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Structure of Single-Wall Carbon Nanotubes: A Graphene Helix

Jae-Kap Lee , * Sohyung Lee , Jin-Gyu Kim , Bong-Ki Min , Yong-Il Kim , Kyung-Il Lee , Kay Hyeok An , and Phillip John

1. Introduction

Single-wall carbon nanotubes (SWNTs) have raised con-siderable interest worldwide [ 1,2 ] because of their unique shape and the resulting versatile and unique properties. Numerous studies have been performed since they were fi rst reported. [ 3,4 ] Previous work has been mainly focused on understanding the structure of SWNTs and the proper-ties of this scientifi cally and technically important material. The deceptively simple structural model of SWNTs, that is, a seamless concentric tube has been virtually universally adopted. [ 24 ] The model was based on the currently accepted structure of turbostratic stacking of seamless concentric gra-phene sheets [ 5 ] of multi-wall carbon nanotubes (MWNTs). Recently, however, we have shown that MWNTs are com-posed of graphene helices with widths of approximately fi ve nanometres. [ 6 ] The structure of MWNTs was attributed to the helical growth of the AA stacked graphene ribbons as the minimum energy confi guration in contrast to circular growth at the tube edges. This suggests that the growth of a curved sheet of graphene, that is, SWNTs, may occur along the min-imum energy pathway. It is questionable whether the growth of seamless narrow diameter cylindrical SWNTs is energeti-cally possible given the high level of stress [ 7 ] and propen-sity to form lower energy structures. In this study, we have analyzed the structure of commercial SWNTs, in the con-text of the previous experimental evidence in the literature. In contrast to the conventional view we show that SWNTs are tubular graphene in the unique armchair confi guration, DOI: 10.1002/smll.201400884

Evidence is presented in this paper that certain single-wall carbon nanotubes are not seamless tubes, but rather adopt a graphene helix resulting from the spiral growth of a nano-graphene ribbon. The residual traces of the helices are confi rmed by high-resolution transmission electron microscopy and atomic force microscopy. The analysis also shows that the tubular graphene material may exhibit a unique armchair structure and the chirality is not a necessary condition for the growth of carbon nanotubes. The description of the structure of the helical carbon nanomaterials is generalized using the plane indices of hexagonal space groups instead of using chiral vectors. It is also proposed that the growth model, via a graphene helix, results in a ubiquitous structure of single-wall carbon nanotubes.

Carbon Nanomaterials

Dr. J.-K. Lee, S. Lee Interface Control Research Center Korea Institute of Science and Technology (KIST) Seoul 130650 , Korea E-mail: [email protected]

S. Lee Department of Semiconductor Science Dongguk University Seoul 100715 , Korea

Dr. J.-G. Kim Division of Electron Microscopic Research Korea Basic Science Institute Daejeon 305333 , Korea

Dr. B.-K. Min Instrumental Analysis Center Yeungnam University Daegu 712749 , Korea

Dr. Y.-I. Kim Korea Research Institute of Standards and Science Daejeon 305600 , Korea

Dr. K.-I. Lee Center for Spintronics Research KIST

Dr. K. H. An Nano Material Research Department Jeonju Machinery Research Center Jeonju 561844 , Korea

Prof. P. John School of Engineering and Physical Sciences Heriot-Watt University Riccarton, Edinburgh , EH14 4AS , UK

small 2014, DOI: 10.1002/smll.201400884

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full papersresulted from a diagonal (30 to the tubule axis) growth of a zigzag graphene ribbon.

The strain energy for a concentric SWNT depends only on the radius of the tubules. [ 7 ] For the smallest diameter SWNT, of about 0.4 nm, which has been experimentally observed [ 8 ] the energy is extremely large, that is, up to about 0.48 eV/atom and 0.85 eV/atom for the zigzag and armchair confi gurations, respectively. [ 7 ] The strain energy of the helical growth of a zigzag or armchair graphene ribbon is just about a quarter that of seamless cylindrical SWNTs. This calcula-tion suggests that the growth of seamless SWNTs may be energetically prohibitive and uncompetitive with the struc-ture proposed here under the conditions of conventional CVD processes.

