## 2 Polymer Nanocomposites for Membranes Applications
The SEM micrograph of the surface of the PIPAA-PM/SNT nanocomposite films obtained (Figure 17) shows a homogeneous dispersion of SNT in the polymer matrix and existence of nanoparticles on the upper membrane surface. Figure 4.2 (**a**) Scheme 1 of the chrysotile hollow tube structure: 85 \(\times\) 53 mm (300 \(\times\) 300 DPI) [130]; (**b**) lattice of chrysotile (Scheme 2 [135]). Figure 4.3 SEM photomicrograph of the surface of PIPAA-PM/SNT nanocomposite film (volume fraction of SNT is 19.6%) [4]. Figure 18 illustrates the relative permeability of oxygen as a function of the volume % SNT in PIPAA-PM/SNT nanocomposite films. The curves represent the theoretical barrier behavior of composites filled with particles of different geometries: Randomly distributed spheres (curve 1), randomly distributed disks aligned perpendicular to the direction of penetration with aspect ratio r/h = 10 (curve 2), uniformly distributed rods with a random and homogeneous distribution in the plane, perpendicular to the direction of permeability with L/d = 1 (curve 3), 5 (curve 4) and 20 (curve 5). The relative gas permeability of composites filled with impermeable spheres was predicted using the Maxwell equation, \(\mathrm{P_{NC}/P_{M}=(1-\phi)/(1+\phi/2)}\), where \(\mathrm{P_{NC}}\) is the permeability of the composite medium and \(\mathrm{P_{M}}\) is the matrix permeability, \(\phi\) is volume fraction of impermeable phase. Relative permeability of composites filled with aligned disks was predicted using the [PERSON]'s equation, \(\mathrm{P_{NC}/P_{M}=(1-\phi)/(1+(f\times r/h))}\), where r is the disk radius and h is the disk thickness. Relative permeability of rods was predicted using an expression derived by [PERSON] and [PERSON]. Figure 18 shows that theoretically the oxygen permeability for PIPAA-PM/SNT tends to decrease between the value for a composite filled with random spheres and the value for a composite filled with randomly distributed disks characterized by a r/h = 10 aspect ratio and aligned perpendicularly to the direction of penetration. The authors emphasize that the ratio r/h \(\sim\)5-10 is a characteristic value of typical mineral additives such as talc, calcite and kaolin. It was found that the values of the oxygen barrier for all the PIPAA-PM/SNT systems studied were significantly lower than the predicted theoretical values, assuming that the rods were randomly dispersed, but aligned with the aspect ratio 20 (curve 5). The aspect ratio L/d = 20 represents the characteristic dimensions of SNT nanoparticles, which were used in the work under discussion, L \(\sim\)400 nm and d \(\sim\)20 nm (Figure 18). The question arises as to why the experimentally measured gas barrier PIPAA-PM/SNT turned out to be lower than the theoretical prediction depicted by curve 5 in Figure 187 According to the authors, one possible reason for this discrepancy is that the SNTs are not aligned exactly in a plane perpendicular to the direction of penetration, which is one of the central assumptions of the model. Figure 4.4 Relative oxygen permeability as a function of vol % of SNT in PIPAA-PM/SNT nanocomposite films. The curves represent theoretical predictions of composites filled with fillers exhibiting different geometries: spherical (1), disks with r/h j 10 (2), and rods with L/d j 1 (3), 5 (4) and 20 (5). Note that subscripts NC and M in the y-axis legend represent PIPAA-PM/SNT and PIPAA-PM, respectively, as described in the text [4]. Another reason for the discrepancy mentioned above is related to the probability of change in the aspect ratio of the nanoparticles actually introduced into the polymer due to the selected conditions for the formation of the composite. For example, brittle failure of CNT as a result of ultrasonic treatment is possible. The barrier of oxygen and water vapor of nanocomposite films was studied in Reference [130], depending on the amount of chrysotile NTs, the degree of their dispersion, and the orientation in the matrix (Table 1).