Membranes and Membrane Technologies

, Volume 1, Issue 3, pp 168–182 | Cite as

Transport Characteristics of Homogeneous and Heterogeneous Ion-Exchange Membranes in Sodium Chloride, Calcium Chloride, and Sodium Sulfate Solutions

  • V. V. SarapulovaEmail author
  • V. D. Titorova
  • V. V. Nikonenko
  • N. D. Pismenskaya


Structural (volume fractions of the gel phase and the intergel solution) and transport (electrical conductivity, diffusion permeability, transport numbers of counterions and coions) characteristics of cation-exchange (CMX, MK-40) and anion-exchange (AMX, MA-41) membranes in NaCl, CaCl2, and Na2SO4 solutions have been studied. The investigated membranes have the same chemical nature of the ion-exchange matrix and similar values of ion-exchange capacity, but they differ in the degree of heterogeneity and chemical nature of the reinforcing materials. The difference in the properties between heterogeneous (MK-40 and MA-41) and (conventionally) homogeneous (CMX and AMX) membranes is due to the fact that the heterogeneous membranes have macropores, whereas the homogeneous membranes do not have such pores. It has been shown that the largest macropores, which basically determine the high diffusion permeability of heterogeneous membranes, are formed at the boundaries of reinforcing fabric threads and the composite material. Regarding the influence of the electrolyte nature, the sorption of coions of the membrane gel phase (not containing macropores) is of primary importance; the sorption of coions, as well as diffusion permeability and the transport number of coions, increase in the order: 1 : 2 < 1 : 1 < 2 : 1, where the first numeral is the charge of the counterion and the second one is that of the coion. An important role, especially in the case of heterogeneous membranes, is played by the electrolyte diffusion coefficients in the electroneutral solution that fills the central part of meso- and macropores.


ion-exchange membranes structure electrical conductivity diffusion permeability selectivity 


By combining baromembrane and electromembrane technologies with classical separation methods, it is possible to obtain highly efficient process technological system for the decontamination of wastewater and recovery of valuable components from them, production of high-quality drinking water and water for irrigated agriculture in areas with insufficient natural precipitation, concentration of reverse-osmosis retentates, and other applications [1, 2, 3]. An important role in the implementation of such technological system is played by both pretreatment, during which most substances critical for fouling and scaling are removed [4], and the use of new configurations of membrane electrodialysis stacks [5], for example, those of electrodialysis metathesis [6, 7]. By using this new method, it is possible to avoid scaling during the processing of fairly concentrated multicomponent solutions, which usually contain scalant ions, such as Ca2+ and \({\text{SO}}_{4}^{{2 - }}\). The idea of this method is to use two compartments instead of a single concentration compartment, as in conventional electrodialysis. Singly charged cations and all anions are concentrated in one of these compartments, and singly charged anions and all cations, in the other. Thus, the contact of doubly charged cations and doubly charged anions, which leads to scaling, is excluded [6, 7]. Ion exchange membranes, IEMs that can provide high efficiency of electrodialysis metathesis should have relatively low cost and high selectivity for transport of singly charged ions, exhibit low permeability to coions and high electrical conductivity in solutions containing calcium cations and sulfate anions, demonstrate resistance to scaling, etc. The need to solve this complex task has stimulated studies on creating new membranes and improving commercially available membranes. An overview of the studies done in this field can be found in [8, 9]. Successful development of new membranes designed for use in fairly concentrated multicomponent solutions is impossible without an understanding of the structure–property relations of ion-exchange materials with regard to the transport of singly and multiply charged ions. A number of classical works have been devoted to this question; e.g., see [10]. The current state of research in this area is reflected in review papers [11, 12, 13]. Thanks to studies that have already been carried out, the selectivity of membranes (their ability to transfer counterions and interfere with the transport of coions) is known to be mainly determined by electrostatic interactions of ions with fixed groups of the membrane matrix and, to a lesser extent, steric factors including the degree of crosslinking of homogeneous ion-exchange materials and the hydration numbers of transported ions. The transport of multiply charged ions can be slower than that of singly charged ions as a result of both simultaneous electrostatic interaction with not one but also several fixed groups at once and the tendency of many multiply charged ions to form complex or weakly dissociating ion–dipole associates with fixed groups. At the same time, as noted in the review paper [11], there is still a lot of uncertainty in the understanding of the transport of multiply charged ions in ion-exchange and uncharged membranes.

Despite quite a large number of experimental studies on the transport of asymmetric electrolytes in membrane systems, the data that have been published are scattered. For example, only concentration dependences of the surface resistance of CMX and AMX membranes in NaCl, CaCl2, and Na2SO4 solutions are presented in [14]. Papers that simultaneously provide information about the diffusion, electrical conductivity and selectivity of ion-exchange membranes are the exception rather than the rule. Among them, it is worth to mention the papers [15, 16], in which the experimental concentration dependences of the specific electrical conductivity and diffusion permeability of IEMs for a wide range of symmetric and asymmetric electrolytes are reported. However, Zhelonkina and Shishkina [15] studied only heterogeneous cation- and anion-exchange membranes. Demina et al. [16] investigated homogeneous and heterogeneous cation-exchange membranes made of ion-exchange materials with different chemical structures; these membranes differed markedly in ion-exchange capacity. In theoretical studies that have been actively developing recently [17, 18], ideally homogeneous membranes are considered. For example, Filippov and coauthors [18], using calculations based on such a model, showed that the diffusion permeability of IEM in concentrated external solutions of asymmetric electrolytes having a doubly charged counterion and a singly charged coion (2 : 1 electrolyte) is higher than in a 1 : 2 electrolyte. In addition, the possibility of the appearance of maxima in the concentration dependences of the diffusion permeability of IEM in the region of moderately dilute solutions was predicted. To explain the differences in the behavior of MK-40, which has macropores [19], and a homogeneous Nafion-425 membrane in solutions of various electrolytes, De-mina et al. [16] attracted the microheterogeneous model [20, 21]. They found that the nature of the coion has a determining effect on the diffusion permeability of the MK-40 membrane, whereas this parameter in the case of Nafion-425 depends on both the coion and counterion natures. The vast majority of researchers determine the membranes selectivity using the EMF measurement technique [22, 23], by which only the apparent transport numbers of counterions including water transport numbers can be obtained [24, 25], or use the Hittorf method [26], which gives effective transport numbers depending on the concentration of the solution on both membrane sides [27]. We are aware of only few works in which the true transport numbers of counterions in membranes are presented [24, 25, 27, 28], but they have been determined only in NaCl [24, 25, 27, 28] or KCl and LiCl [25] solutions.

The aim of this work is to compare the structural (volume fractions of the gel phase and the solution in intergel spaces) and transport (specific electrical conductivity, diffusion permeability, transport numbers of counterions and coions) characteristics of cation-exchange and anion-exchange membranes in NaCl, CaCl2, and Na2SO4 solutions. The objects chosen for the study were membranes with the same chemical nature of the ion-exchange matrix, as well as similar values of exchange capacity, and differing only in the degree of heterogeneity and chemical nature of reinforcing materials.


