FIGURE 1) Three different polyhedra of carbon and hydrogen; (a)
cubane, (b) dodecahedrane, and (c) a side and top view
of a single-wall exohydrogenated carbon nanotube.
Hydrogen-carbon interactions have been studied extensively both
theoretically and experimentally for many interesting polyhedral molecules,
such as cubane (C8H8), dodecahedrane (C20H20),
and various isomers of C60Hn (see Fig.~1).
Despite its very strained 90o CCC-bond angle
cubane has been synthesized successfully (Fig.~1a).
Similarly, dodecahedrane and various isomers of C60Hn
(up to n=32) have been also synthesized.
These novel polyhedral molecules which represent the zero dimensional
case, exhibit many interesting properties. However, due to the one
dimensional nature and the curvature of carbon nanotubes, the
hydrogen-carbon interactions in these systems may be quite different
than those in polyhedral molecules. Therefore, it is important to know
if it is also possible to hydrogenate carbon nanotubes in a similar way
and if so what their structural and electronic properties would be.
This paper addresses this important issue by performing extensive
first-principles calculations and shows that the chemisorption of
hydrogen is dependent on the radius and chirality of the nanotubes.
Theoretical predictions from first-principles studies played an important
role in guiding experimental studies in the
past and we expect that many findings
reported here may have important implications in this interesting system
as well.
TABLE 1.
Various parameters of the fully optimized structures of exohydrogenated
armchair and zigzag carbon nanotubes and other polyhedral molecules.
For graphene (i.e. RCH --> inf.) dCH and dCC
are 1.066 A and 1.622 A, respectively.
The stability and energetics of CH-bond formation are derived from the
average binding energy per atom for exo-hydrogenated nanotubes defined as
FIGURE 2.
(a) Binding energies EB of (n,n) (square)
and (n,0) (circle) nanotubes as a function of RCH. The solid and
dashed lines are one parameter fits to EB = E0 -C(n,m)/RCH
as discussed in the text. Inset shows the binding energies of cubane,
dodecahedrane, and C60H60.
(b) Full circles indicate the energy to break a single
CH-bond to form a CnHn-1 zigzag nanotubes as depicted in the
top inset. Full squares indicate energy gain DEG by attaching
a single H atom to a nanotube to form a CnH as depicted in the bottom
inset. The solid and dashed lines are two parameter fits as discussed in
the text, indicating 1/RHC behavior.
Even though CnHn nanotubes are found to be stable
with respect to a pure carbon nanotube (Cn) and n H atoms
for all values of the radius, it is of interest to see if they are also
stable against breaking a single CH-bond. We, therefore, calculated
energies of fully optimized hydrogenated nanotubes after breaking one
of the CH-bonds and putting the H atom at the center of supercell as
shown in the top inset to Fig.~2b.
We note that for radius around RHC ~ 6.25 A, the
binding energy becomes negative, suggesting instability.
Hence, (12,0) and (8,8) nanotubes are at the limit for stable, fully
exo-hydrogenated nanotubes. We are currently studying this
problem for half-coverage case as well.
The energy, DEG, gained by attaching a single H atom to a
carbon nanotube is calculated by performing structure optimization of a
CnH-nanotube as depicted in the bottom inset to Fig~2b.
Unlike DEG, there is no change in the sign of DEG,
suggesting that for any radius of carbon nanotube hybridization of
a single carbon atom is always stable. However the energy
gain from two such processes is around 5--6 eV which is
slightly less than the dissosiation energy of H2, 6.65 eV.
Hence Cn nanotube plus H2 system is stable
against forming a CnH2 hydrogenated nanotube. Therefore,
in order to realize the CH-bonding discussed here, one first has to break
H2 molecules into hydrogen atoms, probably by using
a metal catalyst or electrochemical techniques.
FIGURE 3.
Band gap as a function
of tube radius RHC. Inset shows the full scale plot to include
the band gaps of the polyhedral molecules.
