Chirality

Chirality-Dependent Reactivity of Individual Single-Walled Carbon Nanotubes

Bilu Liu , Hua Jiang , Arkady V. Krasheninnikov , Albert G. Nasibulin , Wencai Ren , Chang Liu , Esko I. Kauppinen , * and Hui-Ming Cheng *

Electronic characteristics of a single-walled carbon nanotube (SWCNT) strongly depend on minor variations in its atomic arrangement, specifi cally chirality. Therefore, precise control over nanotube chirality is highly desired for their application. Theoretically, SWCNTs with different structures have different chemical reactivities, which can be further used for their chirality selection. Here, an approach is developed to examine the relationship between the chirality of SWCNTs and their intrinsic chemical reactivity. By oxidizing individual, high-quality, suspended SWCNTs and using the nanobeam electron diffraction technique, it is shown that the reactivity of SWCNTs to O 2 is intricately related to their diameters, metallicity, and chiral angles. In particular, even minor differences in chiral angles lead to big differences in their reactivity, which concords with fi rst-principles calculations. Based on the experimental observations, a chirality-dependent reactivity sequence is constructed for SWCNTs. These fi ndings shed light on effective chiral separation of SWCNTs for their practical application in many fi elds.

1. Introduction

A single-walled carbon nanotube (SWCNT) can be con-

ceptually regarded as a seamless cylinder rolled up from

© 2013 Wiley-VCH Verlag GmbHsmall 2013, 9, No. 8, 1379–1386

DOI: 10.1002/smll.201202761

Dr. B. L. Liu, Dr. H. Jiang, Dr. A. G. Nasibulin, Prof. E. I. KauppinenNanoMaterials Group, Department of Applied Physics Aalto University School of Science FI-00076 Aalto, Espoo, Finland Fax: ( + 358) 924-513-517E-mail: esko.kauppinen@aalto.fi

Dr. B. L. Liu, Prof. W. C. Ren, Prof. C. Liu, Prof. H.-M. Cheng Shenyang National Laboratory for Materials Science Institute of Metal Research Chinese Academy of Sciences Shenyang 110016, China Fax: ( + 86) 242-390-3126 E-mail: cheng@imr.ac.cn

Dr. A. V. KrasheninnikovDepartment of Physics University of Helsinki Helsinki 00014Finland and Department of Applied Physics Aalto UniversityEspoo 00076, Finland

a piece of graphene sheet, and its geometrical structure is

defi ned by a pair of integers, (n, m), namely the chirality. [ 1 ]

Numerous theoretical [ 2 ] and experimental [ 3 , 4 ] studies have

shown that the electronic structure of an SWCNT is deter-

mined by its chirality, or equivalently, its diameter and chiral

angle. As-grown nanotube samples are always a mixture

of both metallic and semiconducting SWCNTs, [ 5 ] which

poses a drawback in their applications. [ 6–9 ] Direct selective

growth [ 10–20 ] and post-growth separation [ 21–25 ] techniques

have been developed in recent years in an attempt to select

SWCNTs with a given chirality. These methods are based on

the different stabilities and chemical reactivities of SWCNTs

with different geometrical structures. [ 26 ] Theoretical studies

have touched this fundamental question, aiming to compare

the energy and chemical reactivity differences among indi-

vidual SWCNTs with different chiralities. [ 27–31 ] However, it

is rather challenging to investigate the chirality-dependent

intrinsic stability and reactivity of individual SWCNTs

experimentally. Previous experiments [ 21 , 32 , 33 ] were only car-

ried out on SWCNT bundles or SWCNTs supported on

substrates or dispersed in solvents, where the interactions

among SWCNTs inside a bundle, [ 34 ] on a substrate, [ 35 ] or in

the solution alter the properties of SWCNTs. Meanwhile,

the purifi cation process [ 32 , 33 ] generally introduces defects in

SWCNTs. For example, acid treatment is commonly used to

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Figure 1 . Characterization of as grown SWCNTs. (a) A low magnifi cation TEM image of nanotube network inside a hole on a Si 3 N 4 grid, where abundant individual suspended SWCNTs can be found for ED analysis. (b) A typical Raman spectrum of the nanotubes. The peak denoted with an asterisk at 303 cm − 1 originates from the Si/SiO 2 substrate. (c,d) Representative HRTEM images of the as-grown SWCNTs.

purify raw nanotubes, while such processes may cause surface

functionalization of nanotubes with oxygenated functional

groups [ 36 , 37 ] and destroy nanotube structure. [ 38 ] On the other

hand, sonication involved in many purifi cation methods

can create vacancy-type defects in nanotubes, disrupt their

tubular structure, and even cut them. [ 22–24 , 39 ] This further hin-

ders the investigation of the intrinsic properties of SWCNTs.