2.1 Membranes

Homogeneous membranes CMX and AMX, manufactured by Astom (Japan), and heterogeneous membranes MK-40 and MA-41, manufactured by Shchekinoazot (Russia), were chosen for research. The ion-exchange matrix of all these membranes is made of a styrene–divinylbenzene copolymer. Both of the cation-exchange membranes (CEMs) CMX and MK-40 contain fixed sulfo groups as functional groups [29, 30]. The fixed groups of the anion-exchange membranes (AEMs) AMX and MA-41 are quaternary ammonium groups and a small amount of secondary and tertiary amino groups [29, 30].

Depending on their preparation procedure and structure, IEMs are conventionally divided into homogeneous and heterogeneous [10]. Homogeneous membranes are obtained by introducing functional ion-exchange groups directly into the structure of the polymer framework. This leads to a relatively uniform distribution of fixed charged groups throughout the membrane. Heterogeneous membranes are obtained by mixing a crushed ion-exchange resin with a polymeric binder. This leads to a structure characterized in that ion-exchange groups, occurring only inside resin particles, are very unevenly distributed throughout the bulk of the membrane.

Homogeneous IEMs are made by the paste method: reinforcing polyvinyl chloride (PVC) fabric (Fig. 1b) is introduced into the membrane at the step of producing a composite material from a paste, which consists of a PVC powder and the monomers styrene and divinylbenzene [31]. When these monomers are copolymerized, a composite ion-exchange material is formed, in which PVC particles are incorporated; the diameter of these particles does not exceed 100 nm (Fig. 1a). There is strong adhesion between the ion exchange material and the reinforcing cloth, which is due to the fact that PVC is included in both materials. This preparation procedure eliminates the possibility of the formation of macropores (larger than 200 nm) in the bulk of homogeneous membranes. Although such membranes are called homogeneous [32, 33], their structure is heterogeneous at the nanoscale level and includes two phases of different polymer materials, as well as reinforcing cloth, with fibers about 30 μm in diameter (Fig. 1b).

Fig. 1.

SEM images of (a, c) surfaces and (b, d) sections of (a, b) a homogeneous CMX membrane and (c, d) a heterogeneous membrane MK-40.

Heterogeneous membranes are made by hot rolling of milled ion-exchange resins KU-2-8 (MK-40) and AV-17-8 (MA-41) and a high-density polyethylene powder. Then reinforcing nylon mesh is introduced (Fig. 1d) using the hot pressing method [30]. The size of ion-exchange resin grains ranges from 5 to 50 μm. The adhesion between individual resin particles, polyethylene, and the reinforcing cloth is low, resulting in gaps that form macropores (about 1 μm in size) when the membrane contacts the solution [24]. The resin particles are quite evenly distributed throughout the IEM (Fig. 1d); their tops extend beyond the polyethylene-coated surface of membranes (Fig. 1c). Some of the characteristics of the membranes under investigation are presented in Table 2, Section 3.1.

Table 1.  

Some characteristics (at 25°C) of ions included in the studied solutions. The data are borrowed from [34, 35]


Crystallographic radius, Ǻ

Stokes radius, Ǻ

Hydration energy,

kJ mol−1

Hydration number

Diffusion coefficient at infinite dilution D0 × 109, m2 s–1



















\({\text{SO}}_{{\text{4}}}^{{{\text{2}} - }}\)






Table 2.  

Some characteristics of the investigated ion-exchange membranes




Ion-exchange capacity,

mmol \({\text{cm}}_{{{\text{sw}}}}^{{ - 3}}\)

Water content*, Н2О \({\text{g}}_{{{\text{sw}}}}^{{ - 1}},\) %

Concentration of fixed groups**,

mmol cm−3 H2O

Volume fraction of intergel solution, f2

Specific conductivity of the gel phase, \(\bar {\kappa }\), mS cm−1







Cation-exchange membranes


175 ± 5

1.86 ± 0.05

22 ± 2









520 ± 20

1.52 ± 0.08

30 ± 2








Anion-exchange membranes


125 ± 5

1.22 ± 0.05

16 ± 2









450 ± 50

1.18 ± 0.06

35 ± 2








 * Swollen membrane equilibrated with 0.02 eq dm–3 NaCl solution. ** The number of millimoles of fixed groups per 1 cm3 of water in the membrane.

2.2 Chemicals

The chemicals used in experiments were distilled water (electrical conductivity 1.1 ± 0.1 µS cm−1, pH 5.5, 25°С), solid NaCl and Na2SO4 of the analytical grade, and chemically pure solid CaCl2 (manufactured by Vekton). The pH values of solutions prepared from these salts were 5.4 ± 0.3 (NaCl) and 5.6 ± 0.3 (Na2SO4). In the case of CaCl2 solution, which was prepared from the material of the chemically pure grade, the pH of the solution increased with increasing salt concentration from 6.3 (0.02 mol dm−3) to 9.0 (1.0 mol dm−3). Some characteristics of ions present in the test solutions are given in Table 1.

2.3 Membrane Characterization Methods

Prior to experiments, all membrane samples underwent standard salt treatment in NaCl solutions [31].

Water content was found by hot air drying [24]. Before the experiment, the samples were equilibrated with 0.02 M electrolyte solution at 25 ± 1°С for 24 h and removed from this solution after equilibration; the liquid film on the ends and surfaces was removed with filter paper. The masses of wet and dry samples (msw and mdry, respectively) were obtained using an Ohaus MB25 moisture analyzer. The evaporation of water was carried out at a temperature of 50°C to a constant mass of the sample.

Water content W, % was found according to the formula:

$$W,\% = \frac{{{{m}_{{{\text{sw}}}}} - {{m}_{{{\text{dry}}}}}}}{{{{m}_{{{\text{dry}}}}}}} \times 100\% .$$

Total ion-exchange capacity(Qsw) was determined using the static method [24]. Membrane samples were preliminarily converted into the OH (AEM) or the H+ (CEM) form and washed in distilled water. The pre-prepared swollen membrane samples of about 2.0 g in mass (msw) were finely sliced into pieces and placed in conical flasks. In the case of AEM, a 0.10 M hydrochloric acid solution in an amount of 100.00 cm3 was added to these flasks. In the case of CEM, the same amount of sodium hydroxide solution with the same concentration was added. Then, the membranes were held in these solutions with periodically shaking until equilibrium was reached (24 h). After that, an aliquot of the solution over the membrane was taken (25.00 cm3) and titrated with a 0.10 M NaOH (AEM) or HCl (CEM) solution in the presence of a mixed indicator (3–5 drops). Titration was performed using a METTLER TOLEDO EasyPlus titrator with the output of the titration results to a computer.

