Formation, structure, and structural properties of a new filamentary tubular form: Hollow conical-helix of graphitic boron nitride

Article abstract of DOI:10.1021/ja030003m

A novel tubular form of graphitic boron nitride (BN) displaying a hollow conical-helix was discovered. It was generated via wrapping a single beltlike filament according to the geometry of an Archimedes spiral. Cone apex angles of helical-conical nanotubes (HCNTs) were found to exhibit specific values, each of which refers to a certain coincidence site lattice. A unique structural property of HCNTs was observed, displaying the transformation of apex angles during the annealing process. The observed apex angles were reduced with decreasing annealing temperature, which is in accordance with an estimated HCNT strain energy decrease for a given tubular radius. It is suggested that the curvature and apex angle of a HCNT are determined by a sole dynamic element, that is, enthalpy (ΔH), whereas the HCNT disclination configuration changes through helical sliding of the filament.

Full text of DOI:10.1021/ja030003m

Published on Web 06/10/2003
Formation, Structure, and Structural Properties of a New
Filamentary Tubular Form: Hollow Conical-Helix of Graphitic
Boron Nitride
Fang-Fang Xu,* Yoshio Bando, Renzhi Ma, Dmitri Golberg, Yubao Li, and
Masanori Mitome
Contribution from the AdVanced Materials Laboratory and Nanomaterials Laboratory,
National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
Received January 3, 2003; E-mail: xu.fangfang@nims.go.jp
Abstract: A novel tubular form of graphitic boron nitride (BN) displaying a hollow conical-helix was
discovered. It was generated via wrapping a single beltlike filament according to the geometry of an
Archimedes spiral. Cone apex angles of helical-conical nanotubes (HCNTs) were found to exhibit specific
values, each of which refers to a certain coincidence site lattice. A unique structural property of HCNTs
was observed, displaying the transformation of apex angles during the annealing process. The observed
apex angles were reduced with decreasing annealing temperature, which is in accordance with an estimated
HCNT strain energy decrease for a given tubular radius. It is suggested that the curvature and apex angle
of a HCNT are determined by a sole dynamic element, that is, enthalpy (∆H), whereas the HCNT disclination
configuration changes through helical sliding of the filament.
Introduction
forming high densities of coincidence lattice sites between
overlapping layers;2b,c they were observed to be 13.2°, 21.8°,
A graphitic-like filament may form various curved structures
such as fullerenes, nanotubes, and cones. Among these, graphitic
nanotube is perhaps the most intriguing nanomaterial that has
been proven to possess unmatched physicochemical properties
and remarkable application potential. Cylindrical C and boron
nitride (BN) nanotubes are composed of graphene sheets parallel
to the tube axis independent of its chirality.1 By contrast,
turbostratic nanofibers of C and BN exhibit abundant morphol-
ogies, for example, so-called jellyfish, backbone, herringbone,
horsetail, and bamboo-like. The last two morphologies contain
cone-shaped compartments, whereas the herringbone-like fibers
are the solid cones.
It has been indicated that the apex angle (θapex) of a stacked
(i.e., nonhelical) cone can only display a limited number of
values, which are determined by the disclination angles (θD) of
multiple n of 60° (where n is a positive integer between 1 and
5).2 Theoretically, due to the higher stability of B-N bonds
relative to B-B and N-N bonds, there is a further restriction
for θD in “hat-stacked” BN cones, which thus show angles of
120° and 240° only.3 However, for helical cones, the apex angles
have a somewhat broad selection due to the introduction of an
overlap angle (θover) in addition to the n60° disclination issue.
The overlap angles are determined according to the criteria of
and 27.8° in overlapping h-BN platelets.3,4
Although curved filamentary nanostructures are fairly clear,
their nucleation and growth mechanisms have not yet been well
understood. Among the various formation models, the ring-
stacking model5 suggested creation of curved surfaces via the
selective assembly of monocyclic rings. In the case of the conical
shape, it has been found that a single polygon defect, for
example, a two- to five-membered atomic ring, is sufficient to
form a twisted nucleus followed by further lateral growth of
hexagons.2,4b This could be the case for solid cone particles. In
the case of conical-shaped bamboo-like fibers with round conical
caps, several reports have claimed similar formation mechanisms
relying on growth on the conical catalytic particles.6,7 Thus, cone
apex angles have been suggested to strongly depend on the shape
of the catalytic templates.
