different. Equation (3.7) was derived for a semi-infinite diffusionprocess. This assumes the absence of any, i.e. forced or natural, convection andthus an unlimited growth of the diffusion layer next to the membrane. Thechronopotentiometric measurements in figure 3.5 indicate that these conditionsare fulfilled using the system with the horizontally positioned membrane with itsdepleted boundary layer in the gravitationally stabilised position. This is a priorinot the case for the system with the vertically positioned membrane since a(convective) solution flow is forced through the membrane cell thereby creating adiffusion layer with finite thickness. However, a system with forced convectioncan still resemble the semi-infinite diffusion problem during a time-scale inwhich no concentration changes have occurred at a distance from the membranesurface equal to the boundary layer thickness. An infinite boundary layer conceptcan thus be used for not too large times, i.e. times in which the root-mean-squaredisplacement 2Dt is small compared to the thickness of the boundary layer [11,

16].


In chapter 2 limiting current densities were measured for the CMX and AMXmembrane in NaCl solutions of different concentrations. When using equation(2.8), derived for the limiting current density, an estimation of the thickness ofthe boundary layer can be obtained. The thickness of the boundary layer calculatedthis way is in the range of 250 - 300 µm. Using 250 µm for the root-mean-squaredisplacement, an upper limit for the transition time is calculated to be 20 seconds.Thus as long as transition times smaller than 20 seconds are determined a semi-infinite diffusion process can be assumed, a condition which is fulfilled in figure3.8. This explains why still a linear relationship is obtained in figure 3.8 for thevertically positioned membrane with solution flow and why in this figure thedetermined transition times coincide with the transition times determined withthe horizontally mounted membrane with its depletion layer gravitationallystabilised.

The previous discussion has shown that both membrane set-ups can be used todetermine the transition time as a function of applied current density. The systemwith the vertically positioned membrane and solution flow is characterised by alimiting current density as can be seen in figure 3.4. In order to measure atransition time, current densities above the limiting current value have to beapplied otherwise the concentration at the membrane surface will not reach zero.This reduces the range of current densities which can be used to investigate thetransition time as a function of applied current density and thus limits acomparison between calculated and experimental transition times (equation (3.7)).This is not the case with the second membrane set-up where no solution flow ispresent. In this case much lower current densities can be applied while stillobtaining a transition time (for a truly infinite diffusion layer thickness thelimiting current density is zero).

Figure 3.9 shows the transition time as a function of the inverse of the currentdensity squared, determined over a broader range of current densities andtransition times. This figure demonstrates that the linear relationship ismaintained up to higher transition times.

80 Chapter 3

ti = 1

-

ti = 0.95

-

0

20

40

60

0 0.005 0.01 0.015 0.02

i-2 (cm4/mA2)

transitiontime (s)

Figure 3.9: Comparison between experimental (open circles, dashed line) andcalculated transition times (solid lines) for the CMX membrane(horizontally, gravitationally stabilised position). The calculatedlines refer to an ideally permselective membrane (counter iontransport number in the membrane equal to 1) and a membranewith counter ion transport number 0.95.

In figure 3.9 a comparison is made with the transition time calculated according toequation (3.7). For the calculation a NaCl diffusion coefficient of 1.48 10-9 m2/sand a Na+ solution transport number of 0.39 were used which are values for a 0.10M NaCl solution [17]. It is seen that the experimentally determined transitiontimes are smaller than the transition times calculated for an ideally permselectivemembrane. Equation (3.7) shows that a reduction in membrane permselectivityresults in an increase in the calculated transition time. In appendix 1 to chapter 2it was shown that the permselectivity of the CMX and the AMX membrane isabout 95%. In figure 3.9 also the calculated line is shown using 0.95 as themembrane transport number which demonstrates that a small reduction inmembrane permselectivity can significantly increase the transition time.

Figure 3.10 shows the comparison between calculated and experimentallydetermined transition times obtained with the AMX membrane, again with themembrane in the horizontal position without solution flow and counter ion fluxupwards.


ti = 1

-t

i = 0.95

-transitiontime (s)

0

20

40

60

0 0.002 0.004 0.006 0.008

i-2 (cm4/mA2)

Figure 3.10: Comparison between experimental (open circles, dashed line) andcalculated transition times (solid lines) for the AMX membrane(horizontally, gravitationally stabilised position). The calculatedlines refer to an ideally permselective membrane (membranetransport number 1) and a membrane with transport number 0.95.

The results in figure 3.10 are similar to the findings with the CMX membrane.Also in this case the experimental transition times are smaller than the valuescalculated for an ideally permselective membrane. When figures 3.9 and 3.10 arecompared, it is observed that at given applied current density the transition timefor the anion exchange membrane is much higher than for the cation exchangemembrane. The difference is caused by the difference in counter ion for the twomembranes. The Cl- solution transport number, which equals 0.615, is muchlarger than the Na+ solution transport number (0.385) and equation (3.7) showsthat, given the same membrane transport numbers, this results in highertransition times for the anion exchange membrane.

The results in figures 3.9 and 3.10 show that the experimentally determinedtransition times are lower than the transition times calculated for an ideallypermselective membrane. It is important to stress that any non-ideal behaviour ofa real system, such as a reduced permselectivity, consumption of non-faradaiccurrents for charging of double layers and the onset of natural convection, canonly result in transition times times higher than predicted by theory [3, 18]. Thisway it can be argued that transition times lower than the values calculated for anideally permselective membrane can only be due to a reduction in availablemembrane area for ion conductance [3]. A reduced permeable membrane areacorresponds to a locally higher current density at those points where the

82 Chapter 3

membrane is conductive. This causes a faster depletion of salt near themembrane, i.e. a lower transition time is measured compared to the situationwhere the complete membrane area is available for ion conduction.

The experimentally determined transition times are lower than the timescalculated for an ideally permselective membrane and thus indicate that the CMXand the AMX membrane used in this study are not uniformly conductive. Thedifference between the experimental slope and the calculated slope for an ideallypermselective membrane in figure 3.9 and 3.10 is very small, the ratio is about0.92 for the CMX and 0.95 for the AMX membrane. Rösler [3, 11] performedexperiments with several commercial and lab-made cation and anion exchangemembranes and also found experimental transition times lower than predicted bytheory. The commercial membranes showed a similar small difference betweenexperimental and calculated transition times measured in CuSO4 and KClsolutions. The difference however was much larger when the lab-made cationexchange membranes were studied (the ratio in slopes varied between 0.64 and0.87 in this case). Sulfonated polysulfone membranes had been prepared withsimilar permselectivity but differing in ion exchange capacity. A correlation wasfound between the ion exchange capacity and the transition times. A decrease inion exchange capacity resulted in a larger difference between the experimentaltransition times and the ones calculated for an ideally permselective membrane.A membrane with a lower ion exchange capacity can be regarded as being moreheterogeneous than a membrane with higher ion exchange capacity. Based onthese results the conclusion seems justified that a reduction in transition timecompared to theory is due to a reduced permeable membrane area. At present it isnot possible to quantify the conductive heterogeneity based on thesechronopotentiometric measurements since no mathematical model exists whichcorrelates the reduced transition time with such heterogeneities [3].

Mizutani [19] published a review about the structure of Neosepta membranesproduced by Tokuyama Soda. Although the Neosepta CMX and AMX membraneare not mentioned, it can be assumed that the results obtained in this paper areapplicable to these two membranes as well [20]. The Neosepta membranes areprepared by the paste method. A paste consists of a monomer with a functionalgroup appropriate to introduce an ion exchange group (e.g. styrene, chloro-methylstyrene, 4-vinylpyridine, 2-methyl-5-vinylpyridine), divinylbenzene as acrosslinking agent, a radical polymerization initiator and finely powderedpoly(vinylchloride). The paste is coated onto a PVC cloth as reinforcing material


and the monomers are copolymerised by heating to produce a base membrane,which is subsequently sulfonated or aminated to produce ion exchangemembranes with sulfonic acid or quaternary ammonium groups. The structure ofthe membranes was studied by removing the ion exchange material using a H2O2treatment, resulting in the formation of microporous membranes. Pore sizes upto 0.1 µm were found to be present in the surface of the membranes, larger poresizes were found to be present in the cross-sections. Microscopic techniquescombined with water permeability experiments revealed that the membranescontain microheterogeneities, i.e. the membranes consist of two continuousphases, a PVC phase and the ion exchange resin component, which are closelyintertwined. These studies on Neosepta membranes are thus in agreement withthe chronopotentiometric results shown here for the CMX and AMX membraneswhich also indicated the presence of heterogeneities.

3.5 Conclusions

Chronopotentiometric measurements were performed with a CMX cationexchange membrane with the same set-up configuration that was used in chapter2 to determine current - voltage curves. In this case the membrane was present ina vertical position in the membrane cell while a solution flows through the cell.When a current below the limiting current density was applied the voltage dropincreases slowly and a steady state value was reached. If a current larger than thelimiting current density was applied, the chronopotentiometric curves werecharacterised by a sharp increase in voltage drop at the transition time. After thisthe voltage drop leveled off and a quasi steady state was reached showing strongfluctuations around an avarage value. This is in agreement with the considerablescatter in data points in the overlimiting region of the current - voltage curvesdetermined in chapter 2. The amplitude of the fluctuations in voltage dropincreased with increasing applied current density. The fluctuations occurring inthe overlimiting current range indicate the presence of hydrodynamic instabilitiesin this region. The quasi steady state values of the different chronopotentiometriccurves were found to coincide with the current - voltage curve.

Chronopotentiometric curves were determined both with the CMX and the AMXmembrane using a set-up configuration without any solution flow where themembrane is placed horizontally with the counter ion flux upwards. The resultsfor the two types of membranes were very similar. The measurements showed

84 Chapter 3

that no steady state voltage drop was reached, but the voltage drop continuouslyincreased in time. This was due to the stabilisation of the concentration gradientsin the depleted solution by gravitation. The occurrence of natural convection wasminimised allowing for the concentration profile to grow into the solution intime. These measurements also showed the presence of fluctuations in voltagedrop. Since there was no flow through the membrane cell, this demonstrates thatthe fluctuations are not a result of a forced convection.

Transition times were determined as a function of the applied current density forboth the CMX and the AMX membrane. As predicted by theory, a linearrelationship was obtained between the transition time and the inverse currentdensity squared. Experimental transition times were compared with transitiontimes calculated for an ideally permselective membrane. The experimental valueswere smaller than the calculated transition times. This indicates a reducedpermeable membrane area for the two investigated membranes.

The results obtained are in agreement with the theory describing electrocon-vection. As was shown in chapter 2, the overlimiting current for the CMX andAMX membrane could not be explained by a loss in permselectivity nor by theoccurrence of water dissociation. Thus the counter ions remain responsible forcarrying the current in the overlimiting region. The chronopotentiometricexperiments in this chapter have shown that large fluctuations in voltage dropoccur even with the set-up where no solution flow is applied and the depleteddiffusion layer is stabilised by gravitation. These fluctuations indicate that indeedhydrodynamic instabilities occur, i.e. convective phenomena are present close tothe membrane surface which destabilise the polarised boundary layer and enableto obtain overlimiting currents. In the electroconvection theory it is assumed thata non-uniform electric field exists due to the presence of a non-uniform ion con-ductance through the membrane. This condition agrees with the chrono-potentiometric results; comparison between experimental and calculatedtransition times have indicated the presence of heterogeneities in the CMX andAMX membrane.

3.6 List of symbols







P permselectivity (-)

R area resistance (Ω cm2)

t time (s)

ti transport number in solution (-)

ti transport number in membrane (-)

V voltage drop (V)



τ transition time (s)


0 value at time zero

corr corrected

ideal value for an ideally permselective membrane

m membrane

meas measured

s solution

Ω ohmic

3.7 References

1 I. Rubinstein and F. Maletzki, Electroconvection at an electrically inhomogeneous

permselective membrane surface, J. Chem. Soc. Far. Trans. 87 (1991) p. 2079-2087.

2 I. Rubinstein, Electroconvection at an electrically inhomogeneous permselective interface,

Phys. Fluids A3 (1991) p. 2301-2309.

3 H.-W. Rösler, F. Maletzki and E. Staude, Ion transfer across electrodialysis membranes in

the overlimiting current range: chronopotentiometric studies, J. Membrane Sci. 72 (1992) p.

171-179.

4 A.J. Bard and L.R. Faulkner, Electrochemical methods: fundamentals and applications,

John Wiley & Sons, New York (1980).

5 P. Delahay, Chronoamperometry and chronopotentiometry, in Treatise on analytical

chemistry, I.M. Kolthoff and P.J. Elving (Eds.), John Wiley & Sons, New York (1963) p.

2233-2265.

6 D.T. Sawyer and J.L. Roberts, Experimental electrochemistry for chemists, John Wiley &

Sons, New York (1974).



8 R. Audinos and G. Pichelin, Characterization of electrodialysis membranes by chronopo-

tentiometry, Desalination 68 (1988) p. 251-263.

86 Chapter 3

9 M. Taky, G. Pourcelly, C. Gavach and A. Elmidaoui, Chronopotentiometric response of a

cation exchange membrane in contact with chromium (III) solutions, Desalination 105 (1996)

p. 219-228.

10 P. Sistat and G. Pourcelly, Chronopotentiometric response of an ion-exchange membrane in

the underlimiting current range. Transport phenomena within the diffusion layers, J.

Membrane Sci. 123 (1997) p. 121-131.

11 H.-W. Rösler, Untersuchungen zum überkritischen Ionentransport durch Elektrodialyse-

membranen mit Hilfe der Chronopotentiometrie, Rauschanalyse und Diffusions-Relaxation,

PhD thesis, University of Essen, Germany (1991).

12 C.N. Reilly, Fundamentals of electrode processes, in Treatise on analytical chemistry, I.M.

Kolthoff and P.J. Elving (Eds.), John Wiley & Sons, New York (1963) p. 2109-2160.

13 H.J.S. Sand, On the concentration at the electrodes in a solution, Phil. Mag. 1 (1901) p. 45-

79.

14 I. Rubinstein, E. Staude and O. Kedem, Role of the membrane surface in concentration

polarization at ion-exchange membrane, Desalination 69 (1988) p. 101-114.




16 K.J. Vetter, Elektrochemische Kinetik, Springer-Verlag, Berlin (1961).


(1959).

18 A.J. Bard, Effect of electrode configuration and transition time in solid electrode chrono-

potentiometry, Anal. Chem. 33 (1961) p. 11-15.

19 Y. Mizutani, Structure of ion exchange membranes, J. Membrane Sci. 49 (1990) p. 121-144.

20 Tokuyama Soda Inc., personal communication (1997).

Appendix 3.1

Ohmic resistance and relation to current - voltage curves

Introduction

In chapter 3 several chronopotentiometric curves were shown. As soon as a fixedcurrent density is applied, an instantaneous jump in voltage drop is observed(part 1 of the chronopotentiometric curve as shown in figure 3.2). In this appendixit will be shown that this jump is due to the initial ohmic resistance of the systembetween the voltage measuring capillaries. Furthermore a comparison will bemade between the jump in voltage in a chronopotentiometric measurement andthe ohmic region in a current - voltage curve.

Results and conclusions

First attention is paid to the jump in voltage drop which occurs as soon as aconstant current density is applied. As an example the chronopotentiometriccurves shown in figure 3.3 will be used. The jump in voltage drop increases withincreasing current density. The jump is presumably due to an ohmic resistancesince it occurs instantaneously. In this case it refers to the ohmic resistance of thesystem consisting of solution plus membrane in between the voltage measuringtips of the capillaries. If the capillaries are maintained in exactly the same positionin the membrane cell, the ohmic resistance of this system of solution andmembrane is constant prior to each chronopotentiometric measurement. Thismeans that the ratio of the voltage jump to the applied current density (Ohm’slaw) would be the same in each experiment. Table A3.1 shows the jump involtage at the different applied current densities. The values in this tabledemonstrate that the calculated resistance is indeed constant.

