Page 97 - Carbon Nanotubes

MODEL STRUCTURE OF PERFECTLY GRAPHITIZABLE
COILED CARBON NANOTUBES

A. FONSECA, K. HERNADI, J. B.NAGY, PH. LAMBIN and A. A. LUCAS
Institute for Studies in Interface Sciences, Facultts Universitaires Notre-Dame de la Paix,
Rue de Bruxelles 61, B-5000 Namur, Belgium
(Received 20 April 1995; accepted in revised form 3 August 1995)
Abstract-The connection of two straight chiral or achiral cylindrical carbon nanotube sections of
approximately the same diameters connecting at a “knee” angle of 45 is described. Such knees are based
on the insertion in the plane of the knee of diametrically opposed pentagonal and heptagonal rings in
the hexagonal network. Relationships are also established between the nanotubes and their concentric
graphitic layers. A growth mechanism leading to perfect carbon tubules and tubule connections on a
catalyst particle at a molecular level is described. The mechanism suggested explains the formation of
curved nanotubes, tori or coils involving the heptagon-pentagon construction of Dunlap.
Key Words-Carbon fibers, nanofibers, nanotubes, nanotube knees, fullerenes, tubules.

1. INTRODUCTION 2. -E STRUCTURES
During the last years, several authors have reported 2.1 Labeling tubules
the production of carbon nanotubes by the catalytic Following a standard notation[ 12,131, a cylindri-
decomposition of hydrocarbons in the presence of cal tubule can be described by the (L,M) couple of
metals[ 1-51. More recently, carbon nanotubes were integers, as represented in Fig. 1. When the plane
also found as by-products of arc-discharge [ 61 and graphene sheet (Fig. 1) is rolled into a cylinder so
hydrocarbon flame [ 71 production of fullerenes. that the equivalent points 0 and M of the graphene
The appearance of a large amount of curved and sheet are superimposed, a tubule labeled (L,M) is
coiled nanotubes among the tubes produced by the formed. L and M are the numbers of six membered
catalytic method stimulated several studies on the rings separating 0 from L and L from N, respectively.
theoretical aspect of the coiling mechanism[ 8-1 11. Without loss of generality, it can be assumed that
Based on observations from high resolution electron L> M.
microscopy and electron diffraction, it was proposed Among all the different tubules, and for the sake
in these studies that curving and coiling could be of simplicity, mostly (L,O) and (L’,L’) nonchiral
accomplished by the occurrence of “knees” connect- tubules will be considered in this paper. Such tubules
ing two straight cylindrical tube sections of the same can be described in terms of multiples of the distances
diameter. Such knees can be obtained by the insertion 2 and 8, respectively (Fig. 2).
in the plane of the knee of diametrically opposed The perimeter of the (L,O) tubule is composed of
pentagonal and heptagonal carbon rings in the hexag- L “parallel” hexagon building blocks bonded side by
onal network. The heptagon with its negative curva- side, with the bonded side parallel to the tubule axis.
ture is on the inner side of the knee, and the pentagon
is on the outer side. The possibility of such construc- Its length is equal to L1.
The perimeter of the (L’,L’) tubule is composed of
tion was suggested by Dunlap[ 12,131. Theoretical
models of curved nanotubes forming tori of irregular L’ “perpendicular” hexagon building blocks bonded
diameters have also been described by Itoh et al. head to tail by a bond perpendicular to the tubule
axis. Its length is equal to Ed.
c141.
In this paper we elaborate models of perfect tubule
connections leading to curved nanotubes, tori or
coils using the heptagon-pentagon construction of
Dunlap[ 12,131. In order to understand the mecha-
nisms of formation of perfectly graphitized multi- M
layered nanotubes, models of concentric tubules at
distances close to the characteristic graphite distance
and with various types of knee were built. (Hereafter,
for the sake of clarity, “tubules” will be reserved to
the individual concentric layers in a multilayered
nanotube.) Fig. 1. Unrolled representation of the tubule (5,3). The OM
distance is e ual to the perimeter of the tubule.
OM = a J m , where a is the C-C bond length.
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