Endo M., Iijima S., Dresselhaus M.S. (eds.) Carbon nanotubes

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Fig. 15. Growth of a (5n,5n) tubule on the catalyst surface, illustrated by that of the (5,5) tubule. The

central grey circle represents the catalyst particle with

coordination sites, and the small grey circles

represent the other

catalyst coordination sites. The normal and bold lines represent single and double

bonds, respectively, while coordinative bonds are represented by dotted lines [(a), (b) and (c)]; (a'),

(b)

and (c') are the corresponding planar representations.

sites already coordinated to the growing tubule and,

finally, they are inserted between the tubule and the

catalyst coordination sites Fig. 15(b) and (b)]. This

leads to the formation

the first additional crown

of perpendicular six membered rings to the growing

tubule. In this growing structure, the

units arrive

and are inserted perpendicularly to the tubule axis.

Further arriving

units will behave as the latter

one did, and

on [Fig. 15(c) and (c')].

From Fig. 15, it can be seen that

coordination

sites

the catalyst are involved in the growth

the

(5,5) tubule, and in general,

20n

coordination sites

will be involved in the growth

the (5454 tubule.

It is obvious that the related catalyst particle must

Graphitizable coiled carbon nanotubes

have more than the

coordination sites used, at

least for the decomposition of acetylene.

3.2.2.2

Growth mechanism

(9n,0)

tubule,

over

24n

coordination sites

the catalyst.

The

growth of

general

(9n,O)

tubule on the catalyst

surface is illustrated by that of the

(9,O)

tubule in

Fig. 16 which shows the "unsaturated" end of

(9,O)

tubule in a planar representation. At that end, the

carbons bearing

vacant bond are coordinatively

bonded to the catalyst (grey circles)

growing

cis-polyacetylene chain (oblique bold lines in Fig. 16).

The vacant bonds of the six cis-polyacetylene chains

involved are taken to be coordinatively bonded to

the catalyst [Fig. 16( b)]. These polyacetylene chains

are continuously extruded from the catalyst particle

where they are formed by polymerization of

units

assisted by the catalyst coordination sites. Note that

in order to reduce the number of representations of

important steps, Fig. 16(b) includes nine new

units

with respect

Fig. 16(a).

The

catalyst coordination sites

drawn further

away from the surface of the particle (closer to the

tubule)

are acting in pairs, each pair being always

coordinatively bonded to one carbon of an inserted

(1")

or of a to-be-inserted

(2")

unit and to two

other carbons which are members of two neighbour-

ing cis-polyacetylene chains

(3").

It should be empha-

sized that, as against the

(5n,5n)

tubule growth, the

units extruded from the catalyst particle are

positioned in this case parallel to the tubule axis

before their jnsertion.

Two coordinative bonds of two neighbouring cis-

polyacetylene chains of the growing tubule are speci-

fically displaced from a pair of catalyst coordination

sites by the insertion of one carbon of a

unit

[2"

in Fig. 16(b)]. The second carbon of that

unit is

still1 bonded to the pair

coordination sites. It will

later be displaced from that pair

coordination sites

by the srrival of the next two

segments

the two

growing cis-polyacetylene chains considered

[

Fig. 16(c)]. The

unit and cis-polyacetylene

segments are hence inserted into the growing tubule.

The further arriving

units or cis-polyacetylene

segments will act as the latter one did, and

[Fig. 16(c)].

can be seen from Fig. 16,

coordination sites

of the catalyst are involved in the growth

the

(9,O)

tubule

and,

in general,

24n

coordination sites will be

involved in the growth of the

(9n,0)

tubule.

3.2.2.3

Growth mechanism

(9n,0)-

(5n,5n)

knee, involtiing

from

,7411

20n

coordi-

nation sites

the

catalyst.

Across the knee, the

growth of the tubule starts as explained for the

(9n,0)

tubule (Fig. 16) and

must

end as explained for the

(5n,5n)

tubule (Fig. 15)

eice versa.

starting point,

growing

(9,O)

tubule on the

catalyst surface is illustrated in Fig. 17(a). In that

growing structure, the

units arrive and are inserted

parallel to the tubule axis.

there

enough space

probably thanks to the distortion caused by the

elastic folding of the growing tubule

[Fig.