The total ion-exchange capacity Qsw, mmol \({\text{g}}_{{{\text{sw}}}}^{{ - 1}}\) of the membrane was calculated by:
$${{Q}_{{{\text{sw}}}}} = \frac{{(100 - 4{{V}_{1}})}}{{10{{m}_{{{\text{sw}}}}}}},$$
where V1 is the volume of titrant consumed for titration, cm3.

The calculation of the total ion-exchange capacity of the ion-exchange membranes in mmol \({\text{g}}_{{{\text{dry}}}}^{{ - 1}}\) (Qdry) took into account the water content of the membrane W:

$${{Q}_{{{\text{dry}}}}} = \frac{{(100 - 4{{V}_{1}})}}{{10{{m}_{{{\text{sw}}}}}(1 - W)}}.$$
Concentration of fixed groups was determined using data on the ion-exchange capacity and water content [17]:
$$C_{A}^{{m,{\nu }}} = \frac{{{{Q}_{{{\text{dry}}}}}{{\rho }_{w}}}}{W},$$
where Qdry is the total ion-exchange capacity of the air-dry membrane (mmol \({\text{g}}_{{{\text{dry}}}}^{{-{\text{1}}}}\)), ρw is the density of water (\({{{\text{g}}}_{{{{{\text{H}}}_{{\text{2}}}}{\text{O}}}}}\) cm−3), and W is the membrane water content (\({{{\text{g}}}_{{{{{\text{H}}}_{{\text{2}}}}{\text{O}}}}}\)\({\text{g}}_{{{\text{dry}}}}^{{-{\text{1}}}}\)).

Thicknessof ion-exchange membranes (dm) was measured with a MKTs-25 0.001 precision digital micrometer accurate to 1 μm with an error of 0.1 μm. The membrane thickness value was obtained by averaging the results of 10 measurements made at various points of the sample under study.

Surface imaging of swollen IEMs was performed using a SOPTOP CX40M optical microscope (China) equipped with a digital eyepiece USB camera (5×, 10×, 20×, and 50× magnifications).

Morphology of the surface and sections of air-dry IEMs was studied using a LEO (ex LEICA, ex CAMBRIDGE) Type S260 scanning electron microscope. To improve the quality of the obtained images, air-dry membrane samples were coated with a thin layer of platinum nanoparticles.

Electrical conductivity of IEMs (κ*) was determined by a differential method using a clip cell [36, 37] and a MOTECH MT4080 immitance meter (Motech Industries Inc., Taiwan) at an ac frequency of 1 kHz. All samples were studied in 0.02–1.0 mol eq dm–3 solutions of NaCl, CaCl2, and Na2SO4, starting from the lowest concentration.

The conductivity of the membranes (κ*) was found by the formula:
$${\kappa *} = \frac{{{{d}_{{\text{m}}}}}}{{{{R}_{{{\text{m}} + {\text{s}}}}} - {{R}_{{\text{s}}}}}},$$

where Rm+s is the resistance of the membrane in solution and Rs is the resistance of the solution alone.

The obtained concentration dependences of electrical conductivity were processed using the microheterogeneous model [21] to determine the volume fractions of the gel phase (f1) and the phase of the electroneutral solution that fills the intergel spaces (f2) of the investigated membranes and to estimate the electrical conductivity of the gel phase \(\left( {{\bar {\kappa }}} \right){\text{:}}\)
$${\kappa * = }{{{\bar {\kappa }}}^{{{{f}_{{\text{1}}}}}}}{{{\kappa }}^{{{{f}_{{\text{2}}}}}}},$$
where κ is the specific electrical conductivity of the “intergel” solution, assumed to be equal to that of the external equilibrium solution.
According to the microheterogeneous model, an IEM is considered as a two-phase system (f1 + f2 = 1) in the simplest case. The gel phase is a microporous swollen medium. It includes the polymer matrix, which bears charged fixed groups, and the charged solution of mobile counterions and, in a smaller number, coions that compensate for the charge of fixed groups. The reinforcing cloth fibers and the inert filler (polyethylene) are also included in the gel phase. The second phase is formed by an electrically neutral solution (identical to the external solution) that fills the intergel spaces. This solution includes the fluid in the central part of the meso- and macropores and in the structural defects of the membrane. In the first approximation (when the presence of coions in the gel phase is neglected), the electrical conductivity of this phase \(\bar {\kappa }\) is considered to be constant, depending on the counterion diffusion coefficient in the gel phase of the membrane, \({{\bar {D}}_{i}},\) and on its exchange capacity \(\bar {Q}{\text{:}}\)
$$\bar {\kappa } = \frac{{{{z}_{i}}{{{\bar {D}}}_{i}}\bar {Q}{{F}^{2}}}}{{RT}},$$
where F is the Faraday constant, R is the universal gas constant, T is the temperature, and zi is the counterion charge. The value \(\bar {Q}\) is related to the ion-exchange capacity Q of the membrane by \(\bar {Q} = {Q \mathord{\left/ {\vphantom {Q {{{f}_{1}}}}} \right. \kern-0em} {{{f}_{1}}}}.\) The numerical value of \(\bar {\kappa }\) can be determined from the value of the membrane electrical conductivity (κ*) at the isoconductivity point in which the conductivities of the membrane (κ*) and the solution (κ) are identical. It is clear that according to Eq. (6), the following equality holds in this case: κ * = κ = \(\bar {\kappa }.\)

Diffusion characteristics of the IEMs were investigated using a two-compartment flow cell. The membrane separated two channels: distilled water was pumped through one of them (channel I), and a salt solution of a given concentration was pumped through the other channel (II). Before the experiments, all samples were equilibrated with 0.02 eq dm−3 electrolyte solution at 25 ± 1°С for 24 h. The first measurements were made for a concentration of 0.02 eq dm−3 of salt solution in channel II. Then, this concentration was successively increased to 1.0 eq dm−3. The membrane under investigation was in contact with each of the solutions for at least 5 h. The cell design, the experimental procedure, and the data processing method are detailed in [38].

