## 2 Structure of Ion-Exchange Membranes
[39]) methods have shown that the homogeneous IEMs (namely, perfluorinated MF-4 SK membranes (Plastpolymer, Russia) [39; 41; 42]), as well as Nafion-112, Nafion-115, Nafion-117 membranes [40]) do not contain macropores (the pores, whose effective radius size is larger than 100 nm), while heterogeneous membranes have such pores. It was found [37; 39; 42] that the pore size distribution of Russian heterogeneous MK-40 and MA-40 membranes has two maxima, the first one is at about 10 nm (which is the range of micro- and mesopores) and the second one relates to macropores with size of about 1000 nm. According to [39], the pores of the first type are situated within the ion-exchange resin particles and the pores of the second type are formed by the spaces between different membrane constituents (resin, binder, cloth). The solution filling the clusters where the fixed functional groups are concentrated is charged. It contains mainly counterions coming from the dissociation of functional groups. The counterions being in thermal motion are attracted by the fixed charged groups, forming in this way an EDL. A pore also contains a small amount of co-ions carrying a charge of the same sign as that of the fixed ions. The co-ions are repelled from the pore by electrostatic forces; this effect is called the Donnan (co-ion) exclusion [31]. The distribution of ions within the EDL formed at inner or outer interfaces is described by the Gouy-Chapman theory, which takes into consideration both electrostatic and thermal interaction. Figure 2 schematically shows the ion distribution in the proximity of a pore wall represented as a charged plane. The concentration of counterions in the pore solution increases and that of co-ions decreases with decreasing the ratio of the pore radius to the Debye length. The latter characterizes the EDL thickness. Therefore, the less the pore radius, the higher the membrane selectivity (and the higher the membrane resistance). When the pore radius is higher than the Debye length, there is an electrically neutral solution in the pore centre. When the water molecules are close to the functional groups, they are structured and lose to a great extent their mobility [3; 5]. As a result, the relative dielectric permittivity, \(\varepsilon\), decreases when approaching a functional group. The mobility of counterions concentrated near the functional groups is very low mainly due to strong electrostatic interaction [3; 5]. The side-chains also contribute to their low mobility by encumbering the space [43]. Due to the finite size of hydrated counterions, their concentration decreases when the distance from a fixed group becomes lower than about 0.5 nm. When getting close to the pore centre, the counterion concentration decreases as well, according to the Gouy-Chapman law of ion distribution in EDL (Figure 2). The transport properties of the central zone of a hydrophilic domain are different from those of a zone, which is close to the internal interface. The water molecules located in the centre of sufficiently large pores behave as in free solution. In particular, \(\varepsilon\) approaches the value of 81 there, as in free solution [44]; the proton transport mechanism in the pore centre is identical to that in free solution. The Grothuss shuttling dominates over the vehicular transport (solvation diffusion): proton jumps from one H\({}_{3}\)O+ (or H\({}_{5}\)O\({}_{2}\)+ or even greater) complex to a neighbouring one rather than moves within its aqueous environment-hydration shell [44]. The contribution of the vehicular transport increases with increasing the degree of water structuring, which takes place in the vicinity of the fixed charged groups. The volume fraction of bulk-like water depends on the membrane water content. Electronic structure calculations [45] show that 2-3 water molecules (n) per sulfonic acid group are needed in perfluorinated membranes (such as Nafion(r) for proton dissociation. The dissociated proton is separated from the sulfonate anion, when 6 water molecules are added in a membrane.