Material point method simulation 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. The polymer membrane near the surface of a nanoparticle exhibits enhanced penetrant diffusion relative to that of the bulk polymer. In our model this region of enhanced diffusion is treated as a “skin” with a penetrant diffusion coefficient 100 times that of the bulk matrix. 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. 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.