A general scaling for the barrier factor of composites containing thin layered flakes of rectangular, circular and hexagonal shape

Abstract

We propose a general scaling which allows for the results of 3D mass transfer computations in layered flake composites containing square, circular or hexagonal flakes to collapse on a single master curve. We show that the Barrier Improvement Factor (BIF ~ 1/Deff) of such composites is well represented by a power function of that scale (M) namely BIF=(1+M)2. Our simulations are carried out in three-dimensional multi-particle RVEs each containing up to 4000 randomly placed individual flakes. The flakes are represented as two-dimensional squares, disks or hexagons; this representation is suitable for very thin flakes, such as exfoliated nano-platelets. Around 3000 simulations are carried out, and the effective BIF is computed for different values of flake orientation, shape, dimensions and number density. We show that our scaling is consistent with the traditional representation of the BIF as a power function of (αϕ), (α) and (ϕ) being the aspect ratio and the volume fraction of the flakes, while at the same time offering a generalized approach that is valid for all flake shapes. When the flakes are layered at an angle (θ) to the direction of macroscopic diffusion, we propose a model for the BIF in terms of the principal diffusivity and (θ); this is found to be in very good agreement with computational results, which show that while the BIF increases with increasing (M), this increase is no longer monotonic but, instead, BIF approaches an asymptotic plateau value which is determined by (θ).