ARTICLE IN PRESS

CIS-00944; No of Pages 26 

Abstract 

Characterization of ion-exchange membrane materials: 

Properties vs structure 

N.P. Berezina ⁎ , N.A. Kononenko, O.A. Dyomina, N.P. Gnusin 

Department of Physical Chemistry, Kuban State University, 149, Stavropolskaya St., Krasnodar, 350040, Russia 

This review focuses on the preparation, structure and applications of ion-exchange membranes formed from various materials and exhibiting 

various functions (electrodialytic, perfluorinated sulphocation-exchange and novel laboratory-tested membranes). A number of experimental 

techniques for measuring electrotransport properties as well as the general procedure for membrane testing are also described. The review 

emphasizes the relationships between membrane structures, physical and chemical properties and mechanisms of electrochemical processes that 

occur in charged membrane materials. The water content in membranes is considered to be a key factor in the ion and water transfer and in 

polarization processes in electromembrane systems. We suggest the theoretical approach, which makes it possible to model and characterize the 

electrochemical properties of heterogeneous membranes using several transport-structural parameters. These parameters are extracted from the 

experimental dependences of specific electroconductivity and diffusion permeability on concentration. 

The review covers the most significant experimental and theoretical research on ion-exchange membranes that have been carried out in the 

Membrane Materials Laboratory of the Kuban State University. These results have been discussed at the conferences “Membrane 

Electrochemistry”, Krasnodar, Russia for many years and were published mainly in Russian scientific sources. 

© 2008 Elsevier B.V. All rights reserved. 

Keywords: Ion-exchange membrane; Water content; Electroconductivity; Diffusion permeability; Electroosmotic transport 

1. Introduction 

Charged synthetic membranes with high conductivity and 

selectivity are used as separating films in various electromembrane 

devices: electrodialyzers, fuel cells and electrolyzers. Two 

characteristics of electromembrane processes are particularly 

important: (1) they are ecologically safe and (2) the electrical 

energy required for these processes is comparatively low. The 

efficiency of electromembrane processes depends on physicochemical 

characteristics and electrotransport properties of ionexchange 

membranes (Fig. 1) placed in the external electric 

field, when the electrolyte concentration and temperature are 

changed simultaneously [1–5]. 

Recently, the substantial advances in synthesis and modification 

of ion-exchange polymeric membranes have been made. 

Nevertheless, the extensive studies are continued to develop 

novel materials and methods for membrane modification and to 

⁎ Corresponding author. Tel./fax: +7 861 2199573. 

E-mail address: berezina@chem.kubsu.ru (N.P. Berezina). 

0001-8686/$ - see front matter © 2008 Elsevier B.V. All rights reserved. 

doi:10.1016/j.cis.2008.01.002 

ARTICLE IN PRESS 

Advances in Colloid and Interface Science xx (2008) xxx–xxx 

www.elsevier.com/locate/cis 

produce more complex membrane structures with a wide range 

of functionalities and desired operating behaviors. The problem 

of membrane characterization has been broadly discussed in 

several reviews on the preparation and application of ion-exchange 

membranes [6–8]. Physicochemical properties of ionexchange 

membranes were extensively investigated by O. 

Kedem, P. Meares, A. Narebska, R. Paterson, C. Gardner, R. 

Buvet, B. Auclair and others [9–21]. The membrane characterization 

problem continues to attract attention in current research 

due to the recent significant expansion of the types of polymeric 

matrices [22,23] and development of composite membrane 

materials [24–28]. 

Membrane characterization includes the comprehensive studies 

on equilibrium and physical–mechanical properties (exchange 

capacity, water content, sorption properties, thickness of 

films, thermal and chemical stability); those on transport properties 

(electroconductivity, diffusion and electroosmotic permeability, 

transport numbers of ions) and structural characteristics 

measured by various physical methods (X-ray, spectral and 

optical methods that allows for investigating the structure of 

Please cite this article as: Berezina NP et al, Characterization of ion-exchange membrane materials: Properties vs structure, Adv Colloid Interface Sci (2008), 

doi:10.1016/j.cis.2008.01.002

membranes at different length scales). These properties are 

commonly mentioned in the catalogs of commercially available 

ion-exchange membranes [29–34]. However, there remain several 

outstanding questions: is it possible to find a compromise 

between exchange capacity, water content, conducting properties 

and thermal–mechanical stability of a material? How to 

establish the relationships between the transport properties of 

membranes (selectivity, conductivity, diffusion and electroosmotic 

permeability)? How to measure the changes in electrotransport 

properties of membranes in separation process, when the 

membrane behavior is influenced by the electric and concentration 

fields? To answer these questions, which are very important 

for fabricating of membrane materials and controlling their 

properties, the approach to the characterization of membranes 

remains to be developed using the summarized data on membrane 

properties. 

The objectives of this review are as follows: (1) to summarize 

the results of experimental studies on physicochemical 

characteristics and electrotransport properties of ion-exchange 

membranes, (2) to sketch some of the important factors 

that contribute to the ion and water transfer mechanisms, and 

(3) to suggest a model approach that allows the characterization 

of electrodiffusion properties of structurally heterogeneous 

membranes. 

2. Membrane materials and pre-testing procedures 

The commercial ion-exchange membranes were obtained from 

different companies (Russia, Japan, USA and China). Laboratory 

samples were prepared from aromatic polymers (polysulphone 

and polyether-ether-ketone) and from perfluorinated materials 

(Table 1). 

The pre-testing treatment of polymeric membranes is a vitally 

important factor for the understanding of several aspects of 

these systems including (1) influence of synthesis conditions 

on some physicochemical properties of membrane material, 


2 N.P. Berezina et al. / Advances in Colloid and Interface Science xx (2008) xxx–xxx 

Fig. 1. Schematic diagram of an electromembrane system. 

(2) influence of operating conditions on membrane properties, 

(3) reliability of model parameters, and (4) reproducibility of the 

experimental results. Membrane materials used with no additional 

pre-testing treatment are unstable and often contaminated 

with various (organic) substances. 

The pre-testing treatment of membranes is a stepwise procedure. 

The heterogeneous polymer membranes are first treated 

with ethanol for 6 h to extract the monomer residues and 

surfactant inclusions that remain in the material after the synthesis. 

Then the membranes are treated with the solutions of 

salts, acids or bases [46]. Finally, the membranes are rinsed with 

distilled water. Single processing step requires about 48 h. 

The structure of unlinked polymeric membranes based on 

perfluorinated matrices is very sensitive to pre-testing treatment 

protocol [47]. We used different methods to process perfluorinated 

membranes. For the “salt-based” method, the rinsing of 

membranes with 2 М NaCl solutions was followed by equilibrating 

with NaCl solutions of lower concentration (down to 

0.05 M) under isothermal conditions at 25 °C. In “thermalbased” 

procedure, the membranes were subsequently treated 

with boiling solutions of 3% Н 2О 2, Н 2О, 0.5 МНNO 3 or 

Н 2SO 4, and, finally, Н 2О (each single step required 3 h). The 

samples processed in this fashion were thermally equilibrated 

with water, and, finally, with NaCl or НCl solutions of various 

concentrations at 25 °C. 

3. Experimental section 

Several standard techniques have been used to test membranes 

[19]. The ion-exchange capacity (IEC) was determined 

for H + -form samples by titration of the H + -ions produced in a 

course of base neutralization [48]. The water was evaporated at 

105 °С, and the water content w was determined as the mass 

ratio of water to dry membrane by the gravimetric method [49]. 

The membrane hydration capacity nm (average molar content of 

H 2O molecules/1 mol of functional groups) was calculated from 


doi:10.1016/j.cis.2008.01.002


doi:10.1016/j.cis.2008.01.002 

Table 1 

Membrane materials 

Membrane/produced by Membrane type Fixed groups Application Reference 

MK-40 “Schekinazot” (Russia) Composites formed from the cation-exchange resins KU-2 (polystyrene 

(PS) matrix cross-linked with divinylbenzene (DVB) and fixed groups), 

polyethylene and nylon 

MK-41 “Schekinazot” (Russia) Composites formed from the cation-exchange resins KF-1 (PS matrix 

cross-linked with DVB and fixed groups), polyethylene and nylon 

− 

–HPO3 MA-41 “Schekinazot” (Russia) Composites fabricated from the anion-exchange resins AV-17 (PS 

cross-linked with DVB and fixed groups), polyethylene and nylon 

–N + (CH3)3 

MA-40 “Schekinazot” (Russia) Composites on the base of resin EDE-10P produced via condensation 

` N _ NH–N 

of diamine with epichlorhydrine, polyethylene and nylon 

+ 

Neosepta СМ-1 Tokuyama Soda (Japan) Composites prepared by a former method on the base of PS and DVB and 

reinforced with polyvinylchloride; these membranes are interpolymer materials 

(CH3) 3 20% 

–SO3 − 

Neosepta АМ-1, АМ-Х, Tokuyama Soda (Japan) –N + (CH3)3 

CR 67-HMR-412 “Ionics” (USA) Composite prepared from vinyl monomer and acrylic fiber –SO 3 − 

AR 204-SZRA-412 “Ionics” (USA) –N + 3361-BW Shanghai (China) Composite fabricated from powder of cation-exchange resins (PS cross-linked 

with DVB) and polyethylene and reinforced with nylon 

(CH3)3 

–SO3 − 

3362-BW Shanghai (China) Composite from powder of anion-exchange resins and polyethylene and 

reinforced with nylon, membranes have blue or green color 

–N + (CH3) 3 

RALEX MEGA (Czechia) Composites formed from ion-exchange resins, polyethylene and 

polyamide as the reinforcing material 

–SO3 − 

RALEX MEGA (Czechia) –N + (CH3) 3 

KESD (Poland) Composites formed from the PS cross-linked with DVB and polyethylene –SO 3 − 

AESD (Poland) –N + Nafion 115, 117, 120, 425 Dupon de 

Films fabricated from polytetrafluorethylene and perfluorvinylether 

(CH3)3 

–SO3 

Nemoure (USA) 

with fixed charges 

− 

MF-4SK various modifications 

Films fabricated from polytetrafluorethylene and perfluorvinylether 

–SO3 

“Plastpolymer” (Russia) 

with fixed charges 

− 

SPS-1, 2 University of Twente (The Netherlands) Films fabricated from polysulphone matrix with varied degree of sulphurization –SO 3 − 

SPEEK University of Twente (The Netherlands) Films fabricated from polyether-ether–ketone matrix with varied 

degree of sulphurization 

Kaspion, Karpov Institute (Russia) Films fabricated from aromatic polyamides with varied phenylon content –SO3 − 

