## 1 Introduction
The results confirm our expectation that the morphology of the nanoparticles (platelets, tubes or isometric form) and especially their aspect ratios strongly influences the viscoelastic properties of the nanocomposites in both their solid and liquid states. Therefore, understanding the role of the nano-filler variables such as morphology, aspect ratio and composition on the properties of polymer nanocomposites could lead to development of new materials with optimal properties for targeted application areas. It was shown that tensile strength and deformation-at-break of the PI-PM-based nanocomposite films decreased slightly with increasing concentrations of the nano-filler used to an extent that depends on the specific characteristics of the nano-filler used, in particular, on its ability to aggregate. This decrease in tensile strength may be attributed to the less than optimum adhesion between the nano-fillers and the matrix and the possible formation of an inhomogeneous network structure density in the nanocomposite. Despite the reduction of the tensile strength caused by the incorporation of the nano-fillers in the polyimide nanocomposites, authors noted that the incorporation of relatively high concentrations of SNT and ZrO\({}_{2}\) (up to 10 vol %) do not lead to a drastic decrease of elongation-at-break (\(\varepsilon_{\mathrm{t}}\)) that is widely reported in the literature for a number of PI nanocomposites containing organo-clay nano-fillers [13; 14]. This important benefit offered by the SNT and ZrO\({}_{2}\) was believed to be due to the desirable intrinsic properties of these particles that can be prepared with the prescribed properties for specific applications including polymer nanocomposites, as already mentioned [11; 15]. It was shown that an improvement in the mechanical characteristics of the material was achieved by introducing into the polymer matrix (poly[1,3-bis(3,4-dicarboxyphenoxy)benzene [4,4-bis(4\"-N-phenoxy)-diphenyl sulfone]imide) (PI P-SOD)) about 10% MMT [16]. For this purpose, the MMT has been pre-modified (aminoethylaminomethyl)phenethyltrimethoxysilane. After the filling of PI P-SOD with magnesium silicate nanoparticles modified with silane (10 wt %), the nanocomposite strength increased by 15%, bending elastic modulus and shear elastic modulus by a factor of 1.4. Incorporation of magnesium hydrosilicate NTs in polymer films improved their mechanical properties without notable increasing of brittleness. It was shown that the average increase in the modulus value of a nanocomposite was equal 0.15 GPa per 1 wt % of incorporated NTs. Increasing in mechanical properties was observed in composites containing up to 15 wt % of magnesium NTs, simultaneously with increasing of thermo-stability. These nanocomposites possessed low dielectric constants also (\(\sim\)2.0) [4]. A number of other properties and potential applications are of interest including thermal stability, flammability resistance, electrical/electronic properties, barrier properties, membrane properties and others [1; 2; 4; 11; 17; 18]. Normally, the addition of low-permeability fillers (such as silica) into non-porous polymer film reduces penetrant diffusion simply by volume-fraction effects [19]. The free volume decreases in these types of composites and leads to decreased molecular transport of permeate, because their molecules do not dissolve in the crystalline region of a polymer. The development of polymer membranes with inorganic crystalline fillers was considered for increasing their barrier properties with respect to gases and liquid medium [20; 21; 22]. In some cases, when nano-particles are intercalated into polymeric matrices, they are known to increase the overall mechanical strength and barrier properties [23]. Since the issue of the transport properties optimization of nanocomposite polymer membranes remains relevant to this day, there have been attempts to make some generalizations known; review papers [1; 5; 13; 24; 25; 26; 27; 28; 29].