According to FESEM images, f-MWNTs are well dispersed inside the polymer matrix at different loadings, whereas r-MWNTs are agglomerated at high concentration. When CNTs are well distributed in the polymer matrix the gas molecules pass through nanotubes channels, which offer high permeability. However, in the case that nanotubes agglomerate in the polymer matrix, it is likely that the tortuosity around the agglomerated CNTs decreases the gas permeability. This behavior was predicted by the ‘‘torturous path’’ model by detouring the penetrants along a longer path while defusing across the membrane [67]. According to this model, the reduction in gas permeation rates of MMMs with the addition of r-MWNTs is attributed to the agglomeration of nanotubes through the polymer matrix. In this case, the effective diffusion coefficient decreases with increasing crystallinity due to the longer/more tortuous path that the gas molecules should bypassed the impermeable regions while defusing through the membrane [68]. Besides, gas permeation results made it clear that increase in f-MWNTs loading decreased the gas permeability and increased the ideal selectivity of MMMs. The decrease in gas permeability and the increase in the ideal selectivity of MMMs containing f-MWNTs are due to the inappropriate orientation of nanotubes inside the polymer matrix. This is because the unsuitable orientation of f-MWNTs through the polymer matrix detours gas molecules along a longer path while defusing through the membrane, which decreases gas permeabilitis, and at the same time increases the ideal selectivity. Embedding the filler into the polymer matrix causes the compacting or loosening of the polymer chain structure. For better clarification, the free volume of MMMs was investigated experimentally [28] and the results are presented in Table 6.