Moreover, optical methods like Raman, optical absorption,

and photoluminescence spectroscopy are usually used to

characterize the chirality of SWCNTs. [ 10–12 , 20 , 22–25 , 32 , 33 , 40 , 4

1 ] These methods are not unambiguous for charactering the

chiralities of large diameter SWCNTs and the nanotube envi-

ronment may have an effect on their chirality assignment.

Here, we devised a novel and robust approach to solve

the above problems and to study the chirality-dependent

intrinsic reactivity nanotubes. We used as grown high quality,

individual suspended SWCNTs to exclude the infl uence from

nanotube bundles and substrates on their properties, and

the nanobeam electron diffraction (ED) technique ensures

a precise characterization of nanotube chirality. Our results

show that the reaction of SWCNTs to O 2 sensitively depends

on their diameters, metallicity, and particularly, chiral

angles, which is in well agreement with the fi rst-principles

calculations.

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2. Results and Discussion

High-quality SWCNTs grown using a

fl oating catalyst (aerosol) chemical vapor

deposition (CVD) method [ 42 , 43 ] were

directly collected on Si 3 N 4 transmission

electron microscopy (TEM) grids (see

Experimental Section). Figure 1 a pre-

sents a typical TEM image of as-grown

SWCNTs inside a hole on a Si 3 N 4 TEM

grid, where the nanotubes form a dense

network. Raman spectroscopic study

(Figure 1 b) shows the presence of radial

breathing modes (RBMs) located at

100 cm − 1 to 300 cm − 1 , indicating a rela-

tively broad diameter distribution, as the

diameters of SWCNTs are determined by

their RBM frequencies. [ 44–47 ] Furthermore,

a low defect-related D-band to tangential

G-band intensity ratio of ∼ 0.03 indicates

the very high quality of the as-grown

nanotubes. [ 20 , 47 ] Detailed high-resolution

TEM (HRTEM) studies reveal that most

of the products are high quality SWCNTs,

which are clean and straight with sus-

pended segments having lengths of ∼ 50–

200 nm (Figure 1 c,d).

We characterized the chiralites of indi-

vidual suspended SWCNTs using ED [ 48 ]

(see Experimental Section) and simul-

taneously recorded their position on the

grid inside TEM (Supplementary Figure

S1). Afterwards, these SWCNTs under-

went oxidation treatment in air at 400 ° C

for 30 min and were characterized by TEM again to examine

whether they had reacted. The samples then underwent

repeated treatments under more harsh conditions, followed by

subsequent TEM examinations. By a series of such oxidation

treatments, recording, and characterization, we constructed a

chirality-dependent reaction sequence for SWCNTs.

Figure 2 presents a TEM image sequence illustrating the

evolution of an individual suspended SWCNT after being

treated at temperatures of 400 ° C, 450 ° C, 470 ° C, and 490 ° C.

The original SWCNT is shown in Figure 2 a (indicated by a

solid arrow). Figure 2 b shows the ED pattern of this SWCNT,

which presents a set of parallel diffracted layer lines in addi-

tion to the bright spot at the centre. An ED pattern analysis

revealed that the chirality of this SWCNT is (11, 10). [ 48 ] The

sample then underwent oxidation treatment at 400 ° C, and

Figure 2 c clearly shows that this nanotube did not react. The

situation was the same for 450 ° C (Figure 2 d) and 470 ° C

(Figure 2 e). However, after treatment at 490 ° C, this SWCNT

disappeared, as indicated by the dotted arrow in Figure 2 f.

Note that we did not observe any signifi cant changes in the

surrounding nanotube network, as evident from the fi gures.

