Using calculations from first principles and harmonic transition state theory, we investigated the permeability of a single graphene sheet to protons and hydrogen atoms. Our results show that while protons can readily pass through a graphene sheet with a low tunneling barrier, for hydrogen atoms the barriers are substantially higher. At the same time, the presence of defects in the membrane can significantly reduce the penetration barrier in a region that extends beyond the defect site itself.

The transition from single-file diffusion to Fickian diffusion in narrow cylindrical pores is investigated for systems of rigid single-walled armchair carbon nanotubes, solvated with binary mixtures of Lennard-Jones fluids (Ar/Ne, Ar/Kr, and Ar/Xe). A range of effects is examined including the mixture concentration, the size ratio of the two components, and the nanotube diameter. The transition from single-file to Fickian diffusion in varying carbon nanotube diameters is analyzed in terms of the Fickian self-diffusivity and the single-file mobility of the mixture components. It is found that the single-file to Fickian carbon nanotube transition diameter is a unique property of the individual molecule’s diameter and remains unchanged regardless of the mixture composition. In applications of binary mixtures, each component may crossover from single-file to Fickian diffusion in a different carbon nanotube diameter, giving rise to bimodal diffusion in some nanotubes. This transition allows for one species to diffuse in single-file while the other diffuses by a Fickian mechanism, yielding orders of magnitude difference between the self-diffusional rates of the two molecules. This phenomenon might be further extended to alter the diffusional motion of molecules in nanoporous materials.