In the present paper, the synthesis of novel BN HCNTs with
high purity is reported. Helical-conical BN nanotubes having
no caps were observed. Because no catalytic particles were
detected at the bottom of the cones, a new formation mechanism
is proposed.
(4) (a) Bourgeois, L.; Bando, Y.; Shinozaki, S.; Kurashima, K.; Sato, T. Acta
Crystallogr., Sect. A 1999, 55, 168. (b) Bourgeois, L.; Bando, Y.;
Kurashima, K.; Sato, T. Philos. Mag. A 2000, 80, 129.
(5) Wakabayashi, T.; Achiba, Y. Chem. Phys. Lett. 1992, 190, 465.
(6) (a) Chen, Y.; Chadderton, L. T.; Gerald, J. F.; Williams, J. S. Appl. Phys.
Lett. 1999, 74, 2960. (b) Chadderton, L. T.; Chen, Y. J. Cryst. Growth
2002, 240, 164. (c) Gerald, J. F.; Chen, Y.; Conway, M. J. Appl. Phys. A
2003, 76, 107.
(7) (a) Blank, V. D.; Gorlova, I. G.; Hutchison, J. L.; Kiselev, N. A.; Ormont,
A. B.; Polyakov, E. V.; Sloan, J.; Zakharov, D. N.; Zybtsev, S. G. Carbon
2000, 38, 1217. (b) Terrones, H.; Hayashi, T.; Munoz-Navia, M.; Terrones,
M.; Kim, Y. A.; Grobert, N.; Kamalakaran, R.; Dorantes-Davila, J.;
Escudero, R.; Dresselhaus, M. S.; Endo, M. Chem. Phys. Lett. 2001, 343,
241.
(1) (a) Iijima, S. Nature 1991, 354, 56. (b) Chopra, N. G.; Luyken, R. J.;
Cherrey, K.; Crespi, V. H.; Cohen, M. L.; Louie, S. G.; Zettle, A. Science
1995, 269, 966. (c) Loiseau, A.; Willaime, F.; Demoncy, N.; Hug, G.;
Pascard, H. Phys. ReV. Lett. 1996, 76, 4737.
(2) (a) Double, D. D.; Hellawell, A. Acta Metall. 1974, 22, 481. (b) Amelinckx,
S.; Luyten, W.; Krekels, T.; Van Tendeloo, G.; Van Landuyt, J. J. Cryst.
Growth 1992, 121, 543. (c) Krishnan, A.; Dujardin, E.; Treacy, M. M. J.;
Hugdahl, J.; Lynum, S.; Ebbesen, T. W. Nature 1997, 388, 451.
(3) Bourgeois, L.; Bando, Y.; Han, W. Q.; Sato, T. Phys. ReV. B 2000, 61,
7686.
9
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J. AM. CHEM. SOC. 2003, 125, 8032-8038
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Hollow Conical-Helix of Graphitic Boron Nitride
A R T I C L E S
Table 1. Products from Different Synthesis Conditions
B O :CNT
heating/postheating
2
3
specimen
(in weight)
temperature (°C)
products
SH1850
SH1700
SL1800
S1800
6:1
6:1
6:1
8:1
8:1
1850/-
BN particles
BN microworms
BN particles
BN HCNTs
1700/-
1700/1800
1700/1800
1700/1750
S1750
BN HCNTs
It should be particularly emphasized that the well-known
bamboo-like fibers consist of cone fragments stacking above
each other; this leads to a tubular form that is periodically
segmented by bridges, that is, conical caps. By contrast, BN
HCNTs described here are made of a single filamentary belt
wrapped conically and helically, which thus displays a continu-
ous inner channel without segments, resulting in a real tubular
morphology similar to C nanotubes.1 The hollow helical rather
than tightly stacked morphology allows a filament slide under
external stress and/or thermal treatments without structural
collapse. This leads to an unmatched structural property of a
BN HCNT filament, that is, transformation of its apex angle
during simple annealing.
