Applied Surface Science 206 (2003) 167±177
Enhancement of ®eld emission in carbon nanotubes
through adsorption of polar molecules
M. Grujicica,*, G. Caoa, Bonnie Gerstenb
a
Department of Mechanical Engineering, Program in Materials Science and Engineering,
Clemson University, Clemson, SC 29634, USA
b
Army Research LaboratoryÐWMRD AMSRL-WM-MD, Aberdeen, Proving Ground, MD 21005-5069, USA
Received 2 September 2002; accepted 22 October 2002
Abstract
First-principle's quantum-mechanical density functional theory (DFT) calculations are carried out to analyze the effect of
single water-vapor molecules, three- and ®ve-molecule water-vapor clusters and several other single-molecules with high dipole
moments absorbed at the tip of capped (5,5) metallic armchair nanotubes on the ionization potential which is a measure of the
ease at which electrons are extracted from carbon nanotubes during ®eld emission. The results obtained show that in the absence
of an externally applied electric ®eld, the adsorption energies of both single- and multi-molecule clusters are quite low (typically
less than 0.7 kcal/mol or 0.03 eV/molecule) suggesting that these adsorbates are not stable and would most likely desorb before a
typical ®eld-emission temperature of 900 K is reached. In sharp contrast, under a typical ®eld-emission electric ®eld of 1 eV/
Ê , the adsorption energy is substantially higher (typically around 20 kcal/mol or 0.867 eV/molecule) making the adsorbates
A
stable. The increased stability of the adsorbates is found to be the result of electrostatic interactions between dipole moments of
the adsorbates and the applied electric ®eld. These interactions increase the energy of the highest occupied molecular orbital in
the nanotube and, in turn facilitate ®eld emission. These ®ndings are generally consistent with the available experimental results.
# 2002 Elsevier Science B.V. All rights reserved.
PACS: 81.05.Tp (fullerenes and related materials)
Keywords: Carbon nanotubes; Field emission; Density functional theory (DFT) calculations
1. Introduction
Since their discovery in 1991 [1], carbon nanotubes
have been the subject of intense research due to
tremendous technological promise. Among different
potential applications of carbon nanotubes, the most
frequently cited are those associated with ®eld-emission
*
Corresponding author. Tel.: ‡1-864-656-5639;
fax: ‡1-864-656-4435.
E-mail address: [email protected] (M. Grujicic).
¯at-panel displays (e.g. [2,3]), novel microelectronic
devices (e.g. [4]), hydrogen storage devices (e.g. [5]),
structural reinforcement agents (e.g. [6]), and chemical and electrochemical sensors (e.g. [7]). Among
these areas of application, the use of carbon nanotubes
in ®eld-emission based ¯at-panel displays [2,3]
appears to be the closest to full commercial realization. Functionality of such displays has already been
demonstrated (e.g. [8]) and recent progress in the
fabrication of self-aligned or patterned nanotube
®lms [9,10] has given con®dence that large-scale
0169-4332/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 9 - 4 3 3 2 ( 0 2 ) 0 1 2 1 1 - 4
168
M. Grujicic et al. / Applied Surface Science 206 (2003) 167±177
production of ®eld-emission based ¯at-panel displays
is a matter of near future.
One of the main objectives in the design of ®eldemission based ¯at-panel display devices is reduction
of the operating voltage. This is generally accomplished by lowering the ionization potential (a measure of the ease of electron extraction during ®eld
emission), which is de®ned as the energy difference
between a system (a carbon nanotube in the present
work) in which one electron has been extracted and the
same system in the neutral state. Experimental investigations of Dean et al. [11] have clearly shown that the
presence of adsorbates with a signi®cant dipole
moment (e.g. water-vapor molecules) at the capped
nanotube tip, signi®cantly enhances the emission current at a given applied electric ®eld. This effect is
attributed to the associated reduction in the ionization
potential. Adsorbate molecules such as those of oxygen and hydrogen with weak dipole moments are
found not to effectively change the ®eld-emission
behavior of carbon nanotubes.
