Modeling of enhanced penetrant diffusion in nanoparticle-polymer composite membranes

We have utilized 2D material point method (MPM) to study the influence of nanoparticles on the diffusivity of penentrants in model polymer membranes comprised of impenetrable spherical nanoparticles dispersed in a matrix with uniform penetrant solubility and diffusivity. Diffusion in the nanoparticle-polymer composite membrane was enhanced by the presence of a thin “skin” of matrix material next to the surface of the nanoparticles with a penetrant diffusion coefficient 100 times that of the bulk matrix. The influence of the skin thickness, nanoparticle area fraction and the manner in which the nanoparticles were distributed in the membrane on penetrant diffusion was studied. For a given skin thickness the penetrant diffusion in the composite membrane was found to increase exponentially with increasing area fraction of nanoparticles both above and below the percolation threshold. Membranes with clustered nanoparticles were found to have higher penetrants diffusivity than the membranes with fully dispersed particles due to the formation of anisotropic nanoparticle clusters. We found the total area fraction of particles + enhanced matrix (skin) to be a valid scaling variable for the effective diffusion coefficient of the nanoparticle-polymer composite membranes for the entire range of skin thickness and nanoparticle loadings investigated. Implications of the observed dependencies of effective penetrant diffusivity in the composite membrane on nanoparticle loading, skin thickness and nanoparticle morphology are discussed.