Effect of interfacial transport on the diffusivity of highly filled polymers

The diffusivity of substances, such as moisture, through polymer composites is often described by an effective macroscopic quantity, even though microscopically the diffusivity might be far from uniform. In this work, we study the theoretical example of a permeable matrix containing equal-sized impermeable spheres. We assume that, due to interface effects, the diffusivity of the matrix in the vicinity of the spheres is higher than its bulk matrix diffusivity. Using numerical simulations of the composite's diffusivity, we show that upon the formation of large clusters of the highly permeable interfaces, i.e. near percolation of the spheres, the diffusivity of the composite rises sharply. For even higher values of the volume fraction of the spheres, up to the close-packing limit, the diffusivity decreases due to the increased tortuosity. This effect is well described by an analytical solution for the composite's diffusivity.