This direct numerical study investigated the effect of orientational randomness on the barrier properties of flake-filled composites. Over 2500 simulations have been conducted in two-dimensional, doubly periodic unit cells, each containing 500 individual flake cross-sections which, besides being spatially random, assume random orientations within an interval [−ɛ, +ɛ] (
). We consider long flake systems (aspect ratio α = 50, 100, and 1000) from the dilute (αϕ = 0.01) to the concentrated (αϕ = 15) regime, where (ϕ) is the flake volume fraction. At each (ɛ) and (αϕ), several realizations are generated. At each of those, the steady-state diffusion equation is solved, the mass flux across a boundary normal to the diffusion direction is computed and an effective diffusivity Deff calculated from Fick’s Law. The computational results for Deff are analyzed and the effects of (ɛ) and (αϕ) are quantified. These differ in the dilute (αϕ < 1) and in the concentrated regimes (1 < αϕ < 15). In the dilute regime, the barrier improvement factor is a linear function of (ɛ) and a power function of (αϕ), with the exponent (∼1.07) independent of orientation. In concentrated systems, we find that for aligned flakes or flakes showing small deviations from perfect alignment, the barrier improvement factor approaches the quadratic dependence on (αϕ) predicted by theory. However, the power exponent is found to decrease as (ɛ) increases, from 1.71 in the aligned system (ɛ = 0) to ∼0.9 in the fully random system (ɛ = π/2). We propose a scaling which incorporates the effects of both (αϕ) and (ɛ) on the barrier improvement factor, resulting in a master curve for all (αϕ) and (ɛ). Our results suggest that the anticipated barrier property improvement may not be realized if the flake orientations exhibit a significant scatter around the desired direction.
