The Barrier Properties of Flake-Filled Composites with Precise Control of Flake Orientation

Abstract

Additive manufacturing, especially in the form of 3D printing, offers the exciting possibility of generating heterogeneous articles with precisely controlled internal microstructure. One area in which this feature can be of significant advantage is in diffusion control, specifically in the design and fabrication of microstructures which optimize the rate of transport of a solute to and from a contained fluid. In this work we focus on the use of flakes as diffusion-control agents and study computationally and theoretically the effect of orientation on the barrier properties of flake-filled composites. We conducted over 1500 simulations in two-dimensional, doubly-periodic unit cells each containing up to 3000 individual flake cross-sections which are randomly placed and with their axes forming an angle ( π 2 θ − ) with the direction of macroscopic diffusion. We consider long-flake systems of aspect ratio ( α ) 100 and 1000, from the dilute ( 0.01 αϕ = ) and into the concentrated ( 40 αϕ = ) regime. Based on the rotation properties of the diffusivity tensor, we derive a model which is capable of accurately reproducing all computational results ( 0.01 40 αϕ < < and 0 π 2 θ < < ). The model requires as inputs the two principal diffusivities of the composite, normal and parallel to the flake axis. In this respect, we find the models of Lape et al. [1] and Nielsen [2] form an excellent combination.Both our model and our computational data predict that at 0 θ > the quadratic dependence of the Barrier Improvement Factor (BIF) on ( αϕ ) is lost, with the BIF approaching a plateau at higher values of ( αϕ ). This plateau is lower as ( θ ) increases. We derive analytical estimates of this maximum achievable BIF at each level of misalignment; these are also shown to be in excellent agreement with the computational results. Finally we show that our computational results and model are in agreement with experimental evidence at small values of ( θ ).

Modeling diffusion mass transport in multiphase polymer systems for gas barrier applications: A review

“…Another recent model has been built by Tsiantis and Papathanasiou, which treated the barrier properties of flake filled composites as a function of fillers orientation. For that purpose, they used a Random Sequential Adsorption (RSA) algorithm to build a RVE of the geometry.…”

A closed-form solution for the barrier properties of randomly oriented high aspect ratio flake composites

“…In all cases, the open-source computational environment OpenFoam was used. Details of the computations have been presented in Tsiantis and Papathanasiou 5 and Papathanasiou and Tsiantis 6 and are omitted here for the sake of brevity. Each geometry (unit cell) contained usually ∼ 3000 randomly placed impermeable flake cross sections; however, unit cells containing 10,000 or 50,000 flake cross sections were also considered.…”

“…In the following, we use the model of Lape et al. 4 for D 11, as it gave the best fit to earlier computational results, 5,6 with a value of λ = 2.5.

Figure 4.Comparison of computational results (points) and the predictions of the arithmetic, harmonic, and geometric averages (equations (2), (6), and (9)) based on the model of Lape et al.

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“…Equation (1) can be used to determine the diffusion coefficient of a system of misaligned flakes, provided D 11 and D 22 are known. In previous work, 5 we investigated computationally the performance of equation (1) and determined that the best agreement with the computational results was obtained when the models of Nielsen 12 and Lape et al. 4 were used for the principal diffusivities, namely D22=D01-ϕ1+ϕ2α and D11=(1-ϕ)(1+αϕ/λ) 2D0 respectively, where D 0 is the diffusivity of the matrix material.…”

“…4 When the flake orientations deviate from perfect alignment, the picture is far less clear. When the flakes assume a fixed orientation with respect to the direction of bulk transport, 5 proposed a model capable of reproducing 2D computational results for (αϕ) up to 40. When the flakes assume random orientations within an interval [−ɛ, + ɛ], numerical results along with an empirical model capable of representing them for (αϕ) up to 15 have been presented in Papathanasiou and Tsiantis.…”