When current - voltage curves are determined, it was found that the voltage dropmeasured across the membrane depends strongly on the position of thecapillaries. In figure A3.1 three current - voltage curves are shown using differentcapillary positions, i.e. the distance between the tips of the capillaries was varied.

88 Chapter 3

Table A3.1: Calculation of the resistance from the initial voltage jump at thedifferent applied current densities, determined from the experi-ments in figure 3.3.

applied current density(mA/cm2)

voltage jump(V)

resistance(Ω cm2)

7.1 0.193 27.2

9.1 0.248 27.3

11.1 0.300 27.0

15.2 0.414 27.2

23.3 0.638 27.4

0

10

20

30

40

0 1 2 3 4 5

current density

(mA/cm2)

voltage drop (V)

1 32

Figure A3.1: Current - voltage curves measured at different capillary positionswith a CMX membrane in 0.10 M NaCl. The distance between thecapillaries increased in the direction going from 1 to 3.

Figure A3.1 shows that increasing the distance between the capillaries results inthe voltage drop spread to higher voltage values. This is caused by moreelectrolyte solution present between the tips of the capillaries causing a higherresistance and voltage drop. Furthermore figure A3.1 shows that the currentplateau is less distinct with large capillary distance indicating that a large capillarydistance is not suited for determining the limiting current density value.

The first part of a current - voltage curve shows a linear relation between current

Appendix 3.1: ohmic resistance 89

density and voltage drop which is therefore usually referred to as the ohmic partof the current - voltage curve. The inverse slope of this ohmic region correspondsto a resistance. Chronopotentiometric measurements were performed usingexactly the same three capillary positions that were used for determining thecurrent - voltage curves shown in figure A3.1. The resistance calculated from theinstantaneous jump in voltage drop in the chronopotentiometric measurementswere compared with the resistance calculated from the initial slope of the current- voltage curves. The results are shown in table A3.2.

Table A3.2: Comparison between the resistance calculated from the initial slopein the current - voltage curve and the resistance calculated from thevoltage jump in chronopotentiometric measurements. Capillarydistance increases from 1 to 3.

capillaryposition

resistance(current - voltage curve)

(Ω cm2)

resistance(chronopotentiometry)

(Ω cm2)

1 11.5 ± 0.8 7.6 ± 0.2

2 32.2 ± 1.1 27.2 ± 0.2

3 94.2 ± 1.5 86.6 ± 0.2

Table A3.2 shows that the resistance calculated from the current - voltage curve islarger than the ohmic resistance calculated from the instantaneous voltage dropoccurring when a fixed current density is applied. This demonstrates thatalthough the linear part of a current - voltage curve is generally denoted as theohmic region, it does not correspond to the initial ohmic resistance of thesolution and membrane in between the voltage measuring capillaries. In case ofthe current - voltage curve an extra resistance is added due to the concentrationpotential, i.e the potential associated with the developed concentration gradientsnear the membrane surface.

The capillary distance has a large influence on the current - voltage curve as wasshown in figure A3.1 due to a difference in the initial ohmic resistance of thesystem. This can be avoided by making a correction for the initial ohmicresistance. In this case the ohmic voltage drop which equals the ohmic resistance,RΩ, times the applied current density, i, is subtracted from the measured voltagevalue V:

Vcorr = V - i RΩ (A3.1)

90 Chapter 3

As was described above, the ohmic resistance determined from chronopoten-tiometric measurements should be used in equation (A3.1). This procedure hasbeen applied to the current - voltage curves shown in figure A3.1. The results areshown in figure A3.2. This figure shows that using the corrected voltage dropresults in the three curves to coincide.

0

10

20

30

40

0 0.5 1 1.5 2

123

current density

(mA/cm2)

corrected voltage drop (V)

Figure A3.2: Current - voltage curves using the voltage drop corrected for theohmic resistance. Numbers refer to the capillary distance, which isincreasing from 1 to 3.

Chapter

4

Salt Transport in Bipolar Membranes

at Low Current Density

4.1 Introduction

Bipolar membranes can be used for the production of acids and bases from thecorresponding salt solutions. This is a result from the unique feature that abipolar membrane is capable to perform enhanced water dissociation whenapplying an electric field across the membrane [1]. The principles of bipolarmembranes are shown in figure 4.1 [2]. Suppose an anion and a cation exchangemembrane are placed between two electrodes, as illustrated in figure 4.1A. Underthe influence of an electric field, the salt ions are removed from the compartmentbetween the two membranes (similar to a desalting compartment in electro-dialysis). After removal of all salt ions present, the only ions that can carry thecurrent in this compartment are the H+ and OH- ions of water (figure 4.1B). Toreduce the high electrical resistance of the deionised water layer in thecompartment between the two membranes, they are placed next to each other anda bipolar membrane is formed as shown in figure 4.1C.

Figure 4.1 shows that upon applying an electrical field, the water dissociation of abipolar membrane does not occur instantaneously but only after removal of allsalt ions. When bipolar membranes are stored in a salt solution, equilibriumbetween the bipolar membrane and the surrounding solution results in thepresence of salt at the interphase between the two charged layers which is called

92 Chapter 4

the transition region. The thickness of this transition region is much smaller thanthe thickness of the monopolar layers and can be estimated to be in the order of 1 -10 nm [1, 3, 4]. The transition region will be discussed in more detail in chapter 5.

H+

Na+ Cl --

-

-

+

+

+

cem aem

Na+ Cl -+

+

+

-

-

-cathode anode

-

-

-

+

+

+

bipolar membrane

A

B

C

H + OH -

H2O

OH -

H2O

H2O

Figure 4.1: Schematic of the principles of a bipolar membrane (cem refers to acation exchange membrane, aem to an anion exchange membrane).

When an electric field is applied, salt ions are removed from the transition regionby migration. This, however, creates a concentration gradient across the mono-polar layers of the membrane resulting in a diffusional flow of salt ions back intothe transition region. In steady state (constant current) the migrational flow ofions out of the transition region is in equilibrium with the diffusional backflowinto the transition region. When the current increases the transition regionbecomes depleted of salt ions. At a certain current density, called the limitingcurrent density, all salt ions are removed from the transition region and the onlyions present in this region are the protons and hydroxyl ions having aconcentration of 10-7 mol/l in completely deionised water. Above the limitingcurrent density water dissociation starts and the bipolar membrane resistancedecreases [5].

Bipolar membranes have been studied frequently by measuring current - voltagecurves [1, 6, 7]. Much attention is paid in these studies to the current range wherewater dissociation occurs. This chapter focuses on the transport processes

Salt transport in bipolar membranes at low current density 93

occurring within a bipolar membrane before water dissociation commences.Experiments are performed in which the removal of salt from the bipolarmembrane interphase and the occurrence of a limiting current are shown. Asimple model to calculate this limiting current is described and calculations areperformed to fit the experimental values of the limiting current density.

4.2 Model to describe the salt transport below the limiting current density

A model will be described predicting the limiting current density for an 1:1electrolyte (NaCl) [4]. For simplicity the following assumptions are made:

• Symmetrical conditions, i.e. the electrolyte concentration on both sides ofthe bipolar membrane is equal, the two layers constituting the bipolar membrane have the same fixed charge density and the same thickness and the transport number of the sodium ions in the cation exchange membrane equals the chloride transport number in the anion exchange membrane.

• The concentration gradients of the sodium and chloride ions across the monopolar layers are linear.

• The condition of electroneutrality holds throughout the entire mem-brane.

• Transport of protons and hydroxyl ions is neglected as ion transport is regarded prior to the onset of water dissociation.

Due to the assumption of symmetrical conditions, the concentration profiles ofsodium and chloride ions in the bulk solutions and in the bipolar membrane atzero current (no applied electric field) can be represented as shown in figure 4.2.When the current increases, salt ions are removed from the transition region andconcentration gradients develop across the monopolar layers as is schematicallyshown in figure 4.3.

94 Chapter 4

bulksolution

bulksolutioncem aem

transitionregion

Xcem Xaem

C

x

CNaCl CNaCl

CNa+m

CCl-m

CCl-m

CNa+m

CNa+tr

CCl-tr

=

Figure 4.2: Ion concentration profiles in a bipolar membrane at zero currentconditions. For illustration purposes the thickness of the transitionregion is enlarged with respect to the thickness of the cationexchange (cem) and anion exchange (aem) layer. C denotes theconcentration, X the fixed charge density, superscript m refers to themonopolar layer, tr to the transition region.

bulksolution

bulksolutioncem aem

transitionregion

Xcem Xaem

C

x

CNaCl

C=0

CNaCl

CNa+tr

CCl-tr

=

CNa+m

CNa+m

CCl-m

CCl-m

Figure 4.3: Change in ion concentration profiles in a bipolar membrane whenan electric current is applied (0 ≤ i ≤ il im). Arrows indicate thedirection of change with increasing current density.

As illustrated in figure 4.4, the following ion fluxes have to be considered:1. Migration of counter ions out of the transition region to the bulk

solutions,2. Migration of co-ions from the bulk solutions into the transition region

(non-ideal permselectivity of the monopolar layers that constitute the bipolar membrane), and

3. Diffusion of co- and counter ions from the bulk solutions into the transition region.


bulksolution

bulksolution

cem aemtransition

region

JNa+mig1

1

2

3

JNa+mig2

ClJmig1

-

Jmig2Cl -

JNa+diff

Cl -,JNa+diff

Cl -,

= CCl-tr

CNa+tr

anodecathode

Figure 4.4: Salt ions fluxes in a bipolar membrane for current densities smallerthan the limiting current density. Superscript mig1 refers to themigrational flux of counter ions, mig2 to the migrational flux of co-ions and diff to the diffusional flux.

In the transition region the sodium ion concentration is equal to the chloride ionconcentration (electroneutrality). Since symmetrical conditions are assumed, onlythe transport of sodium ions has to be regarded in the following.The depletion of sodium ions in the transition region (which is equal to thedepletion of chloride ions due to the electroneutrality condition) is given by amass balance over the transition region:

V.dCNa+

tr

dt = A . JNa+∑ (4.1)

Here V is the volume of the transition region, C the concentration, t the time, Athe membrane area and J the flux. Superscript tr refers to the transition region. Asillustrated by figure 4.4, the total flux of sodium ions is given by:

JNa+∑ = JNa

+mig1

+ JNa+

mig2 + 2 JNa

+diff

(4.2)

Within the cation exchange layer Na+ is the counter ion, within the anionexchange layer it is Cl-. The counter ion transport number in both layers isassumed equal and represented by t. The migrational flux of sodium ions throughthe cation exchange layer (superscript cem) from the transition region to the bulksolution is given by:

96 Chapter 4

JNa+

mig1 = -

i tNa+

cem

F = - i t

F(4.3)

where i is the current density and F the Faraday constant. The migrationalsodium ion flux through the anion exchange layer (superscript aem) into thetransition region is given by:

JNa+

mig2 =

i tNa+

aem

F =

i 1 - tCl-

aem

F = i 1- t

F(4.4)

Figure 4.5 shows the schematic concentration profile across the cation exchangelayer. An analogue figure can be drawn for the anion exchange layer.

C

C=0x

bulk NaClsolution

transitionregion

δm

cem

=

CmtrCl

-

CmtrNa

+

CNa+b CCl

-b=

CmbCl

-

mbCNa

+

Xcem

CCl-trCNa

+tr

Figure 4.5: Ion concentration profile across the cation exchange layer of abipolar membrane. Superscript b refers to the bulk solution,mb refers to the membrane interface with the bulk solution, mtrrefers to the membrane interface with the transition region and trrefers to the transition region; δm is the thickness of the monopolarlayer where the concentration gradient is developed.

Figure 4.5 shows that the concentration gradient across the monopolar layer isdetermined by the thickness of the monopolar layer, δm, and the concentrations atthe interfaces with the bulk solution, Cmb, and the transition region, Cmtr. Thediffusional salt flux is determined by the concentration gradient across themonopolar layers of the bipolar membrane. Due to a difference in mobilitydifferent ions tend to diffuse through a membrane with a different velocity. Thiswould disturb the electroneutrality and a so-called diffusion potential is createdwhich slows down the faster ion and accelerates the slower ion [8, 9] . As a result


co- and counter ions diffuse with the same velocity through the membranethereby maintaining electroneutrality. This is the reason why a commondiffusion coefficient (DNaCl) can be used instead of the ionic diffusion constants(DNa+ and DCl-). The diffusional flux of sodium ions into the transition region isnow given by:

JNa+

diff = DNaCl .

CNa+

mb - CNa

+mtr

δm (4.5)

In steady state, combination of equations (4.1) to (4.5) results in:

0 = - i t F

+ i 1-t F

+ 2 DNaCl . CNa

+mb

- CNa+

mtr

δm (4.6)

The sodium concentration at the membrane surface between the outer solutionand membrane, CNa

+mb

, can be calculated from the Donnan equilibrium [8]:

CNa+

b

CNa+

mb =

CCl-

mb

CCl-

b(4.7)

The chloride ion concentration at the membrane surface between the outersolution and the cation exchange membrane, CCl-

mb, in equation (4.7) can becalculated with help of the electroneutrality condition:

0 = -X + CNa+

mb - CCl

-mb

(4.8)

Introducing equation (4.8) into equation (4.7) with CNa+b = CCl-

b results in:

CNa+

b

CNa+

mb =

-X + CNa+

mb

CNa+

b(4.9)

Rearranging equation (4.9) leads to:

98 Chapter 4

CNa+

mb =

X + X2 + 4 CNa

+b 2

2(4.10)

In a similar way the concentration of sodium ions in the transition region, CNa+tr ,is related to the concentration at the membrane and transition region interface,CNa+mtr , by the Donnan equilibrium. It is calculated according to equation (4.9)where the bulk concentration CNa+b is replaced by the concentration in thetransition region, CNa+tr :

CNa+

tr = CNa

+mtr 2

- X CNa+

mtr(4.11)

Introducing equation (4.10) into equation (4.6) leads to:

CNa+

mtr =

X + X2 + 4 CNa

+b 2

2 - i δ

m

2 F DNaCl 2t - 1 (4.12)

Combination of equation (4.11) and equation (4.12) results in an expression for thesodium ion concentration in the transition region as a function of the currentdensity:

CNa+

tr =

X + X2 + 4 CNa

+b 2

2 - i δ

m

2 F DNaCl 2t - 1

2

- X X + X

2 + 4 CNa

+b 2

2 - i δ

m

2 F DNaCl 2t - 1

(4.13)

The limiting current density is the current density at which the salt concentrationin the transition region, CNa+tr , has reached zero. The limiting current density isderived from equation (4.13) and is given by:

ilim = F DNaCl

δm

2t - 1 X

2 + 4 CNa

+b 2

- X (4.14)

Equation (4.14) shows that the limiting current density for the removal of salt


from the bipolar membrane transition region increases with increasing saltdiffusion coefficient, increasing bulk solution concentration, decreasing thicknessof the monopolar layers and a decreasing counter ion transport number in theselayers. In this chapter equation (4.14) will be used to compare measured andcalculated limiting current densities when varying the bulk solution concen-tration.

4.3 Experimental

Current - voltage curves at low current density were determined using the set-upand experimental procedure described in chapter 2. The membrane arrangementin the six-compartment cell is shown in figure 4.6. A 0.5 M Na2SO4 solution wasused for electrode rinsing, a 0.5 M NaCl solution was used in the second and fifthcompartment while a NaCl solution of varying concentration was used in thecentral compartments adjacent to the test bipolar membrane. Bipolar membraneswere equilibrated for at least 12 hours in a NaCl solution of concentration equal tothe concentration to be used in the experiment. All experiments were performedat 23 °C with a solution flowrate of 475 ml/min.

