The Multifractal Model of Sorption Processes for Nanocomposites

As it is known [50-52], introduction of organoclay in a polymeric matrix results in essential reduction of permeability to gas of the nanocomposites obtained by such a mode in comparison with a matrix polymer. As a rule, such permeability to gas reduction is explained by an increase in the meandering trajectory of the gas-penetrant molecules through the nanocomposite by virtue of the availability of organoclay anisotropic particles within it [50, 52]. So, the relative permeability to gas characterising a reduction in this parameter for nanocomposites in comparison with a matrix polymer, is defined as follows [50]  

As it has been shown in paper [58], in stationary diffusion conditions at duration t = const, the relationship is fulfilled  

The multifractal treatment [57] allows the value of Q to be determined as follows  

The authors of paper [59] offered the following equation for estimation of the diffusivity of semi-crystalline polymers  

The direct analogy between nanocomposites and semi-crystalline polymers is contained in the fact that both indicated classes of polymeric materials have regions which are impenetrable for transport processes (nanofiller and crystallites, respectively). Therefore the indicated processes are realised through the polymer matrix and amorphous phase, respectively. Hence, from the comparison of Relationships 7.16-7.18 it can be written [56]  

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