Figure 2 a,c–f exclude any effects of the underlay support on

the disappearance of this (11, 10) SWCNT. Consequently, the

disappearance of this (11, 10) SWCNT at 490 ° C is attributed

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Individual Single-Walled Carbon Nanotubes

Figure 2 . Sequential images illustrate the evolution of an SWCNT sample after air treatment at different temperatures. (a) A TEM image of a pristine SWCNT. (b) A nanobeam ED pattern of the SWCNT suggesting a chirality of (11, 10). (c–f) TEM images of the same SWCNT after air treatment for 30 min at 400 ° C (c), 450 ° C (d), 470 ° C (e), and 490 ° C (f). The solid arrows in images (a,c–e) indicate the SWCNT, while the dotted arrow in image (f) indicates the disappearance of this SWCNT.

to its reaction during air treatment. Using this approach, we

systematically investigated the reaction of over 80 individual

suspended SWCNTs, and on the basis of which we con-

structed a chirality-dependent intrinsic reaction sequence of

SWCNTs.

Figure 3 shows chirality maps of reacted and unreacted

SWCNTs for the four reaction temperatures. In each map,

unreacted SWCNTs are marked with green hexagons while

the reacted SWCNTs are colored in blue (400 ° C, Figure 3 a),

dark brown (450 ° C, Figure 3 b), red (470 ° C, Figure 3 c), and

orange (490 ° C, Figure 3 d). As shown in Figure 3 a and the

Supporting Information Table 1, only two SWCNTs, i.e., (11,

2) and (12, 1), reacted after the treatment at 400 ° C. Inter-

estingly, the (11, 3) SWCNT, which possesses a diameter

and a chiral angle slightly larger than the (12, 1) SWCNT,

survives the treatment. We remark that both (11, 3) and

(12, 1) SWCNTs are semiconducting nanotubes. The above

results indicate that even SWCNTs with similar geometrical

structures and the same electronic properties, they exhibit

distinctly different reactivity in air. The smallest SWCNT

observed in this study, a (7, 6) nanotube, did not react during

400 ° C treatment, despite it having a smaller diameter than

the (11, 2) and (12, 1) SWCNTs. It is noted that a (7, 6)

SWCNT has a chiral angle of 27.5 ° , much higher than that of

the (11, 2) and (12, 1) SWCNTs with chiral angles of 8.2 ° and

4.0 ° , respectively. Furthermore, the (19, 3) SWCNT, which

possess a small chiral angle of 7.2 ° , but a large diameter of

1.62 nm, remained unreacted. Overall, the above results indi-

cate that the reactivity of SWCNTs does not depend solely

on a single structural parameter, but more on the interplay of

both their diameters and chiral angles.

By increasing the treatment temperature up to 450 ° C,

nine more SWCNTs reacted, among which two (11, 3)

SWCNTs reacted simultaneously (Figure 3 b and Supporting

© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheimsmall 2013, 9, No. 8, 1379–1386

Information Table 2). These nanotubes

possess diameters in the range of 1.04–

1.34 nm, which are much smaller than most

of the unreacted SWCNTs in Figure 3 b,

e.g., the (19, 3) and (26, 4) SWCNTs. This

fact indicates that small diameter

SWCNTs possess an intrinsically higher

reactivity in air. Once again we observed

that some small-diameter SWCNTs like

(7, 6), (9, 7), (9, 8), (10, 8), and (11, 7)

remain unreacted after 450 ° C treatment.

These nanotubes share a common feature

of large chiral angles. This observation is

in good agreement with the 400 ° C reac-

tion case, suggesting that high chiral angles

imbue SWCNTs with high stability against

the air treatment. However, it is worth

noting that the metallic (10, 7) nanotube

reacted at 450 ° C, even though it has a

similar dia meter and chiral angle com-

pare to the semiconducting (9, 7), (9, 8),

(10, 8), and (11, 7) nanotubes mentioned

above (Figure 3 b). This result suggests

that metallic SWCNTs intrinsically pos-

sess higher reactivity than their semicon-

ducting counterparts with similar diameters and chiral angles.

The reaction tendency observed at 400 ° C and 450 ° C also

appeared at 470 ° C and 490 ° C. As shown in Figure 3 c and

in Supporting Information Table 3, several nanotubes with

diameters in the range of 0.88-1.43 nm reacted after 470 ° C

treatment. These nanotubes either possess relatively smaller

diameters or smaller chiral angles than the unreacted ones.