Experimental Section
Materials Preparation. BN HCNTs were synthesized by employing
a synthetic route similar to that previously reported, which led to
cylindrical BN nanotubes via a substitution reaction from C nanotube
(CNT) templates by B2O3 in N2 atmosphere.8 However, a postheating
process at a high temperature was additionally performed in the present
synthesis. First, CNTs were prepared from the starting mixture of N2
(99.999%), H2 (99.999%), and CH4 (99.9%) by a plasma-assisted
chemical vapor deposition (CVD) onto a Ti plate sputtered by Co
nanoparticles. The substrate temperature was approximately 500 °C
during the deposition. The obtained CNT powder then underwent a
redox reaction with B2O3 in N2 atmosphere inside a cylinder graphite
crucible in a high frequency (21 kHz) induction furnace JHF-VFX 110
QZ (JEOL). The B2O3 powder was put at the bottom of the crucible,
while CNTs were mounted on a graphitic disk ∼0.8 cm above the B2O3
powder. The material was first heated at ∼1700 °C for 30 min. A
postheating process at higher temperature (1750-1900 °C) was then
performed over 60 min. The reaction chamber was finally cooled to
room temperature within 90 min in flowing N2. The main experimental
parameters that influenced the structures of the resultant products were
found to be starting compositions and heating/postheating temperatures.
Therefore, syntheses with different experimental conditions have been
performed as listed in Table 1.
Annealing Processes. Annealing was performed to examine the
specific structural properties of BN HCNTs. After being postheated at
1800 °C over 60 min, as described above (for specimen S1800, see
Table 1), the material underwent an annealing process at a lower
temperature in Ar atmosphere over 30 min. Two annealing temperatures
(1700 and 1600 °C) were chosen in this study.
Structural and Chemical Analysis. The X-ray diffraction (XRD)
data were collected by a powder diffractometer (Rigaku Rint 2000S)
with graphite-monochromatized Cu KR radiation (λ ) 0.15405 nm).
The microstructural analysis including measurement of apex angles was
taken on a scanning electron microscope (SEM, JSM-6700F) and a
300 kV field-emission transmission electron microscope (TEM, JEOL-
3000F). Chemical composition and elemental maps were acquired by
using electron energy loss spectra (EELS) on a Gatan DigiPEELS 766
parallel detection spectrometer and an Omega filter JEOL-3100FEF
transmission electron microscope, respectively. Carbon tetrachloride
Figure 1. SEM (a) and TEM (b) images of BN HCNTs in the S1800
specimen. Inset in (b) shows a typical EEL spectrum of the material.
CCl4 (>99.99%) was used during TEM specimen ultrasonic treatment
followed by deposition on a standard C-coated-Cu TEM grid.
Results and Discussion
Structural Characterization. Table 1 indicates that only
specimens S1800 and S1750 contain BN HCNTs. The SEM
image (Figure 1a, for the specimen S1800 as an example)
illustrates isomorphic one-dimensional nanostructures exhibiting
a very high aspect ratio (∼1000). An enlarged SEM image (inset
of Figure 1a) and a TEM micrograph (Figure 1b) show clearly
a tubular morphology. XRD and chemical analysis by EELS
(inset in Figure 1b) reveal a pure graphite-like BN phase with
the lattice parameters of a ) 0.2502 nm and c ) 0.3333 nm.
Opposite from straight cylindrical BN nanotubes, typically
displaying a length of several micrometers,1c the present
nanostructures exhibit much higher length and bending curva-
ture. The average length of BN nanotubes exceeds 100 µm, and
the tubular radius ranges from 30 to 170 nm for the S1800
specimen, for instance. The lattice image (Figure 2a and b)
displays oblique fringes (peculiar to graphene planes) with
respect to the tube axis. This, along with the typical electron
diffraction pattern (Figure 2c), which is characteristic of a
conical geometry,4 gives evidence of a hollow cone structure.