–SO 3 − 

–SO 3 − 

Electrodialysis separation 

processes, water desalination 

Bipolar electrodialysis 

separation processes 











[33] 

[33,35] 

[33,36] 

[33,36] 

[29] 

[31] 

[19] 

[36] 


process, water desalination 

[34] 

Diffusion dialysis [37] 

Membrane electrolysis, fuel [8,30,38,39] 

cells, medicine, sensors and others 

Membrane electrolysis, fuel cells [40–42] 

and others 

Laboratory-made samples [22,43,44] 

Laboratory-made samples 

Laboratory-made samples [23,45] 

N.P. Berezina et al. / Advances in Colloid and Interface Science xx (2008) xxx–xxx 

3 

ARTICLE IN PRESS

Table 2 

Schematic drawings of the experimental set-up 

Cell schematics Calculation equation Experimental 

conditions 

Km ¼ l 

RS 

l, membrane thickness; 

S, area; 

R, resistance; 

Pm ¼ VlDc 

ScDt 

V, chamber volume; 

c, concentration; 

t, time; 

V ⁎ 

W ¼ 

Sit 

tw ¼ WF 

18 

i, current density; 

F, Faraday number; 

V⁎, volume of water 

transfer 

Graphic determination 

of limiting current and 

other parameters of 

current–voltage curve 

AC frequency 

200 kHz 

Reference 

[64] 

i=0 [19,70] 

Δc≠0 

Δp=0 

i≠0 [19,71] 

Δc=0 

Δp=0 

i≠0 [72] 

Δc=0 

Δp=0 

(1) Membrane; (2) measuring electrodes; (3) polarizing electrodes; (4) impedance 

meter; (5) potentiostat; (6) measuring capillaries; (7) ammeter; (8) stirrings; 

(9) mercury. 

the values of the water content and exchange capacity of the 

samples; the accuracy of the determination of nm was of 0.1 mol 

H2O/mol SO3 − [50–52]. 

The porous structure of ion-exchange membranes was 

studied with various methods: electron microscopy, atomic 

force microscopy, small-angle X-ray scattering, mercury 

porosimetry etc [2,11,53–59]. The thermodynamic method of 

standard contact porosimetry allows the determination of water 

distribution in the pores [59–63]. This method has been 

developed at the A.N. Frumkin Institute of Electrochemistry by 

Yu.M. Volfkovich and E.I. Shkolnikov. This method is useful 

for studying the properties of heterogeneous membranes 

with S-shaped isotherm of water desorption in a wide range of 

effective pore radii as well as that of homogeneous membranes 

MF-4SK and Nafion [59,60] with narrow distribution of pore 

sizes and low content of water. 

In the standard porosimetry method, the water content is 

measured for the membranes equilibrated with the standards of 

determined porous structure. The curves of integral distribution 

of pore volume on the pore radius were obtained for the 



standards via independent techniques (mercury porosimetry or 

capillary condensation). The size of the molecules (about 1 nm) 

of the measuring liquid limits the use of this method. 

The specific internal surface area S (m 2 /g) and the distance 

between the fixed groups L (nm) were calculated from the 

porosimetry curves of the relative water content V (cm 3 Н2О/g) 

as a function of the effective radii of pores r (nm) in the 

membrane. 

Z l 

1 

S ¼ 2 

r2 0 

dV 

dlnr 

Z l 

dr ¼ 2 

0 

dV 

r 

; L ¼ 

sffiffiffiffiffiffiffiffiffi 

S 

; 

QNA 

ð1Þ 

where dV is the differential of water content, Q is the ionexchange 

capacity, NA is the Avogadro's number. 

Schematic drawings of the electrochemical cells, the 

equations used for calculations and some experimental parameters 

are summarized in Table 2. The membrane conductivity 

κm (S/m) is a common characteristic of electrochemical properties 

of these systems. A wide range of experimental techniques 

has been developed for the determination of materials 

conductivity [17,64–66]. The value of κm is commonly determined 

from the value of membrane resistance measured as an 

active portion of membrane impedance [64]. We used the mercury-contact 

electrode operating at 200 kHz AC. The mercurycontact 

method is very attractive for studying polymer films 

since this technique provides an ideal contact between the 

electrodes and a sample. Moreover, this method is not limited 

by the concentration of the equilibrium solution or by the water 

content which might vary in different polymer materials. 

The polarization effects in membranes translate into the 

discrepancy between the conductivity of ion-exchange membrane 

measured under alternating current (κ AC) and that measured 

under direct current (κ DC) [34,67]. The simple equation 

that establishes the relationship between these characteristics 

has been derived and confirmed by the experimental data for 

heterogeneous electrodialytic membranes [68]: 

jDC ¼ jACt f2 

i 

where ti is transport numbers of counter-ions in solution; f2 is 

the volume fraction of equilibrium solution in the membrane. 

For homogeneous membranes, when f2→0, it is however 

possible to neglect discrepancies between κAC and κDC. 

The diffusion of salt through a membrane is described by 

several quantitative parameters (the salt diffusion flux ( jm, mol/ 

m 2 s), the integral (Рm, m 2 /s) and differential (P⁎) coefficients 

of diffusion permeability). The relationships between these 

parameters are defined by the following equations: 

R c 

Pm ¼ 

0 P⁎dc Dc 

; jm ¼ Pm ; jm ¼ P 

⁎ dc 

: ð3Þ 

c 

l 

dl 

Several papers regarding the experimental methods for measuring 

these diffusion characteristics have been published 

[17,69,70]. We studied the diffusion of salt solution through a 

membrane to the “pure” water (Table 2). The rate of increase of 

the salt concentration in a chamber filled with water (dc/dt) was 

controlled via conductometry method. 


doi:10.1016/j.cis.2008.01.002 

ð2Þ

Electroosmotic permeability of the membranes in NaCl 

solutions W (m 3 /C) and the number of water transport t w (mol 

Н 2О/F) were measured in a two-chamber cell with reversible 

silver chloride electrodes by the volumetric method [19,71] 

(Table 2). 

The voltammetry curves were obtained in a cell equipped 

with platinum polarizing and silver chloride measuring electrodes 

[72]. The value of the electrodiffusion limiting current 

density i lim (A/m 2 ) was found graphically from the voltammetry 

curves. 

Testing of membranes was carried out in NaCl solutions, 

since this salt is one of the most abundant mineral component of 

natural waters, industrial and physiological solutions. For the 

electrodialytic membranes, the 0.1 М solution of NaCl was 

used as a standard. The membranes for other applications must 

be studied in more concentrated solutions of salts as well as in 

acid and base solutions (NaCl, HCl and H 2SO 4). Herein, the 

electrotransport characteristics of membranes were determined 

for a wide concentration range. 

The isothermal experiments were carried out at 25 °С. The 

measurement errors for all determined parameters amounted to 

3–5%. 

4. Results and discussion 

4.1. Structure of ion-exchange membranes investigated by 

standard porosimetry method 

Ion-exchange membranes are multiphase systems harboring 

polar and non-polar components in a polymeric matrix. Dry ionexchangers 

are dielectrics with a conductivity of 10 − 5 S/m. The 

conducting state of a membrane is induced by water or electrolyte 

solution that results in an abrupt increase in the conductivity 

of material (by 2–3 orders of magnitude) in a narrow 

range of water content values. This effect indicates the formation 

of ion and water transport channels in the membrane 

structure influenced by the external electric and concentration 

fields. The spatial distribution of water molecules and their 

specific concentration within the membrane both determine its 

structural, mechanical, thermodynamic and electrochemical 

properties. More recently, theoretical concepts regarding the 

ion aggregation in membranes have been suggested in several 

studies on the data obtained by modern physical methods 

[8,17,53,55,63,73–76]. 

The analysis of the standard porosimetry data provides a 

rational picture of various interactions between the material and 

water. The model represented schematically in Fig. 2 includes 

energetic, hydration and geometrical parameters of membrane 

microstructure. The concept of “free” and “bonded” water in 

ion-exchangers allows simple calculations of the water capacity 

of a gel phase and hydration numbers of counter-ions [63]. 

The “bonded” water confined in hydrate shells of ion–dipole 

associates fixed ion–counter-ion is immobilized in channels 

with effective radii ranging from 0.4 to 1.5 nm [77]. This water 

state is related to the hydrate capacity of a gel phase. The region 

of “bonded” water in the curve of water distribution on the pore 

radii corresponds to the energy of water bonding A≥1.7 kJ/mol 



and to the effective value of pore radii r≤1.5 nm (A ¼ 2Vmr 

cos H 

r , where Vm is the molar volume of water, σ is the 

surface tension and Θ is the contact angle). This value of A is 

less by approximately two orders of magnitude than the hydration 

energy of ions that is comparable with the energy of 

hydrogen bonds [78]. The maximum in a region that corresponds 

to the macropores indicates that structural defects are 

formed at the interface between the resin and polyethylene 

particles. 

The method of standard porosimetry was successfully used in 

several studies of resin-based heterogeneous membranes with 

different porosities and degrees of DVB cross-linking. It is also 

useful for studying membranes with different chemistry of 

matrix, functional groups and counter-ions and for evaluating the 

degradation of membrane properties after freezing, sterilization 

etc [61,62,79]. The data presented in Fig. 3 confirm the high 

sensitivity of standard porosimetry with respect to the synthetic 

methods used for membrane fabrication. This sensitivity makes 

the standard porosimetry technique very convenient to determine 

the structural characteristics of new membrane materials. 