Two types of bipolar membranes were used in the experiments. The first type,denoted as BP-1, is a reinforced single film bipolar membrane supplied byTokuyama Soda Inc. (Japan). Its thickness is 200 µm. The second type was suppliedby WSI Technologies Inc. (USA). It consists of two separate, non-reinforced, ionexchange membranes which have to be laminated together by hand to form thebipolar membrane. The two layers are Pall Rai films consisting of a fluorocarbonpolymer matrix in which functional groups have been introduced by radiationgrafting [10]. The thickness of the anion exchange layer is 43 µm, the thickness ofthe cation exchange layer is 73 µm. Both the WSI and BP-1 bipolar membranecontain sulfonic acid groups in the cation exchange layer and quaternaryammonium groups in the anion exchange layer. The monopolar membranesused in the membrane cell are the Tokuyama Soda AMX and CMX anion andcation exchange membrane, respectively.

100 Chapter 4

O2

H+

Na+

SO42-

H2

Na+ Na+ Na+

Cl-Na+

SO42-

Na+

OH-

Cl-

bm

Na+

cemcem cemaem

0.5 M 0.5 Mvar0.5 M 0.5 M

anode cathode

var

Cl-

Figure 4.6: Membrane arrangement in the six-compartment cell (cem refers toa cation exchange membrane, aem to an anion exchange membraneand bm to a bipolar membrane, var indicates a varying NaClconcentration).


Figure 4.7 shows a typical current - voltage curve for a bipolar membranemeasured up to a current density of 80 mA/cm2. The measured voltage dropincreases rapidly at low current density which means a drastic increase in thebipolar membrane resistance due to the removal of salt ions from the bipolarmembrane transition region. Then the slope of the current - voltage curveincreases. This is a result of the onset of water dissociation; the generation ofprotons and hydroxyl ions at the transition region causes the bipolar membraneresistance to decrease [5].

0

20

40

60

80

0 0.5 1 1.5voltage drop (V)

current density(mA/cm2)

Figure 4.7: Current - voltage characteristic of bipolar membrane BP-1 measuredin 0.5 M NaCl.


Figure 4.7 is based on a measurement up to relatively high current densities, i.e.current densities at which water dissociation occurs. If one is interested in theremoval of salt ions initially present at the bipolar membrane transition region,attention must be paid to the current - voltage curve at low current density.Figure 4.8 shows two examples of current - voltage behaviour at low currentdensities (note the difference in current density scale compared to figure 4.7).

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8voltage drop (V)

WSI BP-1current density

(mA/cm2)

Figure 4.8: Current - voltage curves measured with the WSI and BP-1 bipolarmembrane in 0.5 M NaCl at low current density. Arrows indicatethe limiting current density.

Figure 4.8 shows that the current density through the bipolar membrane increasesinitially with a very small increase in voltage drop. This indicates a low bipolarmembrane resistance and is due to the presence of salt at the transition regionkeeping it highly conductive. Increasing the current density causes the saltconcentration at the transition region to decrease and at a certain value theconcentration in this region will go to zero. The current at which this occurs is thelimiting current density indicated by the arrows in figure 4.8. As the limitingcurrent density is reached, the transition region will have a very low conductivitydue to the lack of ions resulting in a strong increase in membrane resistance.Figure 4.8 shows a current plateau indicating the drastic increase in voltage drop.When the salt ion concentration has dropped to zero, water dissociation starts andthe bipolar membrane resistance will decrease; this is seen in figure 4.8 by thesteep current increase after the limiting current plateau and will be treated inchapter 5.

The model described in section 4.2 explained that at low current densities (before

102 Chapter 4

the onset of water dissociation) the conductivity of the transition region dependson the salt ion concentration in this interphase layer. This concentration dependson the balance of the migrational flow of ions out of the transition region due tothe electric field and the diffusional transport of ions back into this region due tothe established concentration gradient across the monopolar layers of the bipolarmembrane. Equation (4.14) shows that the limiting current density of a bipolarmembrane is a function of the external salt concentration. To check the validity ofequation (4.14), current - voltage measurements were performed at low currentdensity and varying external NaCl concentrations. Using the NaCl diffusioncoefficient as a fitting parameter, calculated and experimental limiting currentdensities were compared. The results are shown in figure 4.9.

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8

calc 2.00M

calc 1.00M

calc 0.25M

2.00M1.00M0.25M

voltage drop (V)

current density

(mA/cm2)

Figure 4.9: Current - voltage curves of bipolar membrane BP-1 measured indifferent NaCl solutions. Dotted lines indicate the calculatedlimiting current densities. Parameters used for the calculations: X=1500 mol/m3, t = 0.95, δm= 100 µm, DNaCl= 2.3 10-12 m2/s.

Figure 4.9 demonstrates that the experimentally observed limiting current densityincreases with increasing bulk NaCl concentration. A similar influence of thesolution concentration was measured by Dang [11] with two different bipolarmembranes. The higher the bulk concentration the more salt is initially present atthe transition region and therefore a higher current density is needed to removeall salt from this region. The increase in limiting current density with bulksolution concentration is also obtained with equation (4.14). A good fit betweencalculated and experimental limiting current density is possible using typicalvalues for the fixed charge density and the counter ion transport number. Rapp[12] reports that the NaCl diffusion coefficient measured across commercial cationexchange membranes which resemble the cation exchange layer of the BP-1


bipolar membrane, is in the order of 5 10-12 m2/s. The NaCl diffusion coefficientused in the calculations in figure 4.9 is 2.3 10-12 m2/s which thus seems to be arealistic value.

It has to be noted that in calculating the limiting current densities in figure 4.9, itis assumed that the transport number of the counter ion in the membraneremains constant for the different bulk solution concentrations investigated. Inpractice this may not hold as the membrane transport number is related to thesolution concentration. As was described in chapter 1, an increase in solutionconcentration results in the Donnan exclusion to become less effective and moreco-ion transport can take place. Furthermore some limitations of the model haveto be mentioned. In describing the salt transport, symmetrical conditions aretaken for simplicity. The two layers constituting the bipolar membrane areassumed to be of equal thickness and have the same fixed charge density, whichin practice is not necessarily correct.

4.5 Conclusions

The behaviour of bipolar membranes at low current density was studied. In theabsence of an electric field, equilibrium between membrane and outer solutionresults in the presence of salt ions at the transition region between the twocharged layers. When a small electric current is applied, salt ions removed fromthe transition region are replaced by salt diffusing and migrating from the bulksolutions into the transition region resulting in a steady state with a constant saltconcentration in the transition region. When the applied current increases, themigration from the transition region can no longer be compensated by thediffusive flux into this region which then becomes depleted of salt ions and alimiting current density is reached.

Current - voltage curves were measured at low current density, clearly showingthe presence of a limiting current density. Initially the current increases with avery small increase in voltage drop due to the presence of salt at the transitionregion. At a certain current density the salt ions have been removed from thetransition region thereby strongly increasing the bipolar membrane resistance anda distinct current plateau (limiting current) is observed. After the current plateaua strong increase in current density is observed due to the onset of waterdissociation.

104 Chapter 4

Measurements using NaCl solutions of different concentrations have shown thatthe limiting current density increases with increasing bulk solution concen-tration. A simple model was described in which the limiting current density canbe calculated from bulk solution concentration and membrane characteristicssuch as fixed charge density, counter ion transport number and salt diffusioncoefficient. The change in measured limiting current density in different NaClsolutions could be described adequately by the model.

4.6 List of symbols

A membrane area (m2)






t transport number in membrane (-)

V volume (m3)



δ thickness monopolar layer (m)

Sub-and superscripts

aem anion exchange membrane

b bulk solution

cem cation exchange membrane

diff diffusion

lim limiting

m monopolar layer

mb interface membrane - bulk solution

mig migration

mtr interface membrane - transition region

tr transition region

4.7 References



2 H. Strathmann, B. Bauer and H.-J. Rapp, Better bipolar membranes, Chemtech 23 (1993) p.

17-24.


3 A.V. Sokirko, P. Ramírez, J.A. Manzanares and S. Mafé, Modelling of forward and reverse

bias conditions in bipolar membranes, Ber. Bunsenges. Phys. Chem. 97 (1993) p. 1040-1049.



5 J.J. Krol, Chapter 5 of this thesis.


68 (1988) p. 279-292.




9 N. Lakshminarayanaiah, Transport phenomena in membranes, Academic Press, New York

(1969).

10 R. Simons, Preparation of a high performance bipolar membrane, J. Membrane Sci. 78 (1993)

p. 13-23.

11 N.-T. Dang and D. Woermann, Efficiency of the generation of protons and hydroxyl ions in

bipolar membranes by electric field enhanced water dissociation, Ber. Bunsenges. Phys.

Chem. 97 (1993) p. 149-154.



Chapter

5

Water Dissociation in

Bipolar Membranes

5.1 Introduction

The purpose of electrodialysis with bipolar membranes is the production of acidand base from the corresponding salt solution. This function results from thefeature that a bipolar membrane is capable to dissociate water at a highly accele-rated rate [1]. In chapter 1 it was described that the water dissociation in bipolarmembranes is at least 107 times faster than expected from the ordinary waterdissociation reaction, which is given by:

2 H2O H3O+ + OH

-k1

k-1(5A)

An explanation for this enhanced water dissociation might be related to thesecond Wien effect [2] which describes an increase in the degree of dissociation ofweak electrolytes by high electric field strengths. According to Onsager’s treatmentof the second Wien effect [3], the increase in dissociation rate constant at highelectric field, assuming that the recombination rate constant is unaffected, can beapproximated by:

108 Chapter 5

k1(E)k1

= 2π

. (8b)-3/4. exp 8b (5.1)

with: b = 0.09636 E

εr . T2

(5.2)

In these equations k1 is the dissociation rate constant, E the electric field strength,εr the dielectric constant and T the temperature. The use of the second Wien effectas being responsible for the enhanced water dissociation has some drawbacks aswas described earlier [4], the main limitation being that it predicts a similar waterdissociation behaviour for monopolar cation and anion exchange membranes.This is not in accordance with experimental findings reported in literature (e.g. [5-

9]), as well as with the data presented in chapter 2.

The difference in water dissociation behaviour between anion and cationexchange membranes was also observed by Simons [10-12] who concluded thatthe fixed charged groups are therefore involved in the water dissociation process.The produced protons and hydroxyl ions are believed to be a result fromprotonation and deprotonation reactions according to the following schemes:

B + H2O BH+ + OH

-k2

k-2(5B)

BH+ + H2O B + H3O

+k3

k-3(5C)

for a neutral base group B, and

A- + H2O AH + OH

-k4

k-4(5D)

AH + H2O A- + H3O

+k5

k-5(5E)

for a neutral acid group AH.In case of anion exchange membranes containing quaternary ammonium groups

Water dissociation in bipolar membranes 109

(which can not participate in the above described protonation - deprotonationreactions) the base group B would be a tertiary amine resulting from thedegradation of the quaternary ammonium groups [8, 13].

Recently Rapp [14] developed a model to calculate current - voltage curves forbipolar membranes, based on the proton transfer reaction scheme while also thesecond Wien effect is assumed. In this chapter the model is described.Experimental results will be discussed in the light of this model and discrepanciesbetween model and experimental data, and their origin in the assumptions of themodel, will be identified. Particular attention will be paid to the effect of thedielectric constant which appears to be an important parameter in the descriptionof the enhanced water dissociation process.

5.2 Concentration and potential profiles

The equilibrium between an ion exchange membrane and the surrounding bulksolution can be described by the Donnan relation [15]. As was shown in chapter 1,the Donnan equilibrium relates the concentration of the ionic species in themembrane to the concentration in the solution. In 1962 Mauro [16] presented amodel describing the interphase between the membrane and the electrolytesolution. The model is based on an analogy between the p-n semi-conductorjunction (as described by Shockley [17]) and the fixed charged membranes. Byapplying the Maxwell-Boltzmann and the Poisson equations, the concentrationand potential profiles can be calculated.

The concentration of the charged mobile species Ci is related to the electricalpotential ϕ(x) by the Maxwell-Boltzmann relation:

Ci ϕ(x) = Ci ϕ=0 . exp - zi ϕ(x) e0

k T(5.3)

where e0 and k are the elementary charge and the Boltzmann constant,respectively. In chapter 1 the Donnan potential was derived according to aprocedure in which the electrochemical potential in the membrane and in thesolution was set equal. The Donnan potential for ion exchange membranes inequilibrium with a surrounding solution is a special solution of equation (5.3).The potential ϕ is arbitrarily taken zero in the bulk solution phase, i.e. at a large

110 Chapter 5

distance from the membrane. The corresponding concentration is the bulksolution concentration, thus Ci(ϕ=0) = Ci

b. In the membrane the potential then isϕm ≠ 0 and equation (5.3) can be represented as:

Cim

Cib

= exp - zi (ϕ

m - ϕb) e0k T

(5.4)

In equation (5.4) superscript m refers to the membrane phase, b refers to the bulksolution phase. The Donnan potential, ϕDon, is given by the potential differencebetween membrane and bulk solution and can be calculated from equation (5.4)according to:

ϕDon = ϕm - ϕb = k Tzi e0

ln Ci

b

Cim (5.5)

The Boltzmann constant is given by the gasconstant R and the Avogadro numberNA according to:

k = RNA

(5.6)

The Faraday constant F is given by:

F = e0 NA (5.7)

Introducing equation (5.6) and (5.7) into (5.5), the Donnan potential now becomes:

ϕDon = ϕm - ϕb = R Tzi F

ln Ci

b

Cim (5.8)

which is the same relation as was derived in chapter 1.

It is further assumed that the electrical potential satisfies the Poisson equationwhich is given by:

d2ϕ

d x2 = -

ρeε0 εr

(5.9)


Here ε0 is the permittivity of free space, εr the relative permittivity (dielectric

constant) and ρe the space charge density which can be calculated from:

ρe = F ω X + zi Ci∑i=1

n(5.10)

Here X is the fixed charge density of the membrane and ω the electrochemicalvalence of the fixed charges.

By solving the Poisson and Maxwell-Boltzmann equation the potential andconcentration profiles can be calculated that describe the transition from the bulksolution to the membrane. Figure 5.1 shows schematically the profiles of a cationand an anion exchange membrane separated by an electrolyte solution. Thisfigure shows that at the interfaces between membrane and solution theelectroneutrality is disturbed due to the increasing or decreasing concentration ofcounter ions and co-ions in the membranes and the bulk solution: there exists aso-called space charge at the interfaces.

x = 0 d-d

ϕ = 0

ϕ = -

ϕ = +

x

ϕ , Cbulkcation-

exchangemembrane

anion-exchange

membrane

Xcem

=

Xaem

mcationC

manionC

bcationC b

anionC

manionC

mcationC

Figure 5.1: Concentration and potential profiles for a cation and anionexchange membrane separated by an electrolyte solution asdescribed by the Poisson and Maxwell-Boltzmann equations.

A bipolar membrane is formed by placing an anion and a cation exchangemembrane together. This is equal to a reduction of the distance 2d between thetwo membranes shown in figure 5.1. When the distance is zero an abruptjunction is present within the bipolar membrane. The concentration andpotential profiles for this situation are shown in figure 5.2. For the abruptjunction the space charge is located completely within the membrane and

112 Chapter 5

uncompensated fixed charges exist in the region where the anion and cationexchange layer meet. The region of uncompensated fixed charges is usuallyreferred to as the transition or depletion region.

XaemXcem

x = 0

ϕ = +

ϕ = -

- x

ϕ , C cation-exchange

membrane

anion-exchange

membrane

mcationC

manionC m

cationC

manionC

Figure 5.2: Concentration and potential profiles for a bipolar membrane withan abrupt junction. The transition region extends from -λ to λ .