2. Results and Discussion

Figure 1 shows typical high-resolution transmission elec-tron microscopy (HRTEM) images of bundles of purifi ed SWNTs synthesized by an arc-discharge technique. At rela-tively low magnifi cation (observed by JEM-2100F operating at 200 kV), the contours of SWNTs are observable and a node-like morphology appears as shown in Figure 1 a. Under high magnifi cation (observed by FEI Titan Cubed with aber-ration corrector and a monochromater operating at 80 kV), Figure 1 b, wavy and disconnected atomic lattice fringes, which correspond to the nodal tubules, are evident (Figure 1 b and b). The profi le of the nodal morphology is evident in the atomic force microscopy (AFM) image of a SWNT as shown

in Figure 2 . The line scans along the tubule axis (Figure 2 d) reveal the trace of the nodal morphology.

The nodal morphology of SWNTs has been evident in previous HRTEM [ 4,912 ] and scanning tunnelling micros-copy (STM) [ 13 ] images. Particularly, the digitalized HRTEM images of Meyer et al. [ 9 ] and Suenaga et al. [ 12 ] show atomi-cally resolved nodal morphologies of SWNTs where the traces of graphene helices are observable (Supporting Infor-mation Figure S1). Other morphological evidence has been provided by the work of Kiang et al. [ 14 ] who showed, via HRTEM images, that SWNTs were twisted and folded but not fractured. Such twisting and folding of a perfect tube are impossible without fracture since the three-dimensional structures of SWNTs have acceptable strains of only 25% in both the zigzag and armchair structures. [ 15 ] On the other hand, a tubule comprising graphene ribbons can be twisted or folded without fracture. The thermal conversion of the bun-dles of SWNTs into graphitic ribbons (2200 C under a high vacuum of 10 5 Torr where graphite is stable at 3000 C) reported by Gutirrez et al. [ 16 ] provides indirect evidence that SWNTs are composed of graphene ribbons. Morpho-logical evidence from the literature [ 3,4,1012,14 ] indicates that graphene ribbons are common structural building blocks of SWNTs. The direct observation of the rotational aspects of the growth of SWNTs, via a fi eld emission microscopy reported by Marchand et al., [ 17 ] supports the spiral model of a graphene ribbon growth although the authors explained the phenomenon in terms of a screw-dislocation where an atom is the unit of the screw growth forming a concentric tube. But, this model cannot explain the prevailing nodal morphology

of SWNTs. Furthermore, helical growth of graphene ribbons reduces the conforma-tional energy from 0.85 to 0.22 eV/atom for a 0.4 nm diameter armchair SWNT as shown in Figure 3 .

Graphene is a two-dimensional net that appears morphologically as a layer of honeycombed sp 2 carbon. We can describe the structure of graphene using the space group for the simple hexagonal #191 for AA graphite wherein c is 0 and the other structural factors are the same as those of AA crystals ( Figure 4 a). Here, the struc-tural lines (we use the term line for two-dimensional graphene) can be described as plane indexes (i.e., ( hk0 )), which are more general and directly comparable with other graphene based structures, namely, AA, AB, and AA stacking. [ 6,18 ] In the crystal structure of graphene, there are two kinds of distinctive lines, that is, (100) and (110), wherein the corresponding d-values are 2.13 and 1.23 , respectively. The zigzag (100) line is the closest-packed line, indicating that the direction of a graphene sheet is the preferential growth direction. Moreover the higher surface energy of the (100) line, 1.3 eV/, compared with that of the armchair

small 2014, DOI: 10.1002/smll.201400884

Figure 1. HRTEM images of commercial arc-SWNTs. a) A low resolution TEM image of SWNTs. a) An enlarged image of the region indicated in (a). b) HRTEM image (FEI Titan Cubed) of the SWNTs. b,b) Inverse FFT images taken from the regions indicated in (b).


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(110) line, 1.0 eV/, [ 19 ] can strongly drive the growth of graphene along the direction.