The diffraction pattern consists of two rows of 00l reflections
meeting at an angle equal to 180° - θapex and hk0 arcs along
the direction perpendicular to the cone axis.
Blank et al.7a and Terrones et al.7b have observed open
graphitic cones forming on the conical catalytic particles. They
(8) Han, W. Q.; Bando, Y.; Kurashima, K.; Sato, T. Appl. Phys. Lett. 1998,
73, 3085.
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A R T I C L E S
Xu et al.
BN filamentary belt helically and conically rather than through
packing of monolayer cones (for θD ) n60), as is schematically
illustrated in Figure 2d. Thus, a novel tubular form is obtained
displaying a geometry of a hollow conical-helix or Archimedes
spiral. The observed disclination angles at 180° and 240° may
refer to either a helical or a nonhelical cone structure, which
could not be distinguished by any of the available techniques.
For the present BN HCNTs, only θover ) 21.8°, 27.8°, and 13.2°
were observed. These three values correspond to three coinci-
dence site lattices (CSLs) with lattice parameters of x7, x13,
and x19‚a0 (a0 refers to the in-plane dimension of h-BN unit
cell), respectively.9 They are the three smallest CSLs, indicative
of an actual configuration with high densities of coincidence
lattice sites between overlapping layers.
While CSLs and θover show well-defined configurations, the
magnitudes of apex angles and radius, that is, the overall bending
curvature, vary; the values and distribution are determined by
the temperature. Table 2 displays the increase of an average
radius, and hence decrease in overall bending curvature, when
the synthesis temperature is decreased. However, apex angles
change synchronically with temperature. Figure 3 demonstrates
that these values for the S1800 specimen are centered at the
higher apex angle, that is, 52°, whereas the distribution peak
moves toward a smaller value (θapex ) 46°) for the S1750
specimen (synthesized at lower temperature). The two peaked
apex angles are peculiar to the disclination angles of 180 +
21.8° and 240 - 21.8°, respectively. It appears that a small
apex angle is energetically more favorable. This particular
structural phenomenon will be further documented by an
annealing process described later. It is noted that a hollow
channel of conical tubes allows the cone axis not necessarily
to be the tube axis; this explains a curved morphology of a rigid-
bonded BN structure even if no C impurities and/or topological
defects are introduced in it. The C impurities, which were always
present in the BN nanotubes prepared via substitution from
CNTs, were found at negligible levels in the present HCNTs,
implying a different formation mechanism.
Formation Mechanism. It can be seen from Table 1 that
BN HCNTs could only be observed in specimens S1800 and
S1750, which were prepared using a significant excess of B2O3
in the starting powder mixture (high B2O3/CNTs ratios, see
Table 1) and higher postheating temperatures. Synthesis without
the postheating process at 1500-1850 °C has led to either
cylindrical BN nanotubes10 or nanofibers, or BN particles.
Reaction at 1700 °C was found to form a new BN microstruc-
ture, as shown in Figure 4a, which displays a morphology
similar to the bamboo-like fibers but with a uniform wall
thickness and curvature, and a short spacing between neighbor-
ing compartments. These “wormlike” BN microfibers are found
to play a crucial role in the formation of BN HCNTs. The curved
surfaces of “microworms” behaved as templates for nucleation
and growth of HCNTs, as is evidenced in Figure 4b. Therefore,
the formation of BN HCNTs can be described by the following
reactions.
Figure 2. High-magnified image (a) of an individual BN HCNT in the
S1800 specimen and the lattice image (b) of the framed region in (a) showing
graphitic-like planes which are oblique to the tube axis. (c) and (d) are a
diffraction pattern and a structural model of the present BN HCNT.
