APPLIED PHYSICS LETTERS 100, 203901 (2012)
Migration mechanism for atomic hydrogen in porous carbon materials
Badri Narayanan,1 Yufeng Zhao,2,a) and Cristian V. Ciobanu3,a)
1
Department of Metallurgical & Materials Engineering, Colorado School of Mines, Golden, Colorado 80401,
USA
2
National Renewable Energy Laboratory, Golden, Colorado 80401, USA
3
Department of Mechanical Engineering and Materials Science Program, Colorado School of Mines, Golden,
Colorado 80401, USA
(Received 1 April 2012; accepted 30 April 2012; published online 14 May 2012)
To explain the fast kinetics of H in porous carbon, we propose that the migration relies on H
hopping from a carbon nanotube (CNT) to another. Using density functional theory, we have found
that the barrier for H hopping becomes smaller than that for diffusion along a tube for certain CNT
separations, decreasing to less than 0.5 eV for separations of 3.1 Å. Such significant reduction
occurs irrespective of radius, chirality, registry, and orientation of the two CNTs: the diffusion is
thus facilitated by the porous nature of the material itself. The mechanism proposed is applicable
C 2012 American Institute of Physics.
for any porous carbon-based nanomaterials. V
[http://dx.doi.org/10.1063/1.4718351]
Covalent carbon-hydrogen (C–H) bonds are among the
strongest chemical bonds known in nature and are generally
considered unreactive. C–H activation is a classic problem in
chemistry dating back to the beginning of last century, and is
now becoming ever more important in fundamental chemistry and chemical technology.1,2 Normally, the activation of a
C–H bond must be catalyzed by transition metal atoms.
However, recent progress in atomic hydrogen storage in
nanoscale carbon materials through the so-called spillover
technique3–13 suggests that the chemisorbed H atoms in carbon migrate relatively easily, with kinetics much faster than
that have been theoretically expected.14–16 Fast kinetics is
understandable for traditional H spillover17 in metals or
oxides, in which the hydrogen species involved are active
protons or anions; however, atomic H migration in carbon
materials runs obviously against the current understanding of
C–H chemistry. Therefore, a mechanistic study of such process is necessary both on the fundamental science level and
from the perspective of practical applications.
Here, we propose a mechanism for hydrogen transport
in pure carbon nanotube (CNT) materials, in which the
migration of hydrogen proceeds via hopping of H atoms
between different CNTs. This mechanism occurs because of
a significant lowering of the hopping when CNTs are sufficiently close. Using density functional theory calculations,
we have calculated the pathways for H migration (a) via the
diffusion along the axis of a CNT, and (b) via hopping
between two CNTs. We have found that the barrier for H
hopping between CNTs becomes smaller than that for diffusion along a tube for certain CNT separations, decreasing to
less than 0.5 eV when such separations are 3.1 Å. This substantial reduction of the hopping barrier is present irrespective of the radius, chirality, registry, and relative orientation
of the two CNTs: the H-diffusion is thus facilitated by the
porous nature of the material itself, which allows for fluctuations of the distance between CNTs. The mechanism proa)
Authors to whom correspondence should be addressed. Electronic
addresses: cciobanu@mines.edu and yufeng.zhao@nrel.gov.
0003-6951/2012/100(20)/203901/4/$30.00
posed is applicable for any porous carbon-based materials,
including, e.g., graphitic structures where the natural interplanar separations are already sufficient to facilitate H hoping between carbon layers.
Using the nudged-elastic band (NEB) method18,19 as
implemented in the Vienna Ab-Initio Simulation Package,20,21 we have optimized the pathways for the diffusion of
an H atom along a CNT, and for the hopping of H between
two perpendicular CNTs (Fig. 1). The density functional
theory calculations were performed in the local density
approximation, using projector augmented wave pseudopotentials22 and the Perdew-Wang exchange-correlation functional.23 To study the hopping behavior, the computational
FIG. 1. (a) A hydrogen atom adsorbed on a CNT; the barrier for H diffusion
to a nearby carbon site is over 1 eV. (b) and (c) Hopping of an H atom
between two perpendicular CNTs that have the closest carbon atoms in
registry at a distance d along the z direction [panel (b)], or off-registry, in
which a shift s exists in the x direction for one of the CNTs [panel (c)].
100, 203901-1
C 2012 American Institute of Physics
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203901-2
Narayanan, Zhao, and Ciobanu
supercell was constructed using two CNTs in desired orientation relative to each other to simulate spatial arrays of CNTs.