The conceptual structure of graphene can be extended to describe SWNTs. This enables us to use plane indexes, which are convenient for describing the structures of SWNTs whether they are armchair or zigzag in structure as shown in Figure 4 b,c. This structural unit cannot describe the entire tubule. The preferential growth direction, , appears diagonally at 30 for the armchair and 60 for the zigzag con-fi gurations to the tubule axis (Figure 4 b,c). This indicates that the armchair confi guration is the energetically lower form of SWNTs because its strain energy is about one-third that of a zigzag (ribbon) SWNT as shown in Figure 5 . The strain energy for a commonly observable armchair (ribbon) SWNT with a diameter of 1 to 2 nm is as low as 0.02 eV per atom.

Longitudinal, that is, overlapping views of a SWNT differ signifi cantly from the azimuthal orientations. This difference implies that their electron diffraction (ED) patterns depend on the incident direction of the electron beam. [ 20 ] Two views

small 2014, DOI: 10.1002/smll.201400884

Figure 2. AFM analysis of a SWNT. a) A non-contact mode AFM image of a SWNT. It appears to be broadened (15 nm in width) due to the AFM tip effects. b) A corrected AFM image where the nodal morphology is evident. c) From the heights of the tubule, 0.8 nm, which is much smaller than the diameters of the tubules, 23 nm (Figure 1 ), we expect that the tubule (i.e., a graphene helix) was fl attened (4 nm in width) during the severe sonication. The green and red arrows indicate the scan directions of the line profi les shown in (c) and (d), respectively. The blue arrows indicate the periods of the helix, that is, the width of the helix.

Figure 3. Strain energy per atom versus the radius for helical growth of a graphene ribbon and tubular growth of a seamless graphene tube, calculated by Xin et al. method, [ 7 ] which was based on the electronic band structure without introducing any empirical potential. We assumed that the graphene ribbon was suffi ciently narrow not to induce relevant additional strain energy.

Figure 4. Schematic showing the structural unit of graphene and SWNTs. a) The structural unit of graphene described by the space group, simple hexagonal (# 191) ( a = b = 2.46 , c = 0, and the angle between a and b = 120). The (100) line of the two crystalline lines is the close-packed line, and the directions become the preferred growth orientation. b), c) The structural units of an armchair and a zigzag SWNTs. Both structures can be described by the plane indexes of hexagonal groups, such as in graphene. The angles of the preferred growth direction to the tubule axis are 30 and 60, respectively. The red dotted lines represent imaginary boundaries of a zigzag graphene helix that drives the helical growth.

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of AA and AA armchair SWNTs and their simulated ED patterns are presented in Figures 6 ad. The ED patterns also vary with inclinational tilts of SWNTs on the TEM grid as shown in Figure 7 . The ED pattern for an untilted AA armchair SWNT has the 2 mm symmetry, in which each 6 spots for the (100) and (110) planes appear on each Ewalds sphere, and is directly comparable to that of the AA stacked MWNTs. [ 6 ]

The digital diffractogram for a tubule reveals evidence of the armchair confi guration as shown in Figure 6 e. Many ED patterns identical or similar to the expected patterns of the armchair structure have been reported in the litera-ture. [ 3,2129 ] Arepalli et al. [ 30 ] showed an ED pattern identical to the expected pattern for the untilted AA armchair SWNT (Figure 6 c) from a bundle of SWNTs using a nano-diffraction technique.

The majority of other reported ED patterns have revealed the features of distorted armchair SWNTs, in which graphene was rotated by 312 and each ED spot was split into two and appeared as a twin. Previous authors have interpreted the split of ED spots as due to chirality. [ 3,2128 ]

All of the ED patterns of SWNTs reported in the liter-ature, with the exception of two, reported by Liu et al., [ 22 ] showed the features of armchair SWNTs. [ 3,2330 ] It is true that the data of Liu et al. are exceptions since they show zigzag structure-like patterns (Supporting Information Figure S2). The observations of these patterns cannot be unequivocal evidence of zigzag SWNTs because the (110) spots of the two ED patterns were not presented. Such ED patterns, that is, six (100) spots for the zigzag confi guration appeared whereas (002) spots were absent were obtained from MWNTs with only a few layers, that is, double-wall carbon nanotubes (DWNTs). DWNTs exhibit a zigzag confi gura-tion, [ 6 ] and their (002) signals are absent. Thus, the previous ED analyses in the literature support our interpretation

namely the armchair confi guration is the preferred structure of SWNTs.