Currently, a wide range of Nafion-type perfluorinated membranes 

MF-4SK (Russia) is manufactured. The expansion of the 

class of novel membrane materials requires careful consideration 

of the relationships between cluster morphology and transport 

properties of membranes. The content and distribution of 

water in these materials are particularly important because they 

are commonly used as solid polyelectrolytes in fuel cells. The 

morphology of perfluorinated membranes and models of their 

structure are the subjects of continuing experiment and theorybased 

research. The generally accepted concept of water clusters 

(4–5 nm in diameter) connected by narrow channels of 1– 

1.5 nm has been extended recently to a new model of Nafion 

structure. This model suggests the formation of networked 

bundles of elongated polymeric aggregates and cylindrical 

channels in the membrane [80]. Fig. 4 shows the porosimetry 

Fig. 2. Integral (1) and differential (2) functions of water distribution on the pore 

radii and energy of bonded water (A, J/mol) for MK-40 membrane; V is the 

relative water content of the swollen membrane (cm 3 /g); r is the effective pore 

radius (nm); nm is the water capacity of the swollen membrane (mol H2O/site). 


doi:10.1016/j.cis.2008.01.002 

5



Fig. 3. Integral (a, b, c) and differential (a, d, e) functions of water distribution on the effective pore radii (r, nm) and energy of bonded water (A, J/mol) 

for heterogeneous membranes with various counter-ions (a, b, c) and altered DVB content (d and e). The hydrate microstructures are drawn schematically (a, b, c). 

a) MK-40 in Li + (1), Na + (2) and K + (3) ionic form; b) MK-40 in Na + (1), Ni 2+ (2), Cu 2+ (3) and Zn 2+ (4) ionic form; c) MK-41 in Na + (1), Ni 2+ (2), Cu 2+ (3) and Zn 2+ 

(4) ionic form; d) MK-40 (2. 4 and 8% DVB); e) MK-41 (4 and 8% DVB). 


doi:10.1016/j.cis.2008.01.002

Fig. 4. Distributions of integral pore-volume (V, cm 3 H 2O/cm 3 membrane) on pore radii (r, nm) for (1) Nafion-115, (2) Nafion-112, (3) Nafion-117 and (4) MF-4SK 

membranes (a) [60], and the scheme of Nafion membrane structure (b) [80]. 

curves for membranes Nafion and MF-4SK described in [60], 

and a model of Nafion structure which accounts for membrane 

heterogeneity scaling from nanometers to microns. 

The effects of water redistribution between structural elements 

are even more pronounced when the organic ions are 

introduced into the membrane material. Fig. 5 represents the 

integral functions of water distribution on the effective pore radii 

for membranes MK-40 and MF-4SK with varied degree of 

Fig. 5. Integral functions of water distribution on effective pore radii for the 

membranes MF-4SK (a) and MK-40 (b). The saturation (θ) of membranes with 

ТBА + ions varies as follows: (a) (1) 0, (2) 0.17, (3) 0.25, (4) 0.49, (5) 0.70, 

(6) 1.00 and (b) (1) 0, (2) 0.24, (3) 0.72, (4) 0.88. 



membrane saturation with tetrabutylammonium ions (TBA + ). 

The degree of saturation (θ) is the ratio of the number of absorbed 

organic ions q (mol/g) to the maximum IEC of a membrane 

with respect to organic counter-ions (Qorg): θ=q/Qorg 

[81]. The values of internal specific surface S, distance between 

the fixed groups L and the amount of TBA + ions on the internal 

surface in membrane cs (cs=q/S) calculated from porosimetric 

curves for various θ values are summarized in Table 3. 

Several suggestions regarding the localization of organic 

ions at the internal interfaces in charged membranes have been 

made on the basis of the experimental data. Different scales of 

heterogeneity in polystyrene and perfluorinated membranes 

results in the accumulation of organic ions at the interface 

between gel phase and internal solution in the macro- and 

mesopores (Fig. 6a). This hypothetical interface is somewhat 

discrete because 40% of the membrane volume is occupied with 

polyethylene [33], which does not interact with organic counterions; 

instead, it is involved in the formation of transport 

channels. 

The saturation of MF-4SK membrane with TBA + ions is 

accompanied by the polymer dehydration and structural reorganization 

that decreases the diameter of hydrophilic channels 

approximately down to that of organic ions (1 nm) (Fig. 6b). This 

Table 3 

Structural characteristics of sulphocationic membranes with a varied degree of 

saturation with TBA + ions 

θ V0,cm 3 /g S, m 2 /g L, nm cs10 6 , mol/m 2 

MF-4SK 

0 0.27 146 0.50 0 

0.17 0.24 129 0.47 0.9 

0.25 0.20 72 0.34 2.4 

0.49 0.16 55 0.31 6.0 

0.70 0.13 33 0.24 14.5 

1.00 0.05 12 0.14 55.3 

MK-40 

0 0.46 121 0.27 0 

0.24 0.36 113 0.27 3.6 

0.72 0.33 99 0.25 13.8 

0.88 0.30 96 0.24 17.3 


doi:10.1016/j.cis.2008.01.002 

7

decrease in the distance between functional groups indicates the 

shrinking of material that inhibits the hydrophilic transport and 

results in the complete loss of membrane conductivity. 

Overall, the consideration of water distribution within the 

equilibrated membrane provides a comprehensive understanding 

of changes in electrotransport properties of membranes 

influenced by various internal and external factors. 

4.2. Ion transport in ion-exchange membranes 

4.2.1. Membrane conductometry 

The electrochemical behavior of ion-exchange membranes is 

generally described by a number of macroscopic properties: 

conductivity, transport numbers of ions and water, diffusion and 

electroosmotic permeability, value of limiting current in the 

current–voltage curve. These properties depend on the concentration 

of equilibrium electrolyte solution, which concentrations 

are altered in a course of separation process (Fig. 1). 

The membrane conductivity thus depends on the solution 

concentration, exchange capacity, type of counter-ions, fixed ions 

and polymeric matrix [17,19,43,45,82–84]. The most important 

factor is the dependence of membrane conductivity on concentration. 

The measurements of membrane conductivity in a wide 

range of NaCl concentration revealed three different concentration 

regions for the Κ M−С dependence (Fig. 7). For diluted 

solutions with the concentration ≤0.5M,anincreaseoftheΚ M 

value has been observed for all measured samples. When the 

membrane conductivity (κ M) is equal to the equilibrium solution 

conductivity (κ), the “isoconductivity” point (κ iso) is a characteristics 

of conducting properties of membranes in diluted solutions, 

jisoujm ¼ j: ð4Þ 

In most cases, the conductivity increased at the medium 

concentrations ranging from 0.5 M to 1.5 M. For the con- 



Fig. 6. Schematic representation of the ТBА + ions immobilized in a heterogeneous cation-exchange membrane (а) and the ТBА + ions moving in cluster-channelcluster 

structure of a perfluorinated membrane (b). 

centrations exceeding 1.5 M, the extreme character of the Κ M−С 

function has been observed for some membranes [84]. The 

conductivity decrease in the concentrated solutions is related to 

the increase in the Donnan's sorption of electrolyte, membrane 

dehydration and ionic association. This study of conductivity VS 

concentration dependences (Figs. 7, 8) confirmed the key role of 

water molecules and their content in the membrane material on 

the conductivity of ion-exchange membranes. 

There are two different ways to vary water content in the 

membrane: (1) synthetically (by varying the degree of polymeric 

matrix cross-linking and the amount of inert component 

in heterogeneous membranes; by changing the conditions 

of alkaline saponification of sulphonyl fluoride groups or 

by varying the time of exposure in glycol at 110 °C for 

Fig. 7. Membrane conductivity vs concentration dependences obtained in 

equilibrium NaCl solutions: (1) MK-40 with 4% DVB, (2) MK-40 with 8% 

DVB, (3) MA-41, (4) MK-41 with 8% DVB, (5) MK-41 with 4% DVB, (6) BW- 

3361, (7) MA-40, (8) MF-4SK with nm=11.9, (9) MF-4SK with nm=36.5, 

(10) MF-4SK with nm=20.2, (11) MF-4SK with nm=7.1, (12) Kaspion. 


doi:10.1016/j.cis.2008.01.002

perfluorinated membranes), and (2) by post-synthetic processing 

of the already synthesized membranes (temperature treatment, 

pre-testing processing of perfluorinated membranes, 

immobilization of hydrophobic organic ions etc.) [19,41,43, 

47,63,71,85]. 

The conductivity as function of water capacity for perfluorinated 

membranes preliminary rinsed with water is shown 

in Fig. 9. The nm value was varied both by changing the 

counter-ion type and by using different pre-testing procedures. 

The n m increased in the H + -form compared to that of K + -form, 

especially after successive boiling of membranes in acidic 

solutions and water [47]. The κm increases with nm (Fig. 9), that 

corroborates the general relationship between the hydrate characteristics 

and electrotransport properties of the ion-exchange 

membranes. 

The analysis of anion-exchange membranes conductivity has 

been described in details [36] and the type of functional groups 

and polymeric matrix have been suggested to be the key factors 

contributed to the ionic transfer. 

4.3. Percolation effects in ion-exchange membranes 

Studying the percolation transitions during the preparation of 

a polymeric composite is very important for the optimization of 

a composition of raw materials. The changes in conductivity are 

commonly observed when the ratio between the conducting and 

non-conducting components is varied for ion-exchange sticks 

(granulates), membranes from a resin and polyethylene, or 

membranes formed from sulpho-containing polyarylenamides 

(conducting component) dispersed in phenylone (inert component) 

[86]. 

Percolation transition in the mixed system composed of 

swollen gel, solution and inert component particles is sche- 



Fig. 8. Concentration dependences of the conductivity of electrodialytic membranes (a) and perfluorinated membranes reinforced with tetrafluoroethylene fibers (b): a) 

(1) Neosepta AM-1, (2) MK-40, (3) Neosepta CM-1, (4) CR 67-HMR-412, (5) MA-41, (6) AR 204-SZRA-412, (7) NaCl solutions; b) (1) Nafion-117, (2) Nafion-425, 

(3) MF-4SK, (4, 5, and 6) MF-4SK with fibers, (7) NaCl solution. 

matically represented in Fig. 10a. Fig. 10b shows a clear set of 

dependences of the relative conductivity value (κ m/κ) on the 

volume fraction of the conducting phase in the composite 

(factor fc). 

The equation proposed by S. Kirkpatrick on the basis of 

the percolation phenomena theory developed by S. Broadbent 

and J. Hammersly [87,88] has been used for the calculations of 

membrane parameters: 

jm ¼ j0 ð/ / jÞ 

t ; ð5Þ 

where κ0 is the parameter dependent on the mechanism of 

conductivity, which has been determined experimentally (the κ 0 

Fig. 9. Conductivity vs hydration capacity curve for perfluorinated membranes 

in various ionic forms. 


doi:10.1016/j.cis.2008.01.002 

9

Fig. 10. 2D schematic representation of the swollen membranes as percolating 

systems (a). Percolation curves (b) for various membrane materials: 

1 — heterogeneous ion-exchange sticks (granulates), fabricated from extruded 

mixture of sulphocationic resin KU-2 and polyethylene; 2 — heterogeneous ionexchange 

membranes with the varied ratios of the resin KU-2 and polyethylene; 

3 — homogeneous cation-exchange films formed from sulphonate-containing 

polyaryleneamide. 

value is the same as electroconductivity of the conducting 

phase); ϕ and ϕ k are the volume fractions of conducting phase 

in the polymer and the critical value, at which the percolation 

transition isolator–conductor is observed; t is critical index of 

electroconductivity or universal constant. 