12(b)]

two carbons

(1")

can be inserted instead of one

between a pair of coordination sites [Fig. 17(b)]. The

knee is started by the arrival of a

unit perpendicu-

lar to the tubule axis, each carbon

which has a

vacant bond for coordination. These

two

carbons

(instead of the carbon with two vacant bonds

usually

involved) displace one carbon from a pair

coordi-

nation sites. This perpendicular

unit constitutes

the basis of the future seven-membered ring. Note

again that nine new

units are shown in Fig. 17(b)

as compared with Fig. 17(a).

Among the three

units arriving together, two

are parallel to the tubule axis

(2')

and one

ortho-

gonal to the tubule axis

[I"

in Fig. 17(b)]. First,

only

the parallel units are inserted into the tubule structure

[Fig. 17(c)]. These two inserted

units

(2')

were

displaced by the arrival of two orthogonal

units

(3")

and all further arriving

units will be ortho-

gonal to the tubule axis.

Meanwhile, the coordinative bonding of the two

units within the pairs of coordinative

sites

forces

the occupied sites to spread.

result, in the

direction opposite to the place where the first ortho-

gonal

unit arrived, there is only enough room for

single site

(")

instead of for a pair of sites

[Fig. 17(c)]. That site now coordinates the two cis-

polyacetylene

segments, but without the possibility

of inserting a new

unit. The displacement of that

site from the growing nanotubule leads to the closure

Fig.

16. Growth of a

(9n,O)

tubule on the catalyst surface illustrated by that

the

(9,O)

tubule. The

normal and bold lines represent single and double bonds, respectively.

I I

'8.

Fig.

17.

Growth mechanism of a

(9n,0)-(5n,5n)

knee

involving from

coordination sites

the catalyst. (a)-(g) Planar representation of the successive tubule growing steps;

(g') Schlegel diagram representation of the whole knee with the

numbering corresponding to that of the individual steps (a)-(g).

Graphitizable

coiled

carbon nanotubes

101

the five-membered ring [Fig. 17(d)]. Note also

that only six new

units are shown in Fig. 17(c)

with

respect to Fig. 17(b).

Once the pair of sites is disconnected from the

growing tubule [Fig. 17(d)], an orthogonal

unit

inserted below the five membered ring

[4"

Fig. 17(e)]. The latter inserted

unit and the remain-

ing two cis-polyacetylene

segments are finally

displaced by the arrival two orthogonal

units

in Fig. 18(f)].

The carbon atoms linked to the remaining twenty

coordination sites have now finished to rearrange to

fivefold symmetry [Fig. 17(f)]. Consecutive inser-

tion of the five orthogonal

units

[lo,

and

5")

displaced from the catalyst by the arrival of five new

Orthogonal

units closes the seven-membered ring

and completes the knee [Fig. 17(g) and (g')]. Further

growth will yield a (5n,5n) tubule. It will proceed

as already explained in Fig.

15.

Figure 17(g') is

Schlegel diagram explanation of the (9,O)-(

5,5)

knee,

equivalent

Fig. 17(g). In that diagram

is possible

to identify the

units introduced at the different

steps [Fig. 17(a)-(g)] by their numbering.

3.2.2.4

Growth

mechanism

(5n,5n)-

(9~0)

knee,

involving

from

20n

24n

coordina-

tion

sites

the

catalyst.

The explanation given

here to pass from

(9n,0) tubule to

(5n,5n)

tubule

can also be used backwards to pass from a (5n,5n)

tubule to a (9n,O) tubule. The progressive steps are

illustrated in Fig.

18.

The starting point of the knee

is again the blockage

tubule growth

the seven-

membered ring

[

Fig. lX(a)J. The later formation

the five-membered ring is only

consequence of

tubule growth blockage at the seven-membered ring.

Secondly, probably because of the large space created

the other side of the tubule by the elastic bending

[Fig. 12(b)] after tubule blockage,

cis-butadiene

[2" in Fig. 18(b)] can be inserted instead

the usual

orthogonal

units. This cis-butadiene arriving with

four new coordination sites [black points on

Fig. 18(b)] will be the head of

two

cis-polyacetylene

chains

C3"

Fig. 18(c)]. (The freshly arrived

segments

the cis-polyacetylene chain, not yet

inserted in the tubule, are represented by dotted lines

for the sake of clarity.) These two chains are started

at the five-membered ring [Fig. 18(e)]. The insertion

that cis-butadiene also disturbs the other coordina-

tion sites,

that

four other cis-polyacetylene chains

[4" and

in Fig. 18(c)] are also inserted into the

growing tubule. The other logical growing steps

the (53-(9,O) knee are very close to the mechanism

explained for the

(9n,0)

tubule. The insertion of the

first cis-polyacetylene units

[3"

