Diffusion in Lamellae, Cylinders, and Double Gyroid Block Copolymer Nanostructures

We study transport of penetrants through nanoscale morphologies motivated by common block copolymer morphologies, using confined random walks and coarse-grained simulations. Diffusion through randomly oriented grains is 1/3 for cylinder and 2/3 for lamellar morphologies versus an unconstrained (homopolymer) system, as previously understood. Diffusion in the double gyroid structure depends on the volume fraction and is 0.47-0.55 through the minority phase at 30-50 vol % and 0.73-0.80 through the majority at 50-70 vol %. Thus, among randomly oriented standard minority phase structures with no grain boundary effects, lamellae is preferable for transport.