Assuming the space charge density in the transition region equal to the fixedcharge concentration, the thickness of this region 2λ can be calculated for thesymmetrical case (Xcem = Xaem = X) by [16]:

2λ = 2 ∆ϕtr ε0 εr

X F(5.11)

Here ∆ϕtr is the potential difference across the transition region. The symmetricalcase also assumes equal bulk solution concentration Cb on either side of thebipolar membrane. In this case the Donnan potential ϕDon

1 between solution andmembrane on both sides are equal and ∆ϕtr is given by [18]:

∆ϕtr = 2 ϕDon1 (5.12)

If it is assumed that the system contains only monovalent ions and that Cb << Xthen:

Ccounter-ionm ≈ X (5.13)

The potential difference across the transition region can now be calculated:


∆ϕtr

= 2 RTF

ln X

Cib

(5.14)

For a fixed charge density of 1.5 mol/l the calculated potential difference across thetransition region at T= 25 °C is 0.85 V (bipolar membrane in water, CH+ = COH- =10-7 mol/l). According to equation (5.11) this corresponds to a transition regionthickness of 4.0 nm.

Equation (5.11) describes the thickness of the transition region if no externalelectric field is applied. When an external voltage Vex is established across thebipolar membrane the voltage drop across the depletion region will be changedaccordingly. The transition region is characterised by a high resistance as it isdevoid of mobile charge carriers. Therefore it is usually assumed that anexternally applied voltage falls completely across this region [18]. Figure 5.3displays the simplified slope of the electric potential across the entire bipolarmembrane when an external voltage Vex is established and the diffusionpotential of the monopolar layers is neglected (constant concentration andpotential profile within the monopolar layers). Figure 5.3 shows that with anexternal applied voltage the potential difference across the transition regionbecomes:

∆ϕtr = 2 ϕDon1 + Vex (5.15)

The thickness of the transition region is now given by:

2λ = 2 2 ∆ϕDon

1 + Vex ε0 εrX F

(5.16)

Equation (5.16) shows that with increasing applied reverse bias (positive value forVex) the thickness of the transition region increases.

114 Chapter 5

ϕ = 0

∆ϕtr

ϕDon1

ϕDon1

1/2 Vex

1/2 Vex

λ- λ

cem aem

Figure 5.3: Schematic potential profile across a bipolar membrane. ϕDon1 refers

to the Donnan potential between solution and membrane. In thedrawing it is assumed that an equal amount of the external voltageV e x falls across the anion and the cation exchange side of thetransition region.

5.3 Model for the water dissociation in bipolar membranes

Rapp [14] developed a model describing the current - voltage behaviour of bipolarmembranes. The fundamental aspects of this model will be described in thisparagraph. The following assumptions are made:

• The water dissociation occurs in the depletion anion exchange layer of the bipolar membrane.

• The water dissociation is accelerated by protonation and deprotonation of weakly basic groups (reactions (5B) and (5C)).

• All reactions involved in the water dissociation are accelerated by the second Wien effect (equation (5.1)).

• The voltage drop across the monopolar layers is neglected, i.e. the complete externally applied voltage drop falls across the transition region.

• As the model focuses on the water dissociation, the transport of electrolyte across the bipolar membrane is neglected.

• The generated protons and hydroxyl ions are removed from the transition region by migration and the electric current is calculated from this migration flux.

• The driving force for the migration of protons and hydroxyl ions dϕ/dx is Vex/2λ, since 2 ϕDon

1 is in equilibrium with the diffusion of ions into


the transition region.• Water is transported into the transition region by diffusion.

Since the water dissociation is assumed to be accelerated by the protonation anddeprotonation of weakly basic groups B, not only the ordinary water dissociationequilibrium, reaction (5A), but also the reactions (5B) and (5C) have to beconsidered:

2 H2O H3O+ + OH

-k1

k-1(5A)

B + H2O BH+ + OH

-k2

k-2(5B)

BH+ + H2O B + H3O

+k3

k-3(5C)

JH2Odiff

reactions

5A

5B

5C

2λ

JH2Odiff

H3O+migJ

OH-J mig

Figure 5.4: Simplified system for the mass balance.

For each species considered in the simplified system the following mass balance isobtained in the transition region, as illustrated in figure 5.4:

2 λ dCi

tr

dt = Ji

diff + Jimig + 2 λ ri (5.17)

Here ri are the reaction rates of the different components in the transition layer.Note that the diffusion term in equation (5.17) applies to water, the diffusion of

116 Chapter 5

protons and hydroxyl ions is neglected in this model. Based on the reactions (5A)to (5C) the reaction rates for the different components are given by:

rH3O+ = k1CH2OCH2O - k-1CH3O+COH- + k3CBH+CH2O - k-3CH3O+CB (5.18)

rOH- = k1CH2OCH2O - k-1CH3O+COH- + k2CBCH2O - k-2CBH+COH- (5.19)

rB = k3CBH+CH2O - k-3CH3O+CB - k2CBCH2O + k-2CBH+COH- (5.20)

rBH+ = - rB (5.21)

rH2O = k-1CH3O+COH- - k1CH2OCH2O - k2CBCH2O

+ k-2CBH+COH- + k-3CH3O+CB - k3CBH+CH2O

(5.22)

The reaction rate constants can be obtained in the following way. For the waterdissociation equilibrium, reaction 5A, the forward and backward reaction rates aregiven by:

r1 = k1CH2OCH2O = k1"CH2O (5.23)

r-1 = k-1CH3O+COH- (5.24)

In equilibrium r1 and r-1 are equal, which leads to:

k1"

k-1 =

CH3O+COH-

CH2O =

KwCH2O

(5.25)

With Kw = 10-14 mol2l-2 and k1" = 2 10-5 s-1 [19] k-1 is calculated from equation

(5.25) to be 1.1 1011 l mol-1 s-1. The dissociation rate constant k1 can be calculatedfrom equation (5.23) and is 3.63 10-7 l mol-1 s-1. The reaction rate constants for theprotonation and deprotonation reactions can be expressed in terms of the pKbvalue of the basic group B involved. For reaction (5B) is:


CBH+COH-

CB = Kb =

k2"

k-2(5.26)

or

k2" = k-2 Kb = k-2 10-pKb (5.27)

For reaction (5C) the equilibrium constant is given by:

CBCH3O+

CBH+ = Ka =

k3"

k-3(5.28)

With pKa + pKb = 14 equation (5.28) becomes:

k3" = k-3 10- (14 - pKb) (5.29)

Furthermore k2 and k3 can be calculated from:

k2 = k2

"

CH2O =

k-2 10-pKb

CH2O(5.30)

k3 = k3

"

CH2O =

k-3 10- (14 - pKb)

CH2O(5.31)

From literature it is known that the rate constants k-2 and k-3 in aqueoussolutions are in the range of 1010 - 1011 l mol-1 s-1 [11, 20]. Here for k-2 and k-3 avalue of 1011 l mol-1 s-1 is taken. In the model it is assumed that the dissociationrate constants depend on the electric field strength through the second Wieneffect. This means that the rate constants k1, k2 and k3 are modified according toequation (5.1). The electric field strength is given by E = Vex/2λ (see theassumptions at the beginning of this paragraph).

When water is consumed in the water dissociation process a water concentrationgradient is developed in the bipolar membrane. This gradient is assumed to belinear as shown in figure 5.5. The diffusional water transport into the membrane

118 Chapter 5

is described by Fick’s law:

JH2Odiff

= - DH2O dCH2O

dx ≈ DH2O

CH2Omb

- CH2Otr

δ - λ(5.32)

Since λ<<δ, the term δ-λ can be replaced by δ.

bulksolution

bulksolution

x

cem aem

CH2Omb

CH2O

trCH2O

δ δ

λ-λ

Figure 5.5: Profile of the water concentration in the bipolar membrane(superscript tr refers to the transition region, mb to the membraneinterface with the bulk solution).

The migration flux of protons and hydroxyl ions is calculated with the Nernst-Planck equation (diffusion and convection neglected):

JH3O+mig

= uH3O+tr CH3O+tr

Vex

2 λ(5.33)

JOH-mig

= uOH-tr COH-tr

Vex

2 λ(5.34)

Introducing the derived relations for the reaction rates and the fluxes of thedifferent species into the mass balance given by equation (5.17):

dCH3O+tr

dt = k1CH2OCH2O - k-1CH3O+COH- + k3CBH+CH2O

- k-3CH3O+CB - uH+ CH+

2 λ Vex

2 λ

(5.35)


dCOH-tr

dt = k1CH2OCH2O - k-1CH3O+COH- + k2CBCH2O

- k-2CBH+COH- - uOH- COH-

2 λ Vex

2 λ

(5.36)

dCBtr

dt = k3CBH+CH2O - k-3CH3O+CB - k2CBCH2O + k-2CBH+COH- (5.37)

dCBH+tr

dt = -

dCB tr

dt(5.38)

dCH2Otr

dt = k-1CH3O+COH- - k1CH2OCH2O - k2CBCH2O + k-2CBH+COH-

+ k-3CH3O+CB - k3CBH+CH2O + 2 DH2O

2 λ CH2O

mb - CH2Otr

δ

(5.39)

Because of their higher mobility the protons will first move faster than thehydroxyl ions. This disturbs the electroneutrality and leads to an additionalelectric field which increases the migration of the hydroxyl ions and slows downthe protons. To take this phenomenon into account both mobilities are assumedto be uH3O

+tr = uOH-tr = 30 10-8 m2V-1s-1. The electric current density, i, can be

calculated from the hydroxyl ion or proton flux (which are equal):

i = F zi Ji∑i=1

n = F uOH-tr COH-

tr Vex

2 λ(5.40)

With the above described model current - voltage curves can be calculated basedon an electric field enhanced proton transfer reaction scheme. The voltage dropacross the membrane (Vex) is used as an input parameter and by solving theabove described equations the current density can be calculated. In order todetermine the steady state current density the five differential equations (5.35) to(5.39) have to be solved. A semi-implicit Euler procedure (subroutine EULSIM)was used for this numerical treatment [14].

120 Chapter 5

5.4 Experimental

Bipolar membrane current - voltage curves were determined using the setup andthe experimental procedure described in chapter 2. The membrane arrangementin the six-compartment cell is shown in figure 5.6. A 0.5 M Na2SO4 solution wasused for electrode rinsing, a 0.5 M NaCl solution was used in the second and fifthcompartment while NaCl solutions with different concentrations were used inthe central compartment adjacent to the bipolar membrane to be characterised.All experiments were performed at 23 °C with a solution flowrate of 475 ml/min.

Two different bipolar membranes were used in the experiments. The first one isthe single film BP-1 bipolar membrane supplied by Tokuyama Soda Inc. (Japan).The second membrane is the laminate bipolar membrane supplied by WSITechnologies Inc. (USA) and referred to as the WSI membrane. Details aboutthese membranes can be found in the experimental section of chapter 4. Themonopolar membranes used in the cell are the Tokuyama Soda AMX and CMXanion and cation exchange membrane, respectively.

O2

H+

Na+

SO42-

Na+ Na+

Cl-

bmcemcem

0.5 M0.5 M

anode

Cl-

var

OH- H+

H2

Na+

Cl-Na+

SO42-

Na+

OH-Na+

cemaem

0.5 M 0.5 M

cathode

var

Figure 5.6: Membrane arrangement in the six-compartment cell (cem refers toa cation exchange membrane, aem to an anion exchange mem-brane, bm to a bipolar membrane and var to a varying NaClconcentration).

5.5. Results and discussion

Experimental current - voltage curves

Current - voltage curves of bipolar membranes were determined up to a currentdensity of 100 mA/cm2. Figure 5.7 shows the curve for the BP-1 bipolarmembrane while the curve for the WSI membrane is shown in figure 5.8. The


two curves shown in figure 5.7 and 5.8 are similar. Initially there is a strongincrease in voltage drop. This is related to the removal of salt from the bipolarmembrane transition region as was described in chapter 4. When the salt isremoved the concentration of charge carriers is very low in this region whichcorresponds to a high resistance of the bipolar membrane. Figure 5.7 and 5.8 showthat at a certain value of the voltage drop the current - voltage curve increasesstrongly. This is due to the onset of (enhanced) water dissociation. The waterdissociation generates new charge carriers, i.e. protons and hydroxyl ions, therebycausing the membrane resistance to decrease.

0

20

40

60

80

100

120

0 0.5 1 1.5 2

current density

(mA/cm2)

voltage drop (V)

Figure 5.7: Current - voltage curve measured with BP-1 bipolar membrane in0.5M NaCl.

0

20

40

60

80

100

120

0 0.5 1 1.5 2

current density

(mA/cm2)

voltage drop (V)

Figure 5.8: Current - voltage curve measured with the WSI bipolar membranein 0.5M NaCl.

122 Chapter 5

To demonstrate the performance in producing acids and bases, figure 5.9 isincluded as an example. This figure shows that the pH of the solutions on eitherside of the bipolar membrane changes drastically as soon as a current is appliedthrough the membrane cell.

0

2

4

6

8

10

12

14

0 10 20 30 40 50 60

pH

time (min)

Figure 5.9: Change in solution pH as a function of time when a fixed currentdensity of 40 mA/cm2 is applied through the BP-1 bipolar mem-brane. The experiment was started with an 0.5M NaCl solution oneither side of the membrane. Closed circles in the figure refer to thepH change of the solution on the anodic side of the membrane,open circles to the cathodic side solution.

Model calculations

As described earlier in this chapter, the water dissociation is believed to be a resultof protonation and deprotonation reactions involving the fixed groups in themembrane. Based on this reaction scheme a model was derived describing thecurrent - voltage curve of a bipolar membrane. To show the effect of differentparameters on the water dissociation behaviour, some results of the calculationswill be shown here.

Current - voltage curves correspond to steady state situations. To determine thesteady state, the five differential equations (5.35) to (5.39) were solved as a functionof time. The (start-) parameters used are listed in table 5.1. The concentration ofbasic groups at the depletion anion exchange layer is difficult to estimate. Here itwill be assumed that all quaternary ammonium groups are degraded to tertiaryamines. Therefore the concentration of basic groups is taken equal to the fixedcharge concentration in table 5.1. The start concentration of water at the transition


region in this table is estimated from the swelling and density of the BP-1 bipolarmembrane.

Table 5.1: Initial parameters used for the determination of the steady state.

fixed charge density X 1500 mol/m3

start concentration basic groups CB(t=0)

(equal to X)

1500 mol/m3

(CBH+ (t=0) = 0 mol/m3)

start concentration water CH2O (t=0) 10000 mol/m3

start concentration H+ and OH- (t=0) 10-4 mol/m3

water diffusion coefficient DH2O 10-9 m2/s [21]

thickness monopolar layers δ(taken as half the total bipolar membrane thickness)

10-4 m for BP-1

5.8 10-5 m for WSI

k1 3.6 10-10 m3/mol s

k-1 1.1 108 m3/mol s

k-2, k-3 108 m3/mol s

mobility H+, OH- 30 10-8 m2/Vs

bulk solution concentration Cb 100 mol/m3

water dielectric constant εr 78 [22]

When a certain external voltage is applied the concentrations of water, H+, OH-, Band BH+ in the transition region change as a function of time according toequations (5.35) to (5.39) until a steady state is reached. Here we are interested inthe current - voltage curve, i.e. the steady state values, only. Typical timedevelopment of the concentrations in the transition region can be found in [23].

An important parameter in calculating a current - voltage curve is the pKb, i.e. thebasicity, of the fixed groups involved. The pKb directly determines the values ofthe dissociation rate constants in the proton transfer reactions. Figure 5.10 showsthe influence of the pKb on the current - voltage curve. With increasing pKb(decreasing basicity) the current density at given applied voltage drop increases.

124 Chapter 5

0

20

40

60

80

100

0 0.5 1 1.5

p Kb=5p K

b

= 7

p Kb=6current density

(mA/cm2)

voltage drop (V)

Figure 5.10: Calculated current - voltage curves using different values for thepKb.