The reaction of a very small diameter (7, 6) SWCNT at such

a high temperature further demonstrates the importance of

chiral angles on the reactivity of nanotubes. After further

treatment at 490 ° C (Figure 3 d and Supporting Information

Table 4), we observed four remaining SWCNTs with chirali-

ties of (14, 13), (15, 13), (16, 14), and (23, 16). As expected,

they all share the common features of large diameter, high

chiral angle, and are semiconducting. Therefore, starting

from samples containing individual and suspended SWCNTs,

one can increase the concentration of SWCNTs with such

characteristics by simply heating them in air. We noted that

the intensity ratios of D bands to G bands do not change

signifi cantly after each treatment (Supporting Information

Figure S2), suggesting the unreacted nanotubes keep high

quality. The preferential reaction of small diameter SWCNTs

is also confi rmed by Raman spectra (Supporting Informa-

tion Figure S2). However, the in-depth chirality-dependent

reaction behavior cannot be extracted from Raman spectra

owing to its inaccuracy for chirality assignment for large

SWCNTs.

Figure 4 a shows SWCNTs that reacted at different tem-

peratures in a single chirality map. This suggests a clear trend

of the reaction towards SWCNTs with larger diameter and

higher chiral angle as the reaction temperature increased

from 400 ° C to 490 ° C (indicated by the red arrow). Note that

this trend is applicable to both semiconducting and metallic

SWCNTs, as presented in Figure 4 b,c.

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Figure 3 . Reactivity of SWCNTs at different temperatures. (a–d) Chirality maps of SWCNTs reacted and unreacted at 400 ° C (a), 450 ° C (b), 470 ° C (c), and 490 ° C (d). In each map, the green area represents unreacted SWCNTs while other colors stand for SWCNTs that reacted at the corresponding temperatures. The hexagons with red frames indicate that more than one SWCNTs with the same chirality reacted (denoted as reacted, > 1) or unreacted (denoted as unreacted, > 1) at the corresponding temperatures. The (n, m) numbers in black stand for semiconducting SWCNTs, while the blue ones represent metallic nanotubes.

The primary reaction taking place during air treat-

ment is the oxidation of SWCNTs by O 2 molecules. There-

fore, the above results suggest a preferential oxidation of

small SWCNTs, which is in line with previous experiments

addressing the chemical reactivity of SWCNTs. [ 21 , 32 , 40 ] This

is attributed to large curvature inducing high strain in small

SWCNTs, which arises from misalignment of π -orbitals. [ 26 ]

The metallicity-dependent oxidation is also in agreement

with previous studies [ 21 , 40 ] where the higher reactivity of

metallic SWCNTs originates from delocalized electronic

states near the Fermi level. Nevertheless, our results reveal

that the metallicity-dependent reactivity trend is applicable

only to SWCNTs with similar diameters to each other, and

large diameter metallic SWCNTs are more stable than small

diameter semiconducting ones. For example, large diameter

metallic SWCNTs (19, 10) and (21, 6) left even many small

diameter semiconducting SWCNTs reacted at 470 ° C treat-

ment (Figure 3 c).

The most intriguing fi nding here is the chiral-angle-

dependent reactivity of individual SWCNTs, which was rarely

observed previously. As shown in Figure 4 b,c, SWCNTs with

higher chiral angles are less reactive and thermodynamically

more stable than those with small chiral angles, providing

they have similar diameters and the same metallicity. This

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differs from another study [ 32 ] where a larger oxidation rate

of SWCNTs with high chiral angles was observed than for

those with small chiral angles. In solution phase reaction of

nanotubes, the redox potential is typically used to describe

the reaction process. [ 49–51 ] However, previous studies show

that the redox potential of SWCNTs does not scale with their

chiral angles. [ 51 ] Therefore, it is clear that the gas phase reac-

tion trend we observed here is not governed by the redox

properties of nanotubes. Our detailed HRTEM examinations

show partial destruction of SWCNT sidewalls under air treat-

ment (Supporting Information Figures S3 and S4), which is

similar to a very recent study based on in situ environmental

TEM observations of the oxidation of multi-walled CNTs. [ 52 ]

As the typical lengths of SWCNTs range from a few microns

to tens of microns in our sample, [ 42 , 43 ] we speculate that the

oxidation of the SWCNTs takes place at SWCNT sidewalls

in the monitored segments, although oxidation from the ends

cannot be excluded.