We have studied configurations of parallel and perpendicular
CNTs (only the latter shown in Fig. 1), nanotubes with different radii, different chiralities (zigzag and armchair), and
different relative registries (Figs. 1(b) and 1(c)). The NEB
optimization of the various transition pathways was carried
out using 9 intermediate points (images) that spatially connect the initial and final states. The plane wave energy cutoff was set to 450 eV for all the ionic relaxations and the
Brillouin zone was sampled using a 2 2 1 MonkhorstPack grid. The atomic coordinates were optimized using a
conjugate gradient algorithm until the residual force on any
atom was smaller than 0.03 eV/Å. For the electronic structure calculations, we used a higher plane wave energy cutoff, 600 eV, and a finer k-point grid, 15 15 1.
In order to illustrate the main ideas of the hydrogen
migration mechanism, we focus here on our results for armchair (n,0) CNTs with n ¼ 7 and 11. The (starting) geometry
of H diffusion along a nanotube is shown in Fig. 1(a), while
Figs. 1(b) and 1(c) show the initial configurations for the
hopping of H between two perpendicular CNTs. In Fig. 2(a),
we show the energy for different configurations (i.e., NEB
images) along the optimized diffusion pathway along the
tube, for armchair tubes with n ¼ 7 and 11. The axial diffusion barrier is rather high, 1.3 eV, for the (11,0) CNT, and
decreases somewhat (by 20%) for the (7,0) CNT; this
small decrease is to be expected because the binding energy
of H with the CNT increases with nanotube radius.24 For the
hopping between two CNTs, the energy barrier is also larger
than 1 eV [Fig. 2(b)] when the CNTs are separated by a distance d ¼ 3.7 Å [as defined in Fig. 1]. At this distance, the
barrier for hopping is very close to the binding energy of H
FIG. 2. Variation of energy along the transition paths for (a) the diffusion of
H along a CNT, and (b) the hopping of an H atom between two perpendicular CNTs.
Appl. Phys. Lett. 100, 203901 (2012)
to one CNT, and also to the barrier associated with the H diffusion along the tube. Interestingly, lowering the distance d
between CNTs to d ¼ 3.1 Å leads to a significant decrease of
the barrier for hopping, to less than 0.5 eV [Fig. 2(b)]. Such a
decrease of the hopping barrier (as compared to the diffusion
along the tube, which is always higher than 1 eV) means that
hopping between nanotubes becomes the dominant mechanism for diffusion of H in nanotube materials—in which the
separation between CNTs can fluctuate by more than 1 Å
even at modest temperatures.
The decrease of the hopping barrier with the inter-tube
distance is a robust result, as it holds for nanotubes of different diameters, as well as for deviations of the relative configuration between the nanotubes [e.g., Fig. 1(c)]. Since the
binding of H to zigzag CNTs is weaker than that corresponding to armchair ones,24 the barriers for H atoms hopping
between zigzag nanotubes are even lower than those shown
in Fig. 2(b). Furthermore, we have found that the decrease of
the barrier for the hopping process holds not only for perpendicular CNTs [Figs. 1(b) and 1(c)], but also for parallel
CNTs as well. The hopping barrier depends critically only
on the proximity of the H atom to a carbon atom on another
CNT. We therefore predict that the marked decrease of the
hopping barrier obtained by bringing the CNT separation to
3 Å is a general characteristic of the H transport in porous
carbon materials. As such, we expect it to hold for any angle
between the CNT axes, and for CNTs of any radius. This
mechanism is also expected to hold in graphitic carbon,
where the layers already have separations that make the
migration by hopping (between carbon layers) favorable.
To investigate the physical origin of the dependence of
the hopping barrier on the proximity of CNTs, we have analyzed the electronic structure of a system containing two perpendicular (7,0) tubes d ¼ 3.1 Å apart at various points along
the optimized hopping pathway of the H atom from one
CNT to another. Figure 3 shows a cross-section of the electron density in the supercell at different positions of the Hatom along the pathway. The position of H atom is identified
by the distance between H and (1) the carbon (C1) in the primary CNT to which it is bonded initially (r1) and (2) the carbon atom (C2) of the (secondary) CNT to which the H hops
(r2).
Initially, the electron density around the H atom overlaps with that of C1 [refer to Fig. 3(a)], indicating the presence of a C1–H bond. The C1–H bond length was observed
to be 1.11 Å, which is close to the value known for methane
and is consistent with bond lengths observed in earlier calculations on chemisorbed H on (7,0) CNT.24 The average bond
angle around C1 was found to be 109.43 , which, along with
the bond length value, suggests that the C1 is in an sp3-hybridized state. The average bond angle around C2 was observed
to be 118.36 , indicating that C2 is predominantly sp2 hybridised. As the H-atom moves away from C1 [see Fig. 3(b)],
the length of the C1–H bond increases from 1.11 Å to
1.18 Å; the charge density of the H-atom, however, continues
to overlap with that of C1 and does not interact with C2. Figures 3(c) and 3(d) illustrate that, as the H atom approaches
C2, the electron density between C1 and H decreases so the
C1–H bond weakens. At the same time, the interaction
between H and C2 increases, as indicated by a gradual
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203901-3
Narayanan, Zhao, and Ciobanu
Appl. Phys. Lett. 100, 203901 (2012)
FIG. 3. Cross-sectional view of the electronic charge distribution in a supercell containing two CNTs oriented perpendicular to each other [as in Fig.
