Numerical simulation and mathematical modeling of 2D multi-scale diffusion in lamellar nanocomposite

In this work, FE analysis was used to study steady-state diffusion into 2 D polymer nanocomposites. The developed FE model is made of randomly distributed and randomly oriented permeable lamellar stacks made of a certain number of platelets, separated by galleries. The model is able to account for diffusion occurring between lamellar stacks, as well as within stacks, inside lamellar galleries. This allows to account for different morphologic features of the nanofiller, including the number of lamellae in each stack, which defines the degree of dispersion, and the lamellar gallery thickness, indicative of the degree of intercalation. 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 nanocomposite. Besides the aspect ratio and volume fraction of the nanofiller, also the degree of intercalation and the degree of dispersion play a significant role in determining the barrier properties of nanocomposites. The behavior of nanocomposites made of permeable lamellar stacks was represented by introducing a geometrical model, which is based on 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.