In a recent letter, Maiti et al. [12] carried out a
preliminary ®rst-principle's quantum-mechanical
investigation of the interactions between hydrogen
and water-vapor molecules and the carbon nanotube
tip. In the present work, the analysis of Maiti et al. [12]
has been extended to include a comprehensive study of
the effect of the cluster size of water-vapor adsorbates
and of the magnitude of the adsorbate dipole moment
on the ionization potential.
The organization of the paper is as follows: a
description of the computational clusters used in the
present work is presented in Section 2.1. In Section 2.2,
a brief overview is given of the ®rst-principle's densityfunctional theory (DFT) code DMol3 developed by
Accelrys Inc. [13] and the details of the calculations
carried out in the present work. The main results
obtained in the present work are presented and discussed in Section 3, while the key conclusions resulted
from the present study are summarized in Section 4.
2. Computational procedure
2.1. Computational clusters
All calculations in the present work are carried
out using a 60-atom carbon structure consisting of a
three-layer (30-atom) (5,5) metallic armchair carbon
nanotube stem capped with a half of a C60 molecule. A
need for the nanotube stem is deemed necessary in
order to attain consistency with the uniform electric
®eld applied in the direction of the nanotube axis
(discussed later). The nanotube is taken to be capped
since this type of structure is energetically favored
over the open-ended structure even in the presence of a
large electric ®eld [14] and, hence, is generally
observed during ®eld-emission microscopic examinations of the nanotube tips (e.g. [15]). In addition, ®eld
emission from the capped nanotubes has been found to
be nearly as ef®cient as that from the open-ended
nanotubes (e.g. [16]). To mimic the effect of long-stem
nanotubes used in ®eld-emission experiments [11], 10
carbon atoms at the open end of the 60-atom cluster
are ®xed at their initial positions during the geometry
optimization (energy minimization) calculations. All
other atoms are allowed to adjust their positions during
the calculations.
It is customary in the ®rst-principle's quantummechanical calculations of carbon nanotubes to ``saturate'' the dangling bonds at the open end of the
nanotubes with hydrogen atoms. This is not done in
the present work since a relatively large difference in
electronegativity between hydrogen and carbon gives
rise to the development of a ``non-physical'' dipole
moment in the 60-atom nanotube cluster. Such a
moment is found to have a profound effect on the
strength of computed interactions between the nanotube and the adsorbate molecules, especially when the
adsorbate molecules are polar, like water.
To mimic the effect of the electric ®eld under
normal ®eld-emission conditions, a uniform external
®eld, EFE, directed along the nanotube axis from the
tip to the stem is applied. Since a required minimal
level of the ®eld-emission current in carbon nanotubes
is typically attained at an electric ®eld of the order of
Ê , this value is assigned to the uniform external
1 eV/A
®eld EFE. This value of the electric ®eld is approximately equal to 0.02 a.u. (a.u. ˆ Hartree/Bohr), the
electric-®eld atomic units used in DMol3. One may
argue that the electric ®eld near the nanotube tip is
generally neither unidirectional nor uniform but rather
consists of the ®eld lines converging radially toward
the nanotube tip. Introduction of such a ®eld would
require the use of a complex arrangement of external
point charges which is not supported by the current
M. Grujicic et al. / Applied Surface Science 206 (2003) 167±177
Materials Studio implementation of the DMol3 code
from Accelrys Inc. [17] used in the present work. This
limitation is not considered as very critical, since over
the distance of few angstroms comparable with the
separation of adsorbate molecules and the nanotube
tip, the electric ®eld can be reasonably well approximated as unidirectional and uniform.
2.2. Computational method
All calculations in the present work are carried out
using a cluster approach and the quantum mechanical
density-functional theory (DFT) code DMol3 developed by Accelrys Inc. [13]. In this code, each electronic
wave function is expanded in a localized atom-centered
basis set with each basis function de®ned numerically
on a dense radial grid. No pseudopotential approximation is used for the near-core electrons. Instead, allelectron calculations are performed with a double
numerical polarized (DNP) basis set, the most complete
basis set available in the DMol3 code. This basis set is
equivalent to the commonly used analytical 6±31g
basis set, a split-valence basis set with polarization
functions from p to H and d to C, and the halogens [18].
