Graphene: A perfect nanoballoon

Abstract

We have performed a first-principles density functional theory investigation of the penetration of helium atoms through a graphene monolayer with defects. The relaxation of the graphene layer caused by the incoming helium atoms does not have a strong influence on the height of the energy barriers for penetration. For defective graphene layers, the penetration barriers decrease exponentially with the size of the defects but they are still sufficiently high that very large defects are needed to make the graphene sheet permeable for small atoms and molecules. This makes graphene a very promising material for the construction of nanocages and nanomembranes.Graphene is one of the most studied materials these days, which has resulted already in a large amount of proposals for possible applications. 1 These applications range from very sensitive gas sensors 2 to carbon-based electronics 3 and are mainly based on the essentially twodimensional (2D) form of graphene and the Dirac-like behavior of the electrons at the Fermi level. 4 Recently it was experimentally shown that perfect graphene sheets are impermeable to standard gases, including helium. 5 This introduces a new range of applications for graphene as an ultrathin, but still impermeable, membrane. In Ref. 5, Bunch et al. suggested also that the graphene samples should be free of defects to explain the impermeability. This suggestion was based on a simple classical effusion theory calculation of the penetration of point particles through single atom vacancies in graphene. In this letter, however, we demonstrate through ab initio calculations that defective graphene is still impermeable and that large defects are needed to destroy this impermeability. In our study we concentrate on the penetration of helium atoms through graphene with increasingly large defects. Helium atoms are the smallest atoms that do not chemically interact with graphene. We limit ourselves to point defects that keep the sp 2 hybridization of the carbon atoms of graphene more or less intact. Such defects are more stable 6,7 and easier to treat in first-principles calculations.We make use of the density functional theory (DFT) formalism in both the local density (LDA) and general gradient approximation (GGA). All our DFT calculations are performed with the ABINIT 8 software package. The simulation of most defects is done in a 4 × 4 × 4 graphene supercell with a distance of 16Å between adjacent graphene layers. A plane-wave basis with a cutoff energy of 30 Hartree (816 eV) was used and the Brioullin zone (BZ) is sampled with a 6 × 6 × 6 Monckhorst-Pack (MP) 9 k-point grid which is equivalent to a 24 × 24 × 24 MP grid in a single unit cell. We used pseudopotentials of the Troullier-Martins type 10 for both the LDA and GGA calculations. There is no need to perform spinpolarized calculations because the defects were chosen to preserve the sp 2 hybridization of the carbon atoms in the simulated defective graphene sheets and the He atom is inert.We first examine the penetration of a helium atom throug...

Janus graphene from asymmetric two-dimensional chemistry

“…Graphene is composed of carbon atoms that are held together by strong covalent bonds, which are theoretically predicted 35 and experimentally confirmed [36][37][38][39][40] to be impermeable to small atoms and molecules as a perfect nanoballoon at room temperature. This is a prerequisite for its bifacially nonsymmetrical modification.…”

Ab initiostudies of hydrogen adatoms on bilayer graphene

“…As suggested by Leenaerts et al, 39 the implication is that both sides of the bilayer graphene has to be exposed to hydrogen for the transformation to occur because graphene is hard to penetrate. 63,64 In configurations c 2 and c 7 , the bond lengths in the hydrogen-free bottom layer still retain their graphitic values of 1.42 Å. The difference between the H-adsorption sites in configurations c 2 and c 7 (see Fig.…”

Porous graphene: Properties, preparation, and potential applications

“…Apart from its atomic thickness, graphene is an excellent electrical conductor and capable of enduring large trans-membrane pressures [44,45]. Theoretical investigations have proved the feasibility of its use [20], and experiments are also making progress.…”

“…Since the membrane permeability is inversely proportional to its thickness [43], these traditional membranes seem inferior to graphene, which is only one-atom thick. However, a perfect graphene is impermeable even to the smallest gas atom, helium, since the densely packed honeycomb crystal lattice is strong enough to prevent atoms and molecules from passing through it [44,45]. To explore its potentially high permeability, it is therefore necessary to introduce pores into the graphene planes.…”