1(c)] separated by a distance of d ¼ 3.1 Å and a hydrogen atom at various
points along the hopping pathway. Panel (a) corresponds to the initial state,
(b)-(e) correspond to four (of the nine) intermediate states, and (f) to the
final state.
increase in electron density between them [Figs. 3(c) and
3(d)]. In the intermediate state [Fig. 3(c)], the H atom is present in the zone of influence of both carbon atoms C1 and C2.
Finally, we observe that the C1–H bond breaks [see Fig.
3(d)] while the C2–H bond forms, as shown in Figures 3(e)
and 3(f). The final C2–H bond length was found to be 1.11 Å
and the average bond angle around C2 to be 109.43 . This
shows that the hybridization state of C2 changed from sp2
[in Fig. 3(a)] to sp3 [in the final state of Fig. 3(f)], due to hopping of H and its bonding with C2.
To further illustrate that in an intermediate state the H
atom interacts with both C1 and C2 and that the hopping barrier decreases as a result of this interaction (which weakens
the C1–H bond), we have also analyzed density of states.
Figure 4 shows the projected density of states (PDOS) on
atoms C1, C2, and H for (a) initial, (b) intermediate, and (c)
final states of H hopping between the two CNTs. In the initial state [Fig. 3(a)], six different bonding peaks (i.e., situated
below the Fermi level) of H have common positions with
those of C1 [shown by the dash lines in Fig. 4(a)], indicative
of the C1–H bond and consistent to the electron distribution
in Fig. 3(a); as seen in Fig. 4(a), there are also two antibonding peaks (above the Fermi level, dotted lines), but they are
relatively small. Figure 4(b) shows that two bonding peaks
are common to H, C1, and C2 in the intermediate state [Fig.
3(c)]. Thus, in the intermediate configuration, the H atom
interacts (albeit weakly) with both C1 and C2; the strong
antibonding peaks common to C1 and H [dotted lines above
the Fermi level in Fig. 4(b)] indicate that at somewhat higher
electron energies breaking of the C1–H bond can readily
FIG. 4. Site PDOS for the carbon atom to which the hydrogen is initially
bonded (C1, red line), the carbon atom to which H hops (C2, black line),
and the hydrogen atom (H, blue line) at various stages along the hopping
pathway between two perpendicular CNT’s separated by d ¼ 3.1 Å (a) the
initial state, (b) an intermediate state with H slightly closer to C2 than to C1,
and (c) the final state. The vertical dashed (dotted) lines are a guide to the
eye to show the bonding (antibonding) peaks that overlap. All the energies
are relative to the Fermi level of each structure.
occur. In the final configuration, the bonding peaks of H
coincide with only with some of the peaks of C2 [Fig. 4(c)],
consistent with the formation of the C2–H bond and the
breaking of C1–H. Our electronic structure analysis (Figs. 3
and 4) therefore shows that when the CNTs are sufficiently
close to one another, the H atom begins to interact with the
C2 atom prior to the breaking of C1–H; this interaction
weakens the C1–H bond and facilitates the hopping process
(i.e., decreases the barrier associated with it).
In summary, we have proposed that the hopping of H
atoms between nanotubes is the mechanism responsible for
the fast kinetics of hydrogen in pure carbon materials. We
have shown that energetic barrier for the hopping of H from
one CNT to another in porous carbon can be lowered to
below 0.5 eV by bringing the distance between CNTs to
3 Å: this makes the hopping between CNTs the dominant
mechanics over axial diffusion of H along any one CNT,
since the latter has always barriers of at least 1 eV. Our
results provide an explanation for the experimentally
observed rapid migration of H through porous materials, and
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203901-4
Narayanan, Zhao, and Ciobanu
suggest that the kinetics of hydrogen in these materials can
be relatively easily controlled by modifying the spacing
between CNTs (e.g., by applying small strains). In fact, even
thermal activation of breathing modes can cause the distance
between two carbon surfaces to decrease down to 3 Å or less,
which effectively promotes the diffusion of hydrogen
through the porous carbon material.
We gratefully acknowledge support from the DOE
Office of Basic Energy Sciences through Grant No. DEFG02-07ER46397 (B.N.), DOE Office of Energy Efficiency
and Renewable Energy Hydrogen, Fuel Cell, and Infrastructure Technologies Program through the Hydrogen Sorption
Center of Excellence under Grant No. DE-AC3699GO10337 (Y.Z.), and from NSF through Grants No.
CMMI-0846858,-0825592 (C.V.C.). Computations were carried out at the NREL facilities and at the Golden Energy
Computing Organization.
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