Connecting carbon nanotubes with pentagon-heptagon pair defects

Introduction

A single-wall nanotube is a rolled-up sheet of graphene which can be metallic or semiconducting depending on its chiral vector (L,M), where L and M are two integers. The rule is that a metallic or a semiconducting nanotube is obtained when the difference L-M is or is not a multiple of 3, respectively. It is possible to connect two nanotubes with different chiralities by just introducing a pair of heptagon and pentagon in the otherwise perfect hexagonal graphite lattice [1]. Quasi one-dimensional heterojunctions can therefore be realized in this way, including metal-semiconductor hybrids for which interesting properties may be expected [2].

The figures shown hereafter illustrate the structure of some nanotube hybrids realized with 5-7 pair defects. When the pentagon and heptagon are positioned at two diametrically-opposed sides of the structure, the axis of the two connected nanotubes make an angle around 35°. Bending angles of that order of magnitude have been observed experimentally by transmission electron microscopy [3]. The angle can be made smaller by putting the pentagon and heptagon closer to each other [4], and it is even possible to connect two different nanotubes without bending the structure by aligning the pentagon and heptagon along the same side [5].

Large-angle connections

(9,0)-(5-5) knee

The (9,0)-(5,5) knee illustrated here connects a nanotube with the parallel orientation (bottom) to one with the perpendicular orientation (top). The diameters of the two half nanotubes are close to 0.35 nm. The structure of this metal-metal nanojunction was optimized with a simplified molecular mechanics model [6], the bending angle was 36°. More recently, a Quantum-Mechanical CNDO method applied to the same system also yielded 36° [7]. The electronic structure of the system was investigted by tight-binding recursion. Atomic coordinates of this structure can be downloaded from here.

(10,0)-(6,6) knee

The (10,0)-(6,6) knee is a semiconductor-metal hybdrid. The structure illustrated here was optimized with a simplified molecular mechanics model [6], the bending angle was 36°. The electronic structure of the system was investigted by tight-binding recursion. The calculations indicate that the band gap requires a distance of the order of 1 nm to settle in the semiconducing nanotube. In the metallic nanotube, oscillations of the computed local density of states are observed. These oscillations are due to the interferences between incoming and reflected Bloch waves, which form a standing pattern at the entrance of the semiconductor where they cannot propagate when their energies lie within the forbidden band. Atomic coordinates of this structure can be downloaded from here.

Small-angle connections

A group in Berkley University has investigated the electronic properties of small-bend heterostructures in which the pentagon and heptagon are adjacent [4]. Local densities of states were computed by Green's functions for several systems, including the (8,0)-(7,1) hybrid illustrated on the left (by courtesy of Leonor Chico). The lower half of this hybrid is a semiconductor, the upper part is a metallic chiral nanotube. The bend angle of this connection is 12° [8]. Atomic coordinates of this structure can be downloaded from here.

Straight connections

(11,0)-(12,0) connection

The (11,0)-(12,0) connection is a semiconductor-metal hybrid. Two nanotubes with the parallel (or zig-zag) orientation are connected with a pair of edge-sharing pentagon (red) and heptagon (blue) oriented parallel to the tubule axis. The structure illustrated here was relaxed by tight-binding molecular dynamics [9]. The electronic structure was computed by tight-binding recursion. Atomic coordinates of this structure can be downloaded from here.

(9,0)-(12,0) connection

The (9,0)-(12,0) connection illustrated on the left was constructed with a pair of pentagon and heptagon (by courtesy of Riichiro Saito). This system, which connects two quasi-metallic zig-zag tubules, has been considered for tunneling conductance calculations [10].

References

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