## 3 Pseudo-Homogeneous and Grafted Membranes
This approach does not prevent the preservation of sufficiently large pores inside the polymer, but in some cases, it is possible to obtain membranes with high selectivity, which can be judged, for example, by their high efficiency in fuel cells. Depending on the application, membrane materials with high ionic conductivity or selectivity are necessary, but in any case, both of these parameters are important. In particular, for electrodialysis, the ratio of conductivity to cation transfer numbers is most important. The relationship between them can be found from a consideration of the transport of counterions and coions through membranes on the basis of the irreversible thermodynamics [131]. The authors concluded that cation transfernumbers should increase with ionic conductivity increasing. However, due to the reasons discussed in the previous section, their ratio usually turns out to be the reverse. To compare membrane conductivity and selectivity, a two-dimensional diagram can be used (Figure 3). Membranes with the best transport properties are near the so-called ''upper bound''. Homogeneous perfluorosulfonic acid membranes have the best properties among the commercial membranes. They are followed by pseudo-homogeneous and heterogeneous ones. At the same time, the best of the samples of grafted membranes based on polymethylpentene and sulfonated polystyrene match the best perfluorosulfonic acid membranes. It should be noted that many commercially available ion-exchange membranes used in electromembrane processes, for example, Neosepta(r), Fumatech(r), FujiFilm(r) membranes and others have the pseudo-homogeneous morphology. When designing pseudo-homogeneous IEMs, it is possible to adjust their properties by changing the nature and proportion of the hydrophobic polymer matrix, the degree of functionalization, the nature of the functional group, using reinforcement or crosslinking. Let us consider how the above factors affect the water uptake of ion-exchange membranes and, hence, their selectivity. Typically, an increase in the proportion of the hydrophobic polymer matrix and its rigidness leads to a decrease in water uptake [84; 109; 115; 133; 134; 135; 136]. For example, [PERSON] et al. showed that an increase in the grafting degree of sulfonated polystyrene for the radiation grafted FEP-g-polystyrenesulfonic acid membranes from 6 to 40% leads to an increase in water uptake from 2-3 to 63 water molecules per sulfonic-acid group [137]. The authors of [138] demonstrated that an increase in the crystallinity of the cation exchange membranes from 8 to 25% leads to a decrease in their water uptake from 32 to 19 water molecules. It should be noted that the CMX Neosepta(r) membrane, which made of high rigid polyvinyl chloride, is one of the most mechanically tough and selective commercial IEMs. This is due to the fact that the limitation of the swelling of the hydrophilic ionic domains is accompanied by an increase in their selectivity. Another important parameter is the amount of functional groups [82; 136; 139; 140]. For example, an increase in the sulfonation degree of polystyrene in the cation-exchange membranes based on block copolymers from 12 to 49% leads to an increase in water uptake from 3 to 165 water molecules per sulfonic-acid group. Figure 3: Dependence of apparent transport numbers (0.5/0.1 M NaCl) on the Na+ conductivity of various cation exchange membranes. 1—grafted membranes based on UV-oxidized polymethylpentene [84], 2—homogeneous and pseudo-homogeneous materials, 3—heterogeneous membranes, 4—grafted membranes based on polyethylene [115; 132]. Some trade names of commercially available membranes are shown in the Figure. For anion-exchange membranes, the nature of the functional group represented by various quaternary amines is especially relevant [82; 141]. Therefore, [PERSON] et al. [82] showed that AEM based on substituted imidazoles have higher selectivity than those with the trimethylamine functional groups, which was associated with their lower hydration degree.