To improve the computational speed, the localdensity approximation (LDA) is often used within
the DFT calculations which assumes that the electron
charged-density varies slowly on the atomic length
scale. However, the LDA method is found not have
the correct asymptotic behavior and generally overestimates the magnitude of the chemical-bond energy
(strength). To overcome this overbidding phenomenon,
one of the existing density gradient expansion schemes
(also referred to as generalized gradient approximations, GGA), which include the effect of chargedensity inhomogeneity, needs to be utilized. Following
Maiti et al. [12], the Perdew±Burke±Ernzerhof (PBE)
gradient-corrected functional [19] is used in the present
Ê is assigned to the ®nite
work. A standard value of 5.5 A
basis-set cutoff radius.
3. Results and discussion
3.1. Zero electric ®eld calculations
3.1.1. Single-molecule water-vapor adsorbates
In this section, the results of the present ®rstprinciple's density functional theory calculations of
169
the interactions between a single water-vapor molecule and the carbon-nanotube tip in the absence of an
external electric ®eld are presented and discussed.
Side and top views of the 60-atom carbon-nanotube
cluster whose structure is optimized with respect
to the positions of 50 non-open end carbon atoms
are as shown in Fig. 1(a and b), respectively. A
ball (atom) and stick (bond) representation is used
in Fig. 1(a and b). However, to improve clarity,
in most of the subsequent ®gures, the structure
of the carbon nanotube is displayed using a stick
representation.
Geometrical optimization of the structure of a
single H2O molecule (the structure not shown for
Ê ) and
brevity) yielded the H±O bond length (0.959 A
the H±O±H bond angle (104.78) which are in excellent
agreement with their experimental counterparts
Ê and 1058, respectively.
0.958 A
Side and top views of the geometrically optimized
structures of two atomic complexes consisting of the
60-atom carbon-nanotube cluster and a single H2O
adsorbate molecule are as shown in Fig. 1(c and d) and
Fig. 1(e and f), respectively. The ``down-water'' H2O
structure in which the two hydrogen atoms face the
nanotube tip, Fig. 1(c and d), is slightly (by 0.1 kcal/
mol or 0.004 eV/molecule) more stable than the
``up-water'' structure as shown in Fig. 1(e and f). A
detailed quantitative examination of the structures as
shown in Fig. 1(a±f) reveals that the interaction of
single H2O adsorbate molecules with the nanotube
Ê and the H±O±H
alters H2O bond-lengths by <0.005 A
bond angle by <2.28. Similar changes are found in the
carbon-nanotube bond lengths and bond angles. The
vertical distance of the two H-atoms of the H2O
molecule from the tube tip is found to be 2.9 and
Ê for the down- and up-water con®gurations,
3.8 A
respectively.
The adsorption energy of a single water-vapor
molecule to the nanotube tip in the absence of an
electric ®eld [E ˆ 0], Eadsorption is next computed
using the following expression:
Eadsorption ‰E ˆ 0Š ˆ Enanotube ‰E ˆ 0Š
‡ Eadsorbate ‰E ˆ 0Š
Enanotube‡adsorbate ‰E ˆ 0Š
(1)
where the use of different subscripts is self-explanatory.
This expression yielded Eadsorption ˆ 0:70 kcal/mol ˆ
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M. Grujicic et al. / Applied Surface Science 206 (2003) 167±177
Fig. 1. Side and top views of the optimized molecular structures of: (a and b) a capped single-wall (5,5) metallic armchair carbon nanotube; (c
and d) the same nanotube containing a single H2O adsorbate in the ``down-water'' orientation; and (e and f) the same nanotube containing a
single H2O adsorbate in the ``up-water'' orientation in the absence of an applied electric ®eld.