The behaviour shown in figure 5.10 can be understood if the dissociation rateconstants k2 and k3 for the reactions (5B) and (5C) are regarded. The values ofthese rate constants are calculated from the pKb according to equations (5.30) and(5.31). Figure 5.11 shows the influence of the pKb on the dissociation rateconstants demonstrating that for strongly basic groups (low pKb) k2 is very highbut k3 very small. This means that the protonation reaction (5B) is very fast butthe deprotonation reaction (5C) is very slow and thus hinders the overall waterdissociation process. The fastest water dissociation would be possible for pKb = 7.Note that in this case k2 and k3 are about 50 107 times larger than k1, thedissociation rate constant for the ordinary water dissociation equilibrium, andthat thus the proton transfer reactions are capable of explaining the enhancedwater dissociation. Based on this reasoning it can be concluded that for a fast waterdissociation weakly basic (or acidic) groups must be present in the membrane.

Figure 5.12 shows the influence of the concentration of the basic groups Binvolved in the water dissociation reactions. At given voltage drop, a higherconcentration of basic groups results in a larger production of protons andhydroxyl ions and thus in a higher current density.


10- 4

10- 2

100

102

104

106

108

2 4 6 8 10 12

k

(l mol- 1 s- 1)

pKb

k2

k3

Figure 5.11: Influence of the basicity of the membrane groups on the disso-ciation rate constants k2 and k3 in reactions (5B) and (5C).

0

20

40

60

80

100

0 0.5 1 1.5 2 2.5 3

CB = 1500 500 1001000current density

(mA/cm2)

voltage drop (V)

Figure 5.12: Influence of the concentration of basic groups, CB (mol/m3), onthe calculated current - voltage curve (pKb=5).

Comparison between calculated and experimental current - voltage curves

The determined current - voltage curves for the BP-1 and the WSI membranewere compared with calculated curves as shown in figure 5.13 and 5.14,respectively. Figure 5.13 and 5.14 show that a reasonable fit is possible when a pKbof 4.6 or 4.7 is used. As was shown in figure 5.10, the calculated current - voltagecurve is very sensitive to the value of the pKb used. Unfortunately no experimen-

126 Chapter 5

0

20

40

60

80

100

120

0 0.5 1 1.5 2 2.5

current density

(mA/cm2)

voltage drop (V)

Figure 5.13: Comparison between experimental current - voltage curve (opencircles) and calculated curve (solid line) for the BP-1 bipolarmembrane in 0.5M NaCl. (For the calculation pKb = 4.7 was used aswell as the parameters listed in table 5.1).

tal data exists about the exact pKb value of amino groups within the membraneand one has to rely on solution properties. The pKb of trimethylamine, N(CH3)3,in solution is 4.2 while for ammonia, NH3, it is 4.8 [24]. The values used in thecalculations in figure 5.13 and 5.14 thus seem to be realistic.

0

20

40

60

80

100

120

0 0.5 1 1.5 2 2.5

current density

(mA/cm2)

voltage drop (V)

Figure 5.14: Comparison between experimental current - voltage curve (opencircles) and calculated curve (solid line) for the WSI bipolarmembrane in 0.5M NaCl. (For the calculation pKb = 4.6 was used aswell as the parameters listed in table 5.1).


Figure 5.13 and 5.14 show that the fit is better at higher current densities whilethere is a large discrepancy at low current density. The model described in thischapter is focussed on the water dissociation and does not take into account thecomplete transport processes involved in a bipolar membrane. Transport of saltions by migration, diffusional transport of salt, acid and base back into thetransition region are all neglected. In chapter 4 it was described that these aspectsshape the current - voltage curve of a bipolar membrane at low current density.This may therefore explain the difference between the calculated andexperimental curves observed at lower current density in figure 5.13 and 5.14.

Current - voltage curves were determined with the BP-1 bipolar membrane inNaCl solutions with different concentrations. The results are shown in figure5.15. The curves are very similar in shape. The figure shows that increasing theNaCl concentration shifts the curves to higher voltage drops. This shift withincreasing solution concentration was also observed in [25-27].

0

20

40

60

80

100

120

0 0.5 1 1.5 2

0.1M NaCl

0.5M 1.0M

2.0M

current density

(mA/cm2)

voltage drop (V)

Figure 5.15: Experimental current - voltage curves measured with the BP-1bipolar membrane in varying NaCl solution concentrations.

The bulk solution concentration is also an input parameter in the waterdissociation model described in this chapter. Figure 5.16 shows the calculatedinfluence of the bulk solution concentration on the current -voltage curve. Hereit is seen that an increase in the solution concentration causes a shift of the curveto lower voltage drop. This is exactly the opposite trend as observed with theexperimental curves in figure 5.15. In the calculations the solution concentrationdirectly affects the calculated thickness 2λ of the transition region as can be seen byequation (5.11) and (5.14). As a result a higher electric field strength (Vex/2λ) is

128 Chapter 5

calculated at given applied voltage. A higher electric field corresponds to a largerincrease in the dissociation rate constants due to the second Wien effect and thusin a faster water dissociation. The result is a higher current density calculatedwhen the solution concentration is increased.

0

20

40

60

80

100

0 0.5 1 1.5

0.10M2.00M NaCl

0.50Mcurrent density

(mA/cm2)

voltage drop (V)

Figure 5.16: Calculated influence of the bulk solution concentration on thecurrent- voltage curve. (For the calculation pKb = 4.6 was used aswell as the parameters listed in table 5.1).

The reason for the discrepancy between the calculated curves in figure 5.16 andthe experimental curves in figure 5.15 must be found in the underlyingassumptions in the model. In the model it is assumed that the complete externalapplied voltage falls across the transition region and is therefore “used” forcreating an electric field strength in this region equal to Vex/2λ . In practice this isnot a correct assumption. When an external voltage is applied any initial saltpresent at the transition region is removed as was shown in chapter 4. Duringoperation of the bipolar membrane the situation thus arises in which there is avery low ion concentration (typically in the order of 10-7 mol/l) in the transitionregion with a higher ion concentration on either side of the membrane in thesolution. This concentration difference between outer solution and the transitionregion corresponds to a diffusive driving force into the transition region. Part ofthe external applied voltage is necessary to counterbalance this driving force.With higher solution concentration this effect is stronger. In other words, withhigher solution concentration at given external voltage a larger part of this


voltage is used for the above mentioned counterbalance and effectively a smallerpart falls across the transition region. This would thus result in a lower electricfield strength at the transition region and hence in a lower current density. Theabove described effects are not included in the model.

The dielectric constant

In this part, the role of the dielectric constant will be discussed. According to thesecond Wien effect the dissociation rate constant of a weak electrolyte is increaseddue to the presence of an electric field. At high electric field strengths this increaseis given by [3]:

k1(E)k1

= 2π

. (8b)-3/4. exp 8b (5.1)

with: b = 0.09636 E

εr . T2

(5.2)

These equations show that the increase in dissociation rate constant is alsodetermined by the dielectric constant εr.

The dielectric constant of a medium is the ratio between the capacity of thedielectric and that of vacuum [28]. It is strongly related to the polarisability andthus to the presence of dipoles in the medium as well as the presence ofassociating effects between the molecules such as hydrogen bonding. Water has adielectric constant of 78 at 25 °C while, for example, it is 2 for benzene [22]. Thevalue of the dielectric constant depends on many factors as will be shown here bya few numeric examples. The water dielectric constant decreases with increasingtemperature (at 100 °C it is 56 [22]). Its value decreases also with increasingconcentration of electrolytes. For example, the dielectric constant decreases from78 for pure water to 60 when the NaCl concentration is 2 mol/l [22]. The state ofwater has a large influence on the dielectric constant. Close to an ion, watermolecules are highly oriented in the hydration shell and here the dielectricconstant takes a value of about 6 [28].

In the calculated current - voltage curves shown so far in this chapter, a dielectricconstant of 78 was used. Figure 5.17 shows the influence of the value of thedielectric constant on the calculated current - voltage curve. This figure shows

130 Chapter 5

that a decrease in the dielectric constant results in a strong shift in the curves tolower voltage drops indicating that the calculations are very sensitive to thisparameter.

0

20

40

60

80

100

0 0.5 1 1.5

current density

(mA/cm2)

voltage drop (V)

20 6040 = 80rε

Figure 5.17: Influence of the dielectric constant on the calculated current -voltage curve. (For the calculation pKb = 5 was used as well as theparameters listed in table 5.1).

In chapter 1 it was shown that the water dissociation rate in bipolar membranes isat least 107 times faster than can be expected from the ordinary water dissociationequilibrium. The electric field strength at the bipolar membrane transition regionis in the order of 108 - 109 V/m [23, 29]. Figure 5.18 shows the increase in thedissociation rate constant for the ordinary water dissociation reaction according toequation (5.1) due to the second Wien effect when the dielectric constant is varied.Here it is seen that the second Wien effect might in principle explain theenhanced water dissociation, i.e. no proton transfer reactions are needed, whenthe dielectric constant takes a value of about 10. However, as discussed before, thesecond Wien effect is assumed not to be able to explain the enhanced waterdissociation completely as it would be identical for both anion and cationexchange membranes above the limiting current density which in practice is notthe case [30].

It is clear that the value of the dielectric constant in the membrane plays animportant role for decribing the electric field effect on the water dissociation.Usually a constant value for the dielectric constant is used in calculating the fieldeffects. In [12, 31, 32] a value in the order of 20 to 30 is taken to be realistic within a


101

102

103

104

105

106

107

108

109

10 20 30 40 50 60 70 80

kd(E) / k

d

dielectric constant (-)

E = 5 108 V/m

E = 9 108 V/m

Figure 5.18: Increase in the dissociation rate constant due to the second Wieneffect as a function of the dielectric constant at two different valuesof the electric field strength.

bipolar membrane. While the correct value of the dielectric constant involved isdifficult to estimate, an even more complex situation arises when it is consideredthat the dielectric constant of pure water is also a function of the electric fieldstrength. In [33] it is calculated that the dielectric constant changes gradually from78 to about 16 when the electric field strength is increased to 2 109 V/m.Furthermore it should be recognized as well that the concentration of water at thetransition region decreases when a larger voltage is applied. Thus it is reasonableto assume that when a current - voltage curve is determined, the dielectricconstant of the water is not a constant value but decreases with increasing electricfields.

5.6 Conclusions

Current - voltage curves were determined up to a current density of 100 mA/cm2

with the BP-1 and the WSI bipolar membrane. The curves show a large increasein voltage drop at low current density due to the removal of salt initially presentwithin the bipolar membrane interphase. Once the salt is removed, enhancedwater dissociation starts. New charge carriers are created and the resistance of thebipolar membrane decreases. As a result the current - voltage curve ischaracterised by a strong increase in current density with only a small increase involtage drop. The water dissociation is manifested by significant pH changes in

132 Chapter 5

the solutions adjacent to the bipolar membrane.

A model was described accounting for the mechanism of water dissociation inbipolar membranes. The model is based on a proton transfer reaction schemeinvolving the fixed groups in the membrane. The dissociation rate constants areinfluenced by the electric field according to the second Wien effect. Current -voltage curves were calculated based on this model. The calculations showed thatfor a low resistance bipolar membrane weakly basic (or acidic) groups should bepresent at the transition region, in the most ideal case groups with a pKb of 7should be involved. Furthermore it was shown that the current - voltage curve isshifted to higher current densities, i.e. lower resistance, if the concentration ofthese groups increases.

The influence of the pKb and the concentration of basic groups on the calculatedcurrent - voltage curves give an intuitively correct picture if the field enhancedproton transfer reactions are assumed for the water dissociation mechanism.Comparing experimental curves with calculated ones, however, shows that themodel has its limitations. At low current density the fit is rather unsatisfactory.This is due to the absence of salt transport in the model. Experimental curves atdifferent solution concentrations showed a shift of the curves to higher voltagedrops with increasing concentration. The model predicts the opposite trend whichresults from not taking into account the voltage drop that is necessary tocounterbalance the concentration gradient between outer solutions and thetransition region.

In a brief discussion it was shown that an important parameter in calculating theeffect of the electric field on the dissociation rate constant is the water dielectricconstant. This is a complex property which depends on various parameters and itsvalue in the bipolar transition region is difficult to estimate. The dielectricconstant decreases with increasing electric field strength and decreasing waterconcentration. Thus the dielectric constant may decrease when the voltage dropincreases when a current - voltage curve is determined.

5.7 List of symbols


d half distance between two membranes (m)


e0 elementary charge (1.602 10-19 A s)


E electric field strength (V m-1)




Ka acid constant (mol m-3)

Kb base constant (mol m-3)

k Boltzmann constant (1.38 10-23 J K-1)

k rate constant (m3 mol-1 s-1)

k” rate constant (s-1)

NA Avogadro’s number (6.023 1023 mol-1)

pKa -log KapKb -log Kbr reaction rate (mol m-3 s-1)


t time (s)

T temperature (K)

u mobility (m2 s-1 V-1)

V voltage (V)




δ thickness monopolar layer (m)

ε0 permittivity of free space (8.85 10-12 A s V-1 m-1)

εr dielectric constant (relative permittivity) (-)

2λ transition region thickness (m)

ϕ electrical potential (V)

ρe space charge density (A s m-3)

ω valence of the fixed charge (-)


aem anion exchange membrane

b bulk solution

cem cation exchange membrane

Don Donnan

i species i

m membrane

tr transition region

134 Chapter 5

5.8 References



2 M. Wien, Uber eine Abweichung von Ohmsen Gesetze bei Elektrolyten, Ann. Physik 83

(1927) p. 327-361.

3 L. Onsager, Deviations from Ohm's law in weak electrolytes, J. Chem. Phys. 2 (1934) p. 599-

615.



(1957) p. 780-784.





8 R. Simons, The origin and elimination of water splitting in ion exchange membranes during

water demineralisation by electrodialysis, Desalination 28 (1979) p. 41-42.




10 R. Simons, Strong electric field effects on proton transfer between membrane bound amines

and water, Nature 280 (1979) p. 824-826.


275-282.



13 I. Rubinstein, A. Warshawsky, L. Schechtman and O. Kedem, Elimination of acid-base

generation ("water splitting") in electrodialysis, Desalination 51 (1984) p. 55-60.




16 A. Mauro, Space charge regions in fixed charge membranes and the associated property of

capacitance, Biophys. J. 2 (1962) p. 179-198.

17 W. Shockley, The theory of p-n junctions in semiconductors and p-n junction transistors, Bell

Syst. Techn. J. 29 (1949) p. 435-489.

18 H.G.L. Coster, A quantative analysis of the voltage-current relationships of fixed charge

membranes and the associated property of "punch-through", Bioph. J. 5 (1965) p. 669-686.

19 R. Simons and G. Khanarian, Water dissociation in bipolar membranes: experiments and

theory, J. Mem. Biol. 38 (1978) p. 11-30.

20 M. Eigen, Methods for investigation of ionic reactions in aqueous solutions with halftimes as

short as 10-9 sec., Disc. Faraday Soc. 17 (1954) p. 194-205.

21 W.H. Rose and I.F. Miller, A model for bipolar membranes in an acid-base environment, Ind.

Eng. Chem. Fund. 25 (1986) p. 360-369.



(1959).



24 R.C. Weast, Handbook of chemistry and physics, CRC Press Inc., Florida (1984).

25 K.N. Mani, F.P. Chlanda and C.H. Byszewski, Aquatech membrane technology for recovery

of acid/base values from salt streams, Desalination 68 (1988) p. 149-166.

26 K.N. Mani, Electrodialysis water splitting technology, J. Membrane Sci. 58 (1991) p. 117-

138.

27 N.-T. Dang and D. Woermann, Efficiency of the generation of protons and hydroxyl ions in

bipolar membranes by electric field enhanced water dissociation, Ber. Bunsenges. Phys.

Chem. 97 (1993) p. 149-154.

28 J. O’M. Bockris and A.K.N. Reddy, Modern electrochemistry, 3rd Edition, Plenum Press,

New York (1977).

29 P. Ramírez, J.A. Manzanares and S. Mafé, Water dissociation effects in ion transport through

anion exchange membranes with thin cationic exchange surface films, Ber. Bunsenges. Phys.

Chem. 95 (1991) p. 499-503.