Several STM images interpreted as zigzag SWNTs have been reported previously. [ 3136 ] However, the present analysis of the STM images shows no evidence for zigzag SWNTs (i.e., STM images directly revealing the graphene lattices in the zigzag direction of the tubules). Venema et al. [ 32 ] inter-preted the triangular (or rhombic) lattices in the STM images of a tubule in terms of a zigzag structure, in which the lat-tices were indicative of zigzag SWNTs (Supporting Informa-tion Figure S3). [ 34,35 ] However it is unreasonable for zigzag SWNTs to reveal the rhombic lattices instead of the hexag-onal confi guration of graphene, which appears for armchair SWNTs. [ 31,34 ] It is conceivable that the samples exhibiting the rhombic lattice in the STM images were MWNTs and could

small 2014, DOI: 10.1002/smll.201400884

Figure 5. Strain energy per atom versus the radius for armchair and zigzag SWNTs formed by helical growth of a graphene ribbon, calculated by Xin et al. method, [ 7 ] which was based on the electronic band structure without introducing any empirical potentials. The red dotted lines in b indicate the imaginary boundaries of the graphene ribbons in the form of a tubule. We assumed that the graphene ribbon was suffi ciently narrow not to induce any relevant additional strain energy.

Figure 6. Schematic showing two typical overlapping views of armchair SWNTs and their simulated and expected ED patterns. a,b) AA and AA overlapping views. The structural units and planes are drawn in the schematic views. c,d) Simulated ED patterns for AA and AA overlapping views of an armchair tubule (diameter, 2 nm and length, 4 nm). e) HRTEM image (FEI Titan Cubed) of a tubule. e) Inverse FFT image taken from the region indicated in (e). e) Digital diffractogram taken from the region indicated in (e). The arrows in (e) and (e) indicate the trace of graphene helix.



be DWNTs consistent with the diameter of their sample, 1.4 nm. [ 32 ] When the graphene sheets of DWNTs, which have the AA stacked zigzag confi guration, [ 6 ] are circumfer-entially translated by several percent, the rhombic symmetry can be projected in their STM images due to an additional effect of the electrons of the alternate atoms from beneath the AA stacked graphene sheet. The rhombic images are the signals amplifi ed from incoherently overlapped two atoms (Supporting Information Figure S3). An STM image showing rhombic lattices was presented [ 37 ] from a clear MWNT with a diameter of about 25 nm. Furthermore, the zigzag hexag-onal STM image was directly measured from a MWNT. [ 35 ] The two STM images obtained from MWNTs indicate that AA stacked zigzag MWNTs can project the zigzag hexag-onal directly or the triangular lattice-like images indirectly depending on the degree of the translation of the graphene. The hypothesis that the samples that produce triangular STM images are derived from MWNTs needs further confi rmation.

Venema et al. [ 32 ] claimed that their sample comprised SWNTs from measuring the nanotube diameters to be 1.4 nm, although MWNTs (i.e., DWNTs) can also exhibit similar diameters [ 38 ] although the means by which the structures of the samples [ 31,3335 ] were established were absent. Further-more, all types of CNTs generally coexist. [ 38 ] Unlike the result

of ED analysis, the frequent observation of SWNTs with the zigzag features in STM measurement indirectly suggests that a portion of their samples were indeed MWNTs. [ 3134 ] On the other hand, STM images of distorted SWNTs, showing arm-chair hexagonal lattices, have been reported [ 31,32,34 ] in which, graphene revealed mismatched and contorted lattices with distortion angles of 10, which are in the range of the angles measured by the ED signals. In summary, the inspection of STM images cannot unequivocally distinguish between the types of CNTs and, moreover, the existence of a zigzag SWNT has yet to be confi rmed.