0.030 eV/molecule and Eadsorption ˆ 0:61 kcal/mol ˆ
0.026 eV/molecule for the down- and up-water adsorbates, respectively. These values are comparable to the
average atomic thermal energy at room temperature
(3/2kBT ˆ 3/2kB298 K 0:039 eV/atom, kB is the
Boltzmann constant) which implies that the adsorption
of single water-vapor molecules to the nanotube tip is
quite weak and that these molecules would most likely
desorb before a typical ®eld-emission temperature
(900 K) is reached. Hence, adsorption of the single
H2O molecules to the nanotube tip in the absence of an
electric ®eld cannot be used to explain the observed
H2O-adsorbate enhanced ®eld-emission in carbon
nanotubes [11].
To better understand the adsorption of single watervapor molecules to the carbon nanotube, an orbital
analysis is carried out in the present work. The resultÊ 3) electron density isosurfaces assoing (0.015 e/A
ciated with the highest occupied molecular orbital
(HOMO) for the geometrically optimized ``clean''
carbon nanotube and the nanotube containing single-molecule down- and up-water adsorbates are as
shown in Fig. 2(a±c), respectively. The energy levels
of the HOMO (approximately 5.5 eV) and of a
number of orbitals below the HOMO (the results
not shown for brevity) are found to be essentially
identical in the three cases suggesting that these
orbitals belong to the carbon nanotube. However, as
seen in Fig. 2(b and c), some delocalization of the
HOMO takes place resulting in charge transfer
from the nanotube to the H2O adsorbate. Due to its
higher electronegativity, the oxygen atom in the H2O
molecule is seen to be primarily responsible for the
observed charge transfer.
3.1.2. Three- and ®ve-molecules water-vapor
adsorbates
In order to examine the full potential of water-vapor
molecules on the enhancement of ®eld emission in
carbon nanotubes, the effect of a larger number of
adsorbate molecules in the absence of an electric
®eld is studied next using the ®rst-principle's density
functional theory calculations. The results of these
calculations for water-vapor clusters consisting of
three- and ®ve-molecules are presented and discussed
in this section.
M. Grujicic et al. / Applied Surface Science 206 (2003) 167±177
171
Ê 3 electron-density isosurfaces associated with the highest occupied molecular orbitals (HOMO) in the three-molecular
Fig. 2. The 0.015 e/A
structures as shown in Fig. 1(a, c and e).
Due to hydrogen bonding, water molecules are
known to form clusters which, in turn can adsorb to
the nanotube tip. Three- and ®ve-molecule clusters
and their adsorption to the nanotube tip are studied
Ê elechere. Since in the presence of an EFE ˆ 1 eV/A
tric ®eld (Section 3.2), H2O molecules in the downwater orientation are found to be more stable than the
ones in the up-water orientation, only the results
pertaining to the three- and ®ve-molecule water-vapor
clusters in the down-water orientation are presented
and discussed in this section. The corresponding
results pertaining to the H2O clusters in the up-water
orientation are found to follow the same general trend
as the ones for the down-water clusters discussed later.
Side and top views of the optimized structures of
H2O three- and ®ve-molecule clusters in the downwater orientation adsorbed to the nanotube tip are as
shown in Fig. 3(a and b) and Fig. 3(c and d), respectively. As in the case of single H2O adsorbates,
adsorption-induced changes in the bond lengths and
the bond angles in the nanotube are found to be quite
small. Application of Eq. (1) to the H2O three- and
®ve-molecule clusters yielded the adsorption energies
(divided by the number of molecules in the cluster)
as Eadsorption ˆ 0:4 kcal/mol ˆ 0:017 eV/atom and
Eadsorption ˆ 0:6 kcal/mol ˆ 0:026 eV/molecule, respectively. These ®ndings suggest that adsorption of
the larger molecular cluster of water-vapor to the
nanotube tip in the absence of an electric ®eld is
even weaker than that of the single H2O molecules
and, hence, cannot either account for the observed
H2O-adsorbate enhanced ®eld emission in carbon
nanotubes. It should be noted that the ®ve-molecule
cluster is adsorbed more strongly to the nanotube tip
than the three-molecule cluster which can be related
to the fact that both the (5,5) nanotube and the ®vemolecule cluster posses ®ve-fold symmetries.
