## 2 Structure of Ion-Exchange Membranes  
Synthetic IEMs are built using flexible polymer chains with aliphatic, aromatic or perfluorinated residues, which contain functional groups such as -SO3H, -COOH, -NH3 OH and others. Protons or OH- ions of these groups can be replaced by cations or anions, respectively, from bathing solutions. The diversity of practical applications of membranes conditions a variety of specific requirements expected from them and, eventually, promotes the development of a wide range of membrane materials. A considerable number of membranes and membrane materials are now available [6; 7; 8]. Depending on the material structure and the method of preparation, IEM are usually divided into homogeneous and heterogeneous membranes. Homogeneous membranes (Figure 1a) are generally obtained by copolymerization of monomers [9] that produces homogeneous material at least at the scale of 100 nm or more, which is determined by the size of polyvinyl chloride (PVC) particles used as a non-conductive binder in the Neosepta(r) membranes [10]. Heterogeneous membranes include macroparticles (with the size from 1 to 50 \(\upmu\)m) of different polymer materials. For example, the MA-40 anion-exchange membranes (AEMs) (Shchekinoazot, Tula Region, Russia) contain particles of polystyrene crosslinked with divinylbenzene (DVB) anion-exchange resin and polyethylene used as the binder (Figure 1b). Both homogeneous and heterogeneous membranes contain reinforcing cloth (Figure 1a,b). This cloth not only plays an important role as a means to improve the mechanical properties but also causes a certain undulation of the membrane surface, which seems important for initiating electroconvection in overlimiting current regime [11]. Recently, Svoboda et al. [13] developed a specific scanning cell for the analysis of heterogeneous IEM structure by micro-computed tomography, which provides volume reconstruction of the studied material. The unique working principle of the cell allows one to scan membranes not only in their dry state but also in fully swollen state. The micro-computed tomography showed that there are profound changes in the structure of the IEM associated with their transition from the dry state into the swollen one. This study applied to the heterogeneous cation-exchange membrane (CEM) coming from Mega a.s., Ceska Lipa District, Liberce Region, Czech Republic showed that swelling of the membrane is caused by the swelling of the ion-exchange resin. Its volume increased nearly three times after exposure to deionized water, while the overall membrane volume increased by 50%. If the membrane contained approximately 28%vol. of the resin in the dry state, this content increased to 52%vol. after swelling. Micro-computed tomography not only allows one to analyse volumetric composition of the membrane bulk but also to quantify the composition of the surface. By using two different methods, [PERSON] et al. [14] evaluated the fraction of the conductive area (e.g., the ion-exchange resin) on the surface of an AEM and CEM in the swollen state. The obtained results showed that the volume fraction of the conductive domains does not correspond to the surface fraction of these domains and thus the volume composition is not reflected on their surface. For example, the volume fraction of the conductive domains for the studied AEM was 0.45 and its surface fraction only 0.26. Similar results were obtained earlier by [PERSON] et al. [15] and other authors [16]. The reason is that during the hot pressing of heterogeneous membranes, polyethylene, which is more fluid than polystyrene, moves from the membrane bulk on the surface. A membrane can include one or several layers. Generally, monopolar IEM have a single-layer structure [17].