In order to gain microscopic insight into the oxidation

process and assess the relative reactivity of different struc-

ture SWCNTs with O 2 , we carried out extensive fi rst-princi-

ples calculations within the framework of density-functional

theory (DFT, see Experimental Section). In agreement with

previous calculations, [ 53 ] we found that there is a potential

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Individual Single-Walled Carbon Nanotubes

Figure 4 . Chirality-dependent reaction sequence of SWCNTs. (a) A chirality map of SWCNTs reacted at different temperatures with a red arrow pointing toward the large diameter and high-chiral-angle direction. (b,c) Diameter- and chiral-angle-dependent reactivity of semiconducting (b) and metallic (c) SWCNTs.

barrier of ∼ 1 eV for an O 2 molecule to chemisorb on an

SWCNT surface by cyclo-addition ( Figure 5 , C). Once the O 2

molecule is chemisorbed, it easily splits into two close oxygen

adatoms in an epoxy (or bridge, Figure 5 , B) confi guration.

The factor that governs the stability of the SWCNTs is the

formation of the fi rst vacancy by evolving a CO 2 molecule,

which requires energy input. When the fi rst vacancy is cre-

ated, the process of oxidation becomes exothermic. The

energetics of the process depends on the diameter and chi-

rality of the SWCNTs. The reactivity of the SWCNTs natu-

rally decreases with diameter, so that in our calculations we

focus mainly on the intriguing dependence of the reactivity

on chirality. Four different SWCNTs with roughly the same

diameter were studied (Figure 5 and Table 1 ). In perfect

agreement with the experimental results, our simulations

indicated that SWCNTs with higher chiral angles are more

© 2013 Wiley-VCH Verlag Gmbsmall 2013, 9, No. 8, 1379–1386

stable than those with smaller ones. This is associated with

the energies of the bridge confi gurations, as in armchair

SWCNTs (the highest chiral angle) there are C–C bonds

(parallel to the y axis, Figure 5 ) perpendicular to the nano-

tube axis (parallel to the x axis) in a three-dimensional space.

This makes it easier for an oxygen adatom in the bridge con-

fi guration to break up the underlying C–C bond, thus low-

ering the total energy of the system. The situation is opposite

in zigzag SWCNTs, while chiral ones fall in between. As seen

from Figure 5 , the energy required to create the fi rst single

vacancy and CO 2 molecule, E etch , is simply the difference

between the energies of the fi nal (SV) and the B states plus

a barrier energy (E bend ) of ∼ 0.5 eV, which is associated with

the bending of the angle between the C–O bonds in the CO 2

molecule when it approaches the vacancy (Supporting Infor-

mation Figure S5). We stress that for any thermally activated

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Figure 5 . Energetics of the SWCNT oxidation process. The data points are the results of the fi rst-principles calculations, and the curves are schematic representations of the energy diagrams. Once an O 2 molecule is chemisorbed by cyclo-addition (C), it easily splits to form two close oxygen adatoms in an epoxy confi guration (bridge, B). The stability of the SWCNTs is determined by the energy ( E etch ) required for the formation of the fi rst vacancy defect by evolving a CO 2 molecule. E etch is the difference between the energies of the fi nal (SV) and the bridge states plus a barrier energy ( E bend ∼ 0.5 eV), which is associated with the bending of the angle between the C-O bonds in the CO 2 molecule when it approaches the vacancy. The etching process proceeds through an intermediate (M) state where two oxygen atoms are bonded to the carbon atom to be removed. For clarity, only the carbon atoms in front of the SWCNTs are shown.

process (diffusion, chemical reactions, etc.), the reaction rate

of the process is exponentially related to the energetic of

the process. Consequently, even a small difference in initial

and fi nal energies can lead to considerable changes in reac-

tion rates. Further close inspection reveals that the etching

process proceeds through an intermediate (M) state where

two oxygen atoms are bonded to the same carbon atom to

be taken away. We also calculated the barrier for the direct

oxidation reaction, where a carbon atom is 'pulled' away

from an SWCNT and interacts with a nearby O 2 molecule.

However, we found that the barrier for this reaction is quite

high, over 3 eV. As the vacancy formation energy is lower

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Table 1 . Comparison of the energies of different confi gurations. The last column (Diff.) showconfi gurations.

Chirality (n, m) Diameter [nm] Chiral angle [ ° ] “C” [eV] “B” [eV]

(9, 0) 0.71 0.0 1.00 −0.70

(8, 2) 0.72 10.9 1.13 −1.24

(6, 4) 0.68 23.4 0.96 −1.74

(5, 5) 0.68 30.0 0.92 −1.97

in metallic SWCNTs, [ 54 ] our model also

explains why metallic SWCNTs are less

stable than semiconducting ones under

oxidation.