It has been found, that percolation transitions occur upon 

changing both water contents and the energetic state of water 

molecules in ion-exchange membranes. Fig. 11 (curve 3) illustrates 

percolation transition for the MK-40 membrane during 

freezing and thawing processes. We did not observe percolation 

effects for Neosepta СМ-1 and MF-4SK membranes under the 

similar experimental conditions [89]. 

These observations suggest that the “free” water is responsible 

for the percolation nature of ion transport in hetero- 

Fig. 11. Time-dependent curve of the logarithm of specific membrane conductivity 

(κm, S/m) in a course of freezing–thawing processes: (1) MF-4SK, 

(2) Neosepta СМ-1, (3) МK-40. 



geneous membrane (MK-40). Dehydrated heterogeneous 

membranes exhibit an abrupt dependence of conductivity on 

water content. We observed this so-called “antipercolation transitions” 

in successively dried Nafion-117 and heterogeneous 

membranes MK-40, MA-41 and MA-41⁎ (isoporous structure 

of resin) equilibrated with water (Fig. 12), and membranes MA- 

40 equilibrated with sodium, nickel (II), copper (II) and zinc (II) 

chloride solutions [90–92]. As indicated in Fig. 12, the conductivity 

changed by more than four orders of magnitude with 

increasing water content. For highly hydrated membranes, the 

conductivity values depend on a chemistry of co-ions because 

of their complexation with the membrane material. 

The accumulation of organic ions in membranes causes the 

formation of structural elements with lower conductivity. This, 

in turn, induces the changes both in the membrane hydrophilicity 

and electrotransport properties. The membrane conductivity 

decreases in a course of saturating of the material with 

low-mobility organic counter-ions. In fact, the membranes with 

θ≤0.4 generally exhibit similar behavior (Fig. 13a). However, 

the ТBА + ions somewhat decrease the conductivity of sulphocationic 

membranes MK-40 and MF-4SK, when the saturation 

exceeds θ=0.4. We hypothesized, that this decrease was caused 

by an influence of membrane structure. 

For the system TBA + /MF-4SK, the change of membrane 

hydration state induced by the corresponding change in saturation 

with organic counter-ions results in an abrupt decrease in 

conductivity. This effect might be attributed to the percolation 

conductor–dielectric transition. The calculations on the percolation 

theory equation confirmed that the experimental value of 

parameter ϕk for all membranes correlated well with the 

theoretical ones [86]. The calculated value of the conductivity 

critical index (parameter t) however exceeded those mentioned 

in the literature for typical percolation systems. This discrepancy 

follows, most likely, from an approximate character of 

calculating the volume fraction (ϕ) of conducting component in 

perfluorinated membranes. The parameters in percolation theory 

equation do not correspond well to an actual geometry and 

packing of conducting regions in the membrane [93,94]. We 

assumed that the volume fraction of water, which formed 

Fig. 12. Dependence of the membrane conductivity (κ m, S/cm) on the water 

content: (1) MA-41, (2) MK-40 and (3) MA-41⁎ membranes impregnated with 

water [90]. 


doi:10.1016/j.cis.2008.01.002

hydrophilic channels for ion transfer, corresponded to the volume 

fraction of the conducting phase. The ϕ value was determined 

using the experimental dependences of the water content 

on the degree of saturation with organic ions and on membrane 

density [95,96]. 

In summary, the introduction of TBA + ions into membrane 

material provided an opportunity for direct observation of new 

percolation conductor–dielectric transitions related to the 

interplay between the membrane dehydration and formation 

of the phase with low conductivity in homogeneous membranes. 

The small value of the t parameter indicates the strong 

influence of membrane dehydration on the type of a conductivity 

decrease. We note, that the similar effects were not 

observed for heterogeneous МK-40 membranes under the same 

experimental conditions. 

The experimental data on the conductivity of ion-exchange 

membranes in dry and swollen states in a wide range of electrolyte 

concentrations provide a basis for a clear set of most 

important factors for understanding polymer behavior: (1) critical 

value of water content corresponding to the percolation 

conductor–dielectric transition, (2) “isoelectroconductivity” 

point corresponding to the equilibration of the conductivity of 

membrane and that of solution, and (3) membrane conductivity 

maximum. 

4.4. Water electrotransport and selectivity of membranes 

The transport of ions through membranes under external 

electric field is accompanied by the transport of solvent molecules. 

The mechanism of water electrotransport depends on the 

membrane hydrophilic properties as well as on the degree of ion 

hydration [71]. The electroosmotic permeability of ion-exchange 

membranes has been studied systematically in several 

works [19,41,71,97,98]. 

The concentration dependences of water transport numbers 

in a wide range of NaCl concentration for electrodialytic and 



perfluorinated membranes are presented in Fig. 14. For diluted 

solutions, water transport numbers (t w), which depend strongly 

on the water content, remain constant for the majority of the 

investigated membranes. When the concentration of solution 

decreases, the tw increases substantially (up to 10 mol H2O/F) in 

strongly swelling membranes (MF-4SK, N M=36.5 mol H2O/ 

mol SO3 − , KESD N M=19 mol H2O/mol SO3 − ). For the higher 

values of concentrations (from 0.5 M to 1.5 M of NaCl), this 

value remains stable in electrodialytic membranes. However, 

the decrease of t w was observed for some perfluorinated membranes. 

For the concentrated solutions, the t w value approaches 

the number of primary hydration of ions (4 for Na + and 3 for 

Cl − ) for all investigated membranes. 

The type of counter-ions may have an essential influence on 

the electroosmotic permeability of membranes. The high numbers 

of water transport by tetrametylammonium and trimethylbenzylammonium 

cations have been found in [98]. A similar 

effect has been described in [99] for Nafion-117 membrane 

saturated with alcylammonium cations (the number of hydrocarbon 

radicals varied from 1 up to 4). The authors hypothesized 

that electroosmotic flow increased because of hydrodynamic 

conditions that induced “the pumping effect”, i.e., the transport 

of the excessive amount of solvent. However, the detailed 

mechanism for this type of water transport has not been proposed. 

High electroosmotic flow has been also observed for 

dicarboxylic acids [100] and amino acids [101,102] transferred 

through membranes. 

Herein, we studied the transport of water by TEA + ions 

through perfluorinated MF-4SK membrane. The anomalous 

electroosmotic transport as compared to NaCl solution was 

observed. For tetraethylammonium chloride (TEACl), the tw 

value reached 22 mol of H2O/F that correlated well with the data 

obtained in [98,99]. To determine the contribution of “the 

pumping effect” to the overall water transport, we studied the 

electroosmotic transport in mixed NaCl and TEACl solutions by 

the method of isonormal series. A total electrolyte concentration 

Fig. 13. Conductivity vs saturation degree curves for membranes with immobilized organic counter-ions TBA + and DDS − : (1) MK-40, (2) MA-41, (3) MF-4SK 

(a). Graphical determination of the parameters of percolation theory (b). (The parameter κm refers to the membrane conductivity after saturation with the TBA + ions 

and parameter κm 0 refers to the same characteristic of initial membrane). 


doi:10.1016/j.cis.2008.01.002 

11

Fig. 14. Concentration dependence of the water transport numbers in NaCl solutions for (a) electrodialytic and (b) perfluorinated membranes: a) (1) MK-40 with 

8% DVB, (2) MK-40 with 4% DVB, (3) MK-41 with 8% DVB, (4) MA-41, (5) MA-40, (6) BW-3361; b) (1) MF-4SK with nm=11.9, (2) MF-4SK with nm=20.2, 

(3) MF-4SK with n m=36,5, (4) Nafion 425, (5) Nafion 117, (6) MF-4SK with n m=9.8, (7) MF-4SK with n m=10.1. 

was kept constant (0.1 M). The experimental results are shown 

in Fig. 15. The convex dependence of tw on the equivalent 

fraction of organic ions in the mixture indicates that, unlike 

individual NaCl and TEACl solutions, the t w values obtained 

for the mixture of Na + and TEA + ions are not additive ones The 

conservative value of tw can be related to the membrane selectivity 

toward organic counter-ions [103,104]. For the mixture of 

the TEA + ions with hydrophilic Na + , there are two parallel 

flows transferring ions through the membrane. 

Table 4 summarizes the equilibrium and dynamic hydration 

characteristics for the MF-4SK membrane (Na + -form) saturated 

with TEA + ions. The t w/n m coefficient [105] facilitates the 

comparison between dynamic and equilibrium hydration characteristics. 

The transport number of water, tw, characterizes the 

flow of solvent through the labyrinth of transport channels in a 

Fig. 15. Dependences of (1) the water transport numbers and (2) conductivity of 

the MF-4SK membrane on the equivalent fraction of TEACl in 0.1 M NaCl 

solution. 



membrane. The water capacity nm is determined by the amount 

of water absorbed by the membrane upon swelling under equilibrium 

conditions. 

As evidenced by the data given in Table 4, the t w/n m coefficient 

for Na + is smaller than 1. This value indicates that the 

water is only partially involved into electroosmotic transport 

with Na + ions. Here, the transport of water immobilized in the 

hydration shells of ions is the primary mechanism of electroosmotic 

process. For the TEA + , the tw/nm coefficient increases 

to 1.93 that suggests the additional mechanism of water trans- 

port. The electroosmotic transport in perfluorinated membranes 

is, most likely, induced by the pressure gradient ( dP) 

promoting 

dx 

the opening of additional channels that are highly selective to 

the transport of Na + ions [78]. 

The formation of aqueous clusters around tetraalkylammonium 

ions in a free solution thus manifests itself in the electromigration 

of TEA + ions through the membrane. The proposed 

mechanism of water transport with Na + and TEA + ions through 

ion-exchange membrane is drawn schematically in Fig. 16. We 

suggest, that the ‘pumping effect” ( dP ¼ 0) does not occur during 

dx 

the translational motion of Na + ions when the water molecules 

are transported only in immobilized form, that is, in ion hydration 

shells. 

The function of the equivalent fraction of TEA + ions obtained 

by conductometry measurements for the membranes in 

a mixed Na + -TEA + form is shown in Fig. 15. Even small 

amounts of TEA + ions cause a considerable decrease in the 

Table 4 

Hydration characteristics of the MF-4SK membrane 

Ions Ion radius, nm n m, mol Н 2О/mol SO 3 − 

Na + 

TEA + 

t w, mol Н 2О/F t w/n w 

0.095 16.6 10.60 0.64 

0.41 11.4 22.92 1.93 


doi:10.1016/j.cis.2008.01.002

membrane conductivity. This might be attributed to the membrane 

selectivity toward organic counter-ions. The degree of 

membrane saturation by TEA + ions tends to unity (θ→1) after 

the contact of the membrane with the TEACl solution of 

minimal concentration. A similar loss of conductivity was 

observed also for Nafion-117 membrane in NaBr and TMABr 

solutions [42]. The anomalous water transport through MF- 

4SK membrane and the simultaneous decrease in membrane 

conductivity can be therefore explained by specific interaction 

between tetraalkylammonium ions and water and by the pressure 

gradient acting as an additional force in the electromembrane 

system. 