Figs 18(c) and (d)]

and the coordination of the first parallel

units

[6"

in Fig. 18(d)], followed by the insertion

the cis-

polyacetylene units [4O in Figs 18(d) and (e)] and the

coordination of parallel

units

[7"

in Fig. 18(e)]

leads to positioning of the five membered ring. The

closure of that ring, followed by the insertion of the

cis-polyacetylene units

[5"

and

in Figs 18(e) and

in Fig. 18(f)] leads to positioning of the seven-

membered ring. The closure of that ring, during

normal (9n,O) tubule growing step [Fig. 19(g) and

(g')], completes the knee and the following steps will

be the growth of the

(9n,O)

tubule proceeding as

explained in Fig.

16.

Figure 18(g') is a Schlegel

diagram of the (5,5)-(9,O) knee, equivalent to Fig.

18(g). In that diagram

possible to identify the

units introduced at the different growing steps

[Fig. lS(a)-(g)] by their numbering.

important conclusion obtained from the model

based

the variation of the number of coordination

sites at the catalyst surface is that all double bonds

can be localized on the (9n,0)-(5n,5n) knee and

connected nanotubes.

fact, in that model, only

single C-C bonds are formed and there

no double

bond formation during the nanotubule growth.

All

of the double bonds are already localized on the

units or on the inserted cis-polyacetylene chains.

seen from Figs 17 and 18, there is no double bond

on the sides

the five membered ring and there is

only one double bond

the seven membered ring.

It should also be pointed out that localizing the

double bonds on the (9n,0)-(5n,5n) knee and con-

nected tubules was

very difficult task before the

establishment of this model. Once the double bonds

are localized, after replacing the vacant bonds of the

(9n,0)-(

5n,5n)

knee of Fig. 17(g') by hydrogens,

possible to have a three dimensional view

the knee

(Fig. 19). The introduction of the parameters of

Fig. 19 into

more sophisticated program can also

be used in order to minimize the energy and simulate

the real knee angle[18,19].

Concerning the multi-shell tubules, the graphitic

layers

the growing nanotubule described are sup-

posed to grow on the same catalyst particle, at the

same time

the inner layer does. This

in agreement

with the observations of Fig.

11,

where it is possible

to see that the diameter range of the young tubes

minute) is about the same as that of the

old

ones

(20

minutes). Moreover, it has also been observed that

during

long exposure time (5 hours) of the tubules

to the reaction conditions, only amorphous carbon

is deposited on the outer layer[4,5], and no tubes

with larger diameters were observed.

the diameter of the catalyst particle is supposed

to be close to that of the single-shell tubule[20], or

to that of the inner tubule[8], the number of graphitic

layers might depend on the flow rate

acetylene at

the catalyst particle. The graphitic layers are supposed

to be formed by the

units formed

the catalyst

particle, exceeding those needed for the growth of the

multi-shell tubule inner layer. This generalisation

multi-layer tubules

just a hypothesis, since we do

not have any experimental proof yet.

CONCLUSIONS

The building of knees, tori

and

helices

described

simple formalism.

(f)] and coordination

three parallel

units

[So

Relationships are established between the tubules

Fig. 18. Growth mechanism of

(5n,5n)-(9n,O)

knee involving from

coordination sites of the catalyst. (a)-(g) Planar representation

the successive tubule growing steps;

(g') Schlegel diagram representation

the whole knee with the

numbering corresponding to that

the individual steps (a)-(g).

Graphitizable coiled carbon nanotubes

103

(5ninJn)

H’

Fig.

19.

Schlegel diagram of the

(9,O)-(5,5)

knee after replac-

ing the vacant bonds by hydrogen. All of the double bonds

are localized according to the growth process represented

in Figs

17(g’)

and

18(g’).

and their graphitic layers. Hence, after measurement

of a nanotube diameter by HREM, it is possible to

establish the order

its graphitic layer.

All the double bonds can be localized

the

(9n,0)-(

5n,5n)

knee and connected tubule. There

no double bond

the sides

the five-membered

ring and only one double bond on the seven-

membered ring.

Acknowledgements-The

authors acknowledge the Region

of Wallonia and the Belgian Prime Minister Office (PAI-

projects) for financial support. Thanks are also addressed

to D. Bernaerts for the

TEM

images, to D. Van Acker for

the photographs and to

Vallette for the drawings.