Transport numbers of the counterion in IEMs, in accordance with the generally accepted definition (the fraction of the charge transferred through the membrane by ions of a given kind) [10], give an idea of membrane selectivity. The values for the transport numbers of counterions, for example, Cl\((t_{{{\text{Cl}}}}^{*})\), and coions, for example, Na+\((t_{{{\text{Na}}}}^{*})\), in the membranes under study were obtained using the concentration dependences of the specific conductivity and the integral diffusion permeability coefficient of the membranes (P). Their determination procedure and formulas for calculation are presented in [25]. In the case of NaCl solution, they are as follows:
$$t_{{{\text{N}}{{{\text{a}}}^{{\text{ + }}}}}}^{*} = \frac{1}{2} + \sqrt {\frac{1}{4} - \frac{{P{\text{*}}{{F}^{2}}C}}{{2RT\kappa {\text{*}}}}} ,$$
$$t_{{{\text{C}}{{{\text{l}}}^{{\text{ + }}}}}}^{*} = 1 - t_{{{\text{N}}{{{\text{a}}}^{{\text{ + }}}}}}^{*},$$
where F is the Faraday constant; R is the universal gas constant; T is the temperature; C is the electrolyte concentration (eq dm−3) determined as C = zi c (c in mol dm–3); and P* is the differential diffusion permeability coefficient of the membrane, which is related to the integral diffusion permeability coefficient by:
$$P{\text{*}} = P + C\frac{{dP}}{{dC}}.$$

With allowance for Eq. (10), the values of the differential diffusion permeability coefficient were determined using the formula [39]:

$$P{\text{*}} = P\left( {\beta + 1} \right).$$

The coefficient β = dlnP/dlnC was found as the slope of the concentration dependence of the integral diffusion permeability coefficient presented in log–log coordinates.


3.1 Electrical Conductivity

Figure 2 shows the concentration dependences of the specific electrical conductivity of the investigated membranes in NaCl, CaCl2, and Na2SO4 solutions. Values found using the microheterogeneous model for the volume fraction of the intergel solution phase are presented in Table 2. In the case of NaCl solution, the f2 values found are in good agreement with those obtained by other researchers (see review [28]).

Fig. 2.

Concentration dependences of the specific conductivity of (a) cation-exchange and anion-exchange (b) membranes in NaCl, CaCl2, and Na2SO4 solutions. The dashed lines show the electrical conductivity of the NaCl solution.

As follows from Eq. (6), at C < Ciso (where Ciso is the concentration at the isoconductivity point), the greatest contribution to the conductivity of the membranes is made by the conductivity of its gel phase. With an increase in the concentration of the external solution, an increasing contribution to the value of κ* is made by the conductivity of the electroneutral solution filling the intergel spaces. This contribution increases with increasing f2. From Fig. 2a, it is seen that the κ* value for the homogeneous CMX membrane in a NaCl solution of a low concentration in the vicinity of the isoconductivity point (Ciso values for all the investigated membranes fall within the range of 0.02–0.1 eq dm−3) exceeds the corresponding value for the heterogeneous membrane MK-40. Since the concentration of fixed groups (number of millimoles of fixed groups per cm3 of water sorbed by the membrane [10, 17]) and the conductivity of the gel phase in the CMX membrane are higher than in the case of MK-40 (Table 2), this experimental result is easy to understand in light of the above discussion of Eq. (6). However, in the area of higher sodium chloride concentrations, the conductivity of MK-40 becomes greater than that of CMX. In accordance with Eq. (6), the conductivity of the solution in the intergel spaces plays a dominant role in this concentration region, and the membrane with the larger value of f2 has a higher conductivity. (Note that the conductivity of 1 eq dm–3 NaCl solution is 15-fold greater than the conductivity of the gel phase of the CMX membrane.) Similar trends are observed for the κ*(C) functions of anion-exchange membranes, the homogeneous AMX and the heterogeneous MA-41 (Fig. 2b).

In the case when a singly charged coion is replaced by a doubly charged one (the Na2SO4/CEM and CaCl2/AEM systems), there is a slight decrease in electrical conductivity for all the membranes studied (Fig. 2). This well-known fact is explained by stronger Donnan (electrostatic) exclusion of a doubly charged ion compared to a singly charged ion [10]. Since the Stokes radius of the Ca2+ ion is larger than that of the \({\text{SO}}_{{\text{4}}}^{{{\text{2}} - }}\) ion (Table 1), the electrostatic exclusion of the latter is higher [10]. For this reason, the decrease in κ* by replacing the singly charged coion with the doubly charged one in CEM (coion \({\text{SO}}_{{\text{4}}}^{{{\text{2}} - }}\)) (Fig. 2a) is more pronounced than in AEM (coion Ca2+) (Fig. 2b).

A more significant decrease in the electrical conductivity of the investigated membranes is observed when a singly charged counterion is replaced with a doubly charged one (CaCl2/CEM and Na2SO4/AEM systems). In the case of anion-exchange membranes, the decrease in conductivity ranges from 25% (MA-41) to 40% (AMX). In the case of cation-exchange membranes, the conductivity drops by a factor of 2.5 (MK-40) or 6 (CMX) as compared to NaCl solutions. Similar changes in specific conductivity were reported by other researchers for CMX, AMX [14] and MK-40, MA-41 [15, 16, 18]. The reason for the decrease in κ* can be slowing down of the doubly charged counter-ions as a result of ion–ion interactions simultaneously with two fixed groups, not with one as in the case of NaCl solution [10, 17]. It is also possible that steric hindrances to the transport of the larger, highly hydrated (Table 1) sulfate ions and calcium ions play a certain role [14, 16]. A more drastic decrease in the electrical conductivity of the CEM is most likely due to the formation of the weakly dissociating “sulfo group–calcium ion” ion–ion associates [10]. Interactions of this kind are also considered in [22]. The formation of such associates is due to the fact that the product of the concentrations of fixed groups (Table 1) and Ca2+ ions in cation-exchange membranes greatly exceeds the solubility product constant of the salt CaSO3, which is 3.1 × 10−7 (mol dm−3)2 in free solution at 25°C [40].

3.2 Diffusion Permeability of Ion Exchange Membranes

Figure 3 shows the concentration dependences of integral diffusion permeability coefficient P of the investigated membranes in NaCl, CaCl2, and Na2SO4 solutions. A common feature is that the P value of the heterogeneous cation- and anion-exchange membranes is substantially (by a factor of 3–8) higher than that of the homogeneous membranes. This trend was noted, for example, in the review [24] and the recent paper [16]. Obviously, electrolyte diffusion through macropores, which are present in heterogeneous membranes and absent in homogeneous ones, is of crucial importance for this difference. Another common feature is that the replacement of a singly charged coion (the CEM/NaCl and AEM/NaCl systems) with a doubly charged one (the CEM/Na2SO4 and AEM/СaCl2 systems) leads to a decrease in diffusion permeability. As in the case of electrical conductivity, the effect is due to stronger Donnan exclusion of doubly charged coions: a decrease in the concentration of coions leads to a decrease in the diffusion of the electrolyte. This effect is more pronounced for homogeneous membranes, since Donnan exclusion occurs only in the gel phase, the volume fraction of which is significantly greater in homogeneous membranes. The third common feature is that the replacement of a singly charged counterion (CEM/NaCl and AEM/NaCl systems) with a doubly charged one (CEM/CaCl2 and AEM/Na2SO4 systems) leads to an increase in the diffusion permeability. It is known [10] that in the presence of a doubly charged counterion, there is enhancement of electrolyte sorption due to an increase in the attraction force between the coion and the counterion. The observed ratio between the P values for the systems with the singly charged and the doubly charged counterion is explained by a higher concentration of coions, whose transport limits the electrolyte diffusion rate [10]. Although in the case of permeability, there is a certain analogy with the effects observed for the change in membrane conductivity in response to a change in the electrolyte nature, the relations between the P values depending on the contact of the membrane with solutions of different electrolytes are more complex. Apparently, along with electrostatic interactions, which are described by the Donnan relationships, there are more complex interactions of mobile ions with the functional groups and the matrix of the membrane. Some of the relations, for example, the hydration of ions and their place in the Hofmeister series, are discussed in the review by Zhu et al. [14].