The characteristics of water electrotransport are directly 

related to the selectivity of ion-exchange membranes. This 

parameter is especially important for the membranes used as 

ion-selective electrodes in electromembrane processes (e.g. 

water desalination, concentrating of electrolyte solutions etc.). 

The transport numbers of ions (ti ⁎) are quantitative and complex 

characteristics of the selectivity of membranes. This parameter 

represents the fraction of current transferred by certain ions and 

depends strongly on the experimental conditions. In fact, the 

effective transport numbers of ions [17] are “apparent” (t+app) 

because ion transport is accompanied by water transport. For 

this reason, some authors argue that these characteristics should 

not be used in technical data sheets. Nevertheless, the development 

of new methods to measure actual transport numbers still 

continues since these values are important for calculating the 

electric energy required for the electromembrane processes. A. 

Narebska et al. [4,106] analyzed the dependences of transport 

numbers of counter-ions on concentration and electric current 

density and suggested that this parameter as well as electroosmotic 

permeability might be included into the set of six 

“compulsory” properties for membrane characterization. The 

following equation suggested in [107] provides yet another 

approach for calculating transport numbers using the values of 

conductivity, diffusion and electroosmotic permeability coefficients: 

t ⁎ i ¼ 

z2 þL⁎þ c ðÞ 

z2 þL⁎ þðÞþz c 2 L⁎ ; ð6Þ 

ðÞ c 

Here, the electrodiffusion coefficients Li ⁎ (с) are defined in the 

following equations using the values of the specific conductiv- 



Fig. 16. Schematics illustrating the mechanism of water transport with Na + and TEA + ions in ion-exchange membrane. 

ity and diffusion permeability coefficient at certain concentration 

of the solution: 

L ⁎ þ c ðÞ¼j⁎ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 

ðÞ c 

2P 

⁎ 1 þ 1 

zþF 2 ⁎ðÞcF c 2 

RTj⁎ " s 

# 

; ð7Þ 

ðÞpF c ðÞ c 

L ⁎ ðÞ¼ c 

j⁎ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 

ðÞ c 

2P 

⁎ 1 1 

z F2 ⁎ðÞcF c 2 

RTj⁎ " s 

# 

: ð8Þ 

ðÞpF c ðÞ c 

where π ±(c) is the function accounted for the non-ideality of 

equilibrium solution: 

pFðÞ¼1 c þ dlngF=dlnc: ð9Þ 

The data on the ti ⁎ value calculations for membranes with 

various structures are summarized in Table 4. Herein, the t+ ⁎ 

values were obtained using the well-known Scatchard equation 

[108]: 

t ⁎ þ ¼ tþapp þ 0:018mFtw; ð10Þ 

This equation establishes the relationship between “true” and 

“apparent” transport numbers of counter-ions and it accounts 

for the additional contribution of water transport. We used the 

experimental data obtained in our laboratory and those published 

in [43] for our calculations. The transport numbers calculated 

from the concentration dependences of specific conductivity and 

diffusion permeability of counter-ions are in very close agreement 

with those estimated from the experimental data with Eq. 

(10); the discrepancy amounted to 3–5% (Table 5). The concentration 

dependences of conductivity, diffusion and electroosmotic 

permeability provides enough data for calculations of 

ion transport numbers, and the experimental determination of 

these latter parameters is therefore not required. 

We successfully used this approach in [107] for perfluorinated 

membranes (MF-4SK) with various contents of water and 

for heterogeneous membrane МK-40 on polystyrene matrix. 

Our results as well as those of A. Narebska et al. for Nafion-120 

membrane [109,110] were used in a recent work [13] for the 

calculation of ion transport numbers. The authors suggested an 

equation, which was proposed earlier by R. Paterson and O. 

Kedem [9,10], though in different mathematical form. 


doi:10.1016/j.cis.2008.01.002 

13

Table 5 

Transport numbers of counter-ions and water transport numbers for sulphocation 

membranes with varied type of polymer matrix in 0.5 M NaCl solution 

Membrane t + ⁎ calculation 

by Eq. (6) 

t+app 

tw, mol 

Н 2О/F 

SPEEK-1 0.99 0.97 4.8 0.99 

SPEEK-2 0.93 0.91 9.0 0.95 

SPS-2 0.99 0.96 4.0 0.98 

Nafion-117 0.97 – 4.0 – 

MF-4SK 0.98 0.94 10.3 0.99 

t+ ⁎ calculation 

by Eq. (10) 

Fig. 17 demonstrates the concentration dependence of the 

“true” transport numbers, which was calculated with Eq. (6) for 

sulphocationic membranes formed from polysulphone and polyether-ether-ketone 

matrix. The t+ ⁎ values indicated by dots were 

calculated from the experimental data on the water transport 

numbers and “apparent” transport numbers of ions for the same 

membranes [43]. Overall, this method enables, in principle, the 

determination of the “true” transport numbers of counter-ions for 

ion-exchange membranes with various structures. 

The concept of simultaneous water and ion transfer allows 

calculations of the hydration characteristics of ions from the 

concentration dependences of water transport numbers. It has 

been found that the dependence of transport number of water 

(transporting through a gel zone) on “true” transport number of 

ions is linear for many membranes when the transport number 

of counter-ions is below 0.9 [97]. The experimental results can 

be plotted in tw−t+ ⁎ coordinates according to the equation 

jw ¼ jþw þ j w ¼ t ⁎ þ hþ t ⁎ h i=F: ð11Þ 

The dynamic hydration numbers can be therefore found 

graphically: h − as an intersection point of the linear function 

with the ordinate axis (tw), and h+ as a tangent of the linear 

function slope to the x axis (Fig. 18). In Eq. (10), jw is a density 

of the water flow across the membrane, j+w and j−w are the 

densities of the water flow transferred by cations and anions, i is 

the current density, and F is the Faraday constant. The dynamic 

Fig. 17. Concentration dependence of the ion transport numbers in ion-exchange 

membranes with a varied degree of sulphurization (1) SPS-2 with nm=7.0, (2) 

SPEEK-1 with nm=13.7 and (3) SPEEK-2 with nm=20.0 mol H2O/mol. 



Fig. 18. Water transport number vs transport number of counter-ions (Na + ) 

correlation for various membranes: (1, 3) MF-4SK with nm=(1) 36.5 and 

(3) 20.2 mol H2O/mol, (2) SPEEK-2 and (4) MK-40. 

characteristics h+ and h− consist of two parts: (1) volume of 

water involved in hydration, and (2) volume of water, which 

participates in the electrotransport process. 

The calculated values of the dynamic hydration numbers of 

counter-ions and co-ions for sulphocationic membranes with 

different polymeric matrices and water capacity nm are presented 

in Table 6. The dynamic hydration numbers of counterions 

somewhat depend on the nm factor. The h+ values range 

from 7 to 11 mol Н2О/mol Na + , while the differences between 

the dynamic hydration numbers of co-ions Cl − are more pronounced. 

We note that the dynamic hydration numbers of 

counter-ions Na + listed in Table 5 are in agreement with those 

calculated with the model equations for the electroosmotic 

permeability [40,66]. In summary, the values of dynamic hydration 

numbers of ions depend on the water content in a 

membrane and therefore they must be mentioned among other 

technical characteristics. 

4.5. Diffusion permeability of membrane materials 

The concentration field induces the diffusion transfer of the 

electrolyte solution in a course of ion separation, which, in turn, 

influences the membrane behavior. The data on the salt diffusion 

into the chamber filled with distillate water are shown in 

Fig. 19. The integral coefficients of diffusion permeability as 

Table 6 

Dynamical hydration numbers of ions in membranes 

Membrane nm, mol 

Н2О/mol SO3 − 

hNa+, mol 

Н2О/mol Na + 

МK-40 13.0 6.9 7.0 

МF-4SK 36.5 11.4 29.2 

МF-4SK 20.2 7.0 11.2 

SPEEK-2 20.0 8.5 6.0 

hCl 

− ,mol 

Н2О/mol Cl − 


doi:10.1016/j.cis.2008.01.002

Fig. 19. Concentration dependences of the integral diffusion permeability 

coefficient for various membranes in NaCl solution: (1) MK-40 with 8% DVB, 

(2) MA-40, (3) BW-3361, (4) Neosepta AM-1, (5) Neosepta AM-X, (6) MF- 

4SK with nm=11.9, (7) MF-4SK with nm=20.2, and (8) MF-4SK with 

nm=36.5. 

well as other transport characteristics of different membrane 

depend strongly on the concentration. The interpolymeric 

KESD membrane generally used for the diffusion dialysis exhibited 

the highest Р m value in all measured solutions (Р m of 

KESD membrane is 10 times higher than those of electrodialytic 

membranes). In the case of membranes with high water capacity 

(e.g., MC-3361 type), a pronounced maximum of Рm was 

observed in the concentration range from 0.5 to 1.5 M. These 

data suggest that the average water content and, importantly, the 

state and location of water molecules are the factors that 



dominate the dependences of conductivity and diffusion permeability 

on concentration (Fig. 7). Fig. 20a shows the dependences 

of the diffusion flow j on concentration of NaCl 

solution for electrodialytic membranes. The similar curves of 

the integral coefficient of diffusion permeability for perfluorinated 

membranes filled with reinforcing fluorethylene fibers are 

shown in Fig. 20b. 

The concentration dependences of the diffusion permeability 

of about 40 membrane types have been studied systematically in 

[70]. The logarithm of j m value depends linearly on the logarithm 

of electrolyte concentrations. The tangent of these linear 

functions (β=dlnjm/dlnc) varies from 0.5 up to 1.5 depending 

on a type of membrane and chemistry of co-ions, which thereby 

influences the β value. For βN1, the concentration profile in a 

membrane is a convex function, and for βb1, it is of concave 

character (Fig. 21) — the inference, that has been supported by 

the results of theoretical calculations [65]. In the case of poorly 

hydrated membranes (SPS, SPEEK or Kaspion), the β value lies 

near 1. The similar β values were measured for MF-4SK membrane 

with ultra-low content of water (nm≈5 mol H2O/mol) and 

reinforced with thick fluorethylene network (Fig. 20b). The 

concentration profiles and the β parameter can be therefore used 

for the membrane characterization. 