Table 2. Average Radii and Apex Angles in Different Specimens
Rav (nm)
θapex (deg)
specimen
range
peaked
range
peaked
peaked θD (deg)
S1800
S1750
SA1700
SA1600
30-170
70-200
100-300
130-320
60-100
110-150
170-210
200-240
43-60
35-71
30-72
19-46
52
46
35
30
180 + 21.8
240 - 21.8
240 + 13.2
240 + 27.8
characterized the cones as a stacked-type conical structure
exhibiting certain limitations with respect to its apex angle. Our
measurements of cone apex angles on the present BN conical
filaments indicate a helical structure rather than a stacked type.
Apex angles and average tubular radii Rav (Rav ) (Rin + Rex)/2,
where Rin and Rex represent interior and exterior tubular radii,
respectively), of about 30 BN nanotubes were measured for both
S1800 and S1750 specimens and are summarized in Table 2.
The measurements of apex angles were carried out on diffraction
patterns if the cone axis was roughly perpendicular to the
incident beam direction;4a the measurement uncertainty stands
at 1°. The diagram shown in Figure 3 depicts the distribution
of the apex angles. They were found to display some specific
values within a narrow range rather than be randomly distrib-
uted. Moreover, each apex angle coincides with the theoretical
value corresponding to a certain disclination configuration.2,9
It is seen from Figure 3 that the majority of disclination angles
includes a θover in addition to n60°, allowing us to conclude
that the present BN nanotubes are formed via wrapping a narrow
At 1700 °C (for heating):
3C (nanotubes) + 2B2O3 + 2N2 f
4BN (microworms) + 3CO2 (1)
(9) Xu, F. F.; Bando, Y. Acta Crystallogr., Sect. A 2003, 59, 168.
(10) Bando, Y.; Ogawa, K.; Golberg, D. Chem. Phys. Lett. 2001, 347, 349.
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Hollow Conical-Helix of Graphitic Boron Nitride
A R T I C L E S
Figure 3. Distribution of the apex angles in the specimens S1800 and S1750. The corresponding disclination angles are indicated.
At 1750 or 1800 °C (for postheating):
B2O3 + C (crucible) f 2BO + CO
B2O3 + 3CO + N2 f 2BN (HCNT) + 3CO2
6BO + N2 f 2B2O3 + 2BN (HCNT)
BN (microworms) f BN (particles)
(2)
(3)
(4)
(5)
CNTs have been proven to be the templates and reduction
reagents for the formation of BN nanostructures at the initial
reaction stage.11 Because all CNTs have been consumed during
the formation of BN phases at the first heating stage, as
confirmed by the chemical analysis of the specimen SH1700,
the reduction reagent for the reactions in the postheating process
appears along with reaction 2; that is, CO vapor originates from
the graphite crucible used. Thus, CNTs played no role in the
formation of nanostructures at the postheating stage. The
possible contribution of metal particles to the nucleation of
conical nanotubes, as observed in bamboo-like nanofibers by
several authors,6,7 may also be ruled out due to the fact that no
Co crystallites were ever found at tube ends. On the other hand,
the curved surfaces of the microworms could be responsible
for the formation of conical graphitic sheets rather than
cylindrical tubules (see Figure 4b). Because fewer BN micro-
worms were observed in the final HCNT specimens, most of
the thin microworms have eventually been collapsed and
converted to particles at the later stage of postheating at
temperatures over 1750 °C (see reaction 5). Numerous nucle-
ation sites on the surface of microworms led to a high yield of
HCNTs, while postheating at a certain high temperature and
hence the high B2O3 or BO vapor pressure guarantees the fast
formation of a uniform structure. It turns out that packing of
BN layers is more favorable and thus proceeds faster than
continuous growth of an individual BN graphitic-like sheet. This
postulate is in accordance with the rare occurrence of single-
Figure 4. (a) TEM image of BN microworms in the SH1700 specimen.
(b) SEM image of an individual BN microworm (in S1750) on which
HCNTs have been nucleated.
wall BN nanotubes and the fact that typical BN nanotubes are
usually short.1c Helical wrapping of a BN thin belt favors the
packing growth mode of graphene sheets and hence faster
growth of HCNTs and consequently extreme high aspect ratios.
Meanwhile, the high temperature provides energetic support for
the formation of the conical structure.
