Rings of single-walled carbon nanotubes

Abstract

Among the most studied processes of self-organization¹, ² are the coiling and ring formation of biopolymers such as DNA and proteins. These processes are complex, involving several different types of interaction. We have found that single-walled carbon nanotubes (SWNTs), which are renowned for their extremely high flexural rigidity³, ⁴, can also be induced to organize themselves into rings or coils, with high yields of up to 50%. But unlike coils of biopolymers, in which hydrogen bonding and ionic interactions are usually involved, coils of nanotubes can be stabilized by van der Waals forces alone.

Main

Scanning electron micrographs (Fig. 1a) of SWNTs with an average diameter of 1.4 nm were prepared using laser ablation⁵. The nanotubes were shortened and induced to coil by using an acid treatment with ultrasound. Transmission electron microscope (TEM) images (Fig. 1b) confirm that the rings consist of aligned ropes of SWNT. The size of the rings formed is shown in Fig. 1c.

Figure 1: Ring formation in single-walled carbon nanotubes.

a, Scanning electron micrograph of a SWNT sample dispersed on a hydrogen-passivated silicon substrate, with rings clearly visible. Rings are produced by mixing long SWNTs with a solution of concentrated sulphuric acid and hydrogen peroxide and irradiating them with ultrasound for 1-3 h (40 kHz, 190 W) at 40-50° C, which disperses them and shortens the nanotube ropes⁶. After sonication, the solution is filtered through a 0.2-μm membrane filter, and the residue dried and suspended in 1,2-dichloroethane with a brief period of sonication. A high yield requires shortening the raw nanotubes to a length of 2-4 μm. Yield varies with time of exposure to ultrasound and concentration of peroxide solution. b, TEM image of a section of a ring wall (courtesy of L. Gignac). c, Histogram showing the distribution of ring radii.

The structure of rings (tori or coils) can be deduced from several observations. First, long SWNTs are shortened by oxidation, leaving the tube ends functional with carboxylic acid groups⁶, ⁷, arguing against the formation of a torus involving covalent bonds between carbon atoms. Images obtained by TEM and atomic force microscopy show that the rings do not have a constant thickness and height around their circumference (Fig. 1b), indicating that they may be formed by separate ropes being curled together. The rings can be taken apart and the ends of the ropes exposed (not shown), so we conclude that they are indeed produced by a coiling process.

Trace quantities (0.01 to 0.04%) of rings have previously been observed⁸ and larger yields have also been claimed⁹. The rings were assumed to be perfect tori⁸, stabilized by covalent bonds between carbon atoms, but our analysis suggests that they were actually coiled SWNTs.

The simplest model of the ring formation process has a SWNT coiling over itself to form a loop. Coiling involves significant strain energy because of the increased curvature, but van der Waals interactions stabilize the tubes.

The critical ring radius, R, for forming thermodynamically stable rings a few micro-metres long is small, about 0.03 μm for single tubes or ropes of SWNTs 1.4 nm in diameter. According to our calculations, much lower values of R are energetically allowed than are actually observed, indicating that ring formation may be kinetically controlled. The activation energy, E_A, should be of the order of the strain energy, and ΔE_A∝ R^-2. In our experiments, the activation energy is provided by ultrasonic irradiation. The most likely mechanism involves the hydrophobic nanotubes acting as nuclei for bubble formation and being bent mechanically at the bubble-liquid interface as a result of the bubbles collapsing during cavitation¹⁰.