Fig. 3.

Concentration dependences of the integral diffusion permeability coefficient of (a) cation-exchange and (b) anion-exchange membranes in NaCl, CaCl2, and Na2SO4 solutions.

Comparison of the behavior of CEMs and AEMs shows that significant differences are only in the form of concentration dependence of diffusion permeability: the value of P for all the CEMs and electrolytes studied increases with increasing electrolyte concentration in the feed solution, whereas P decreases with an increase in the concentration of the Na2SO4 solution in the case of the AMX and MA-41 anion-exchange membranes (Fig. 3b).

To rationalize the behavior of the obtained concentration dependences of diffusion permeability, let us consider the description of diffusion permeability in solutions of electrolytes of different natures through membranes in the terms of the microheterogeneous model. Note that Filippov et al. [18] proposed a mathematical model by which the P(C) function can be described for asymmetric electrolytes. The model is built in the framework of the Teorell–Meyer–Sievers theory [41]; that is, the membrane is considered as a homogeneous medium and the condition of local thermodynamic equilibrium at the membrane/solution interfaces is assumed. In terms of this model, it is possible to adequately describe the concentration dependences in the case of a cation-exchange membrane and 1 : 1 and 2 : 1 electrolytes (where the first figure is the charge of the counterion, and the second one is the charge of the coion).

According to the microheterogeneous model [21], the differential diffusion permeability coefficient P* of the membrane can be represented as a function of the corresponding coefficients for the gel phase, \(\bar {P},\) and for the intergel solution, P. Since the properties of this solution are considered identical to the properties of the external equilibrium solution, the value of P is simply that of the diffusion coefficient D of the electrolyte in solution. Then we can write [27]:
$$\begin{gathered} P{\text{*}} = \left\{ {{{{\left[ {{{f}_{1}}{{{\left( {\frac{{\bar {P}}}{{{{{\bar {t}}}_{1}}}}} \right)}}^{{\alpha }}} + {{f}_{2}}{{{\left( {\frac{D}{{t_{1}^{*}}}} \right)}}^{{\alpha }}}} \right]}}^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} {\alpha }}} \right. \kern-0em} {\alpha }}}}}} \right. \\ {{\left. { + \,\,{{{\left[ {{{f}_{1}}{{{\left( {\frac{{\bar {P}}}{{{{{\bar {t}}}_{{\text{A}}}}}}} \right)}}^{{\alpha }}} + {{f}_{2}}{{{\left( {\frac{D}{{t_{{\text{A}}}^{*}}}} \right)}}^{{\alpha }}}} \right]}}^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} {\alpha }}} \right. \kern-0em} {\alpha }}}}}} \right\}}^{{ - 1}}}, \\ \end{gathered} $$
where α is a structural parameter determined by the position of the phases relative to the transport axis; α is in the range from −1 (serial connection) to +1 (parallel connection). Usually, α varies from 0.1 to 0.4 [16, 21, 24, 42]. \({{\bar {t}}_{i}}\) and \(t_{1}^{*}\) are the transport numbers of ith ions in the gel phase and in the solution, respectively; the subscript i takes the values 1 and A, respectively, for the counterion and the coion.

According to Eq. (12), P* depends on the permeability of both the gel phase and the intergel solution, with the contribution of the gel phase being more important for homogeneous membranes (f1 ≈ 0.9) and less important for heterogeneous membranes (f1 ≈ 0.8).

For further analysis, the \(\bar {P}\) value is conveniently represented as [27]:
$$\bar {P} = \left( {1 - \frac{{{{z}_{{\text{A}}}}}}{{{{z}_{1}}}}} \right)\overline {{{t}_{1}}} \frac{{{{{\bar {D}}}_{A}}{{{\bar {C}}}_{{\text{A}}}}}}{{{{C}_{{\text{A}}}}}},$$
where z1 and zA are the charges of counterions and coions, respectively (taking into account the sign of the charge). Since the transport number of counterions in the gel phase \({{\bar {D}}_{{\text{A}}}}\) differs little from 1 in a wide range of concentrations, coions play the main role in determining the \(\bar {P}\) value. The value of \(\bar {P}\) is determined by the diffusion coefficient of coions in the gel phase and the ratio of their concentration in the gel phase and in the solution phase (also called the partition coefficient) Ks [43]. The ion concentrations in the gel phase and the partition coefficient are determined by electrostatic interactions of mobile and fixed ions. The values of \({{\bar {C}}_{{\text{A}}}}\) and Ks can be found using the Donnan equilibrium relations and local electroneutrality relationships. Experimental [17, 38] and theoretical [10, 17, 27] estimates show that the \({{\bar {C}}_{{\text{A}}}}\)/CA ratio is much less than unity and the diffusion coefficient of coions in gel membranes is one to two orders of magnitude less than their coefficient in solution. Thus, according to Eq. (13), \(\bar {P}\) is two to three orders of magnitude less than D. From the equation it follows that the greater the value of f1 (the smaller the f2), the closer the P* to the \(\bar {P}\) value. On the contrary, the smaller the f1 (the larger the f2) value, the closer the P* to the D value. Thus, P* for homogeneous membranes (f1 ≈ 0.9) should be smaller than for heterogeneous membranes (f1 ≈ 0.8). Indeed, as discussed above and seen from Fig. 3, this trend holds.

