## 2 Polymer Nanocomposites for Membranes Applications
Splicing interfacial layers with high penetration due to the clustering of nanoparticles can lead to the formation of long, highly permeable, preferred ways for penetrating diffusion. It was found that an increase in the surface area of the filler at its constant volume fraction in the composite, [125] results in a monotonic increase in the penetrant diffusion rate. This is further confirmation that the amount and properties of the polymer modified in the interphase region between the polymer and the filler are key factors determining the amount of gain in the diffusion permeability rate due to the addition of the filler to the polymeric membrane. The authors note that numerical methods, such as finite element method (FEM) and the recently developed material point method (MPM) can be  
Figure 3:9 Relative CO\({}_{2}\)/CH\({}_{4}\) selectivity results for MMMs [124]. Figure 4.0 SEM photos for pure PES membrane and MMMs with different content of MMT. effective in the study of penetrant diffusion in heterogeneous media. In contrast to theoretical solutions based on assumptions about geometric arrangements and distributions over the sizes of different phases, numerical simulation can explicitly study the influence of shapes, sizes and effects of inclusion distribution on the properties of composites [125]. The main assumption of the authors [125] based on experimental data, was that the polymer membrane near the surface of nanoparticles enhances a diffusion of penetrants in comparison with the polymer material. In the model, this region of enhanced diffusion is treated as a \"skin\" on the nanoparticles which in themselves are considered to be impenetrable and are heterogeneously distributed in the polymer matrix. Technology of forming and transport properties of nanocomposites based on latex and layered hydrosilicates depending on content of nano-fillers, surface treatment and nano-fillers distribution in polymer matrix, were investigated in Reference [129]. Transport barrier properties of nanocomposites relative to oxygen and nitrogen increased notably with the increasing of the nano-fillers content in comparison with unfilled polymer. When nanoparticles aggregate then the polymer-inorganic system became not the nano- but micro-composite with insignificant arising of barrier properties. Sometimes the anomalous increase in gas permeability was observed that was explained by the increasing of free volume owing to voids, as a result of nanoparticles aggregations. It has been reported that, depending on the amount of filler used, the aspect ratio of the plates and the state of dispersion of the silicate particles and their orientation, a gas permeability reduction of 20 to 90%, is observed compared to the control of unfilled polymer and of 20 to 60% for nanocomposites based on MMT [130; 131; 132; 133; 134]. An obvious reduction in gas permeability was observed by the authors [4; 130] in the study of polymer-filled composite materials containing nanoparticles of MMTs or synthetic hydrosilicate NTs with chrysotile structure (SNT, Figure 16a,b) [135; 130]. SNTs (Mg\({}_{3}\)Si\({}_{2}\)O\({}_{5}\)(OH)\({}_{4}\)) synthesized under hydrothermal conditions crystallographically and are morphologically similar to the nano-fibrils of a natural asbestos but are considerably shorter [130; 136]. SNTs containing polyimide nanocomposites were prepared by solution mixing-casting method. Figure 4.1 Cont. The introduction of the inorganic phase into the polymer enhances the gas barrier of the polymer. This fact, according to the authors, is associated with a more tortuous diffusion pathway. Oxygen permeability decreased by 24% for PI PAA-PM/SNT containing 4.1 vol % SNT and by 40% for PI PAA-PM/SNT containing 19.6 vol % SNTContrary to expectations, the decrease in water vapor permeability due to the addition of SNT to the polymer was less than the decrease in oxygen permeability. Permeability for water vapor decreased by 1.5% for PIPAA-PM/SNT with 4.7 vol % SNT and 29% for PIPAA-PM/SNT with 19.6 vol % SNT.