3.2. 1-eV/AÊ electric ®eld calculations
3.2.1. Single-molecule water-vapor adsorbates
In this section, the results of the ®rst-principle's
quantum-mechanical calculations of interactions
between a single water-vapor molecule and the carbon-nanotube tip in the presence of a uniform electric
®eld directed along the nanotube axis are presented
Ê
and discussed. As mentioned earlier, an EFE ˆ 1 eV/A
electric ®eld is applied since this value is comparable
with the magnitude of the electric ®eld at which ®eld
emission in carbon nanotubes yields a required level of
the ®eld-emission current.
Side and top views of the optimized molecular
structures of the ``clean'' nanotube and the same
nanotube containing a single down-water and the
up-water adsorbates (the results not shown for brevity)
are very similar to their zero electric-®eld counterparts
as shown in Fig. 1(a±f). The electric ®eld is found to
have the following main effects on the nanotube and
adsorbates molecular structures: (a) the carbon±carbon sp2-s bond lengths in the nanotube are changed
Ê ; (b) the H±O±H bond angles in the downby <0.02 A
and up-water molecules changes from 1038 in the
absence of the electric ®eld to 100 and 1018,
respectively; (c) the vertical distance of the two hydrogen molecules in the down- and up-water molecules
Ê,
changes from 2.9 to 2.6 and 3.8 to 2.5 A
respectively; and (d) the down-water adsorbates
becomes signi®cantly more stable than the up-water
172
M. Grujicic et al. / Applied Surface Science 206 (2003) 167±177
Fig. 3. Side and top views of the optimized molecular structures of: (a and b) a capped single-wall (5,5) metallic armchair carbon nanotube
containing a H2O three-molecule adsorbate; and (c and d) the same nanotube containing a H2O ®ve-molecule adsorbate in the absence of an
applied electric ®eld.
molecule (by 90.36 kcal/mol or 3.92 eV/molecule). Due to their lower stability relative to that of
their down-water counterparts in the presence of an
electric ®eld, H2O single- and three- and ®ve-molecules
clusters in the up-water orientation are not considered
any further.
Taking into account the fact that the electric ®eld
under normal ®eld-emission operating conditions is
highly localized to the nanotube tip, the adsorption
energy under an applied electric ®eld [E ˆ EFE ] is
de®ned as:
Eadsorption ‰E ˆ EFE Š ˆ Enanotube ‰E ˆ EFE Š
‡ Eadsorbate ‰E ˆ 0Š
Enanotube‡adsorbate ‰E ˆ EFE Š
(2)
The adsorption energy de®ned in this way is the
energy required to detach the adsorbate from the
nanotube tip and places it at a distance far away from
the tip, where the electric ®eld can be considered as
negligible relative to its values at the nanotube tip.
Ê , the adsorption energy for a single
For EFE ˆ 1 eV/A
water-vapor molecule in the down-water orientation is
found to be 20.5 kcal/mol or 0.889 eV/molecule. This
value is comparable to the binding energy of a chemical bond suggesting that adsorption of single watervapor molecules to the carbon nanotube tip changes
from physisorption (at a zero applied electric ®eld) to
Ê electric ®eld). To
chemisorption (at an EFE ˆ 1 eV/A
better understand this phenomenon, an attempt is
made to identify the most important contribution to
the increased interaction energy between single watervapor molecules and the nanotube tip in the presence
M. Grujicic et al. / Applied Surface Science 206 (2003) 167±177
of an electric ®eld. In particular, since the H2O
molecule is polar, its interaction with the applied
electric ®eld and the nanotube dipole moment had
to be quanti®ed. All dipole moments analyzed here are
directed along the nanotube axis and are, hence,
completely de®ned by their magnitudes. The following sign convention is chosen for the dipole moment: a
dipole moment is considered as positive when it is
directed from the nanotube tip toward the nanotube
stem.