(11) Golberg, D.; Bando, Y.; Kurashima, K.; Sato, T. Chem. Phys. Lett. 2000,
323, 185.
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A R T I C L E S
Xu et al.
Figure 6. Schematic presentation of the formation mechanism for the
present HCNTs, exhibiting elimination of interior bridges via a chemical
reaction, which eventually led to a tubular morphology. A final stable apex
angle is determined by temperature and has been achieved via the slide of
filaments after microworms were collapsed and converted to particles.
appearing along the exterior surface in Figure 5 is an optical
artifact, not referring to segregation of a certain element. It is
obvious that the chemical reaction occurred inside of the tubes,
which destroyed the bridges. In Figure 5, it looks that the
reaction took place from the right-hand open end of the tube.
By noting the direction of the apex, we found that the
morphology suggests that chemical erosion starts from the open
cap at the conical apical region; this implies that the bottom of
the tube is sealed. The reactants, either CO or BO, flew along
the tubular channel through its open cap. This phenomenon
coincides with the nucleation of HCNTs on the surface of
microworms. The formation mechanism can then be clarified
as is schematically illustrated in Figure 6. It is possible that the
nucleation of HCNTs on the surface of microworms employs a
disclination configuration depending on the curvature of the
microworms and the size of the cones. The absence of polygon
defects results in conical fragment appearance rather than
fullerene-type shells packed onto the curved surface of micro-
worms. However, high temperature postheating destroyed
microworms, resulting in isolated HCNTs which further undergo
reconstruction of disclination configuration, governed by tem-
perature. Change of disclination configuration, and hence the
apex angle, has been observed recently during the deformation
process of HCNTs.12 Reconstruction is achieved via helical
sliding of filaments. Apart from an external stress, thermal
treatment is also found to ensure a driving force for the
reconstruction, as is evidenced by the annealing process
described below.
Figure 5. Bright-field image of an individual HCNT and its elemental
maps that were obtained using energy-loss edges of B-K, N-K, C-K,
and O-K, respectively. The apical direction is indicated on the bright-
field image.
It has been indicated that an enthalpy (∆H) is the driving
force for the formation of curved structures while an entropy
(∆S) plays a dominating role in the distribution of disclinations
formed.2c In some previous nucleation and growth models, a
disclination configuration is determined during the nucleation
stage and does not change after seeding.2 However, the absence
of apexes and catalytic particle at the tube ends, along with the
narrow distribution of apex angles and hence disclination angles,
as observed in BN HCNTs, contradicts the dominant role of
the entropy in the present case. The S1800 and S1750 specimens
postheated at different temperatures show a different distribution
of apex angles, although they had experienced the same heating
temperature (1700 °C) at which microworms were actually
formed. This excludes the possible dependence of final apex
angles on the curvature of microworms. These results imply
changes of disclination configuration during the postheating
process, which transforms the apex angles to a stable value
determined by the temperatures. Thus, the single enthalpy factor
determines the final disclination configuration of HCNTs.
A hollow conical-helix is actually not formed soon after the
nucleation of a wrapping cone on the microworm. Numbers of
bridges were formed along the tube axis segmenting the hollow
chamber, showing a typical bamboo-like morphology (see
Figure 5). A phenomenon that should be noted is that the bridges
were completely removed in the right-hand part of the tube,
whereas they are only broken in the left-hand region. EELS
elemental mapping (Figure 5) shows carbon and a trace amount
of oxygen covering the interior surfaces of the tubes and surfaces
on both sides of the broken bridges. The sharp bright contrast
The round morphology of bridges inside the initial HCNTs
requires the introduction of a considerable amount of topological
defects, for example, four- or five-membered rings depending
on the curvature. For the binary BN system, odd-numbered rings
imply the introduction of B-B or N-N bonds which are less
favorable than B-N bonds under energetic consideration. The
chemical reaction easily proceeds at these defect sites. The
surface of a hollow conical-helix consists of filament edges,
(12) Xu, F. F.; Bando, Y.; Golberg, D.; Ma, R. Z.; Tang, C. C. J. Chem. Phys.,
accepted.