31 S. Mafé, J.A. Manzanares and P. Ramírez, Model for ion transport in bipolar membranes,

Phys. Rev. A 42 (1990) p. 6245-6248.



33 F. Booth, The dielectric constant of water and the saturation effect, J. Chem. Phys. 19 (1951)

p. 391-394 (errata: p. 1327-1328 and p. 1615).

Chapter

6

Behaviour of Bipolar Membranes

at high Current Density:

Water Diffusion Limitation

6.1 Introduction

In the previous chapter bipolar membranes were studied up to medium currentdensities (i.e. 100 mA/cm2). This region is important in rationalising the waterdissociation mechanism. When it comes to practical applications, electrodialysiswith bipolar membranes at high current densities is attractive because ofimprovements in current efficiency. In general the current efficiency increaseswith increasing applied current density [1-4]. A high current efficiency of a bipolarmembrane improves the total effectiveness of the electrodialysis system inobtaining high quality concentrated acids and bases. Therefore an investigation ofthe behaviour of bipolar membranes at high current density is of great practicalrelevance.

When an electric field is applied across a bipolar membrane, water dissociationtakes place at the transition region between the two charged layers that constitutethe bipolar membrane. Water dissociates into protons and hydroxyl ions whichare removed from the transition region by the electric field. Water consumed thisway is replenished by diffusion from the outer solutions through the twomonopolar layers into the bipolar membrane interphase. An increase in current

138 Chapter 6

density requires a faster generation of charge carriers, i.e. protons and hydroxylions. In other words, the rate of water dissociation must increase when thecurrent density is increased. This is accompanied by an increase in waterconsumption at the transition region. When the rate of water dissociation is fasterthan the supply of water a transport limitation occurs. This way it can be reasonedthat at a certain value of the current density the water dissociation occurs so fastthat the transport of water into the bipolar membrane transition region can notkeep up and limits the water dissociation process. A limitation of water supplywould result in a drying out of the bipolar membrane which is highly undesiredsince it will cause a drastic increase in the resistance [1, 4]. However, experimentalstudies on the limitation of water supply into a bipolar membrane are very scarcein literature.

In this chapter the behaviour of two bipolar membranes at very high currentdensity is investigated. This is achieved by measuring current - voltage curves.Furthermore the influence of such high current densities on the membranematerial is studied. The measured current - voltage curves are comparedqualitatively with curves calculated using the water dissociation model describedin chapter 5.

6.2 Experimental

Current - voltage curves

Current - voltage curves were determined with the six-compartment cell and theexperimental set-up described in chapter 2. The membrane arrangement in thesix-compartment cell is shown in figure 6.1. A 0.5 M Na2SO4 solution was usedfor electrode rinsing, a 1.0 M NaCl solution was used in the second and fifthcompartment while a 0.5 M NaCl solution was used as the starting solution in thetwo central compartments adjacent to the bipolar membrane. The bipolarmembrane area was reduced by clamping the membrane in between two glassplates with a circular hole of 4.74 cm2 to allow the application of high currentdensities.

Two different bipolar membranes were used in the experiments. The first one isthe single film BP-1 bipolar membrane supplied by Tokuyama Soda Inc. (Japan).The second membrane is the laminate bipolar membrane supplied by WSI

Bipolar membranes: water diffusion limitation 139

Technologies Inc. (USA) and referred to as the WSI membrane. Details aboutthese membranes can be found in the experimental section of chapter 4. Themonopolar membranes used in the cell are the Tokuyama Soda AMX and CMXanion and cation exchange membrane, respectively.

O2

H+

Na+

SO42-

H2

Na+ Na+ Na+

Cl-Na+

SO42-

Na+

OH-

Cl-

bm

Na+

cemcem cemaem

1.0 M 1.0 M0.5 M0.5 M 0.5 M

anode cathode

0.5 M

Cl- Cl-

H+OH-

Figure 6.1 Membrane arrangement in the six-compartment cell (cem refers toa cation exchange membrane, aem to an anion exchange membraneand bm to a bipolar membrane).

Membrane characterisation

Characterisation of the monopolar layers of the WSI bipolar membrane involvedthe determination of the degree of swelling, the electrical resistance, thepermselectivity and the ion exchange capacity. The degree of swelling wasdetermined from the wet and dry weight of the polymer film. The electricalresistance was determined under direct current by measuring current - voltagerelation both with and without the membrane. The permselectivity wasdetermined by the static method based on measurement of the membranepotential. Details about the procedures for obtaining these quantities can be foundin appendix 2.1 to chapter 2. The ion exchange capacity of the cation exchangelayer was determined by exchanging protons with sodium ions within themembrane and titrating the released protons with a NaOH solution (as wasdescribed in appendix 2.1).

For determination of the ion exchange capacity of the anion exchange layer twodifferent methods were used. The first method was described in appendix 2.1. Theanion exchange membrane was first brought into the hydroxyl ion form byplacing it in a 1 M NaOH solution for eight hours. After this the membrane wasplaced in a 2 M NaCl solution (which was renewed several times) to replace thehydroxyl ions by chloride ions in the membrane. The released hydroxyl ions weretitrated with HCl. The membrane was dried and the ion exchange capacity

140 Chapter 6

(meq/g) was calculated for the dry membrane. The second method was slightlydifferent. In this case the membrane was brought into the hydroxyl ion form.After this the membrane was rinsed in ultrapure water and placed in a HClsolution. The hydroxyl ions now react with the protons of the HCl solution andthe amount of unreacted protons remaining in the solution is determined bytitration with NaOH. The ion exchange capacity was calculated from thedifference between the initial proton concentration in the HCl solution and thefinal concentration (after reaction with the hydroxyl ions from the membrane).


Measurements with the Neosepta BP-1 bipolar membrane

Figure 6.2 shows two current - voltage curves measured with two differentsamples of the BP-1 bipolar membrane up to a current density of 600 mA/cm2.

0 0.5 1 1.5 2 2.5 30

100

200

300

400

500

600

voltage drop (V)

current density

(mA/cm2)

Figure 6.2: Current - voltage curves measured up to high current densityshowing the presence of an inflection point at around 480 mA/cm2.The two curves correspond to different samples of the BP-1bipolar membrane.

Figure 6.2 demonstrates that the voltage drop across the bipolar membraneremains fairly constant up to a current density of approximately 480 mA/cm2. Atthis current density a clear inflection point is observed and a drastic increase involtage drop is measured. The strong increase in voltage drop indicates a sharprise in membrane resistance. The inflection point is due to a limitation of water


supply into the bipolar membrane causing dessication. The presence of aninflection point was also observed by Aritomi [5] and Pivovarov [6]. Figure 6.2shows that the two measured current - voltage curves for the BP-1 bipolarmembrane are very similar indicating a good reproducability.

The inflection point indicates a limited supply of water into the bipolarmembrane. If at a certain current density the water concentration in the transitionregion has reached zero no increase in current can be expected, i.e. a true limitingcurrent density should be observed in the current - voltage curve. Figure 6.2shows that in practice this is not the case. Although the resistance increasesdrastically after the inflection point, still an increase in current density can beobtained. This demonstrates that at the inflection point the transition region isnot completely depleted of water but the concentration is just so low that it limitsthe production of protons and hydroxyl ions.

When currents are applied that are larger than the current density belonging tothe inflection point, the membrane performance is influenced. This wasestablished by successive measurements of a current - voltage curve with thesame membrane sample. Figure 6.3 shows current - voltage curves measured fiveconsecutive times up to a current density of 600 mA/cm2. It is observed that a sys-

0 2 4 6 80

100

200

300

400

500

600

voltage drop (V)

current density

(mA/cm2)

1 2 3 4 5

Figure 6.3: Consecutive measurements of the current - voltage curve of a BP-1bipolar membrane (numbers indicate the sequence).

tematic change in the curves occurs. The curves are shifted to higher voltagedrops and the inflection point not only moves to lower current densities but also

142 Chapter 6

becomes less distinct (and in fact can not be observed in the last twomeasurements). The curves shifting to higher voltage drops indicates that thebipolar membrane resistance has increased. Apparently the bipolar membrane isdamaged irreversibly when such high current densities are applied.

Figure 6.4 shows that the inflection point occurring at high current density is nota well-defined point. The transition in slope in the curve is not instantaneous at asingle current density but it is a continuous trajectory over a certain current range.A deviation of the slope occurs between 350 and 400 mA/cm2 (marked as point Bin figure 6.4) which is considerably smaller than the inflection point value of 480mA/cm2 determined by the intersection of the two slopes (point A).

0.5 1 1.5 2 2.5 3200

300

400

500

600

voltage drop (V)

current density

(mA/cm2)A

B

Figure 6.4: Current - voltage curve showing the transitional region around theinflection point (A denotes the inflection point as determined bythe two tangents, B refers to the onset of the transition).

Consecutive measurements were performed up to a current density of 400mA/cm2 which is smaller than the value of the current density belonging to theinflection point. The results are shown in figure 6.5. Here similar features areobserved as was shown in figure 6.2, indicating that also measurements up to 400mA/cm2 damage the membrane. Consecutive measurements up to 200 mA/cm2

did not show any change in current - voltage curve (not shown here). Themeasurements in figure 6.5 demonstrate that damaging of the bipolar membranestarts as soon as a deviation occurs from the slope in the medium current rangeand that the transition in slopes around the inflection point already indicates apermanent change in bipolar membrane resistance.


0 0.5 1 1.5 20

100

200

300

400

voltage drop (V)

current density

(mA/cm2)

1 2 3

Figure 6.5: Three consecutive measurements of a current - voltage curve forthe BP-1 bipolar membrane up to 400 mA/cm2.

Measurements with the WSI bipolar membrane

Figure 6.6 shows two current - voltage curves measured up to 800 mA/cm2 withtwo different samples of the WSI bipolar membrane. The current - voltage curvesshow a clear inflection point, similar to the findings with the BP-1 bipolarmembrane. Figure 6.6 also shows for both curves a rapid increase in voltage dropat lower current densities after which the voltage drop decreases again and asmooth curve is obtained. This irregular behaviour at lower current densities wasnot always observed. It is believed to stem from the structure of the WSI bipolarmembrane. The membrane consists of two separate layers which have to beplaced on top of each other prior to an experiment. This possibly results in a badcontact between the two layers with an irregular interphase and a thick waterlayer in between. When a current is applied, water is consumed at the interphaseby the water dissociation reaction and the two layers are drawn to each other. Thisway a better contact between the two layers is created causing the resistance(voltage drop) to decrease again. Once a good contact is achieved, a smoothcurrent - voltage curve can be obtained.

144 Chapter 6

0 3 6 90

200

400

600

800

voltage drop (V)

current density

(mA/cm2)

Figure 6.6: Experimental current - voltage curves measured with two differentsamples of the WSI membrane.

Comparing the two curves in figure 6.6 it is observed that the reproducability forthis membrane is much worse than in case of the BP-1 bipolar membrane (figure6.2). This might be due to an inhomogeneous distribution of the charged groupsin the two layers created during membrane manufacturing or it might result fromdifficulties arising from the laminating procedure as described above. Althoughthe two curves in figure 6.6 are different with respect to the voltage values, it isclear that the inflection points are located at similar current densities.

Also with the WSI membrane the influence of applying current densities abovethe inflection point was studied. Figure 6.7 shows two consecutive measurementsperformed with the same piece of membrane. The results are similar to theresults obtained with the BP-1 bipolar membrane. With the WSI membranealready the second measurement did not show an inflection point anymore.Again the curve was shifted to higher voltage drops indicating that themembrane was damaged in the first measurement after applying currents largerthan the current density belonging to the inflection point. Comparing figure 6.7and 6.3 it is clear that the change in current - voltage curve is much morepronounced in case of the WSI membrane.


0 2 4 6 80

200

400

600

800

1 2

voltage drop (V)

current density

(mA/cm2)

Figure 6.7: Two consecutively measured current - voltage curves with thesame sample of a WSI membrane.

The inflection point at high current densities

The presence of an inflection point in the current - voltage curves indicates that ata certain current density the resistance increases drastically, i.e. the amount ofconducting ions (protons and hydroxyl ions) produced at the transition regionbecomes a limiting factor. In principle this limitation can be due to the twoprocesses which are involved in the water dissociation:

1: The increase in resistance might be due to a limitation of the water dissociation reaction itself.

2: The inflection point might be related to the water transport into the bipolar membrane. If the water dissociation reaction is so fast that all thewater at the interphase is consumed by the reaction before water is replenished from the outer solutions, a limitation of conducting ions would be possible to occur as well.

Since the WSI bipolar membrane consists of two separate layers, experiments canbe performed in which the thickness of the bipolar membrane can be varied byplacing several monopolar layers on top of each other. The results are shown infigure 6.8. An increase in the thickness of the monopolar layers constituting thebipolar membrane results in a significant shift of the inflection point to lowercurrent densities. This is a strong indication that the water transport into thebipolar membrane is the reason for the inflection point. Increasing the thicknessof the bipolar membrane results in a longer diffusion pathway for water

146 Chapter 6

molecules and thus a limitation of the water supply (the inflection point) willoccur at lower current densities.

This can also explain the difference in position of the inflection point when theWSI (inflection point around 720 mA/cm2) and the BP-1 bipolar membrane(inflection point around 480 mA/cm2) are compared. The BP-1 membrane ismuch thicker (200 µm) than the WSI membrane (total thickness 116 µm). Ifsimilar water diffusion coefficients are assumed in both bipolar membranes,water diffusion limitation is expected to occur at a lower current density for thethicker, i.e. the BP-1, bipolar membrane.

0 2 4 6 8 100

200

400

600

800A: 116 µm

C: 348 µm

B: 232 µm

voltage drop (V)

current density

(mA/cm2)

Figure 6.8: Current - voltage curves of WSI bipolar membranes with varyingthickness (membrane A: one cation plus one anion exchange layer,membrane B: two cation plus two anion exchange layers, mem-brane C: three cation plus three anion exchange layers).

The experiments described are in agreement with the work presented by Aritomi[5]. He also concluded that the inflection point is related to a limited diffusionaltransport of water into the bipolar membrane interphase. This was based onexperiments in which the bulk solution concentration was varied. The inflectionpoint shifted to lower current densities with increasing solution concentration.The increase in salt concentration gives an increase in the osmotic pressure of thesolution resulting in a decreasing water supply into the membrane.

Physical or chemical cause of the damage

In the previous sections it was shown that both the BP-1 and the WSI bipolar


membrane are irreversibly damaged (increase in resistance) when currentdensities near and above the inflection point are applied, the nature of thisalteration being unclear. As was discussed in chapter 5, the highest resistance in abipolar membrane is located at the transition region. This is not only the region oflow conductivity (deionised water layer) but also the region where drying out ofthe membrane is most likely to start when a limitation of water supply occurs. Asa result an intense heat generation occurs at the transition region. This heatgeneration is easily detected by the increase in solution temperature next to thebipolar membrane (typically a temperature increase of 2 to 10 oC was measuredduring the determination of a current - voltage curve up to very high currentdensities). In one of the experiments with a WSI membrane heat formation waseven so intense that it completely burned away the membrane.

It is known that anion exchange membranes often display a limited chemicalstability when placed in contact with alkaline solutions [7] . Kneifel andHattenbach [8] performed long term stability experiments with differentcommercial ion exchange membranes. Exposure to an alkaline solution changedthe resistance and the ion exchange capacity of most of the membranes. Similarobservations were obtained when placing the membranes in a NaCl solution at 85oC, showing that also elevated temperatures can effect the properties of themembranes. The changes were believed to be related to variations in ordestruction of the polymer matrix or the destruction of ion exchange groups dueto chemical reactions. It was found that acidic solutions hardly influenced theinvestigated membranes.

When a current - voltage curve is measured a rapid change in pH of the solutionsnext to the bipolar membrane is observed [9]. The pH of the solution in the basecompartment (anodic side of the bipolar membrane) typically is in the range of 12to 13 during an experiment when higher current densities are reached. Althoughthe measurements are started with the two layers in the salt form, the intensegeneration of protons and hydroxyl ions will cause the anion exchange layer to bechanged into the hydroxyl ion form. Therefore it can be assumed that a highhydroxyl ion concentration will be present in the anion exchange layer.