The dipole moment for a single isolated waterÊ electric ®eld
vapor molecule under the EFE ˆ 1 eV/A
is found to be padsorbate[E ˆ EFE ] ˆ 2.44 D which is a
23% increase relative to its value (padsorbate[E ˆ 0] ˆ
1.98 D) in the absence of the electric ®eld. In
sharp contrast, the dipole moment of the nanotube
changes drastically from pnanotube[E ˆ 0] ˆ 1.17 D
to pnanotube[E ˆ EFE ] ˆ 29.44 D at the applied
Ê . Likewise, the dipole
electric ®eld of EFE ˆ 1 eV/A
moment of the nanotube containing a single-molecule
water-vapor adsorbate in the down-water orientation
changes from pnanotube‡adsorbate[E ˆ 0] ˆ 1.87 D to
pnanotube‡adsorbate[E ˆ EFE ] ˆ 34.80 D. Finally, the
dipole moment induced by charge transfer and
higher-order polarization effects associated with
adsorption of single water-vapor molecules to the
nanotube tip in the presence of an electric ®eld
E ˆ EFE can be de®ned as:
padsorption ‰E ˆ EFE Š ˆ pnanotube‡adsorbate ‰E ˆ EFE Š
pnanotube ‰E ˆ EFE Š
padsorbate ‰E ˆ EFE Š
(3)
173
Using Eq. (3), the adsorption-induced dipole moment
is computed as padsorbate[E ˆ EFE ] ˆ 34.80 D 29.44
D 2.44 D ˆ 2.92 D.
The computed values for different dipole moments
given above suggest that the main contributions to
be electrostatic interactions between single-molecule
water-vapor adsorbates in the down-water orientation
and the nanotube tip is associated with: (a) the adsorbate/electric-®eld interactions which are proportional
to padsorbate[E ˆ EFE ]EFE; and (b) the adsorbatedipole/nanotube-dipole interactions which are proportional to the padsorbate[E ˆ EFE ]pnanotube[E ˆ EFE ].
Changes in the dipole moments induced by adsorption
of the single H2O molecules in the down-water orientation to the nanotube tip in the presence of an electric
®eld are relatively small and make minor contributions
to the adsorbate/nanotube interactions.
To examine the role of covalent bonding in the
adsorbate/nanotube interactions in the presence of an
Ê electric ®eld, the distribution of the
EFE ˆ 1 eV/A
total charge-density has been computed. The 0.06 e/
Ê 3 total charge-density isosurface for a the carbon
A
nanotube containing a single H2O adsorbate in the
down-water orientation is as shown in Fig. 4(a). Low
values of the charge-density in the region separating
the single-molecule H2O adsorbate and the nanotube
tip suggest that the contribution of covalent bonding to
the adsorbate/nanotube interactions in the presence of
an electric ®eld is relatively small. Thus, the observed
strong bonding between single H2O molecules and the
nanotube tip is primarily due to electrostatic interactions between dipole moments of the adsorbates and
the nanotube and the applied electric ®eld.
Ê 3 total charge-density isosurfaces associated with a carbon nanotube containing: (a) a single H2O molecule in the
Fig. 4. The 0.06 e/A
Ê.
down-water orientation; (b) an H2O three-molecule cluster; and (c) an H2O ®ve-molecule cluster under an applied electric ®eld of 1 eV/A
174
M. Grujicic et al. / Applied Surface Science 206 (2003) 167±177
3.2.2. Three- and ®ve-molecule water-vapor
adsorbates
In this section, the results of the ®rst-principle's
quantum-mechanical calculations of interactions
between three- and ®ve-molecule water-vapor clusters
and the carbon-nanotube tip in the presence of a
Ê uniform electric ®eld directed along
EFE ˆ 1 eV/A
the nanotube axis are presented and discussed.