3. Conclusion

In summary, we experimentally investi-

gated the intrinsic reactivity of individual

suspended SWCNTs with known chi-

ralities and have constructed a map illus-

trating a chirality-dependent reactivity of

SWCNTs. The reactivity of SWCNTs to

O 2 is intricately related to their diameters,

metallicity, and more intriguingly, chiral

angles. The chirality-dependent reactivity

of SWCNTs is further verifi ed based on

fi rst principles calculations of the chirality-

dependent vacancy formation energies of

SWCNTs with different geometrical struc-

tures. Our work demonstrates that oxida-

tion in air can be used to selectively obtain

large diameter and high chiral angle

semiconducting SWCNTs, which provides

an effective approach towards control-

ling the chirality of SWCNTs. Moreover,

the unique tracking method developed

in this study is versatile, robust, and can

be applied to investigate the structure-

dependent reactions and properties of

other materials and systems.

4. Experimental Section

SWCNT Synthesis : SWCNTs were synthe-sized in a vertical CVD furnace at 880 ° C using

CO as carbon source and ferrocene as catalyst precursor. [ 42 , 43 ] A ceramic tube with an internal diameter of 22 mm and a length of 550 mm was used as the reaction chamber. Ferrocene powder was fi lled in a cartridge maintained at room temperature. A CO fl ow (300 cm 3 /min) was passed through the ferrocene and was then introduced directly into the high-temperature zone of the reactor through a water-cooled probe inserted 65 mm deep into the reactor. An additional CO fl ow (100 cm 3 /min) was introduced directly into the reactor for the growth of SWCNTs.

The as-grown SWCNTs were fl oating in the gas phase inside the chamber and directly collected with silicon wafers, carbon TEM grids, and Si 3 N 4 TEM grids (DuraSiN meshes, Protochips Inc.,

, Weinheim small 2013, 9, No. 8, 1379–1386

s the difference between the “SV + CO 2 ” and “B”

“M” [eV] “SV + CO 2 ” [eV] Diff. [eV]

−0.27 1.26 1.96

−0.54 1.43 2.67

−0.67 1.56 3.30

−1.00 1.46 3.43

Individual Single-Walled Carbon Nanotubes

USA) at the outlet of the furnace with the assistance of nitrocel-lulose membrane fi lters (Millipore Corp., USA). [ 43 ] The collection time varied from 10 min to 60 min to obtain samples with optimal density and abundant individual and suspended SWCNTs. The samples were then put above an ethanol tank for 10 min to fi rmly attach the SWCNTs on the substrate surface.

SWCNT Oxidation Treatment and Characterization . The SWCNTs on Si 3 N 4 TEM grids were fi rst treated in air at 300 ° C for 1 h in a horizontal CVD furnace to remove absorbed gas molecules and amorphous carbon and to expose a clean surface. Afterwards, the grid was inserted into a TEM chamber (JEOL 2200FS, double Cs-corrected TEM operated at a low electron accelerate voltage of 80 kV, Japan) for TEM imaging and nanobeam ED analysis. We started from holes close to a corner with a special marker (Sup-plementary Figure S1) and moved the grid parallel so as to monitor SWCNTs in many holes inside the grid. In each hole, we chose only those clean, individual, suspended, and straight SWCNTs so as to exclude the infl uence of catalyst particles, adjacent nanotubes, and substrates. Therefore, we believe that possible concurrent reac-tions, e.g., metal particles catalyzed carbon reactions, [ 55 , 56 ] should not play important roles. Moreover, to get a reliable ED analysis on the chirality of SWCNTs, the suspended segments of the SWCNTs typically possessed a length of ∼ 50–200 nm. We set this criterion based on the consideration that a length shorter than 50 nm is not enough to get high-quality ED patterns, while longer than 200 nm may lead to the bending of SWCNTs, which both may produce uncertainty for chirality analysis. The positions and ED patterns of the same nanotube were recorded simultaneously. By switching to other holes in the grid, we monitored a large number of SWCNTs for statistic analysis. Afterwards, the grid was carefully taken out from the TEM chamber and underwent 400 ° C air treatment for 30 min and was then inserted into the TEM again. Guided by the marker on the grid, we can accurately move to the same holes that were recorded in previous experiments to examine whether the previ-ously recorded SWCNTs remain or were reacted after the 400 ° C treatment. The same procedure was applied to the SWCNTs after air treatment at 450 ° C, 470 ° C, and 490 ° C for 30 min. After each reac-tion, we recorded and analyzed a few more SWCNTs to expand the number of SWCNTs for statistical analysis. We remark that for some SWCNTs, they disappeared after treatment at one specifi c tempera-ture, accompanying with the destroying of the underlying nanotube mattress. For such cases with signifi cant change of SWCNT environ-ment, we only concluded that the SWCNTs were not reacted prior to this specifi c temperature, but not discussed their reactivity at this or even higher temperatures to avoid any uncertainty. It is worth noting that the TEM grids we used are made of Si 3 N 4 mem-brane deposited on the top of Si framework. Both Si and Si 3 N 4 are materials with very low volumetric thermal expansion coeffi cients of ∼ 10 − 6 /K. [ 57 , 58 ] A temperature change from room temperature to 490 ° C (the highest temperature in this study) will only lead to a volume change of ∼ 10 − 4 –10 − 3 , which would not cause any signifi -cant structural deformity to the grids. The electron beam density was established to be 10 15 –10 19 e − /cm 2 · s during TEM and ED char-acterization, which is rather safe and does not introduce noticeable structural defects in SWCNTs (Supporting Information Figures S6, S7, and S8).