Experiments were performed in which the effect of creating a dry bipolarmembrane and the effect of a treatment with NaOH were investigated. A BP-1bipolar membrane was placed in a vacuum oven at 50 oC for 14 days to remove allwater from the membrane. Another BP-1 bipolar membrane was placed in a 0.5 M

148 Chapter 6

NaOH solution at room temperature for 20 hours. Current - voltage curves weredetermined with the treated membranes and compared with an untreated bipolarmembrane. The results are shown in figure 6.9. In this figure also the curves ofdamaged membranes are shown that were determined when performing conse-cutive measurements (same curves as shown in figure 6.3).

0 1 2 3 4 50

100

200

300

400

500

600

dried

NaOH

1

3

2

voltage drop (V)

current density

(mA/cm2)

Figure 6.9: Effect of pretreatment on the current - voltage curve of a BP-1 bipo-lar membrane. Curves 1 to 3 (closed circles) refer to three consecu-tively determined current - voltage curves (no pretreatment), thecurve indicated with “NaOH” refers to the bipolar membranepretreated with a NaOH solution, “dried” refers to the curvemeasured with the bipolar membrane that was dried prior to theexperiment.

Figure 6.9 shows that not only the resistance (voltage drop) of the pretreatedbipolar membranes is higher than for the untreated membrane (curve 1), but it isalso clear that the inflection point is situated at much lower current densities.Thus the two curves of the pretreated membranes resemble the current - voltagecurves of the membranes damaged by consecutive measurements (curve 2 and 3).Therefore, figure 6.9 demonstrates that both drying of the bipolar membrane andan exposure to 0.5M NaOH damages the membrane. However, no conclusionscan be drawn which of the two (or a combination) is responsible for the damageoccurring with a bipolar membrane when current densities near or above theinflection point are applied.


Localisation of the damage in the bipolar membrane

Drying out of the bipolar membrane is most likely to start at the transition regionwhere the water dissociation reaction occurs. It is unknown whether damaging ofthe bipolar membrane occurs only at the transition region (which is a very thinlayer compared to the thickness of the monopolar layers) or if it extends to thebulk of the monopolar layers as well when currents near or above the inflectionpoint are applied. An experiment was developed to establish whether the damageis only located at the transition region. The WSI membrane was damaged bymeasuring a current - voltage curve up to 800 mA/cm2, similar as was shown infigure 6.6. After this, the membrane was turned inside out, i.e. the two sides of thebipolar membrane which originally faced the solutions now formed thetransition region. If only a damage had occurred at the transition region it wasexpected that the bipolar membrane turned inside out showed a similar current -voltage curve to the first measurement. However, these experiments failed as itwas found that the second measurement did not show an inflection pointanymore. It is believed that this might be due to the presence of holes or cracks inthe membrane which enable a large water transport into the bipolar membraneand thereby not showing any water diffusion limitation. The holes or cracksmight be formed during the first measurement. It has to be mentioned that it alsohas been observed in one experiment that no inflection point was obtained evenin the first measurement. The two layers of the WSI membrane are very thin andnot reinforced which results in a poor mechanical stability of this membrane.

Both for a new and a damaged WSI bipolar membrane the surface of the mono-polar films constituting the transition region was studied with Attenuated TotalReflectance Infra Red (ATR-IR) spectroscopy. Assignment of the peaks to thecharged groups in the films was found to fail due to interference with waterpresent. Therefore, no information could be obtained about the nature of thedamages in the bipolar membrane using this technique.

Characterisation of the monopolar layers of the WSI membrane

The advantage of using the WSI bipolar membrane is that it consists of two layerswhich bulk properties can be determined separately. In this part the electricalresistance, swelling, permselectivity and ion exchange capacity of the twomonopolar layers are compared for membranes as received and membraneswhich are damaged. The damaged samples were obtained from the membranes

150 Chapter 6

that were used in measuring current - voltage curves up to current densitiesabove the inflection point (typically up to 800 mA/cm2). An overview of theresults is shown in table 6.1 for the cation exchange layer and in table 6.2 for theanion exchange layer. Each value in these tables was obtained with a differentmembrane sample.

Table 6.1 shows that the determined properties of the cation exchange layer of theWSI membrane are very similar for the new and the damaged membrane. Henceit seems that the bulk properties of the cation exchange layer are not affectedwhen damaging the bipolar membrane.

Table 6.1: Comparison between properties of the cation exchange layer of theWSI membrane as received and the membrane that was damagedby applying current densities above the inflection point. Each valuerefers to a different membrane sample.

membranestatus

swelling(%)

exchange capacity(meq/gr dry)

area resistance(Ω cm2)

permselectivity(%)

new 20.125.027.0

0.760.87

1.251.36

94.495.095.0

damaged 22.726.127.8

0.720.83

1.011.29

93.393.995.0

In table 6.2 the change in properties are shown for the anion exchange layer.Although a considerable spread in swelling values are observed, it seems that theswelling of the damaged anion exchange layer is lower than for the newmembrane. Simultaneously it is observed that the area resistance seems to haveincreased for the damaged membrane. Swelling and area resistance are bothproperties which are closely related to the amount of fixed charged groups in anion exchange membrane. A lower value of the swelling and a higher electricalresistance is an indication that the amount of fixed charges has decreased in themembrane. The determination of the ion exchange capacity of the anion exchangelayer appeared to be difficult as is shown in table 6.2. Two methods were used todetermine the ion exchange capacity of the anion exchange layer. In the firstmethod hydroxyl ions were released from the membrane into a NaCl solution,


Table 6.2: Comparison between properties of the anion exchange layer of theWSI membrane as received and the membrane that was damagedby applying current densities above the inflection point (( 1 ) :determined according to method 1, (2): according to method 2 asdescribed in section 6.2). Each value refers to a different membranesample.

membranestatus

swelling(%)

exchange capacity(meq/gr dry)

area resistance(Ω cm2)

permselectivity(%)

new 30.233.434.7

0.87(1)

0.86(1)

0.51(2)

0.230.23

81.582.6

damaged 24.226.226.4

1.50(1)

1.46(1)

0.45(2)

0.360.39

82.681.8

after which the amount of hydroxyl ions in the solution was determined bytitration with HCl. In the second method the membrane in hydroxyl ion formwas placed in a HCl solution after which the amount of protons reacted from thissolution was determined by titration of the solution with NaOH. According to thefirst method the ion exchange capacity of the damaged membrane was muchhigher than that of the new membrane which is very peculiar. Not only noexplanation can be given why the ion exchange capacity can increase when themembrane is damaged, but it also contradicts the finding that the bipolarmembrane resistance increases when it is damaged. Therefore the second methodwas used. With this method much lower values for the ion exchange capacitieswere obtained. Although the difference is small, the value for the damaged anionexchange layer now was found to be lower than for the new membrane, inagreement with a lower swelling and higher area resistance.

6.4 Model calculations

In chapter 5 a model was described calculating bipolar membrane current - voltagecurves. The model assumes the water dissociation to originate from protontransfer reactions, enhanced by the electric field. Water reacted at the transitionregion is assumed to be replenished by a diffusional transport from the outersolutions into this region. In this section a qualitative comparison will be made

152 Chapter 6

between calculated current - voltage curves and the experimental curvesdetermined up to current densities above the inflection point.

Figure 6.10 shows calculated current - voltage curves, demonstrating the effect ofthe water diffusion coefficient. The shape of the curves resemble the experimentalresults to a large extent; also the calculated curves show an inflection point athigh current densities. The figure shows that a decrease in the water diffusioncoefficient results in a shift of the inflection point to lower current densities.Figure 6.11 shows the steady state water concentration at the transition regioncalculated as a function of the external voltage, corresponding to the calculatedcurrent -voltage curve with a water diffusion coefficient of 5 10-10 m2/s in figure6.10. Comparing figures 6.10 and 6.11 shows that the inflection in the current -voltage curve is a result of the decreasing water concentration in the transitionregion. With increasing external voltage this water concentration graduallyreaches zero. Simultaneously the water dissociation becomes limited by the watersupply and an inflection in the current - voltage curve occurs. In the calculationsthe water concentration reaches truly zero and therefore a true limiting currentdensity is observed at high current density in the calculated current - voltagecurves.

0

200

400

600

800

1000

0 2 4 6 8 10voltage drop (V)

10- 9 m2/s

5 10-10 m2/s

10-10 m2/s

current density

(mA/cm2)

Figure 6.10: Calculated current - voltage curves in which the value of the waterdiffusion coefficient is varied. For the calculations a pKb of 5.0 wasused as well as the parameters listed in table 5.1 in chapter 5.


0

2

4

6

8

10

12

0 2 4 6 8 10

waterconcentration

(mol/l)

voltage drop (V)

Figure 6.11: Calculated steady state water concentration at the bipolar membranetransition region as a function of external voltage. The graphcorresponds to the current - voltage curve calculated with a waterdiffusion coefficient of 5 10-10 m2/s in figure 6.10.

Figure 6.12 shows the influence of the thickness of the monopolar layers on thecalculated current - voltage curves. Increasing the thickness of the membraneresults in a shift of the inflection point to lower current densities. This is inagreement with the experimental curves shown in figure 6.8 where the thicknessof the WSI membrane was varied.

0

200

400

600

800

1000

0 2 4 6 8 10voltage drop (V)

current density

(mA/cm2)60 µm

100 µm

140 µm

Figure 6.12: Calculated current - voltage curves in which the thickness of themonopolar layers of a bipolar membrane is varied. For the calcu-lations a pKb of 5.0 and a water diffusion coefficient of 5 10-10 m 2/ swas used as well as the parameters listed in table 5.1 in chapter 5.

154 Chapter 6

Figure 6.10 and 6.12 are according to expectations; both a decrease in waterdiffusion coefficient and an increase in membrane thickness results in a smallerdiffusional transport of water into the bipolar membrane transition region andtherefore a limitation of water supply occurs at lower current densities.

The experiments with the WSI bipolar membrane indicated that the damageoccurring with the membrane at high current density mainly affected the anionexchange layer. The swelling decreased and the area resistance appeared toincrease. This might be due to a decrease in the amount of fixed charged groupspresent within the anion exchange layer. In chapter 5 it was described that theproton transfer reactions primarily occur at the anion exchange membrane. Areduction in fixed charges in the anion exchange layer of the WSI membranewould also result in a lower concentration of the basic groups involved in thewater dissociation process. Figure 6.13 shows the calculated effect of a decreasingconcentration of these groups in the transition region. The current - voltage curveis shifted to higher voltage drops. This is the same trend as was observedexperimentally when the bipolar membrane was damaged (see figure 6.3 and 6.7).

0

100

200

300

400

500

0 2 4 6 8 10

0.1 M1.5 M 0.5 M

voltage drop (V)

current density

(mA/cm2)

Figure 6.13: Calculated current - voltage curves in which the concentration ofbasic groups at the transition region involved in the water disso-ciation process is varied. For the calculations a pKb of 5.0 and awater diffusion coefficient of 5 10-10 m 2/s was used as well as theparameters listed in table 5.1 in chapter 5.

The damaged bipolar membranes not only showed an increase in resistance but itwas also observed that the inflection point shifted to lower current densities (seefigure 6.3). If the inflection point in the calculated current - voltage curves is taken


as the intercept of the two tangents before and after the inflection, the value of theinflection point is at the same current density for the curves in figure 6.13. This isdue to the presence of a true limiting current density in the calculated curves.Thus only a decrease in the concentration of basic groups involved in the waterdissociation, as shown in figure 6.13, is not sufficient to obtain qualitativeagreement between the calculated and measured current - voltage curves.

The inflection in a calculated current - voltage curve results from a limitation ofwater supply into the bipolar membrane. As was shown in figure 6.10, a shift inthe inflection point to lower current densities can be explained by a reduction inwater diffusion coefficient. A decrease in water diffusion coefficient when thebipolar membrane is damaged can be rationalised by the experimental resultswith the WSI membrane. The anion exchange layer of the WSI membrane ismuch thinner than the cation exchange layer. Furthermore, comparison betweentable 6.1 and 6.2 shows that the swelling of the (undamaged) anion exchange layeris higher than the swelling of the cation exchange layer. Therefore it seemsreasonable to assume that the water supply into the bipolar membrane interphaseis primarily determined by the anion exchange layer of the WSI membrane. Alower degree of swelling and a higher area resistance of the anion exchange layermight result in a lower value of the water diffusion coefficient for the damagedbipolar membrane.

6.5 Conclusions

Current - voltage curves were determined for a Neosepta BP-1 and a WSI bipolarmembrane. At high current density an inflection point is observed at which asharp increase in voltage drop occurs, i.e. at a certain value of the current densitythe bipolar membrane resistance increases drastically. Increasing the thickness ofthe WSI membrane resulted in the inflection point being shifted to lower currentdensities. This indicates that the inflection point is caused by a limited watersupply. Near the inflection point the dissociation of water into protons andhydroxyl ions occurs so fast that the transport of water into the bipolar membranetransition region can not keep up, the membrane dries out and the resistanceincreases.

Performing consecutive current - voltage measurements with the same sample ofbipolar membrane revealed that the second measurement showed a different

156 Chapter 6

curve if the first measurement was performed up to current densities exceedingthe inflection point. The inflection point shifted to lower current densities andthe voltage drop shifted to higher values, which indicates that the bipolarmembrane resistance has increased. Apparently the bipolar membrane isdamaged irreversibly when applying such high current densities.

The transition in slope in the current - voltage curve near the inflection point isnot instantaneous at a single current density but it is a continuous transition overa certain current range. Experiments with the BP-1 bipolar membrane has shownthat the membrane is damaged at current densities well below the inflectionpoint.

When a current - voltage curve is measured and the inflection point is exceeded,water diffusion limitation occurs and the membrane dries out. Since the bipolarmembrane interphase has a high resistance an intense heat generation occurswithin the membrane. During an experiment the anion exchange layer becomesloaded with hydroxyl ions while this layer simultaneously is exposed to analkaline solution with high pH. Two samples of the BP-1 bipolar membrane werepretreated by either a drying process or exposure to a 0.5 M NaOH solution. Bothtreatments resulted in a similar change in the current - voltage curve as wasobtained when performing consecutive measurements with the same sample ofuntreated membrane. No conclusions can be drawn whether the damage(increase in resistance) is due solely to a drying out of the membrane or to adegradation by alkaline solution (or by a combination of both).

The WSI membrane was used to compare the membrane as received and themembrane that was damaged by applying high current densities. The monopolarlayers were characterised with respect to swelling, area resistance, ion exchangecapacity and permselectivity. The properties of the cation exchange layer seemednot to have changed when comparing the damaged and the new membrane. Theswelling of the anion exchange layer was found to be lower for the damagedmembrane. Simultaneously an increase in area resistance was measured. Thisindicates that the amount of fixed charged groups in the anion exchange layer haddecreased when the bipolar membrane was damaged by applying high currentdensities.

In chapter 5 a model was described for calculating current - voltage curves, basedon the mechanism of electric field enhanced proton transfer reactions. In chapter


6 calculations were performed up to higher current densities. The calculatedcurves showed an inflection due to water diffusion limitation, similar to thecurves obtained experimentally. It was shown that the location of the inflectionpoint was determined by water transport into the bipolar membrane interphase; adecrease in membrane thickness and an increase in water diffusion coefficientboth results in the inflection point to shift to higher current densities.

The change in current - voltage curve when a bipolar membrane sample ismeasured consecutive times and damaged (inflection point to lower currentdensities, shift of curve to higher voltage drops) could be described qualitativelywhen it was assumed that both the water diffusion coefficient and theconcentration of basic groups involved in the water dissociation reaction haddecreased. A decrease in the water diffusion coefficient can be related to theexperimental result with the WSI membrane that the swelling of the anionexchange layer had decreased after damaging the bipolar membrane. The decreasein basic groups at the transition region can be rationalised by the measureddecrease in swelling and increase in area resistance of the anion exchange layerwhich indicate a reduction of the amount of fixed charges in this layer.