The results presented in the previous section show
that the presence of an electric ®eld enhances the
adsorption energy of single H2O molecules to the
nanotube tip. It should be noted, however, that single-molecules are free to achieve perfect alignment
with the nanotube, as well to adjust their H±O bond
lengths and the H±O±H bond angle. When multimolecule H2O complexes are adsorbed to the nanotube tip, on the other hand, hydrogen bonding between
the individual molecules constrains them from achieving perfect alignment with the nanotube. This is
expected to reduce the adsorption energy of multimolecule complexes (per H2O molecule adsorbed)
relative to that for single H2O adsorbates.
Using Eq. (3), adsorption energies for the H2O
three- and ®ve-molecule complexes (relative to the
energies of the same complexes at a distance far away
from the nanotube tip) are computed as 35.31 kcal/
mol (1.53 eV/complex) and 65.2 kcal/mol (2.83 eV/
complex), respectively. When divided by the number
of molecules in the complex, the adsorption energies
for the three- and ®ve-molecule complexes per H2O
molecule become 11.77 kcal/mol (0.51 eV/molecule)
and 13.04 kcal/mol (0.57 eV/molecule), respectively.
These values are lower than their single-molecule
counterparts (20.5 kcal/mol ˆ 0:889 eV/molecule)
and, hence, con®rm that formation of the multi-molecule complexes reduces the adsorption energy per
H2O molecule. However, the use of these adsorption-energy values to judge the tendency for individual
molecules to desorb from the nanotube tip may be
misleading since such molecules must not only break
their bonds with the nanotube tip but also with other
molecules in the multi-molecule H2O cluster before
desorbing. An average H2O±H2O bond energy in the
three- and the ®ve-molecule clusters has been determined as 7.31 kcal/mol (0.317 eV/molecule) and
7.24 kcal/mol (0.314 eV/molecule), respectively. If
these values are added to the adsorption energy values
(per H2O molecule) given previously, the following
effective adsorption energies for the three- and the
®ve-molecule clusters are obtained: 19.08 kcal/mol
(0.827 eV/molecule) and 20.39 kcal/mol (0.884 eV/
molecule), respectively. These effective adsorption
energies suggest that the formation of the three-molecule clusters but not the ®ve-molecule clusters somewhat weakens adsorption of the individual H2O
molecules to the nanotube tip. This ®nding is consistent with the absence of ®ve-fold symmetry in the
three-molecule complexes and its presence in ®vemolecule complexes. In addition, one may conclude
that in the presence of an electric ®eld, H2O adsorbates, either as single- or multi-molecule clusters, are
stable and would remain so at a typical ®eld-emission
temperature of 900 K.
Ê 3 total charge-density isosurfaces for
The 0.06 e/A
the nanotube continuing a three- and a ®ve-molecule
H2O adsorbates are as shown in Fig. 4(b and c),
respectively. It is seen that, as in the case of singlemolecule H2O adsorbates, the contribution of covalent
bonding to the adhesion in the presence of an electric
®eld is quite small.
3.2.3. Water-vapor adsorbates enhanced
®eld emission
To explain the experimentally observed watervapor adsorbate-enhanced ®eld emission in carbon
nanotubes [11], ionization potentials are computed
for the clean nanotube and the same nanotube containing one-, three- and ®ve-molecule H2O clusters in the
down-water orientation. For each of these systems, the
ionization potential is calculated as an energy difference between the (‡1 charge) state of that system
from which one electron has been removed and
its zero-charge state. Since the ``hole'' left by an
electron emitted from the nanotube tip is almost
instantaneously ®lled with an incoming electron from
the nanotube stem side, ®eld emission is assumed
not to alter the zero-charge optimized molecular
structures discussed earlier.
