From flakes to ribbons: The barrier factor of composites containing flakes of rectangular shape

We present a comprehensive computational and theoretical analysis of diffusion through flake composites in which the flakes are of rectangular shape, spanning the entire spectrum from squares to ribbons. Following a large number of detailed 3D simulations in realistic Representative Volume Elements (RVEs), each containing 1000s of individual flakes, we propose a scaling which, for the first time in the technical literature, introduces the planar aspect ratio r of the flakes as a parameter affecting the barrier properties of the resulting composite. Subsequently, we examine the effect of r in several cases of practical significance, such as under the assumptions of (i) constant number-density N/ΔV and flake volume fraction ϕ, (ii) constant N/ΔV and flake diagonal and (iii) constant ϕ and varying N/ΔV—describing the problem of the fragmentation of ribbons into flakes. Both deterministic and stochastic systems in terms of r, are considered. One key result is that square flakes offer the best barrier performance compared to flakes of general rectangular shape—as long as N/ΔV and ϕ or the diagonal of the flakes remain constant. Randomness in flake aspect ratio only moderately impacts the barrier improvement factor as long as ϕ and N/ΔV remain constant but has a strong effect under the assumption of constant N/ΔV and flake diagonal. Finally, we show that, for r < 10 and M < 1, the scaling proposed in this work is valid not only for unidirectional flakes but also for flakes showing random in-plane orientations.