This work is aimed to study diffusion in 3-D nanocomposites, characterized by the presence of permeable lamellar stacks, by means of finite element (FE) analysis. To this purpose, a geometric model was developed, based on a random distribution of non-interpenetrating stacks, each one made of regularly spaced platelets. The geometric features of the stacks which define its morphology are the number of lamellae in each stack and the thickness of lamellar galleries. The two quantities, defining the degree of dispersion and the degree of intercalation, respectively, determine the thickness, and therefore the aspect ratio, of the lamellar stacks. Simulation results showed that the normalized coefficient of diffusion only depends on the normalized path length, which is, in turn, dependent on the morphology of the nano-composite. The results also allowed to highlight the relevance of the degree of dispersion and the degree of intercalation on the coefficient of diffusion in the nanocomposites.
The diffusion behavior of nanocomposites made of permeable lamellar stacks was modeled by considering the probability of collision of diffusing particles on the lamellar surface. For a random orientation of lamellar stacks, the developed model showed an excellent agreement with the simulation results. The developed model also allowed to estimate the error arising from the assumption of impermeable stacks when using permeability data in order to calculate the aspect ratio of nanofillers.