The variation of the ionization potential with the
corresponding HOMO energy in the clean nanotube
and the same nanotube containing a single-, three- and
®ve-molecules complexes is as shown in Fig. 5. It is
seen that the ionization potential decreases (and,
hence, the tendency for ®eld emission increases) with
the size of the H2O molecular complex and that this
change is linearly related to the associated increase in
M. Grujicic et al. / Applied Surface Science 206 (2003) 167±177
175
the HOMO energy. These ®ndings can be readily
explained. As the HOMO energy increases, it becomes
easier to extract electrons from this orbital unto the
Ê 3 HOMO electron-density
vacuum. The 0.015 e/A
isosurfaces for the four systems considered here under
Ê applied electric ®eld are as shown
the EFE ˆ 1 eV/A
in Fig. 6(a±d), where it is seen that the HOMO orbitals
are con®ned entirely to the nanotube. Since there
is no projection of the HOMO orbitals to the H and
O atoms of the water molecules and complexes, one
would expect a linear correlation between the HOMO
energy and the ionization potential, as observed in
Fig. 5.
Fig. 5. Variation of the ionization potential with the corresponding
HOMO energy for a pure carbon nanotube and the same nanotube
containing an one-, three-, and ®ve-molecule H2O complexes under
Ê.
an applied electric ®eld of 1 eV/A
3.2.4. Effect of the magnitude of the dipole
moment of adsorbates
In their preliminary work, Maiti et al. [12] reported
that only adsorbates with signi®cant dipole moments
can enhance the ®eld emission in carbon nanotubes.
In this section, an attempt is made to establish a
relationship between the magnitude of the dipole
Ê 3 HOMO electron-density isosurfaces for: (a) a clean nanotube and a nanotube; containing (b) a single-molecule downFig. 6. The 0.015 e/A
Ê.
water adsorbate; (c) a three-molecule H2O adsorbate; and (d) a ®ve-molecule H2O adsorbate under an applied electric ®eld of 1 eV/A
176
M. Grujicic et al. / Applied Surface Science 206 (2003) 167±177
Fig. 7. Variation of the nanotube ionization potential with the magnitude of the dipole moment in a number of linear single-molecule
adsorbates.
moment of an adsorbate and the resulting reduction in
the ionization potential of carbon nanotubes. Toward
that end, the ionization potential is calculated for a
series of linear single-molecule adsorbates (H2, HCl,
HCN and LiH) which cover a range of the dipole
moment between essentially 0 D (for H2) to 5.88 D
(for LiH). In each case, the linear adsorbate molecule
is aligned with the nanotube axis and the molecular
structure optimization carried out. The results of this
calculation are as shown in Fig. 7. The data for a single
H2O molecule in the down-water orientation is also
shown in Fig. 7. It is seen that the adsorption-induced
reduction in the ionization potential increases with
the magnitude of the dipole moment of the adsorbate
molecule. However, the ionization potential versus
dipole moment relationship is not simple suggesting
the contributions of factors other than the dipole
moment. In each of the cases shown in Fig. 7,
however, the reduction in the ionization potential is
found to match the corresponding increase in the
HOMO energy (as in the case of H2O adsorbates,
Fig. 5).
4. Conclusions
Based on the results obtained in the present work,
the following main conclusions can be drawn:
1. In the absence of an electric ®eld, H2O single- and
multi-molecule complexes are quite weakly adsorbed to the nanotube tip at room temperature
and would tend to desorb before a typical ®eldemission temperature of 900 K is reached.
Ê uniform electric ®eld directed
2. Under an 1 eV/A
along the nanotube axis, H2O single- and multimolecule complexes become chemisorbed to the
nanotube tip and are likely to remain stable at the
®eld-emission temperature.
3. Electrostatic interactions between the dipole
moments of H2O single- and multi-molecule
complexes with the nanotube destabilize the
HOMO of the nanotube and, in turn lower
ionization potential and promote ®eld emission.
4. The extent of reduction of the ionization potential
in carbon nanotubes generally increases with the
M. Grujicic et al. / Applied Surface Science 206 (2003) 167±177
magnitude of the dipole moment of singlemolecule linear adsorbates.
Acknowledgements
The material presented in this paper is based on
work supported by the US Army Grant number
DAAD19-01-1-0661. The authors are indebted to
Drs. Walter Roy, Fred Stenton and William DeRosset
of ARL for the support and a continuing interest in the
present work. The authors also would like to thank
Dr. Amitesh Maiti of Accelrys Inc. for assistance in
the initial stage of this work.
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