We used an intrinsic layer distance method [ 48 ] for chirality analysis of individual SWCNTs from their ED patterns, based on the following equations:

© 2013 Wiley-VCH Verlag Gmsmall 2013, 9, No. 8, 1379–1386

n =π

√3∗ 2d3

t − d2t

(1)

m =π

√3∗ 2d2

t − d3t

(2)

θ = a tan

⎡⎣ 1

√3∗ 2d2

d3− 1

⎤⎦

(3)

where d 2 and d 3 are the layer-line distances between the equa-torial line and the second and third layer line for the fi rst-order hexagons in the ED pattern of SWCNTs, and t is the period of the equatorial line oscillations. [ 48 ] The chirality assignments were also cross-checked by using other available layer line combinations, e.g., d 2 and d 6 or d 3 and d 6 , where d 6 is the distance between the equatorial line and the sixth line for the second-order hexagons in the ED patterns of SWCNTs.

Raman spectra (LabRAM, Horiba Yhoriba Jobin Yvon, France) were collected on SWCNTs on Si wafers and Si 3 N 4 TEM grids using a 633 nm He-Ne laser with a laser spot size of ∼ 1 μ m in a back-scattering confi guration.

Theoretical Calculations . The fi rst-principles simulations were performed using spin-polarized DFT as implemented in the plane-wave-basis-set Vienna ab initio simulation package. [ 59 , 60 ] Projector augmented wave potentials [ 61 ] were used to describe the core elec-trons, and the generalized gradient approximation [ 62 ] to describe the exchange and correlation. The kinetic energy cutoff for the plane waves was set to 400 eV, and all the nanotube structures consisting of 80–152 atoms were relaxed until atomic forces were below 0.01 eV/Å. The same accuracy was achieved with regard to the number of k-points in the one-dimensional Brillouin zone (up to 8 k -points). The length of the supercell along the nanotube axis varies from 9.8 to 18.6 Å depending on the nanotube chirality, and the periodic images of the nanotubes in the transverse direction are separated by 12 Å of vacuum. Nudged elastic band calcula-tions with 10 images between the initial and fi nal confi gurations were carried out to fi nd the energy barriers.

Supporting information

Supporting Information is available from the Wiley Online Library or from the author.

Acknowledgements

This work was supported by the Ministry of Science and Technology of China (Grant 2011CB932601), the National Natural Science Foun-dation of China (Grant 50921004), the TEKES of the Academy of Fin-land (LIBACAM 211247), and the CNB-E project at Aalto University through the Multidisciplinary Institute of Digitalization and Energy (MIDE) program. A.V.K acknowledges funding from the Academy of Finland through several projects. We are also grateful to CSC, Fin-land, for generous grants of computer time. Correspondence and requests for materials should be addressed to E.I.K. or H.M.C.

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Received: November 6, 2012 Revised: January 17, 2013 Published online: March 15, 2013

erlag GmbH & Co. KGaA, Weinheim small 2013, 9, No. 8, 1379–1386