The growth mechanism of helical SWNTs can be inferred from the different lengths of the nodes which range from 1 nm to 5 nm as shown in Figure 1 a and b. The growth of a narrow and thin graphene ribbon [ 39 ] (i.e., 1 nm, 4 zigzag hexagon width) in the zigzag confi guration drives the helical growth ( Figures 8 a,b) process. As the top of the graphene ribbon rises from the nucleation site, the edges of the helix become wider to minimize surface energy by lateral growth along to the directions of the edges (Figures 8 b,c). The secondary lateral growth of the zigzag graphene helix fi lls the gaps between the nodes preformed by the primary helical growth, and completes the tubular shape in the arm-chair confi guration. Such two-step growth produces a unique

small 2014, DOI: 10.1002/smll.201400884

Figure 7. Effect of inclination tilt of a tubule on ED spots. With the inclination angle ( ), some of ED spots for a) AA and b) AA overlapping of an armchair SWNT are disappeared ( = 30 of AA overlapping) or evolved ( = 5, 10, 20, 30 of AA overlapping). The inset defi nes the inclination angle.

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back and belly nodal morphology (Figure 8 d), observable in the digitalized HRTEM images of Meyer et al. (Supporting Information Figure S1a). [ 9 ] The unique nodal morphology for armchair SWNTs is also observable in the STM image for the 1-nm tubule reported by Ge et al. [ 36 ] although they interpreted the tubule as a zigzag structure. The angle of their prominent rows, 50 to tubule axis (Supporting Informa-tion Figure S4), demonstrates that the tubule is an armchair SWNT distorted by about 10 which is frequently observed in the literature. [ 2129,31,32,34 ] A zigzag SWNT, if it exists, should reveal prominent rows oriented by about 30 to the tubule axis (Supporting Information Figure S3). We anticipate that the slightly deformed rhombic lattices (which can be regarded as a part of the hexagon-like lattices) is attributed to the steep curvature of the 1 nm-tubule which makes the atoms be seen to be closer in STM analysis and projects the derived images, as in the case of the AA stacking. The cur-rent analysis for the STM image can explain the inconsistent and diverse STM images for SWNTs in the literature where distorted graphene is the unique feature. [ 31,32,34,36 ] The direct armchair hexagons of graphene with lattice distortions [ 31,32,34 ]

and indirect derived symmetries can appear according to diameters and local positions of nodal samples comprising the back and the belly zones (Supporting Information Figures S1 and S4). The line defects in the STM images for SWNTs [ 31,32,34 ] are characteristic of the unzipped zones. Due to the STM imaging mechanism, the three-dimension-ally mismatched graphene helices appear as line defects in their STM images.

We predict that two-step growth, initially via a helical structure followed by zipping of the single strand, distorts the graphene helix (Figure 8 d) and the distorted graphene helix may have been previously interpreted as a chiral SWNT. The atoms on edges of the unzipped zones of a helix may conceivably be H-terminated or modifi ed (i.e., forming a fi ve- or seven-membered ring) to minimize the conformation energy.

The new model explains the diverse HRTEM morpholo-gies of SWNTs in the literature as well as the different dia-meters of the tubules that are determined by the width of the initial graphene ribbons. Ideal matching of the two spatially approaching graphene edges should form a smooth nodal morphology, such as in the HRTEM image of Hashimoto et al. [ 23 ] This explanation addresses the prominent appear-ance of the D band (1350 cm 1 ) as well as its large variation in Raman spectra for SWNTs reported in the literature. [ 40,41 ] The D band can be strong for some samples (incoherently scrolled) or weak for other samples (coherently scrolled). We expect that the D band should be negligible if SWNTs are seamless graphene tubes because the fraction of the dis-ordered portion at the ends of a seamless tube will be very small due to the large aspect ratio of SWNTs. Our graphene helix model also explains the inconsistent physical proper-ties of SWNTs, that is, an approximately four-fold deviation in breaking strength and Youngs modulus, [ 42 ] which should be critically dependent on the perfection of the graphene helix.

