Finite element simulation and analytical modeling of 3D multi scale diffusion in nanocomposites with permeable stacks

This work is aimed to study the mass transport in 3D 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, which are considered representative of an intercalated nanocomposite. The morphological features of the stacks are the number of lamellae and the thickness of lamellar galleries, which determine the thickness, and therefore the aspect ratio. FE simulation results showed the relevance of diffusion within stack, and therefore the unsuitableness of the assumption of stack impermeability. The diffusion behavior of nanocomposites made of permeable stacks was modeled by considering the probability of collision of diffusing particles on the stack surface. For a random orientation of stacks, the developed analytical model showed an excellent agreement with the FE simulation results. It was shown that other analytical models found in literature are not able to capture the dependence of diffusivity on the morphology of intercalated nanocomposites. The developed analytical model allowed estimating the error arising from the assumption of impermeable stacks in the estimation of nanofiller aspect ratio from experimental diffusivity data.