| Summary: | Composite films of a graded miscrostructure hold the promise of achieving optimal use of the filler material, resulting in composites with improved and application-taylored properties. In the context of barrier materials in which the reinforcing phase comes in the form of flakes or platellets, concentrating the filler particles in certain critical regions is thought to achieve economy in filler usage while ensuring superior barrier performance. The objective of the present article is to quantitatively test this hypothesis and provide guidelines on the expected barrier improvement. A model is developed, according to which a graded miscostructure in a composite film offers a quantitative improvement over an equivalent homogeneous microstructure; this improvement is quantified using a coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>, which depends on the form of the graded miscrostructure, specifically the distribution of the number-density of the filler particles across the film. It is shown that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> for a uniform microstructure and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula> for a graded one, indicating that a graded miscrostructure will indeed result in improved barrier properties. Analytical expressions for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> are developed for certain typical distributions; for a linear filler distribution, it is shown that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>=</mo><mn>4</mn><mo>/</mo><mn>3</mn></mrow></semantics></math></inline-formula>. This model is tested against detailed multi-particle simulations and is found to be in excellent agreement with computational results.
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