Two-dimensional and three-dimensional simulation of diffusion in nanocomposite with arbitrarily oriented lamellae

In this work, a new FE model was developed, in order to simulate the diffusion into polymer nanocomposites in 2D and 3D geometries. The simulation model is based on a random distribution of non-interpenetrating impermeable lamellae with an arbitrary average orientation angle. Simulations were run at different filler volume fractions, aspect ratio and orientation angles. 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 composite (volume fraction, aspect ratio and orientation). The dependency of the normalized coefficient of diffusion on normalized path length was found to follow a simple power law model. In order to account for the normalized path length dependence on filler volume fraction and aspect ratio, a geometrical model was developed, which is based on the probability of collision of diffusing particles on the lamellar surface. For a random orientation of particles, both in 2D and 3D geometries, the developed model showed an excellent agreement with the simulation results. In 3D, the model prediction are even better than the Bharadwaj model prediction.