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Hollow Conical-Helix of Graphitic Boron Nitride
A R T I C L E S
further decrease along with a decrease in annealing temperatures.
The peaked apex angle tends to be 35° and 30° for specimens
SA1700 and SA1600, respectively. The smallest apex angle was
observed in SA1600, displaying a value of 19°, that is,
corresponding to the highest disclination angle of 300°. It is
indicated that the reconstructed conical configuration after
annealing also employs ordered stacking modes showing specific
values of θover
.
During deformation of HCNTs, we observed that tension and/
or torsion may cause the apex angle decrease along with a
simultaneous decrease in tubular radius, leading to an increase
of strain energy.12 However, the present thermodynamic phe-
nomenon which shows a decrease of the apex angle at lower
temperatures does not suggest an increase in strain energy which,
on the other hand, is determined by the overall bending
curvature. The overall bending curvature is fully determined
by the average tubular radius, Rav. A notable increase in Rav,
and hence decrease in the overall bending curvature, was
observed for specimens prepared at lower temperatures (see
Table 2). S1800 has the smallest Rav, with a distribution centered
around 60-100 nm, whereas the largest diameters Rav (up to
320 nm) were observed in SA1600 with a peaked value at 200-
240 nm. Anyhow, systematic reduction of apex angles with a
decrease in annealing temperatures is of great importance
because it implies that such an important structural parameter
can be controlled. It may be suggested that the reduction of
apex angles under annealing at low temperatures is favored in
terms of strain energy as described below.
Figure 7. TEM image and diffraction pattern of an individual HCNT in
the specimens SA1700 (a) and SA1600 (b), which have experienced
annealing at 1700 and 1600 °C, respectively.
On the basis of a continuum elastic model, Tibbetts13 and
then Robertson et al.14 pointed out that the strain energy of an
individual atom in a curved filament should increase inversely
proportional to the square of the radius of curvature.
leaving B and N atomic bonds unsaturated. Reactants are then
absorbed on the interior surface. At present, it is not fully clear
whether the chemical reaction takes place on the interior or
exterior surfaces of the tubes, leading to thinning of the tubular
walls. Anyhow, the fact that almost all of the BN HCNTs
display a flat exterior surface but a rough interior surface implies
that the interior region is more reactive than the exterior one,
as revealed by the EELS mapping. Thus, we suggest that some
specific conditions for the dominant chemical reaction inside
the nanoscaled HCNT channel are present.
σi ) λRi-2
(6)
where Ri is the radius of curvature, and λ is a constant
determined by the elastic modulus, filamentary structure, and
atomic size. The strain energy (σ) for a cone can then be
regarded as the sum of σi for all atoms with a linear change of
Ri.
σ ) σ ) λRi-2
(7)
Structural Properties. The above-mentioned chemical and
structural examinations indicate that cone apex angles of HCNTs
are determined by a sole dynamic element, enthalpy. The
reconstruction of disclination configuration after the postnucle-
ation stage is thus achieved through sliding of filaments. This
phenomenon implies an interesting structural property of
HCNTs, which may display a change in apex angles during
annealing. In other words, we can control the apex angle, the
most pronounced structural parameter for the present conical
geometry. Therefore, annealing processes at two different
decreased temperatures (1700 and 1600 °C) were employed.
Systematic TEM observations did reveal a simultaneous reduc-
tion of apex angles but an increase in tubular radius. Figure 7a
and b shows the typical morphologies and diffraction patterns
of HCNTs annealed at 1700 (specimen SA1700) and 1600 °C
(specimen SA1600), respectively. The measured apex angles
and Rav in SA1700 and SA1600 are summarized in Table 2.
Figure 8a illustrates the distribution of apex angles in SA1700
and SA1600, and Figure 8b compares the distribution of Rav in
S1800 and SA1700. As compared to those in S1750, apex angles
∑ ∑
i
or
Rex
∆R
RinRex
σ ) F
λR-2 ) Fλ
(8)
(9)
∫
Rin
∆R ) Rex - Rin ) L sin(θapex/2)
where F is a constant related to the number of atoms per area
on a filament, and L is the generatrix of the cone. For a given
average tubular radius, that is, Rav is a constant, the strain energy
is solely dependent on θapex and gives
4L sin(θapex/2)
4Rav2 - L2 sin2(θapex/2)
σ ) Fλ
(0 < θapex/2 < π/2) (10)
(13) Tibbetts, G. G. J. Cryst. Growth 1984, 66, 632.
