The dispersal of nano-sized fillers into the polymer matrix affects the barrier properties of a homogeneous polymer film in two specific ways.
The first way is by creating a tortuous path for gas diffusion.
Because the filler materials are essentially impermeable inorganic crystals, gas molecules must diffuse around them rather than taking a (mean) straight line path that lies perpendicular to the film surface.
The result is a longer mean path for gas diffusion through the film in the presence of fillers, as illustrated in Fig. 2. Essentially, the tortuous path allows the manufacturer to attain larger effective film thicknesses while using smaller amounts of polymer.