Barrier properties of -mer packings

Lebovka, Nikolaï; Khrapatiy, S. V.; Vygornitskyi,; Pivovarova, N. S.

doi:10.1016/j.physa.2014.04.019

Cited by 6 publications

(5 citation statements)

References 36 publications

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“…The implication of these results is significant. While the BIF of the aligned flake composite shows a near-parabolic increase with (αϕ), as would be expected from theory, 8,9 randomly oriented composites deviate from that behavior and, instead, achieve BIF values which seem to plateau for increasing (αϕ) at a fraction of the BIF of the corresponding aligned composite. A similar result is implicit in the work of Lusti et al.…”

Section: Resultssupporting

confidence: 69%

“…When the flakes are randomly placed and well aligned, the predicted barrier efficiency improvement ranges from being ∼(αϕ) in dilute systems, where (α) is the aspect ratio and (ϕ) the flake volume fraction, to being ∼(αϕ) 2 in more concentrated dispersions. 6,8,9 Considering the usually large flake aspect ratio, significant barrier property improvement can be achieved by adding a small amount of filler. Computational and experimental studies are in agreement with these predictions.…”

Section: Introductionmentioning

confidence: 99%

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Orientational randomness and its influence on the barrier properties of flake-filled composite films

Papathanasiou

Tsiantis

2016

Journal of Plastic Film & Sheeting

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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] ([Formula: see text]). 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.

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Section: Resultssupporting

confidence: 69%

Section: Introductionmentioning

confidence: 99%

Orientational randomness and its influence on the barrier properties of flake-filled composite films

Papathanasiou

Tsiantis

2016

Journal of Plastic Film & Sheeting

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“…This oversimplified approximation was used only for qualitative estimations of the barrier properties of a dense layer on the drying rate. In the general case, the barrier properties can depend on details of the structure, density and thickness of the layer of sticks oriented along the evaporating interface (see [46] and references therein for the details). The transition from the isotropic to the ordered nematic phase was observed at ρ ≈ 7 [23,24].…”

Section: Computational Modelmentioning

confidence: 99%

Vertical drying of a suspension of sticks: Monte Carlo simulation for continuous two-dimensional problem

2018

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The vertical drying of a two-dimensional colloidal film containing zero-thickness sticks (lines) was studied by means of kinetic Monte Carlo (MC) simulations. The continuous two-dimensional problem for both the positions and orientations was considered. The initial state before drying was produced using a model of random sequential adsorption with isotropic orientations of the sticks. During the evaporation, an upper interface falls with a linear velocity in the vertical direction, and the sticks undergo translational and rotational Brownian motions. The MC simulations were run at different initial number concentrations (the numbers of sticks per unit area), p_{i}, and solvent evaporation rates, u. For completely dried films, the spatial distributions of the sticks, the order parameters, and the electrical conductivities of the films in both the horizontal, x, and vertical, y, directions were examined. Significant evaporation-driven self-assembly and stratification of the sticks in the vertical direction was observed. The extent of stratification increased with increasing values of u. The anisotropy of the electrical conductivity of the film can be finely regulated by changes in the values of p_{i} and u.

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“…It is known that incorporation of such fillers aligned perpendicular to the direction of macroscopic diffusion is very effective in increasing the barrier properties. Both theoretical results and computational studies have shown that, for flakes aligned perpendicular to the direction of macroscopic diffusion, the improvement in the Barrier Improvement Factor (BIF) ranges from being ~(αφ) in dilute systems, where (α) is the aspect ratio and (φ) the volume fraction of the flakes, to being ~(αφ) 2 in more concentrated dispersions [3][4][5][6][7]. When the orientation of the flakes deviates from perfect alignment, it is known that the BIF decreases; however no universally accepted models to predict this effect exist and only limited computational results have been presented, with the exception of the recent studies of [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Computational analysis of transport across flake-filled composites of realistic microstructure

Tsiantis

Sumbekova

Papathanasiou

2019

AIP Conference Proceedings

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In this paper we present the results of a computational study of diffusion across disordered flake composites in which the flakes are misaligned with respect to the direction of bulk diffusion. We evaluate the effect of flake orientation as well as the influence of boundary conditions and unit-cell types on the predicted barrier properties. Flake orientation impacts very significantly on the barrier properties in flake-filled composites, and usually the key objective in their fabrication is to orient them as close as possible to being perpendicular to the direction of macroscopic diffusion. Our computations are carried out in two-dimensional, doubly-periodic unit cells, each containing up to 3000 individual flake cross-sections. We consider high aspect ratio (α) systems with α=1000, from the dilute (αφ=0.01) and into the very concentrated (αφ=40) regime. The effective diffusivity of the corresponding unit cells is computed from the imposed concentration difference and the computed mass flux, using Fick's Law. We show that use of cyclic boundary conditions and doubly-periodic unit cells results in effective diffusivities which are in agreement with theory and invariant of the shape of the unit cell. We also show that the use of adiabatic boundary conditions produces erroneous results at high flake concentrations. Finally we compare our results to the predictions of existing literature models and find that the latter deviate significantly from computation at high flake concentrations.

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Barrier properties of -mer packings

Cited by 6 publications

References 36 publications

Orientational randomness and its influence on the barrier properties of flake-filled composite films

Orientational randomness and its influence on the barrier properties of flake-filled composite films

Vertical drying of a suspension of sticks: Monte Carlo simulation for continuous two-dimensional problem

Computational analysis of transport across flake-filled composites of realistic microstructure

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