To analyze the effect of ion charges on the diffusion permeability, it is convenient to use the following equation [27]:

$$\frac{{{{{\bar {C}}}_{{\text{A}}}}}}{{{{C}_{{\text{A}}}}}} = K_{{\text{D}}}^{{\left| {{{z}_{{\text{A}}}}} \right|}}{{\left( {\frac{c}{{\bar {Q}}}} \right)}^{{\left| {{{{{z}_{{\text{A}}}}} \mathord{\left/ {\vphantom {{{{z}_{{\text{A}}}}} {{{z}_{1}}}}} \right. \kern-0em} {{{z}_{1}}}}} \right|}}},$$

derived from the Donnan relation in the approximation of \({{\bar {C}}_{{\text{A}}}} \ll \bar {Q},\) which is true for relatively dilute solutions. Here, KD is the Donnan constant. According to this equation, the concentration of coions in the gel phase of the membrane increases with an increase in electrolyte concentration in the external solution, a decrease in ion-exchange capacity (concentration of fixed groups), and an increase in the |zA/z1| ratio. Substituting Eq. (14) into (13), we get

$$\bar {P} = \left( {1 - \frac{{{{z}_{{\text{A}}}}}}{{{{z}_{1}}}}} \right)\overline {{{t}_{1}}} {{\bar {D}}_{{\text{A}}}}K_{{\text{D}}}^{{\left| {{{z}_{{\text{A}}}}} \right|}}{{\left( {\frac{C}{{\bar {Q}}}} \right)}^{{\left| {{{{{z}_{{\text{A}}}}} \mathord{\left/ {\vphantom {{{{z}_{{\text{A}}}}} {{{z}_{1}}}}} \right. \kern-0em} {{{z}_{1}}}}} \right|}}}.$$

For three possible options (singly charged counterion and coion, doubly charged counterion and singly charged coion, singly charged counterion and doubly charged coion), we obtain three equations:

$$\bar {P} = 2\overline {{{t}_{1}}} {{\bar {D}}_{{\text{A}}}}{{K}_{{\text{D}}}}\left( {\frac{C}{{\bar {Q}}}} \right),\,\,\,\,\left| {{{z}_{{\text{1}}}}} \right| = \left| {{{z}_{{\text{A}}}}} \right| = {\text{1}},$$
$$\bar {P} = \frac{3}{2}\overline {{{t}_{1}}} {{\bar {D}}_{{\text{A}}}}{{K}_{{\text{D}}}}{{\left( {\frac{C}{{\bar {Q}}}} \right)}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}}},\,\,\,\,\left| {{{z}_{{\text{1}}}}} \right| = 2,\,\,\,\,\left| {{{z}_{{\text{A}}}}} \right| = 1,$$
$$\bar {P} = 3\overline {{{t}_{1}}} {{\bar {D}}_{{\text{A}}}}K_{{\text{D}}}^{2}{{\left( {\frac{C}{{\bar {Q}}}} \right)}^{2}},\,\,\,\,\left| {{{z}_{{\text{1}}}}} \right|{\text{ = 1}}{\text{,}}\,\,\,\,\left| {{{z}_{{\text{A}}}}} \right| = 2.$$

If \({c \mathord{\left/ {\vphantom {c {\bar {Q}}}} \right. \kern-0em} {\bar {Q}}}\) is significantly less than unity, then \({{\left( {{C \mathord{\left/ {\vphantom {C {\bar {Q}}}} \right. \kern-0em} {\bar {Q}}}} \right)}^{2}} < \left( {{C \mathord{\left/ {\vphantom {C {\bar {Q}}}} \right. \kern-0em} {\bar {Q}}}} \right) < {{\left( {{C \mathord{\left/ {\vphantom {C {\bar {Q}}}} \right. \kern-0em} {\bar {Q}}}} \right)}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}}}.\) From this relationship, it follows that the values of \(\bar {P}\) are arranged in the following order at close values of \(\left( {1 - \frac{{{{z}_{{\text{A}}}}}}{{{{z}_{1}}}}} \right)\overline {{{t}_{1}}} {{\bar {D}}_{{\text{A}}}}K_{{\text{D}}}^{{\left| {{{z}_{{\text{A}}}}} \right|}}\) for different types of electrolytes: \({{\bar {P}}_{{\left| {{{z}_{1}}} \right| = 1,\,\,\left| {{{z}_{{\text{A}}}}} \right| = 2}}}\) < \({{\bar {P}}_{{\left| {{{z}_{1}}} \right| = 1,\,\,\left| {{{z}_{{\text{A}}}}} \right| = 1}}}\) < \({{\bar {P}}_{{\left| {{{z}_{1}}} \right| = 2,\,\,\left| {{{z}_{{\text{A}}}}} \right| = 1}}}.\) Indeed, as can be seen from Fig. 3, this relation holds for the P value for both homogeneous and heterogeneous membranes, as has been mentioned above.

Regarding the form of the P*(C) curve, \(\bar {P}\) should increase in all cases with increasing concentration of the external solution in accordance with Eqs. (15)(17), with the fastest growth being in the case of |z1| = 1, |zA| = 2. Indeed, in the case of AEM/CaCl2, the function P*(C) grows faster than the others. In accordance with Eq. (17), the increase in \(\bar {P}\) with increasing concentration should be the least rapid in the case of AEM/Na2SO4. However, instead of the expected growth, the experimental value of P(C) decreases in the case of both homogeneous AMX and heterogeneous MA-41 membranes (Fig. 3b). Apparently, this behavior of the membranes is due to the fact that the diffusion coefficient of sodium sulfate in solution decreases significantly with increasing C, unlike that of NaCl and CaCl2, for which this decrease is insignificant (Fig. 4). For example, the ratio of the electrolyte diffusion coefficient D in 1 eq dm−3 solution to its value at infinite dilution D0 is 0.92 (NaCl) [44, 45] or 0.87 (CaCl2) [45] versus 0.64 (Na2SO4) [46], with the sharp drop in the D/D0 value in the case of Na2SO4 being observed already in very dilute (C < 0.01 eq dm−3) solutions (Fig. 4). A more drastic decrease in the diffusion coefficient of the Na2SO4 electrolyte with increasing concentration [44, 46], which is accompanied by a more significant decrease in solution viscosity [47], is attributed to the high ability of sulfate ions to structure water [14] or form ion associates [48]. As the electrolyte concentration increases, the proportion of such associates increases, resulting in a sharp drop in the diffusion coefficients of Na2SO4.

Fig. 4.

Dependence of electrolyte diffusion coefficient D on the solution concentration at a temperature of 25°C. The values of D are normalized to the diffusion coefficient corresponding to each electrolyte at infinite dilution of the solution, D0 (Table 1). The curves were constructucted using experimental data, taken from [44, 45].

Note that in the case of the heterogeneous membrane MA-41, a more dramatic decrease in P is observed with an increase in the concentration of sodium sulfate compared to homogeneous AMX (Fig. 3b). Apparently, this is due to the greater volume fraction of the electroneutral solution in the intergel spaces by which the electrolyte diffuses in the same manner as in the free solution. That is, for this kind of diffusion, the effect of a considerable decrease in the diffusion coefficient with increasing concentration of the solution should be very significant. The effect of reducing the diffusion coefficient of Na2SO4 in the solution with an increase in its concentration should also occur in the case of CEMs, but the magnitude of this effect for the latter membranes seems to be offset by the theoretically expected most rapid growth of the function \({{\bar {P}}_{{\left( {{{C}_{{{\text{N}}{{{\text{a}}}_{{\text{2}}}}{\text{S}}{{{\text{O}}}_{{\text{4}}}}}}}} \right)}}}\), in accordance with Eq. (18).