For all membranes, the specific conductivity and diffusion 

permeability increase up to maximal critical value in concentrated 

solutions, while the activity of water and mobilities of 

counter-ions and co-ions decrease. Similarly, the water transport 

numbers and ion transport numbers decrease simultaneously 

with increasing concentration. For cb1 M, there is a defined 

region of stable tw values in tw−c curve. The threshold character 

of these curves is due to the difference in the physical 

properties of conducting phases in structurally heterogeneous 

membranes, e.g. viscosity. 

Fig. 20. Concentration dependences of diffusion flow for electrodialytic membranes (a) and integral diffusion permeability coefficient (b) for perfluorinated 

membranes in NaCl solution: a) (1) AM-1, (2) Neosepta СM-1, (3) МА-41, (4) MK-40, (5) CR 67-HMR-412, and (6) AR 204-SZRA-412 membranes; b) (1) Nafion- 

117, (2) Nafion-425, (3) MF-4SK, (4, 5, and 6) MF-4SK with tetrafluoroethylene fibers as the reinforcing material. 


doi:10.1016/j.cis.2008.01.002 

15

Fig. 21. Concentration profile in membranes with varied β parameter: c is the 

solution concentration, c 1≈0, c 2 is the electrolyte solution concentration in the 

chamber of a cell, x is the transport axis and l is the thickness of membrane. 

The data on concentration dependences of electrotransport 

properties and those on critical values of physicochemical properties 

provide, in principle, a set of guidelines for the optimization 

of membranes testing protocols, membrane composition 

and concentration ranges corresponding to more efficient electrochemical 

separation. 

4.6. Polarization phenomena in electromembrane systems 

4.6.1. Membrane voltammetry 

The membrane voltammetry method is capable of measuring 

the properties of polarized membranes under the conditions 

approximating those of actual membrane operating. The 

literature on testing of membranes via current–voltage measurements 

(CVC) is however limited by only a few works [111– 

117]. This is due to the difficulties related to the correct interpretation 

of measured CVC signals, which are influenced by the 

variety of factors. 

The current, which reaches certain limiting value and then 

increases sharply, and the following system transition to the socalled 

“overlimiting” state are the distinguishing characteristics 

of CVC curves of ion-exchange membranes. Each portion of the 

voltammetric curve provides information about the electrotransport 

properties of the membrane. The ohmic portion helps to 

determine the membrane resistance. The value of the limiting 

electrodiffusion current (ilim) depends on the membrane selectivity, 

concentration and chemistry of the electrolyte solutions 

as well as on hydrodynamic conditions, which influence the 

thickness of the diffusion layer on the membrane surface. The 

increase of a current above i lim is caused by the coupled effects 

of the concentration polarization inducing the electro-, termoand 

gravitational convective flows. These effects are the generation 

of H + ,OH − ions and formation of the macroscopic spatial 

charge in solution at the membrane/solution interface, and the 

limiting current exaltation [118–128]. Hydrodynamic and structural 

features of the membrane surface dominate the behavior of 

the membrane at the overlimiting currents. 



In the case of cation-exchange membrane, the characteristics 

of hydrodynamic instability, which is proportional to the length 

of a CVC plateau and to the ratio of “overlimiting” resistance to 

“underlimiting” one, depend on the cation radii [129]. The 

intensity of hydrodynamic instability decreases when the 

Stokes' ion radius increases. The coupled convection, which 

manifests itself in the electrochemical noise on CVC curves, 

depends on the ratio of counter-ion/co-ion diffusion coefficients 

[130]. The parameters of CVC curves to be used for testing of 

membrane materials are as follows: the slope of the ohmic 

portion, the limiting current value, the length of limiting current 

plateau, and the potentials, at which the transitions into limiting 

and overlimiting state occur. 

It is well-known fact that the shape of current–voltage curves 

and the value of limiting current density (ilim) substantially 

depend on the amount and chemistry of surfactants [95,131– 

133]. The addition of amphiphiles alters significantly the 

properties of the external membrane/solution interface 

[134,135]. The effect of water redistribution within thin surface 

layers of membranes modified with surfactants has been found 

in [136] using the contact angle measurement and corresponding 

calculations of wetting energy. The adsorption of such 

compounds on a membrane surface can, in principle, favor the 

decrease as well as the increase of the limiting current compared 

to that for non-modified membrane in the NaCl standard 

(Fig. 22). We now have an original “scaling bar” based on 

Fig. 22. Current–voltage characteristics of (1, 3, 5) MK-40 and (2, 4, 6) MA-41 

ion-exchange membranes in (3, 4) 0.05 M NaCl solution and in the same 

solution containing various organic surfactants: (1, 2) camphor, (5) tetrabutylammonium 

iodide, and (6) sodium dodecyl sulphate. 


doi:10.1016/j.cis.2008.01.002

Fig. 23. Schematically drawn structure of a membrane/solution interface with 

adsorbed camphor. The drawing illustrates an effect of adsorbed substance on 

the diffusion layer thickness (from δ′ to δ″). 

limiting current values in the current–voltage curves that helps 

to evaluate the activity of organic surfactants in membranes 

[95,131]. 

The presence of organic counter-ions decreases the value of 

ilim and diminishes the slope of ohmic portion of the CVC curve 

with respect to x axis. This is so, because the interactions 

between surfactants and ion-exchange membranes are accompanied 

by the Coulomb's forces thereby increasing the membrane 

resistance. The continuous loss of i lim observed in a 

course of membrane saturation with organic ions is related to 

electrostatic shielding effect. The membrane selectivity however 

decreases at large θ values and in surfactant solutions 

concentrated over CCM threshold. This selectivity loss translates 

into degeneration of the CVC dependencies, which become 

linear [137]. 

The organic counter-ion can be immobilized in a membrane 

either at the equilibrium [72,95,135] or under applied electrical 

field [135,138]. The degree of membrane saturation might be 

controlled through changing the time, for which the membrane 

is exposed to surfactant solution, or by altering the amount of 

electrical charge transferred through the membrane. The chemistry, 

geometry and activity of organic ions contribute significantly 

to the electrochemical response of modified membranes; 

for instance, the measured values of the limiting current are 

different in a presence of TBA + and DDS − ions, respectively. 

Some substances cause, however, a significant increase in the 

ilim (Fig. 22). These substances belong to the class of camphorlike 

compounds (non-electrolyte) with high attraction constant 

[131,133,139]. Camphor itself is capable of assembling into 2D 

“islands” (or layers) on a membrane surface (Fig. 23). 

The role of the membrane surface on the coupled effects of 

concentration polarization remains an open question [134,140– 

145]. Nevertheless, modern physical methods confirmed that 

chemical and mechanical modification of the membrane surface 

changed its properties and behavior [124,143]. The cluster-like 

adsorption of camphor molecules on membrane surfaces results 

in strong electrical heterogeneity and, consequently, in hydrodynamic 

instability at the interface (Fig. 23). These effects are 

responsible for corresponding decrease in thickness of diffusion 

layer [146] that favors the enhancement of mass transport. 



These effects (so-called the Marangoni–Gibbs effects) are a 

well-known phenomena for the mercury electrode system 

[147,148]. We note, however, that the adsorption of camphor 

molecules on a polymer surface leads to the formation of specific 

discrete layer, which dimensions are comparable to those 

of electrical double layer. 

To establish the relationship between CVC parameters and 

physicochemical properties of membranes, we studied the 

properties of different MF-4SK membranes. Several methods 

were used to modify membranes: 

(a) various chemical pre-testing protocols, 

(b) immobilization of tetrabutylammonium cations, 

(c) polymerization of aniline in perfluorinated matrix. 

The shape of CVC curves and the value of ilim of MF-4SK 

membranes are both sensitive to pre-testing treatment protocol 

(Fig. 24). Thermal pretreatment causes an increase in i lim while 

the potential corresponding to the transition into the overlimiting 

state decreases. Several factors can affect the limiting 

current. Specifically, the water content increases in membranes 

after thermal processing that, in turn, induces an increase in 

conductivity and diffusion permeability [47]. Backward diffusion 

of the electrolyte solution can increase the ilim value in 

accordance with the following equation [149]: 

ilim ¼ DcF 

t⁎ ð i tiÞd 

þ P⁎cF t⁎ : ð12Þ 

ð i tiÞl 

where l is the membrane thickness, δ is the thickness of 

diffusion layer. 

The decrease in overlimiting potential is directly related to 

increased amount of water in the membrane. The data obtained 

with porosimetry method indicate that the number of pores with 

radii more than 100 nm is about 38% greater in thermally- 

Fig. 24. Current–voltage curves of MF-4SK membrane in 0.05 М HCl solutions 

after different pre-testing treatments: (1) thermal pretreatment and (2) salt 

pretreatment. 


doi:10.1016/j.cis.2008.01.002 

17

treated membrane compared to that in membranes after the 

treatment with salt. These cavities in membrane material 

provide a free volume for unbound water which readily dissociates 

under applied electrical field. 

The current–voltage characteristics of the MF-4SK membranes 

variously saturated with the TBA + ions are represented 

in Fig. 25a. An increase in saturation degree θ results in the 

decrease in limiting current by two orders of magnitude. The 

slope of ohmic portion with respect to the x axis in CVC curve 

is also decreased thus pointing to the loss of the conductivity. 

Fig. 25b demonstrates the dependences of the limiting current, 

water transport number and conductivity on the saturation 

degree. The specific conductivity values obtained graphically 

from the ohmic portion of the curves correlate well with those 

measured by the contact technique using the alternating current. 

The conductivity decreases with the increasing θ (other memrane 

properties changes similarly) and the transition to the nonconducting 

state occurs at the θ=0.7. The i lim value decreases 

abruptly and the membrane becomes electrochemically inactive. 

Therefore, there is a clear percolation-overlimiting transition 

correlation in the perfluorinated MF-4SK membranes 

containing TBA + ions. Both effects are firmly related with the 

polymer dehydration induced by the immobilization of TBA + 

ion in the membrane cavities. The standard porosimetry results 

(Fig. 5) confirmed this suggestion. The change in saturation 

degree also causes the decrease in potential of overlimiting 

conductivity. This is so, because the TBA + ions act as catalytically 

active nitrogen-containing centers that form bipolar 

contacts [123]. The more pronounced transition of the system 

into the overlimiting state might arise because of the electroconvection 

resulted from electrical heterogeneity of the membrane 

surface [118,119]. 

The development of the polymers with mixed electron-ion 

conductivity is important for fabricating technologically rele- 



vant materials (e.g. those for electrocatalysis, fuel cells, sensors 

etc.) [150–152]. Electrochemical behavior of composite membranes 

(MF-4SK/polyaniline) has been investigated by the 

membrane voltammetry [153]. The shift of overlimiting transition 

potential was clearly observed Fig. 26). In this particular 

case, the slopes of the ohmic portion of CVC curve and the ilim 

values are similar for the common membranes and composite 

ones. 