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HEMI-TOROIDAL NETWORKS

PYROLYTIC

CARBON NANOTUBES

SARKAR,

KROTO

School

Chemistry and Molecular Science, University

Sussex, Brighton, BN1

9QJ

U.K.

and

ENDO

Department

Engineering, Shinshu University, Nagano, Japan

(Received

May

1994;

accepted

revised

form

August

1994)

Abstract-Evidence for the formation

an archetypal hemi-toroidal link structure between adjacent

concentric walls in pyrolytic carbon nanotubes is presented. The observed and simulated TEM images for

such structures are in excellent agreement. This study suggests that double-walled carbon nanotubes,

which the inner and outer tubes are linked by such hemi-toroidal seals, may be one viable way

over-

coming the reactivity at the graphene edges

open-ended tubes

engineer stable and useful graphene

nanostructures.

Key

Words-Nanotubes, pyrolytic carbon nanotubes, hemi-toroidal nanostructures.

INTRODUCTION

The discovery by Iijima[ 11 that carbon nanotubes

form in a Kratschmer-Huffman fullerene generator[2],

and the subsequent development

techniques by

Ebbeson and Ajayan[3] and others to produce them

in viable quantities, promise to have important impli-

cations for future nanotechnology. The tubes are es-

sentially elongated fuIlerenes[4] and, thus, description

(in particular structural characterisation) in terms of

fullerene chemistry/physics principles is appropriate

and useful.

growth mechanism has been proposed

for the primary tube growth phase[4] which involves

ingestion

carbon fragments (e.g., atoms and chain

molecules)

the reactive hemi-fuuerene closed end-

caps

the tubes. An open-ended growth mechanism

has

also

been proposed[5].

closed-end growth mech-

anism is consistent with the--observations

Ulmer

al.

[6] and McElvany

al.

[7], that fullerenes can

grow by ingestion of carbon fragments into their com-

pletely closed networks. Both growth schemes also are

consistent with Iijima's observation that, in general,

the tubes appear

have their hexagons helically dis-

posed in the tube walIs[l].

The discovery that carbon generates closed-cage

fullerenes spontaneousIy[2,8]

well as nanotubes[l,3]

has

stimulated the question of whether other topolog-

ically accessible networks are feasible. Predictions

the possibility

both small fullerenes[9] and giant ful-

lerenes[lQ,ll] appear to have been vindicated[l2,13].

well as general closed-cage structures, extended

repeat-pattern networks involving seven- and other-

membered rings have been considered by Terrones and

MacKay[l4,l5] and Lenosky

al.1161.

Other struc-

tures have been considered and,

particular, Cher-

nozatonskii[l.7] and Ihara

a1.[18,19] have discussed

toroidal structure.

During the course

detailed study of the struc-

ture and growth of pyrolytic carbon nanotubes

(F'CNTs)

we have found that complex graphitisation processes

occur during

second

stage

heat treatment

these

materials[20,21]. In particular, we here draw attention

to evidence that hemi-toroidal graphite surfaces occur

regularly during nanotube production.

this commu-

nication we present evidence for the formation of

single-

layered hemi-toroid structures, within bulk multi-walled

material during PCNT graphitisation. The structures

occur in material prepared by pyrolysis

hydrocar-

bons at ca. 1000°C and subjected

secondary heat

treatment at 2800°C. The structures have been studied

experimentally by high resolution transmission electror,

microscopy (HRTEM)[20] and the resulting images

compared with simulations. The simulated structures

were generated from hypothetica1 fullerene related

hemi-toroidal networks, which were constructed on

the basis of feasible graphene topologies relaxed by

molecular mechanics. During the course

the present

study

PCNTs, Iijima

al.

[5]

have obtained TEM

images showing related structures

arc-formed car-

bon nanotubes

(ACNTs).

OBSERVATIONS

The PCNTs obtained by decomposition

benzene

ca.

1000-1070°C

ceramic substrate were gath-

ered using

toothpick and heat treated at

tempera-

ture of

2800°C

for

minutes[21]. The heat-treated

PCNTs were then mounted on a porous amorphous

carbon electron microscope grid (so-called carbon

ultra-microgrid). HRTEM observations were made

using a LaB6 filament operating at an accelerating

voltage of 300 kV. The special aberration coefficient

2.0 mm and lambda

0.0197

The under-focus

105

106

SARKAR

al.

value was chosen deltaf

nm, where the sin(x)

transfer function has a large plateau at sin(x) ca. -1

against the interlayer spacing of carbon in the range

5.0-2.8 A. These conditions were optimum for observ-

ing high-contrast

002

lattice fringes form the PCNTs.

