Open or Close Ended Growth for Multiwalled Nanotubes

Assuming first that the tube remains closed during growth, the longitudinal growth of the tube occurs by the continuous incorporation of small carbon clusters (C2 dimers). This C2 absorption process is assisted by the presence of pentagonal defects at the tube end, allowing bond-switching in order to reconstruct the cap topology [13,14]. Such a mechanism implies the use of the Stone-Wales mechanism to bring the pentagons of the tip at their canonical positions at each C2 absorption. This model explains the growth of tubes at relatively low temperatures (~1100°C), and assumes that growth is nucleated at active sites of a vapor-grown carbon fiber of about 1000A diameter. Within such a lower temperature regime, the closed tube approach is favorable compared to the open one, because any dangling bonds that might participate in an open tube growth mechanism would be unstable. However, many observations regarding the structure of the carbon tubes (see Sect. 1) produced by the arc method (temperatures reaching 4000° C) cannot be explained within such a model. For instance, the present model fails to explain multilayer tube growth and how the inside shells grow often to a different length compared with the outer ones [15]. In addition, at these high temperatures, nanotube growth and the graphitization of the thickening deposits occur simultaneously, so that all the coaxial nanotubes grow at once, suggesting that open nanotube growth may be favored.

In the second assumption, the nanotubes are open during the growth process and carbon atoms are added at their open ends [15,16]. If the nanotube has a random chirality, the adsorption of a C2 dimer at the active dangling bond edge site will add one hexagon to the open end (Fig. 2).

Fig. 2. Growth mechanism of a carbon nanotube (white ball-and-stick atomic structure) at an open end by the absorption of C2 dimers and C3 trimers (in black), respectively [14]

The sequential addition of C2 dimers will result in the continuous growth of chiral nanotubes. However, for achiral edges, C3 trimers are sometimes required in order to continue adding hexagons, and not forming pentagons. The introduction of pentagons leads to positive curvature which would start a capping of the nanotube and would terminate the growth (see Fig. 3). However, the introduction of a heptagon leads to changes in nanotube size and orientation (Fig. 3). Thus, the introduction of heptagon-pentagon pairs can produce a variety of tubular structures, as is frequently observed experimen-

Fig. 2. Growth mechanism of a carbon nanotube (white ball-and-stick atomic structure) at an open end by the absorption of C2 dimers and C3 trimers (in black), respectively [14]

Toroidal Carbon Nanotubes

Fig. 3. (a) Model for a +n/3 disclination, pentagon ring which causes a positive curvature in a hexagonal network. (b) Model for a —n/3 disclination, heptagon ring which causes a negative curvature in a hexagonal network. (c) A deflecting singleshell nanotube. Letters P and H represent the locations of pentagons and heptagons, as illustrated in the model. (d) A "candy cane"-shaped nanotube and its possible model, which contains part of a torus structure. (e) An electron micrograph showing a bill-like termination of a multi-shell tube. A positive and a negative disclination are formed at the locations, indicated by A and B, probably due to the correlated presence of pentagons and heptagons, respectively, within the different concentric layers of the nanotube [11]

Fig. 3. (a) Model for a +n/3 disclination, pentagon ring which causes a positive curvature in a hexagonal network. (b) Model for a —n/3 disclination, heptagon ring which causes a negative curvature in a hexagonal network. (c) A deflecting singleshell nanotube. Letters P and H represent the locations of pentagons and heptagons, as illustrated in the model. (d) A "candy cane"-shaped nanotube and its possible model, which contains part of a torus structure. (e) An electron micrograph showing a bill-like termination of a multi-shell tube. A positive and a negative disclination are formed at the locations, indicated by A and B, probably due to the correlated presence of pentagons and heptagons, respectively, within the different concentric layers of the nanotube [11]

