## 5 Hybrid Membranes  
Another approach to increase the selectivity and decrease the water uptake of ion-exchange membranes is to replace part of the water in the pores by the inorganic particle's incorporation. Since the membrane pore size is usually small and does not exceed 5 nm [62; 172], the size of the introduced particles should also be several nanometers. Doping with inorganic nanoparticles has been used to improve the transport properties of membrane materials since the late 1980s [173; 174; 175; 176]. Since organic and inorganic components are simultaneously present in such systems, such membranes are called hybrid membranes. Research in this area was almost simultaneously developed for gas separation membranes, which are often called the Mixed Matrix Membranes [178; 179]. In the case of ion-exchange membranes, this approach is more often used to increase their ionic conductivity. For this purpose, nanoparticles of hydrophilic materials, such as silica [180; 181; 182; 183; 184; 185; 186; 187], or other oxides [188; 189; 190; 191; 192; 193; 194; 195; 196; 197; 198; 199] are used. This often leads to an increase in the membrane water uptake, and therefore it is often believed to be the reason for the conductivity increase. However, in a number of hybrid membranes, the conductivity increases despite the lower water uptake. To explain this effect, a model of limited elasticity of the membrane pore walls was proposed [200]. Upon doping, inorganic nanoparticles should displace a part of water molecules from the pore. Since the counterion concentration remains almost the same, this leads to an increase in the osmotic pressure and a pore expansion (Figure 6a,b), accompanied by an expansion of the channels connecting them and, hence, a conductivity increase. However, with increasing nanoparticle size, the elastic forces of the pore walls increase according to Hooke's law and the osmotic pressure becomes insufficient for their further expansion. Therefore, the membrane water uptake decreases, and new \"bottlenecks\" that limit conductivity appear in the pores (Figure 6c). When the additive content is above two vol %, the conductivity of the hybrid membranes decreases [180; 201; 202; 203]. This model is confirmed by comparing the data on the ionic conductivity of hybrid membranes with the diffusion coefficients of proton-containing groups determined by NMR with a pulsed magnetic field gradient [201; 204]. The authors of [205] developed this model and described with its help the effect of a double electric layer formed around nanoparticles embedded in mesopores and macropores on the electrical conductivity, diffusion permeability of IEMs, and ion transport numbers in them. Figure 5: Formation of a typical highly cross-linked membrane via polymerization of aqueous or amide solutions of ionospheric monomers. Figure 6: Scheme of the pore structure change: the initial membrane (**a**) and membranes modified with nanoparticles of different sizes (**b**,**c**) according to the case of the model of limited elasticity of the pore walls (redrawn from [206]). Increased conductivity is not the only advantage of hybrid membranes. Some authors also note an improvement in their mechanical properties [177, 207, 208]. Although it is not always achieved, the mechanical properties of hybrid membranes are usually sufficient for their practical use [16, 209]. A noteworthy advantage of hybrid membranes is often their reduced permeability of methanol and other fuel gases [202, 210, 211, 212]. This determines, in particular, the widespread use of hybrid membranes in direct methanol fuel cells (DMFCs) [16, 213, 214]. A comparison of proton conductivity and methanol permeability for a number of hybrid membranes is given in Table 1.  
It is worthwhile to note that gas permeability can be considered as a measure of selectivity of membranes used in fuel cells and the transfer mechanism of non-polar gas molecules or alcohols containing voluminous non-polar fragments is much similar to that of coions.