It can be expected that the decrease in the diffusion coefficient of ions with increasing concentration of the external solution occurs not only in the solution, but also in the gel phase of the membrane. However, the change in ionic strength in the gel phase with increasing concentration of the external solution is significantly less than in the external solution, since fixed ions and counterions have the dominant effect and the concentration of the counterions increases (due to an increase in the concentration of coions) slightly with an increase in C. At the same time, there is another reason behind a decrease in the mobility of ions in the gel phase of the membrane with increasing concentration of the external solution. This reason is a decrease in the water content in IEMs with an increase in the concentration of the external solution, which leads to a decrease in pore size and an increase in the concentration of fixed groups per volume of sorbed water. These effects are due to a decrease in the “driving force” of membrane swelling—difference in osmotic pressures in the solution and in the membrane [10, 49, 50]. As shown by Kamcev and coauthors [17], an increase in the concentration of fixed groups should lead to stronger electrostatic exclusion of coions, especially multiply charged ones (Na2SO4/CMX system) and a decrease in pore size should lead to an increase in steric hindrance to the transport of large highly hydrated ions (CMX/CaCl2 and CMX/Na2SO4 systems). Note that B.D. Freeman’s research team [11, 17] studied lightly crosslinked ion-exchange gels, for which the contribution of the factor under consideration in the region of unimolar salt solutions is very noticeable. Our and similar [14] measurements carried out for CMX and AMX membranes showed that a decrease in the water uptake of these membranes with an increase in the concentration of CaCl2 and Na2SO4 solutions from 0.02 to 1 mol dm−3 does not exceed 10%, which is comparable with the measurement error. Based on the data obtained, it can be assumed that for highly crosslinked ion-exchange polymers, including those of the membranes under study, this factor is less significant. Perhaps, a more significant role is played by ion–ion and ion–dipole interactions of the electrolytes with each other and with fixed membrane groups. In [11, 51], for example, it was shown that the formation of weakly dissociating associates of magnesium or aluminum counterions with sulfo groups reduces the ionization of fixed groups (decreases the effective ion-exchange capacity of the membrane), thereby making the CEM behavior close to the behavior of uncharged polymers. This type of interaction (together with Eq. (17)) seems to explain the smaller slope of the P(C) curve in the CMX/CaCl2 system compared to the CMX/NaCl system.

3.3 Transport Numbers of Counterions and Coions

Figure 4 shows the concentration dependences of the counterion transport numbers in the investigated IEMs, as found from their electrical conductivity and diffusion permeability using Eq. (8). For analysis, it is more convenient to write this equation in the following form [34]:

$$t_{A}^{ * } = \frac{{{{F}^{2}}P{\text{*}}C}}{{2RT\kappa {\text{*}}}}.$$

According to Eq. (19), the transport number of coions is directly proportional to the diffusion permeability and inversely proportional to the conductivity of the membrane (taking into account that the transport number of counterions is slightly different from unity).

As can be seen from Fig. 5, the transport number of counterions (characterizing the selectivity of cation-exchange membranes for transport of ions of a certain charge sign) decreases in a certain order in accordance with the increase in the P*/κ* ratio depending on the nature of the electrolyte. For both CEM types, this order is Na2SO4 ≥ NaCl > CaCl2 (Fig. 5a). This series corresponds to the sequence in which the concentration of coions increases in the gel phase of the membrane: \({{\bar {C}}_{{{\text{N}}{{{\text{a}}}_{{\text{2}}}}{\text{S}}{{{\text{O}}}_{{\text{4}}}}}}} < {{\bar {C}}_{{{\text{NaCl}}}}} < {{\bar {C}}_{{{\text{CaC}}{{{\text{l}}}_{{\text{2}}}}}}}.\) This issue has been discussed above. For all electrolytes, the selectivity of the heterogeneous membrane MK-40 is lower than that of the homogeneous CMX membrane. However, these differences are significant only for CaCl2 solutions, in which the \({{t}_{{{\text{C}}{{{\text{a}}}^{{{\text{2}} + }}}}}}\) values decrease to 0.75 (MK-40) and 0.88 (CMX) at the concentration of the external solution of 1 eq dm−3. As discussed above, this behavior of both membranes seems to be due to the specific interaction of Ca2+ ions with fixed \({\text{SO}}_{{\text{3}}}^{ - }\) ions, which is responsible for the low electrical conductivity of the membranes. At the same time, the transport numbers of sodium counterions in both homogeneous and heterogeneous membranes exceed 0.98 in the entire investigated range of NaCl and Na2SO4 concentrations (up to 1 eq dm−3). In the case of NaCl, this result is consistent with the data reported by Larches et al. [25], who used the same method of determination as in this work, and the results obtained by Gnusin et al. [52], who found the true transport number using the EMF method and the transport numbers of water.

Fig. 5.

Concentration dependence of the transport numbers of counterions in (a) cation-exchange and (b) anion-exchange membranes.

Regarding AEMs, as in the case of CEMs, the highest selectivity is observed for the solution with the singly charged counterion and the doubly charged coion, then comes the 1 : 1 electrolyte, and the lowest AEM selectivity is shown in the solution with the doubly charged counterion and the singly charged coion: CaCl2 > NaCl > Na2SO4. As in the case of CEMs, the reason for the decrease in selectivity is an increase in the coion concentration in the gel phase of the membrane with a change in the electrolyte nature. Like CEMs, the heterogeneous membranes are characterized by lower transport numbers of counterions compared to the homogeneous ones. At the same time, in NaCl and CaCl2 solutions in the entire investigated concentration range, they exceed the values of 0.99 (AMX) and 0.97 (MA-41). In the case of Na2SO4 solution with a concentration of 1 eq dm−3, they decrease to 0.98 (AMX) and 0.92 (MA-41).

Since all the studied membranes have similar ion-exchange capacities and are made of identical ion-exchange materials; the difference in conductivity, diffusion permeability, and selectivity between homogeneous and heterogeneous membranes should be attributed to structural differences, which are determined by their fabrication methods. Namely, the reason for the substantially lower selectivity of heterogeneous membranes is the presence in them of macro-pores and structural defects filled with an equilibrium solution, in which there is no transport selectivity.

3.4 Structural Differences between Homogeneous and Heterogeneous Membranes

Figure 6 shows porosimetry curves for the MK-40 and MA-41 membranes, which were constructed using the experimental data [19] obtained by means of standard contact porosimetry.

Fig. 6.

Dependence of the integral volume of sorbed water (V) on the effective pore radius (r) of MK-40 and MA-41 membranes. The vertical dashed lines pass through the inflection points of the curves. The numbers at the top of the figure are the characteristic values of the effective pore radii corresponding to the dashed lines. The curves were constructed using experimental data from [19], with the permission of Elsevier.