(14) Robertson, D. H.; Brenner, D. W.; Mintmire, J. W. Phys. ReV. B 1992, 45,
12592.
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A R T I C L E S
Xu et al.
Figure 8. (a) Distribution of apex angles in the SA1700 and SA1600 specimens, and (b) distribution of Rav in the S1800 and SA1700 specimens.
We then obtain
stepwise. Such deformation behavior results in the striking
flexibility and elasticity of BN, which become comparable to
those of metals. Keeping in mind the inherent high strength
and outstanding chemical and thermal stability, we found that
BN HCNTs exhibit, in some senses, apparent advantages over
metal, polymer, and inorganic compound nanofibers and may
become a key candidate for applications in high-performance
composite materials for both low- and high-temperature usages.
The presently observed structural property of the HCNTs
suggests a possibility for controlling the apex angles artificially.
Although the exact role of the apex angle for the HCNT
physicochemical properties, for example, field emission, is not
yet clear, the present discovery suggests an obvious practicability
of the effect for controlling nanomaterial properties. Neverthe-
less, further theoretical and experimental work is required to
investigate the role of apex angles for HCNT physiochemical
properties.
16Rav2L + 4L3 sin2(θapex/2)
(4Rav2 - L2 sin2(θapex/2))2
∂σ
) Fλ
(11)
∂(sin(θapex/2))
It is noted that eq 11 gives a positive value, indicative of a
synchronous change of strain energy with apex angle. Thus, a
small θapex is energetically more favorable for a given Rav. It is
noted that a large apex angle refers to a large curvature
difference (characterized by sin(θapex/2)) on the curved filament.
The large curvature difference implies that higher density and
a larger variety of distorted bonds in the structure, leading to
the lack of structural rigidity, periodicity, and continuity, and
higher strain energy are involved, and thus it is less stable. Only
enthalpy can provide energetic support for the formation of such
a severely strained structure at the expense of crystal potential.
Strain relaxation is achieved by decreasing the apex angles in
addition to the increase in tubular radius. Reconstruction of the
molecular structure can be performed via the sliding of filaments
and, possibly, the skipping of atoms within a certain range,
leading to a configuration with decreased overall bending
curvature and a moderate curvature difference. The least strained
curved geometry is expected to be achieved when θapex/2 ) 0,
that is, for the conventional cylindrical nanotubes. This accounts
for the fact that cylindrical BN nanotubes were usually obtained
at relatively low temperatures, for example, 1200-1500 °C,
while the higher temperatures (>1750 °C) generated conical
structures.4
Conclusion
We report on the synthesis and structural characterization of
a novel graphitic tubular material displaying a hollow conical-
helix geometry. A new formation mechanism is proposed and
discussed in detail. A sole dynamic element, that is, enthalpy
(∆H) or postheating temperature, is found to determine the
disclination configuration of HCNTs. The specific geometry of
HCNTs leads to an interesting structural property, that is,
transformation of apex angles under annealing. This implies the
possibility of nanostructure design and control of its properties.
The present HCNTs are expected to bring about new properties
and applications in chemistry, physics, and materials science.
The specific geometry of the HCNTs is expected to exhibit
some new properties and promising application potentials as
compared to the cylindrical graphitic tubular form. The conical-
helix allows the easy slide of filaments prior to bending and
fracture. Actually, a novel deformation mechanism for HCNTs
upon external stresses has been observed and will be reported
elsewhere.12 The tubes deform through changing the apex angles
Acknowledgment. The authors thank Mrs. K. Kurashima and
K. Fushimi for assistance in the experimental work.
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8038 J. AM. CHEM. SOC. VOL. 125, NO. 26, 2003