The observed effect might be attributed to the specific energetic 

state of water in the membrane structure. The experimental 

data obtained with standard porosimetry and those found in 

literature suggest that the water is immobilized in the structural 

cavities of a composite. The aromatic nature of polyaniline 

chains promotes the assembling of water molecules into clusters 

that inhibits the proton transfer. The polyaniline forms nanosize 

interpolymer complexes with ion–dipole associates in these 

cluster zones. This change in energetic state of water (water 

dissociation), most likely, hinders the transition of the system 

into the overlimiting state. The CVC parameters as well as all 

electrotransport properties therefore depend on the state of 

water. 

The analysis of electrochemical behavior of MF-4SK/ 

polyaniline composites evidences the enhanced properties of 

this material when compared with common membrane matrices 

[154–156]. The composite membranes have high specific conductivity 

and selectivity and low diffusion permeability; the 

water immobilized in the interpolymer network, which is 

formed in such materials, is stable with respect to dissociation 

under applied electrical field. These properties make composites 

operationally more efficient for fuel cell systems and separation 

processes than the comparable non-composite systems. 

In summary, we believe, that the membrane voltammetry 

method has conclusively proven very useful for membrane 

testing and characterization. 

Fig. 25. Current–voltage curves for MF-4SK membrane with varied saturation with TBA + ions measured in 0.05 M HCl solution (a). Saturation dependences of 

dimensionless parameters: (1) water transport number, (2) density of limiting current, (3) conductivity from CVC (DC), and (4) conductivity under AC (b). (The 

parameter f refers to the membrane property after saturation with the TBA + ions and parameter f0 refers to the same characteristics of initial membrane): a) (1) θ=0, 

(2) θ=0.2, (3) θ=0.3, (4) θ=0.5. 


doi:10.1016/j.cis.2008.01.002

4.7. Theoretical modeling of electrotransport in heterogeneous 

membranes 

The behavior of membranes operating in real separation 

processes is influenced by the electric, concentration, and temperature 

gradients when the circulating flows of electrolyte 

solution pass through the inter-membrane space. Theoretical 

models of the electrotransport processes in membranes should 

therefore rely on an approach provided by the nonequilibrium 

thermodynamics which define the fluid flows as linear functions 

of generalized forces. Nonequilibrium membrane processes are 

accompanied by various cross-effects and associated phenomena 

(electro-, thermo-, barodiffusion, electro- and thermoosmosis 

etc.) [4,17,106,109,110,157–160]. The well-known Nernst– 

Planck equation 

ji ¼ L ⁎ i dA i=dx ð13Þ 

can be used as the differential transport equation for i-type ions 

that move under the electrochemical potential gradient (dµi/dx). 

The ji characterizes the ionic flow and the Li ⁎ is the coefficient 

of proportionality between the ionic flow and the force acting on 

the ion. Phenomenological coefficients Li ⁎ are the electrodiffusion 

characteristics of the ion mobility in heterogeneous 

medium. It has been suggested [161] that these factors are the 

functions of conducting properties of membrane “pseudophases” 

and of membrane geometry. 

The theoretical analysis of some known equations (Kedem– 

Katchalsky, Onsager and Nernst–Planck) in [13,17] evidences 

that the consideration of the structural heterogeneity of membranes 

is more important with respect to estimating transport 

values than the calculations using cross-coefficients — a traditional 

nonequilibrium thermodynamic approach to the description 

of trans-membrane transport [71,107]. 

The studies on the transport properties vs solutions concentration 

that have been carried out for various membranes 

Fig. 26. Current–voltage curves of (1) MF-4SK membrane and composites 

formed from MF-4SK and polyaniline in the emeraldine form (2) and overoxide 

form (3) measured in 0.025 М H2SO4 solution. 



supported the assumption that the heterogeneity of membrane 

structure translated into the specific character of these dependences 

[17,19,65,71,84,162,163]. The Nernst–Planck equation 

was therefore extended to account for Li ⁎ coefficients — the 

functions dependent on the solution concentration. The mathematical 

form of the equation remains unaltered, while the Li ⁎ 

coefficients are now considered as the kinetic electrodiffusion 

characteristics in the structurally heterogeneous medium. 

The closed system of the Nernst–Planck equations defines 

each ion with a charge z i participating in the ion transport and 

accounts for electroneutrality of membrane system. The 

theoretical model therefore relies on the determination of the 

flow values at certain parameters and boundary conditions in 

the system [149,164–167]. When Li ⁎ coefficients are defined as 

functions of concentration, they account for the structural properties 

of material. The values of Li ⁎ coefficients are determined 

from the experimental data on the concentration dependences 

of membrane conductivity (κ m) and salt diffusion flow ( j). The 

κ m−c and j−c dependences represent the power functions: 

jm ¼ Ac a 

ð14Þ 

jm ¼ Bc b : ð15Þ 

The parameters A, a, B and b are constants that depend on a 

membrane morphology and solution type. The electrodiffusion 

coefficients are expressed as follows [149,166]: 

L ⁎ ðÞ¼ c 

Bblzþ 

RTðzzþÞz cb 

ð16Þ 

L ⁎ þ c 

A 

ðÞ¼ 

z2 ca 

ð17Þ 

2 

þF 

where l is the membrane thickness. 

This approach, which is based on concentration dependences 

of electrodiffusion coefficients of counter-ions and co-ions, 

provides an adequate description of electromasstransfer in the 

membrane system. The conductivity values, differential coefficients 

of diffusion permeability (P⁎) and the transport numbers 

of ions at certain concentration (с) are calculated with the 

following equations [149,166]: 

jm ¼ F 2 z 2 þL⁎þ c ðÞþz2L ⁎ ðÞ c 

ð18Þ 

P ⁎ ¼ 

RTðz zþz c 

zþÞ 

t ⁎ i ¼ 

1 

z 2 þ L⁎ þ c 

ðÞþ 

1 

z2 L⁎ ðÞ c 

ð19Þ 

z2 þL⁎þ c ðÞ 

z2 þL⁎ þðÞþz c 2 L⁎ : ð19:aÞ 

ðÞ c 

This approach has been recently corrected for a non-ideality 

of solution [168]. The authors suggested a set of equations to 

calculate the electrodiffusion coefficients L i ⁎ (с) from the data on 

κ m and P⁎ at randomly varied concentrations. 


doi:10.1016/j.cis.2008.01.002 

19

However, the model based on the set of physically relevant 

parameters instead of concentration dependences of electrodiffusion 

coefficients L i ⁎ of the counter-ions and co-ions remains 

to be developed. In this respect, the charged membranes 

are now generally considered as the phase-separated systems in 

which transfer processes occur. The membrane harbors several 

structural fragments which number depends on the preparation 

protocol. 

For instance, the heterogeneous polymeric compositions for 

electrodialysis consist of ion-exchange resin, reinforcing polyethylene 

or polyvinylchloride and equilibrated solution distributed 

in membrane cavities. Perfluorinated ion-exchange 

membranes contain the hydrophobic matrix, charged groups 

and chains of side segments. The hydration of charged entities 

promotes the formation of ion-water clusters connected by 

narrow channels [8,53,78,169]. To model transfer phenomena 

in such heterogeneous structures, the number of structural 

elements is commonly considered as a single conducting phase 

[73,170,171]. The combination procedure varies in different 

studies. In some cases, the certain volume fraction of polymer is 

defined as a portion impermeable for the diffusion of particles 

[17,172]. The so-called winding factor is used to estimate the 

decrease in diffusion coefficient in a membrane when compared 

to that in a free solution. However, this model considering 

separate conducting and non-conducting phases helps to understand 

the decreasing conductivity alone, while the dependences 

of these properties on concentration of equilibrated solutions 

remain largely uncharacterized. 

The theory of generalized conductivity for heterogeneous 

system [161,173] provides a basis for quantitative characterization 

of the electrochemical properties of membranes. The effective 

properties are defined as the characteristics of separated 

phases by the interpolating function (Eq. (21)): 

L ⁎ m ¼ f1L a 1 þ f2L a 2 

1=a 

ð20Þ 

where Lm is the coefficient of generalized conductivity (electroconductivity 

or diffusion permeability coefficient); L 1, L 2 are 

the properties of individual phases; f 1 and f 2 are the volume 

fractions of phases; α is the parameter characterizing the arrangement 

of phases in the material (α=+1 for parallel orientation 

of conducting phases, α=−1 for serially orientated 

phases). The parameters f and α are related with the geometry of 

the dispersion. 

The structure of two conducting “pseudophases” is dictated by 

the mechanism of conductivity. The hypothetical phase I 

comprises: (1) gel phase with high conductivity, that is, gel/ 

cluster structural fragments representing the ion–dipole associates 

fixed ion–counter-ion, and (2) inert, uncharged fragments 

(polyethylene and reinforcing material in heterogeneous membranes 

or microcrystallites of fluorocarbon chains and hydrophobic 

segments in the perfluorinated membranes). The ion 

transport in phase I is a flow of counter-ions. The volume fraction 

of this phase in the swollen membrane is equal to f 1=V 1/V sw.m. 

Phase II represents an internal “free” solution distributed in 

structural cavities and pores of the swollen membrane. This 

solution is not influenced by the local electrical fields of charged 



polymer matrix. Both cations and anions are responsible for the 

charge transfer in phase II. The volume fraction of this phase is 

defined as f 2=V II/V sw.m. Consequently, both phases constitute a 

single integrated conducting structure ( f1+f2=1). 

When influenced by electric potential and concentration 

gradients, the properties of such system depend on the interplay 

between the spatial arrangement of both phases and the directions 

of electrical current or diffusion flow. The conducting 

phases can be assembled in parallel, serially or chaotically; the 

model accounts for the phase arrangement by using a specific 

parameter α. Eq. (20) represents the interpolation between the 

conductivity of the selected pseudophases. 

The first model representations of ion-exchange membrane as a 

biphase system have been published in the monographs [174,175] 

aimed to interpret correctly the conductivity of heterogeneous 

membranes. Similar approach has been used to describe conducting 

properties of the perfluorinated membranes with cluster 

morphology and those of membranes from aromatic polymers 

[41,43,71]. Fig. 27 shows the two-dimensional structural image of 

the membranes applied in electrodialysis. The volume fraction of 

phase I and an equilibrium solution (phase II) are also indicated. 