Hydrogenation of nanotubes is also important in the modification
of the electronic structure for device applications.
Figure 3 shows the density of states (DOS) for a (9,0) exo-hydrogenated nanotube,
which is typical to other nanotubes that we studied. Using projected DOS, we find that
the bottom of the conduction bands are mainly derived from hydrogen
while the top of the valence bands are mainly carbon-origin.
In contrast to pure nanotubes which are metal or semiconductors
depending on their structure, the CnHn nanotubes are found
to be direct band insulators with a gap of 1.5--2 eV at the Gamma-point.
This value is about one-third of those for the molecular polyhedrals,
indicating less stability of hydrogenated nanotubes than molecules.
The band gaps decrease with increasing tube radius but unlike
binding energies there is no apparent 1/RHC type behavior.
Interestingly, the band gaps of armchair
nanotubes are higher in energy by about 0.2 eV than those in
zigzag nanotubes. This is surprising because the band gap is usually
higher for more stable saturated hydrocarbons.
FIGURE 4.
The observed band gap opening via hydrogenation of nanotubes can be used for
band gap engineering for device applications such as metal-insulator
heterojunctions as shown in this figure.
For example, various quantum structures (see Fig.4) can easily be realized on
an individual carbon nanotube, and the properties of these structures
can be controlled by partial hydrogenation of carbon nanotubes.
If the different regions of a SWNT are covered with
hydrogen atoms, the band gap and hence the electronic structure
will vary along the axis of the tube. This way various quantum
structures of the desired size and electronic character
can be formed. In this respect, present scheme is quite similar to our
previous constructions of nanotube heterostructures or quantum dots,
where periodic applied transverse compressive
stress is used for band gap opening.
EB = ( ECnHn - EC
- n EH)/n .
Here ECnHn , EC, and
EH are the total energies
of the fully optimized exo-hydrogenated nanotube, nanotube alone, and
hydrogen atom, respectively. According to this definition, a stable
system will have a negative binding energy. Figure 2a shows the radius
dependence of EB for nanotubes and polyhedral molecules (see inset).
Two interesting observations are apparent. First, as shown by solid and
dotted lines, the binding energies can be very well described by a one
parameter fit;
EB = E0 -C(n,m)/RCH,
where E0 is the limit RCH --> inf. (i.e.
graphene) and calculated to be -1.727 eV. The fit results for
C(n,m) are given in Fig.~2a for zigzag and armchair nanotubes.
The inset to Fig.~2a shows that while EB for cubane falls on the
same curve as nanotubes, dodecahedrane and C60H60 have
lower energies than nanotubes due to the their more spherical shape.
The second interesting observation in Fig.~2a
is that the binding energies of zigzag nanotubes are always lower than
those in armchair nanotubes with similar radius by about 30 meV/atom.
This is a natural result of the fact that the
CCH-bond angles in zigzag nanotubes are closer to the optimum tetrahedral
sp3 bonding than those in armchair nanotubes.
We expect this observation is also valid for hybridization of nanotubes
oith other elements, such as Cl and F and this may have important
implications for separating similar radius nanotubes from
each other by selective chemical functionalization.
CONCLUSION
In summary, we have presented first-principles calculations of the
structural and electronic properties of various nanotubes which are
fully protonated by sp3 hybridization of carbons.
We find that CnHn nanotubes are stable for tube radius
RHC smaller than 6.25 A, roughly corresponding to a (8,8) nanotube.
Hybridization of a single carbon atom is found to be always exothermic
regardless of tube radius. Weak but stable CH-bonding in nanotubes may be
an important consideration for possible hydrogen storage applications. We also
found that hybridization of zigzag nanotubes is more likely than armchair
nanotubes with the same radius, suggesting a possible selective chemical
functionalization of nanotubes.
The fact that other carbon clusters such as cubane,
dodecahedrane, and C60H32 have been synthesized successfully,
suggest that it may possible in the near future
to hydrogenate carbon nanotubes, yielding new structures
with novel properties.