Ab initio investigation of molecular hydrogen physisorption on graphene and carbon nanotubes

Density-functional theory is used to investigate hydrogen physisorption on a graphene layer and on single wall carbon nanotubes. Both external and internal adsorption sites of (9, 0) and (10, 0) carbon nanotubes have been studied with the hydrogen molecular axis oriented parallel or perpendicular to the nanotube wall. A range of hydrogen molecule binding sites has been examined and it is found that hydrogen binds weakly to each of the graphitic structures and at all adsorption sites examined. Calculations using different functionals reveal that the binding energies are a factor of 2 larger for hydrogen bound inside the nanotubes than for adsorption outside the nanotubes or on the graphene layer. Furthermore, configurations of the hydrogen molecular axis parallel to the nanotube wall or graphene layer bind more effectively than configurations where the axis is normal to the carbon nanostructures. The differing behavior between the carbon nanostructures is attributed to the curvature of the structure and the hydrogen-carbon electron interactions, where analysis of the electron density reveals evidence of charge redistribution with little charge transfer. The potential of hydrogen physisorption to carbon nanostructures for hydrogen storage and delivery is also discussed.

Figure 1

Physisorption sites for a hydrogen molecule on a graphene layer. All C–C bonds are $s{p}^2$ hybridized.

Figure 2

Physisorption sites for a hydrogen molecule on a segment of a (10, 0) carbon nanotube. All C–C bonds are $s{p}^2$ hybridized.

Figure 3

Variation of potential energy with the separation between the graphene sheet and the center of mass of the hydrogen molecule in site D using the LDA VWN functional (◻), the GGA PW91 functional (●), and the GGA PBE functional (▵). Inset: close up of the potential-energy minima.

Figure 4

(Color online) Contour map of the change in electron density for a hydrogen molecule placed (a) $7\mathrm{\AA }$ and (b) $2\mathrm{\AA }$ from, and parallel to, the graphene sheet surface across the C–C bond midpoints (adsorption site D). The view is in the plane of the graphene layer, looking end on to the hydrogen molecule (black circle located at the top of the figure). Four carbon atoms in the graphene matrix are labeled by black squares at the bottom of the figure. Scale bar is in units $e∕{\AA }^3$.

Figure 5

(Color online) Contour map of the change in electron density for a hydrogen molecule placed (a) adjacent to a graphene layer at adsorption site D and (b) adjacent to a (10, 0) carbon nanotube at adsorption D. In (a), the ${\mathrm{H}}_2$ is positioned $3.3\mathrm{\AA }$ from the graphene layer. In (b), the ${\mathrm{H}}_2$ is positioned $3.5\mathrm{\AA }$ from the nanotube surface. The ${\mathrm{H}}_2$ is parallel to the surface of both carbon nanostructures. The view of (a) is in the plane of the graphene layer, while the view of (b) is looking down the nanotube axis. Hydrogen atoms are denoted by black circles. Black squares denote carbon atoms. Scale bar is in units $e∕{\AA }^3$.

Figure 6

Variation of binding energies for all carbon nanostructures calculated using the LDA VWN and GGA PW91 functionals. The adsorption sites are listed for binding energies of hydrogen to graphene (◻), (10, 0) carbon nanotube (●), and (9, 0) carbon nanotube (▵).

Figure 7

Potential energy as a function of distance from the (10, 0) nanotube wall. A hydrogen molecule is placed in adsorption site E: parallel to the nanotube surface and the axis of the nanotube.

Figure 8

(Color online) Contour map of the change in electron density for a hydrogen molecule placed inside (a) the (10, 0) and (b) the (9, 0) nanotube. The hydrogen is positioned $3.5\mathrm{\AA }$ away from the nanotube wall (right-hand side of the contour plots) parallel to the surface and the nanotube equator (adsorption site D). Hydrogen atoms are labeled by black circles, while C–C bonds are labeled by black squares that correspond to the nanotube wall. The view is looking down the nanotube axis with the nanotube center line to the left of the map. Scale bar is in units of $e∕{\AA }^3$.