In the case of 1:1 electrolyte, the resulting membrane conductivity 

and diffusion permeability coefficients can be expressed 

as follows: 

jm ¼ f1j a iso þ f2j a 1=a ; ð21Þ 

P ⁎ ¼ f1ðGCÞ a þf2D a 

½ Š 1=a : ð22Þ 

Here κ iso and κ are specific conductivities of the solution 

and of phase I, respectively; c¯ −, c are co-ions concentrations in 

Fig. 27. Schematically drawn structure of a heterogeneous electrodialytic cationexchange 

membrane. 


doi:10.1016/j.cis.2008.01.002

Fig. 28. The data from the computer processing of the dependences of 

dimensionless characteristics Y and X at various solution concentration for 

membranes (1) Neosepta CL-25T, (2) MK-40, (3) SPEEK, (4) SPS, (5) CR 67- 

HMR-412, (6) MF-4SK (7) Nafion-117: ● — electroconductivity data 

(Yj ¼ jm 

jiso ; Xj ¼ j 

jiso ), ○ — diffusion permeability data (YP ¼ P⁎ 

Gc ; XP ¼ D 

Gc ). 

phase I and in solution, respectively; D is the electrolyte diffusion 

coefficient. G is the complex parameter [176] which 

contains the Donnan constant (kD), the co-ion diffusion coefficient 

in the phase I (D¯ −) and the membrane exchange capacity 

P 

G ¼ kDD 

=Q: ð23Þ 

The G parameter plays the same role in the diffusion as does 

the κ iso parameter the conductivity. The κ iso is a characteristic 



of the counter-ions transfer and the G is that of the co-ions 

transport in phase I. 

Using the conductivity and diffusion permeability functions 

normalized on the corresponding characteristics of phase I, the 

(21) and (22) equations can be generalized and represented as 

uniform function [177], 

Y ¼ f1 þ f2X a 

½ Š 1=a : ð24Þ 

For conductivity, we have the following equations: 

Yj ¼ j⁎ 

juMj 

; Xj ¼ j 

juMj 

; ð25Þ 

and for diffusion permeability, the relationships are expressed as 

follows: 

Yp ¼ P⁎ 

Gc ; Xp ¼ D 

: ð26Þ 

Gc 

These Eqs. (24)–(26) confirm the close similarity between 

the conductivity and diffusion transport. 

Fig. 28 shows the dependencies of the Y-function on the X 

for the number of ion-exchange membranes in logarithmic 

coordinates. The shape of the curves depends on some 

transport-structural parameters (TSP): f, κiso, α and G. 

To describe electromasstransfer in membrane systems correctly, 

the model must account for the electroosmotic phenomena. 

The transport of water is expressed by the dynamic 

transport numbers of water and ionic flows. Resulting set of 

TSP contains also the dynamical hydration characteristics of 

ions h+ and h− [107,178]. Membrane characterization based on 

Fig. 29. Scheme of calculation procedure for transport-structural parameters of ion-exchange membrane. 


doi:10.1016/j.cis.2008.01.002 

21

Fig. 30. Dependencies of the transport-structural parameters on the water capacity for the set of membranes MF-4SK: κiso (a), G (b), f2 (c), α (d). 

concentration dependencies of specific conductivity, salt diffusion 

flux and electroosmotic permeability has been described in 

details in [179,180]. Fig. 29 represents a scheme for the determination 

of TSP-set of ion-exchange membrane. We note that 

the approach discussed here is based on the large set of our 

experimental data obtained for various membranes. 

The aforementioned method has been recently used to test 

new membrane materials. In [82], the polyamidoacid membranes 

have been characterized using f2 and κiso, parameters; 

similarly, the membranes fabricated from fibrous materials 

[181] and the heterogeneous membranes pre-treated with polycharged 

ions have been studied [182]. The behavior of MF- 

4SK/polyaniline composites, which comprises the properties of 

ionic and electronic conductors, has been broadly investigated 

with the TSP-set [155]. Yet another approach has been suggested 

in [183,184] to simplify calculations. 

The TSP-set is sensitively influenced by an average content 

of water and its distribution within the membrane. The dependences 

of the TSP of perfluorinated sulphocationic MF-4SK 

membranes on the water capacity are shown in Fig. 30. The 

water content was altered by changing the type and concentra- 



Fig. 31. Dependence of transport-structural parameters ( f2 and α) on a 

membrane structure. 


doi:10.1016/j.cis.2008.01.002

tion of base in a course of alkaline saponification of sulphonyl 

fluoride groups [85]. An increase in the water content enhances 

the transport of counter-ions (Na + ) and that of co-ions (Cl − ) 

through phase I; these types of transport are related with the κiso 

and the G parameters, respectively (Fig. 30). Importantly, the 

enhanced transfer of co-ions can be accompanied by the loss of 

selectivity (Fig. 30b). 

In our model, the f2 parameter changes in the same manner 

as the κ iso and G parameters (Fig. 30c), while the dependence of 

the α parameter on the n m (Fig. 30d) exhibits an opposite trend. 

This behavior suggests an evolution of structural morphology 

from more or less regular arrangement to the chaotic one 

(α→0). The relationship between f and α parameters illustrated 

by Fig. 31 has been established using the database of the 

Membrane Materials Laboratory of Kuban State University. 

5. Conclusions 

This review summarized the state of field and general 

understanding of the physicochemical behavior of charged ionexchange 

membranes for a wide range of applications. In particular, 

we emphasized some of the important questions regarding 

structural and dynamic properties of ion-exchange 

membranes and discussed the theoretical and experimental elements 

that expanded the commonplace representation of these 

systems. 

Charged polymers and composite materials are the essential 

components of many developments related to rapidly advancing 

and demanding technological fields (fabrication of fuel cells, 

water purification and separation, analytical and medical 

sensing etc.). The outstanding progress in polymer synthesis 

during past decades considerably expands the types of materials 

used in electrochemical devices and the variety of functions 

exhibited by membrane structures. The development of common 

approach to optimize membrane structure and composition 

and to test its operating properties is therefore a significant 

challenge for modern analytical chemistry and material science. 

One strategy that provides a convenient experimentally-based 

data-set for comprehensive and reliable analysis of membrane 

properties has been described here in details. Further work will 

be, however, needed to generalize membrane handling protocols 

and to find a common guideline for rationalizing the diversity 

of structures used in electrochemical processes. 

Future progress of the technologies utilizing ion-exchange 

membranes will also depend on theoretical advancing the 

understanding of structural and dynamic aspects of existing 

systems and new types of membrane materials, especially those 

representing nanocomposites. The theoretical consideration of 

nanoscale structures must account for the interactions and 

processes at the multiple inner and external interfaces formed in 

hybrid (organic/inorganic) composite membranes. 

We believe that our approach for theoretical modeling of 

electrotransport in membranes makes it possible to characterize 

adequately the relationship between the structure and electrochemical 

properties of membrane materials. In this method, which 

is based on nonequilibrium thermodynamics consideration, the 

membrane structure is modeled with two conducting pseudo- 



phases thus accounting for different mechanisms of ion transport. 

The structure–properties correlations and the proposed mechanisms 

of conductivity of heterogeneous membranes rely on the 

hypothesis that the phenomenological coefficients are the functions 

of polymeric structure. The model enables the characterization 

of electrochemical processes with a set of structurally-related 

parameters and provides a reasonably clear understanding of 

subtle interplay between the colloidal-scale structure and macroscopic 

properties of various membrane systems. 

Finally, we believe, that the development of new nanostructured 

materials will significantly encourage the theoretical 

and experimental progress in this field in coming years and that 

it will have a large impact on the way the research on ionexchange 

materials approach technologies. 

List of symbols 

A Energy of membrane-bonded water 

c Concentration of electrolyte solution 

c¯ − Co-ion concentration in phase I 

cs Amount of TBA + ions on the internal membrane surface 

Di Ion diffusion coefficient in solution 

D¯ − Co-ion diffusion coefficient in phase I 

F Faraday's constant 

f1 Volume fraction of phase I 

f2 Volume fraction of the inner solution phase 

G Gnusin's parameter, characterizing the diffusion properties 

of phase I 

h+ Dynamical hydration numbers of counter-ions 

h− Dynamical hydration numbers of co-ions 

i Current density 

ilim Electrodiffusion limiting current density 

ji Density of ionic flow 

jm Density of salt diffusion flow 

jw Density of water flow across membrane 

j +w Density of water flow transferred by cations 

Density of water flow transferred by anions 

j−w 

kD 

Donnan constant 

L Distance between the fixed groups 

Li ⁎ Phenomenological coefficients (electrodiffusion characteristics 

of the ion mobility in heterogeneous 

L m 

membrane) 

Membrane generalized conductivity coefficient (electroconductivity 

or diffusion permeability coefficient) 

L1, L2 Conducting properties of individual phases 

l Membrane thickness 

NA Avogadro's constant 

nm Membrane water capacity 

P⁎ Differential coefficient of diffusion permeability 

Integral coefficient of diffusion permeability 

Р m 

Q Ion-exchange capacity (IEC) 

Q org 

Ion-exchange capacity of membrane with respect to 

organic counter-ions 

q Amount of absorbed organic ions 

r Effective radius of pores 

S Area of the internal specific surface 

t Critical index of conductivity, or universal constant in 

the percolation theory 


doi:10.1016/j.cis.2008.01.002 

23

ti Transport number of counter-ions in solution 

ti⁎ Transport number of counter-ions in membrane 

t +app “Apparent” transport number of counter-ions in 

membrane 

tw Electroosmotic transport number of water 

V Relative water content 

Vm Molar volume of water 

W Electroosmotic permeability 

w Water content 

zi Ion charge 

α Parameter characterizing the spatial arrangement of 

membrane phases 

β Slope of the concentration dependences of the salt 

diffusion flow in logarithmic coordinates 

δ Diffusion layer thickness 

θ Membrane saturation with organic ions 

Θ Contact angle 

κ Conductivity of electrolyte solution 

κ0 Parameter of the percolation theory (conductivity) 

κm Conductivity of membrane 

κiso Conductivity of phase I and at isoelectroconductivity 

point 

κAC Conductivity measured under alternating current 

κDC Conductivity measured under direct current 

µ i Electrochemical potential 

π ±(c) Function accounted for non-ideality of equilibrium 

solution 

σ Surface tension 

ϕ Volume fractions of conducting phase in the polymer 

Critical value of volume fraction of conducting phase 

ϕk 

Acknowledgments 

We gratefully thank the Russian Foundation for Basic 

Research for the financial support (projects N 06-08-01424 and 

N 06-03-96675) and to Professor Victor Starov for the kind 

invitation in contributing to this special issue of the Journal. 

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