6.6 References

1 K. Nagasubramanian, F.P. Chlanda and K.J. Liu, Use of bipolar membranes for generation of

acid and base- an engineering and economic analysis, J. Membrane Sci. 2 (1977) p. 109-124.

2 T.A. Davis and T. Laterra, On-site generation of acid and base with bipolar membranes: a

new alternative to purchasing and storing regenerants. 48th annual meeting Int. Water

Conference. Pittsburgh (1987).

3 K.N. Mani, F.P. Chlanda and C.H. Byszewski, Aquatech membrane technology for

recovery of acid/base values from salt streams, Desalination 68 (1988) p. 149-166.


68 (1988) p. 279-292.

5 T. Aritomi, T. van den Boomgaard and H. Strathmann, Current-voltage curve of a bipolar

membrane at high current density, Desalination 104 (1996) p. 13-18.

6 N.Y. Pivovarov and V.P. Greben, Special features of the current-voltage characteristics of

bipolar membranes, Sov. Electrochem. 26 (1990) p. 1002-1006.

7 B. Bauer, H. Strathmann and F. Effenberger, Anion-exchange membranes with improved

alkaline stability, Desalination 79 (1990) p. 125-144.

8 K. Kneifel and K. Hattenbach, Properties and long term behaviour of ion exchange

membranes, Desalination 34 (1980) p. 77-95.


Summary

Monopolar ion exchange membranes are membranes that contain either positiveor negative fixed charges attached to the polymer matrix. These membranes canbe used for example in electrodialysis where a salt solution is separated into asolution enriched in ions and a solution depleted of ions. Operating currents,however, are restricted due to concentration polarisation resulting in a limitingcurrent density. In practice an overlimiting current can be obtained, the nature ofwhich is still widely discussed nowadays. Bipolar membranes consist of both ananion and a cation exchange layer. These membranes are able to dissociate waterinto protons and hydroxyl ions and can thus be used to produce acids and basesfrom the corresponding salt solution. Much attention so far has been paid to thebehaviour of bipolar membranes up to medium current densities. Informationabout the transport processes at very low and very high current densities is scarce.This thesis deals with both monopolar and bipolar membranes. The aim is toinvestigate and describe the transport processes and the transport limitationsoccurring with both types of membranes.

Chapter 2 and 3 in this thesis focus on the ion transport through monopolar ionexchange membranes. In chapter 2 concentration polarisation is studied by deter-mining current - voltage curves with a commercial cation and anion exchangemembrane. General features concerning these curves are presented, e.g. theoccurrence of a limiting and an overlimiting current. The overlimiting region ischaracterised by a considerable scatter. The limiting current density increaseslinearly with increasing bulk solution concentration and depends on the counterion to be transported through the membrane. The contribution of waterdissociation to the overlimiting current is studied. It is shown that pH changesoccur in the solutions adjacent to the test membrane when currents above thelimiting current density are applied. The measurements demonstrate that waterdissociation is more pronounced in case of the anion exchange membranecompared to the cation exchange membrane. This indicates that the waterdissociation depends on the type of membrane, which is in agreement with aconcept of proton transfer reactions as a mechanism for water dissociation.Calculation of the transport number of the water dissociation products revealsthat the contribution of water dissociation to the overlimiting current remainsnegligible. This conclusion is supported by measurements where the salt co- and

160 Summary

counter ion transport numbers in the two membranes are determined.Furthermore, these measurements show that the membrane permselectivityremains high. Thus in the overlimiting region virtually all the current is carriedby the salt counter ions for the two membranes investigated.

In chapter 3 chronopotentiometry is used to characterise the ion transportthrough the two monopolar ion exchange membranes. In chronopotentiometrydynamic measurements are performed in which the transient state of iontransport is investigated when a fixed current density is applied. Themeasurements clearly show fluctuations in voltage drop when currents higherthan the limiting current density are applied, the amplitude of which increaseswith increasing current density. The fluctuations indicate the presence ofhydrodynamic instabilities in this region. Chronopotentiometric curves arecharacterised by a transition time. Experimental transition times are found to besmaller than times calculated for an ideally permselective membrane. Thisindicates the presence of a reduced permeable membrane area. The resultsobtained in this chapter are in agreement with the theory describingelectroconvection as a mechanism for obtaining an overlimiting current.

Chapter 4, 5 and 6 focus on bipolar membranes. In the consecutive chapterstransport processes in bipolar membranes from very low to very high currentdensity are described. In chapter 4 current - voltage curves are measured at lowcurrent densities. The removal of salt ions from the bipolar membrane transitionregion, before water dissociation commences, is studied. The current - voltagecurve is characterised by a limiting current density at which all salt has beenremoved from the transition region. The limiting current density increases withincreasing bulk solution concentration. A model is described in which thelimiting current density can be calculated. The experimental change in limitingcurrent density as a function of the bulk solution concentration can be describedadequately by this model.

Chapter 5 treats bipolar membranes in their normal operating range, i.e. up tocurrent densities of 100 mA/cm2. Experimental current - voltage curves show thatthe bipolar membrane resistance decreases after the salt has been removed. This isdue to the occurrence of water dissociation, which is manifested by significant pHchanges in the solutions adjacent to the bipolar membrane. Attention is paid tothe water dissociation mechanism. A model to calculate current - voltage curvesis described, based on a combination of the second Wien effect and proton transfer

Summary 161

reactions involving the fixed groups in the bipolar membrane. The modeldemonstrates that for a low resistance bipolar membrane a high concentration ofweakly basic (or acidic) groups should be present at the transition region.Comparing experimental with calculated curves shows that the model has itslimitations. At low current density the fit of the experimental curves is ratherunsatisfactory. This is due to the absence of salt transport in the model. Themodel predicts a shift of the current - voltage curve to lower voltage drops withincreasing solution concentration, which is the opposite trend with respect to theexperimental curves. This results from not taking into account the voltage dropthat is necessary to counterbalance the concentration gradient between outersolutions and the transition region.

In chapter 6 the behaviour of bipolar membranes is investigated at very highcurrent densities. Current - voltage curves show the presence of an inflectionpoint, corresponding to a drastic increase in resistance. At this point the waterdissociation reaction is limited by the supply of water. Successive measurementswith the same membrane sample demonstrate that this results in a permanentdamage of the bipolar membrane. The damage might be caused by the intenseheat generation occurring within the membrane or by a degradation due to thealkaline environment which is created by the water dissociation process. One ofthe bipolar membranes investigated consists of two separate layers. The two layersare characterised both for the membrane as received and the damaged membrane.The properties of the cation exchange layer do not seem to have changed. Anincrease in area resistance and a decrease in swelling is found for the anionexchange layer of the damaged bipolar membrane, indicating that the amount offixed charges in this layer has decreased by applying such high currents. Aqualitative comparison between measured and calculated current - voltage curvesis made, using the water dissociation model described in chapter 5. The calculatedcurves also show an inflection point at high current density due to a limitation inwater supply. The calculated curves resemble the consecutively measured curvesif it is assumed that both the water diffusion coefficient and the concentration ofbasic groups involved in the water dissociation decrease.

Samenvatting

Monopolaire membranen zijn membranen die een positieve of een negatievelading dragen, gebonden aan een polymeermatrix. Deze membranen kunnenbijvoorbeeld gebruikt worden in electrodialyse waarbij een zoutoplossinggescheiden wordt in een oplossing rijk aan ionen en een oplossing arm aanionen. De maximale stroomsterkte waarmee gewerkt kan worden is echterbeperkt door concentratie polarisatie, resulterend in het optreden van eenlimiterende stroomdichtheid. In de praktijk kunnen echter bovenlimiterendestroomsterktes bereikt worden. De achtergrond hiervan is nog steeds een puntvan discussie. Bipolaire membranen bestaan uit zowel een positief als eennegatief geladen laag. Deze membranen zijn in staat om water te dissociëren inprotonen en hydroxide ionen en kunnen derhalve gebruikt worden om zuren enbasen te produceren uit de corresponderende zoutoplossing. Dit proefschrift gaatzowel over monopolaire als over bipolaire membranen. Het doel is het onder-zoeken en beschrijven van de transportprocessen en de transportlimiteringen diebij beide typen membranen optreden.

In hoofdstuk 2 en 3 van dit proefschrift staat het ionentransport door mono-polaire membranen centraal. In hoofdstuk 2 is concentratie polarisatie bestudeerddoor het bepalen van stroom - spannings curves van een commercieel anion enkation selectief membraan. Algemene patronen van deze curves wordenbeschreven, zoals de aanwezigheid van een limiterende en een bovenlimiterendestroomsterkte. De bovenlimiterende stroomsterkte is gekarakteriseerd door deaanwezigheid van aanzienlijke fluctuaties. De limiterende stroomdichtheidneemt lineair toe met toenemende bulkconcentratie van het zout en isafhankelijk van het tegen-ion dat door het membraan getransporteerd wordt. Debijdrage van waterdissociatie tot de bovenlimiterende stroomsterkte isonderzocht. Veranderingen in de pH van de oplossingen naast het testmembraantreden op zodra stroomsterktes groter dan de limiterende stroomsterkte wordenaangelegd. Deze metingen laten zien dat waterdissociatie sterker optreedt bij hetanion selectieve membraan dan bij het kation selectieve membraan. Dit duidterop dat de waterdissociatie afhangt van het type membraan, hetgeen in overeen-stemming is met proton overdrachtsreacties als mechanisme van water-dissociatie. Berekening van de transportgetallen van de waterdissociatieprodukten toont aan dat de bijdrage van waterdissociatie tot de bovenlimiterende

Samenvatting 163

stroom zeer gering is. Deze conclusie wordt ondersteund door metingen waarinde transportgetallen van het zout co-ion en tegen-ion bepaald zijn. Verder latendeze metingen zien dat de membranen hun selectiviteit behouden. In hetbovenlimiterende gebied wordt dus vrijwel de gehele stroom in de tweeonderzochte membranen gedragen door de zout tegen-ionen.

In hoofdstuk 3 is met behulp van chronopotentiometrie het ionentransport doormonopolaire membranen gekarakteriseerd. Bij deze techniek wordendynamische metingen uitgevoerd bij een konstante stroomdichtheid. Demetingen laten duidelijke fluctuaties in spanningsval zien wanneer een stroomgroter dan de limiterende stroom aangelegd wordt, waarbij de amplitude vandeze fluctuaties toenemen met toenemende stroomdichtheid. De fluctuaties zijneen indicatie dat er hydrodynamische instabiliteiten in dit gebied optreden.Chronopotentiometrische curves worden gekarakteriseerd door een overgangs-tijd. Experimentele overgangstijden blijken kleiner dan berekende voor eenideaal selectief membraan. Dit geeft aan dat er een gereduceerd membraan-oppervlak voor permeatie beschikbaar is. De resultaten in dit hoofdstuk stemmenovereen met de theorie dat electro-convectie beschrijft als mechanisme voor hetoptreden van een bovenlimiterende stroom.

In de hoofdstukken 4, 5 en 6 staan bipolaire membranen centraal. In deachtereenvolgende hoofdstukken worden de verschillende transportprocessen indeze membranen beschreven, van zeer lage tot zeer hoge stroomsterktes. Inhoofdstuk 4 worden stroom - spannings curves beschreven bij lage stroom-dichtheid. Het verwijderen van zout uit de tussenlaag van het membraan,voordat waterdissociatie begint, is bestudeerd. De stroom - spannings curvesworden gekarakteriseerd door een limiterende stroomdichtheid waarbij al hetzout is verwijderd uit de tussenlaag. De limiterende stroomdichtheid neemt toemet toenemende zout bulkconcentratie. Een model is beschreven waarmee delimiterende stroomdichtheid berekend kan worden. De gemeten verandering inlimiterende stroomdichtheid bij verschillende zoutconcentraties kan goedbeschreven worden door dit model.

Hoofdstuk 5 behandelt bipolaire membranen in hun normale toepassingsgebied,d.w.z. tot een stroomdichtheid van 100 mA/cm2. Experimentele stroom -spannings curves laten zien dat de weerstand van het bipolaire membraanafneemt nadat het zout is verwijderd. Dit wordt veroorzaakt door het optredenvan waterdissociatie, wat zichtbaar is door de sterke pH veranderingen in de

164 Samenvatting

oplossingen naast het membraan. Een model is beschreven waarmee stroom -spannings curves berekend kunnen worden. Het model is gebaseerd op eencombinatie van het tweede Wien effect en proton overdrachtsreacties tussenwater en de geladen groepen in het membraan. De berekeningen laten zien dateen lage membraanweerstand verkregen kan worden door een hoge concentratievan zwak basische (of zure) groepen in de membraantussenlaag. Vergelijkingtussen experimentele en berekende stroom - spannings curves tonen debeperkingen van dit model aan. Bij lage stroomdichtheid is geen goede fit van deexperimentele curves mogelijk. Dit wordt veroorzaakt doordat in het model geenrekening gehouden wordt met het zouttransport. Het model voorspelt eenverschuiving van de curve naar lagere spanningswaarden met toenemendebulkconcentratie, hetgeen tegenovergesteld is aan de gemeten curves. Dit komtdoordat de spanningsval die nodig is om de concentratiegradient tussenoplossingen en tussenlaag tegen te werken niet meegenomen is in het model.

In hoofdstuk 6 is het gedrag van bipolaire membranen bij zeer hogestroomdichtheden onderzocht. Stroom - spannings curves tonen een inflectie-punt, wat een sterke toename in weerstand betekent. Bij dit punt is de water-dissociatiereactie gelimiteerd door de aanvoer van water. Opeenvolgendemetingen met hetzelfde stuk membraan tonen aan dat het membraan hierdoorirreversibel beschadigd raakt. De schade kan een resultaat zijn van intensewarmteontwikkeling in het membraan of van degradatie door het basischemilieu dat ontstaat door de waterdissociatie. Eén van de bipolaire membranenbestaat uit twee afzonderlijke lagen. De twee lagen zijn gekarakteriseerd voorzowel het nieuwe als het beschadigde membraan. De eigenschappen van dekation selectieve laag lijken niet veranderd te zijn. De anion selectieve laag vanhet beschadigde membraan laat een toename in oppervlakteweerstand en eenafname in zwelling zien. Dit duidt erop dat de concentratie van geladen groepenin deze laag afgenomen is door het aanleggen van zeer hoge stroomdichtheden.Op basis van het model beschreven in hoofdstuk 5 is een kwalitatievevergelijking gemaakt tussen gemeten en berekende curves. De berekende curveskomen overeen met de opeenvolgend gemeten curves als aangenomen wordt datzowel de water diffusiecoefficiënt als de concentratie van basische groepenparticiperend in de waterdissociatiereactie afneemt.

Levensloop

John Krol werd geboren op 25 augustus 1969 te Grootegast. In juni 1987 behaaldehij het Gymnasium diploma aan het Drachtster Lyceum in Drachten. In augustusvan datzelfde jaar begon hij met de studie Chemische Technologie aan deUniversiteit Twente. De propaedeuse werd in 1988 behaald. Tijdens zijn studieliep hij stage aan de University of South Australia te Adelaide (Australië). Hierdeed hij onderzoek naar de invloed van temperatuurbehandelingen op en hetslijtage gedrag van een high-performance bismaleimide hars.

In mei 1992 begon hij met zijn afstudeeropdracht bij de groep membraantech-nologie waar hij onderzoek deed naar de ontwikkeling van micro- en ultra-filtratie membranen op basis van polyamides. Het ingenieursdiploma werd inmaart 1993 behaald. Op 1 mei van dat jaar trad hij in dienst als AIO bij dezelfdevakgroep. Onder leiding van prof. Strathmann heeft hij het in dit proefschriftbeschreven onderzoek verricht.