The shape of the porosimetry curves (Fig. 6) is typical for domestic heterogeneous membranes [19, 24, 27]. These membranes are characterized by a wide range of pore sizes. The narrowest pores are in ion-exchange resin grains and ensure selective transport through heterogeneous ion-exchange membranes. The inflection points on the porosimetry curves (Fig. 6) show that pores with radii of 3.5 and 13 nm prevail among the aforementioned pores. In addition, MK-40 and MA-40 contain larger pores, of which pores with the effective radii of approximately 100 and 3000 nm dominate. The former, most likely, are the macropores formed at the sites of contact of ion-exchange resin particles with the inert binder. Such pores, for example, were found in scanning microscopy images of the surface of swollen MK-40 and MA-41 [53]. The larger pores (>3000 nm), apparently, can be formed between the nylon reinforcing fiber and the “ion exchange material + inert binder (polyethylene)” composite. This assumption was made in [19]. Indeed, these pores can be visualized by video recording the drying of swollen MK-40 and MA-41 samples in air. Some of the frames of this video are presented in Fig. 7.

Fig. 7.

Transmission light microscopy images of the MA-41 membrane surface after (a) 10, (b) 720, (c) 900, and (d) 1070 s contact of the swollen sample with air.

Water has a higher optical density than air [54]. Therefore, the membrane areas from which it evaporates have a darker color. There are no such areas on the sample that was exposed to air for a short time (Fig. 7a). However, they appear in a few hundred seconds, first of all, at the points of contact of the reinforcing fiber with the composite material of the membrane. Especially fast evaporation of water occurs at the fibers intersection points (Fig. 7b). Some fibers, according to our data, as well as data from low-vacuum SEM [49], extend beyond the composite material, become bare and come into contact with the membrane-washing solution. It can be assumed that the number of protrusions of reinforcing cloth to the surface, varying from batch to batch of heterogeneous membranes, largely determines the rather wide variation in the values of diffusion permeability and electrical conductivity of these and similar membranes [15, 16, 21, 31, 41]. For example, the integral diffusion permeability coefficient of the MK-40 membrane in 0.5 M NaCl solution, according to different sources, can take the following values (10−8 cm2 s−1): 8 (Fig. 3a), 6 [15], 14 [16], and 7 [24]. However, verification of this assumption requires additional research.

In the case of homogeneous membranes AMX and CMX, surface drying occurs fairly evenly and it is not possible to visualize the “rapid water evaporation” areas, although these membranes contain reinforcing fabric as well. Apparently, this is due to the stronger adhesion of the reinforcing fabric and the composite ion-exchange material of these membranes, because both materials contain or consist of PVC. Note that the characteristics of these membranes are more stable. For example, the concentration dependences of the CMX and AMX conductivity calculated from the data published in [14] coincide quantitatively with those presented in this paper within the measurement error (±5%).

According to estimates made using the porosimetry curves shown in Fig. 6 [19], macropores with a size of >3000 nm (we believe they are located between the reinforcing fiber and the “resin + inert binder” composite) contain about 10% of the total volume of water in the studied heterogeneous membranes MK-40 and MA-41 [27, 55]. It can be expected that the diffusion permeability and selectivity of the investigated heterogeneous membranes MK-40 and MA-41 will approach the corresponding characteristics of the homogeneous CMX and AMX membranes, providing that it is possible to reduce these macropores, for example, by selecting more appropriate reinforcing materials.


The study has shown that homogeneous and heterogeneous membranes with the ion-exchange matrix made of similar materials and the same nature of functional groups have similar properties. All the features listed below relate to the membrane systems studied, which include СМХ, МK-40, АМХ, and МА-41 membranes. On passing from one electrolyte to another, the numerical values of conductivity κ*, diffusion permeability P, and ion transport numbers \(t_{i}^{*}\) for the studied pair of cation-exchange membranes change in the same direction; the same applies to the pair of anion-exchange membranes. The direction of changes in properties is determined by electrostatic interactions of mobile ions and functional fixed groups, this direction depends on the concentration of coions and on the mobility of counterions in the membrane. Doubly charged coions (due to their stronger Donnan exclusion) are sorbed to a lesser extent than singly charged ones. As a consequence, the value of P for such systems is minimal. The value of κ* is barely varied by replacing a singly charged coion with a doubly charged one, since the concentration of coions almost does not affect the membrane conductivity (at least in the concentration range of the external solution up to 1 eq dm−3). The presence of doubly charged counterions, on the contrary, enhances the sorption of coions, thereby determining the maximum value of P. But this sharply decreases κ* because of the low mobility of the doubly charged counterion due to its electrostatic interaction simultaneously with two functional groups, not with one group as in the case of NaCl solution. Regarding the transport numbers of coions, the higher the P value and the lower the κ* value, the greater are the transport numbers. In both CEM and AEM cases, the membrane selectivity decreases in the order of 1 : 2 > 1 : 1 > 2 : 1 electrolytes, where the first figure is the counterion charge and the second one is the coion charge.

The specifics of the behavior of heterogeneous membranes is manifested in that they have a significantly larger value of the volume fraction of macropores, f2: this parameter is 0.20–0.22 in heterogeneous membranes compared to 0.09 in homogeneous membranes (in NaCl solution). The presence of macropores is not very strongly reflected in the conductivity of the membranes. However, this leads to the fact that with an increase in the concentration of the external solution after passing through the isoconductivity point, the value of κ* grows significantly faster in the case of heterogeneous membranes compared to homogeneous ones. This provides an increment in κ* by about one and a half times at a concentration of 1 eq dm−3 as compared with \(\kappa _{{{\text{iso}}}}^{*}\) in the case of heterogeneous membranes and only by a factor of 1.2 in the case of homogeneous membranes. As a result, the electrical conductivity of homogeneous membranes in most electrolytes used in the region of low concentrations is higher than that of heterogeneous ones and the conductivity of heterogeneous membranes is higher in the region of high concentrations. The presence of macropores in heterogeneous membranes has a much more significant effect on the diffusion permeability of membranes: the P value of heterogeneous membranes is two to three times that of homogeneous membranes. As a consequence of this difference, the transport numbers of coions in heterogeneous membranes are two–four times greater than in homogeneous ones.

Imaging of the drying of the surface of heterogeneous membranes leads to the conclusion that the areas of contact of the reinforcing fiber with the composite material of the membrane are the most critical for transport properties: it is from these areas that water evaporates most quickly, suggesting its weak connection with the material. Apparently, it is in these areas that pores with a size of about 1 μm are formed. In the studied homogeneous membranes AMX and CMX, the reinforcing fabric material has good adhesion to the composite material of the membrane, thus precluding the appearance of such macropores.


This work was supported by the Russian Foundation for Basic Research, project nos. 18-08-00397_a (study of transport characteristics in various electrolytes) and. 18-38-00521 mol_a (study of macropore formation in heterogeneous membranes).



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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • V. V. Sarapulova
    • 1
    Email author
  • V. D. Titorova
    • 1
  • V. V. Nikonenko
    • 1
  • N. D. Pismenskaya
    • 1
  1. 1.Kuban State UniversityKrasnodarRussia

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