This model is thus a simple scenario where all the growing layers of a tube remain open during growth and grow in the axial direction by the addition of carbon clusters to the network at the open ends to form hexagonal rings [16]. Closure of the layer is caused by the nucleation of pentagonal rings due to local perturbations in growth conditions or due to the competition between different stable structures. Thickening of the tubes occurs by layer growth on already grown inner-layer templates and the large growth anisotropy results from the vastly different rates of growth at the high-energy open ends having dangling bonds in comparison to growth on the unreactive basal planes (Fig. 4a). Figure 4c is a summary of various possibilities of growth as revealed by the diversity of observed capping morphologies. The open-end tube is the starting form (nucleus) as represented in (a). A successive supply of hexagons on the tube periphery results in a longer tube as illustrated in (b). Enclosure of this tube can be completed by introducing six pentagons to form a polygonal cap (c). Open circles represent locations of pentagons. Once the tube is enclosed, there will no more growth on that tube. A second tube, however, can be nucleated on the first tube side-wall and eventually cover it, as illustrated in (d) and (e) or even over-shoot it, as in (f). The formation of a single pentagon on the tube periphery triggers the transformation of the cylindrical tube to a cone shape (g). Similarly, the introduction of a single heptagon into a tube periphery changes the tube into a cone shape (h). The latter growth may be interrupted soon by transforming into another form because an expanding periphery will cost too much free energy to stabilize dangling bonds. It is emphasized here that controlling the formation of pentagons and heptagons is a crucial factor in the growth of carbon nanotubes. A final branch in the variations of tube morphologies concerns the semi-toroidal tube ends. This growth is characterized by the coupling of a pentagon and a heptagon. Insertion of the pentagon-heptagon (5-7) pair into a hexagon network does not affect the sheet at all topologically. To realize this growth process, first a set of six heptagons is formed on a periphery of the open-tube (i). The circular brim then expands in the directions indicated by arrows. Solid circles represent locations of the heptagons. In the next step, a set of six pentagons is formed on the periphery of the brim, which makes the brim turn around by 180°, as illustrated in (j). An alternative structure is shown in (k), in which a slightly thicker tube is extended in the original tube direction, yielding a structure which has actually not yet been observed. Finally, it should be emphasized that an open-end tube can choose various passes or their combinations. One example is shown in (l), in which the first shell grows as a normal tube but the second tube follows a semi-toroidal tube end.

Although open-ended tubes are only occasionally spotted in the arc-grown deposit, these can be considered as quenched-growth structures, suggesting evidence for an open-ended growth model (Fig. 5). Terminated regions of such tubules are often decorated with thin granular objects which might be carbonaceous amorphous material. This observation suggests that dangling

Fig. 4. Model for the open-end growth of the nanotube. (a) The tube ends are open while growing by accumulating carbon atoms at the tube peripheries in the carbon arc. Once the tube is closed, there will be no more growth on that tube but new tube shells start to grow on the side-walls. (b) Schematic representation of a kink-site on the tube end periphery. Supplying two carbon atoms (o) to it, the kink advances and thus the tube grows. But the supply of one carbon atom results in a pentagon which transforms the tube to a cone shape. (c) Evolution of carbon nanotube terminations based on the open-end tube growth. Arrows represent passes for the evolution. Arrow heads represents terminations of the tubes and also growth directions. Open and solid circles represents locations of pentagons and heptagons, respectively [17] (see text)

Fig. 4. Model for the open-end growth of the nanotube. (a) The tube ends are open while growing by accumulating carbon atoms at the tube peripheries in the carbon arc. Once the tube is closed, there will be no more growth on that tube but new tube shells start to grow on the side-walls. (b) Schematic representation of a kink-site on the tube end periphery. Supplying two carbon atoms (o) to it, the kink advances and thus the tube grows. But the supply of one carbon atom results in a pentagon which transforms the tube to a cone shape. (c) Evolution of carbon nanotube terminations based on the open-end tube growth. Arrows represent passes for the evolution. Arrow heads represents terminations of the tubes and also growth directions. Open and solid circles represents locations of pentagons and heptagons, respectively [17] (see text)

Fig. 5. Transmission electron micrographs showing open-ended multi-wall carbon nanotubes [17]

bonds of carbon atoms at the peripheries of the open tube ends could have been stabilized by a reorganization of the carbon atoms. A rare chance of seeing such open tubes also suggests that under normal growing conditions the tube ends close rapidly.

An electric field 108 V/ cm) was also suggested as being the cause for the stability of open ended nanotubes during the arc discharge [15]. Because of the high temperature of the particles in the plasma of the arc discharge, many of the species in the gas phase are expected to be charged, thereby screening the electrodes. Thus the potential energy drop associated with the electrodes is expected to occur over a distance of ~ 1|j.m or less, causing very high electric fields. Later experiments and simulations confirmed that the electric field is in fact neither a necessary nor a sufficient condition for the growth of carbon nanotubes [18,19]. Electric fields at nanotube tips have been found to be inadequate in magnitude to stabilize the open ends of tubes, even in small diameter nanotubes (for larger tubes, the field effect drops drastically).

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