The simulations were carried out on a Silicon

Graphics Iris Indigo workstation using the CERIUS

molecular modeling and the associated HRTEM mod-

ule. The multislice simulation technique was applied

using the following parameters: electron energy

400

(lambda

0.016 A); C, (aberration coefficient)

2.7 mm; focus value deltaf

66 nm; beam spread

0.30

mrad.

In Fig. 1 is shown a HRTEM image of part of

the end

a PCNT. The initial material consisted of

carbon nanotubes upon which bi-conical spindle-like

secondary growth had deposited[21], apparently by in-

homogeneous deposition of aromatic carbonaceous,

presumably disordered, layers on the primary substrate

nanotube. Prior to further heat treatment, the second-

Fig.

The sealed-off tip of an annealed PCNT

ary growth showed no regular structure in the HRTEM

images (Fig.

l),

suggesting that it might consist largely

some form of “amorphous” carbon. After the sec-

ond stage of heat treatment, at 28OO0C, the amor-

phous sheaths graphitise to a very large degree,

producing multi-walled graphite nanotubes which tend

to be sealed off at points where the spindle-like for-

mations are thinnest. The sealed-off end region of one

such PCNT is shown in Fig.

The detailed analysis of the way in which the over-

all and internal structure of PCNTs apparently arise

is discussed elsewhere[20]. Here, we draw attention to

some particularly interesting and unusual structures

which occur in the body of the nanotubes. An expan-

sion of the section of the central core which lies ca.

below the tip

the nanotube in Fig.

is shown in

Fig. 2. Loop structures occur at points a-d and a‘-d‘

in the walls in directly opposing pairs. This parallel be-

haviour must,

the basis

statistical arguments, be

related and we interpret the patterns as evidence for

a hemi-toroidal connection between the inner and

outer adjacent concentric graphene tubes (Le., turn-

overs similar to a rolled-over sock). That the loops,

seen in the HRTEM, are evidence for very narrow

single-walled closed-ended tubes trapped within the

walls can be discounted, also on statistical grounds.

Perhaps the most important features in the images

are the dark line images that interconnect adjacent

loops. We particularly draw attention to the structure

b-b‘ in the expanded image in Fig. 2. Here, the adja-

cent loops are fairly distinct and well matched on ei-

Fig.

Expanded image

part

the annealed PCNT

Fig.

showing several regions (a/a’-d/d‘), in detail, where

complex looped images appear

be associated with graph-

ite turnover structures. The clearest eliptical image can be

seen between markers b and b’.

Hemi-toroidal networks in pyrolytic carbon nanotubes

107

Fig.

Molecular graphics images of an archetypal flattened toroidal model

a nanotube with

and

at three different orientations

plane perpendicular to the paper. Note the points

the rim where

the cusps are located.

ther side. The image

is,

as discussed below, quite

consistent with

single twin-walled tube connected at

one end.

In Fig.

a set

molecular graphics images

mo-

lecular models

hemi-toroidal structures, which are

the basis

the archetypal double-walled nanotube,

is depicted. The Schlegel-type diagram for the

rim

the smallest likely double-walled tube is depicted in

Fig.

where the fact that it consists

hexagonal

network in which

sets

pentagodheptagon (p/h)

pairs are interspersed in a regular manner is seen. This

diagram results from the connection

five p/h pair

templates

the kind depicted in Fig. 5a. The inside

and outside walls

the hemi-toroid are linked by the

matching p/h pairs in such a way that the curvature

allows optimal graphene sheet distortion and inter-

sheet interaction. For every p/h pair, the outer cylin-

der gains an extra two carbon atoms over the inner

g[-1g

I I I

I-

(b)

Fig.

General templates for inner/outer wall rim connec-

tions: a) simplest feasible template (section between the

dashed lines) in which

one

bond separates the heptagons

the inside rim,

one

bond separates the heptagons and penta-

gons across the rim, and two bonds and a hexagon separate

pengatons

the outside rim; b) The overall circumference

of the hemitoroidal structure can readily be increased with-

out increasing

the

interwall separation

inserting

further

hexagon

two half-length bond units

the kind shown in

the square dashed brackets.

Fig.

Schlegel-type diagram

the hemi-toroidal rim of

double walled nanotube, in which the inner and outer walls

are connected by a set

pentagon/heptagon pairs.