Our analysis of the ED patterns and STM images in the literature shows that the preferred armchair confi guration is possibly the unique structure of SWNTs. Theoretically, SWNTs in the armchair confi guration are metallic. [ 41,43 ] The theory is based on the assumption that SWNTs are perfect tubules. The electrical properties of SWNTs, as metallic or semiconducting, may be attributed to imperfections in the graphene helix and experimental errors in sampling. It is well understood that strain can change the band structure of SWNTs and defects act as conductance barriers. [ 44 ] We propose, on these grounds, that the semiconducting proper-ties may be an intrinsic feature of helical nanotubes. There is evidence that some of the previous STM data [ 3135 ] have been obtained from MWNTs (mostly DWNTs) which show metallic conductivity. [ 40 ] Straight and undistorted tubules with a diameter of 2 nm are DWNTs which reveal the rhombic STM symmetry where the angle of the prominent rows to the tubule axis is about 30 (Supporting Informa-tion Figure S3). [ 3135 ] DWNTs can be relatively free from stress due to the growth mechanism where AA stacked graphene nanoribbons collectively grow, [ 6 ] unlike SWNTs with the typical nodal morphology which is evident in AFM images. [ 45 ]

small 2014, DOI: 10.1002/smll.201400884

Figure 8. The growth model of a SWNT. a) Schematic showing a graphene ribbon diagonally nucleated in the zigzag confi guration. The direction, which is normal to the cross-packed (100) line, is the preferred growth direction. b) Schematic showing the initial stage of the growth of the graphene ribbon. c) Schematic showing the two-step growth of the graphene helix; lateral growth, followed by helical growth of the zigzag graphene ribbon. The length of a node (i.e., a cycle of the helix), l , is smaller than 5.3 d where d is the diameter of a tubule. d) Schematic showing a completed armchair SWNT with a diagonal dislocation in which is the distortion angle.



3. Conclusion

The analysis and experimental data presented in this paper show that SWNTs may be derived from the initial helical growth of a zigzag oriented graphene ribbon. These conclu-sions address previous experimental evidence in the litera-ture, diverse ED patterns, HRTEM and STM morphologies as well as inconsistencies in the measured mechanical and electrical properties of SWNTs. The prevailing nodal mor-phology of SWNTs is direct evidence for our graphene helix model. The results clarify the interpretation of the sci-entifi cally and technically important electrical properties of SWNTs.

4. Experimental Section

Commercial purifi ed SWNTs were synthesized by an arc-discharge technique (Hanwha nanotech) and analyzed by HRTEM and AFM. Samples were sonicated in ethyl alcohol with an ultrasonic power density of 20 W/mL for 2 h. HRTEM images were acquired by a JEM-2100F operating at 200 kV and a FEI Titan Cubed with aberration corrector and a monochromater operating at 80 kV. We confi rmed that the images of the samples did not change when subject to further FEI Titan TEM observation (i.e., there was no any electron damage to the samples). A droplet of the SWNTs suspension was dispersed on a single crystal silicon (100) substrate for AFM sam-pling The surface morphology was probed by a non-contact-mode AFM (PSIA, XE-100) using a commercial cantilever with a tip radius of curvature

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small 2014, DOI: 10.1002/smll.201400884

[40] J. Hodkiewicz , Characterizing Carbon Materials with Raman Spec-troscopy Application note:51901 , Thermo Fisher Scientifi c Inc . 2010 .

[41] (Eds: A. Jorio , M. S. Dresselhaus , G. Dresselhaus) , in Carbon Nano-tubes: Advanced Topics in the Synthesis, Structure, Properties and Applications Springer-Verlag , Berlin, Germany 2008 , pp 84, 256, 387, 502, 548-552, 590 .

[42] M.-F. Yu , B. S. Files , S. Arepalli , R. S. Ruoff , Phys. Rev. Lett. 2000 , 84 , 5552 .

[43] M. S. Dresselhaus , G. Dresselhaus , R. Saito , Carbon 1995 , 33 , 883 . [44] (Eds: A. Jorio , M. S. Dresselhaus , G. Dresselhaus) , in Carbon Nano-

tubes: Advanced Topics in the Synthesis, Structure, Properties and Applications Springer-Verlag , Berlin, Germany 2008 , pp 463 464 .

[45] L. Ding , D. Yuan , J. Liu , J. Am. Chem. Soc. 2008 , 130 , 5428 .

Received: April 1, 2014 Revised: April 19, 2014 Published online:

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