A 3-D approach to model diffusion in randomly distributed nanocomposite

The mass transport properties of a system with impermeable platelets dispersed in a polymer matrix were investigated, through a numerical algorithm, based on finite volume method. Simulations were carried out on 3-D geometries where different shapes of the lamellae were considered, dispersed in both an ordered and random way; different volume fractions φ and aspect ratios α of the platelets were considered, and, in the ordered structures, also different values of the flakes spacing σ were investigated. In the case of random systems, multiple structures were analyzed for a given set of parameters and the results were treated statistically to obtain reliable information. The results show that the permeability in ordered geometries decreases with the product α φ and that the curves corresponding to different filler shapes have a similar qualitative behavior but quantitative differences in the enhancements of the material barrier properties; circular platelets in particular, showed to be less efficient than other geometries in decreasing the effective diffusivity of the composite. All 3-D structures then showed diminished barrier properties with respect to homologous 2-D structures suggesting that the use of the latter approach would lead to an overestimation of the barrier properties increases in real nanocomposites and thus, despite its simplicity, should not be used for this purpose. The data relative to 3-D random dispersions, that show barrier properties even worse than those of ordered dispersions of circular lamellae, can be accurately predicted by the Nielsen's model approach which therefore seems more suitable to describe the properties of real materials.