LETTERS Ring Formation in Single-Wall Carbon Nanotubes Richard Martel, Herbert R. Shea, and Phaedon Avouris* IBM Research DiVision, T. J. Watson Research Center, Yorktown Heights, New York 10598 ReceiVed: May 6, 1999; In Final Form: July 14, 1999 Nanotube rings were fabricated from straight single-wall carbon nanotubes (SWNTs) with yields exceeding 50%. The rings result from the folding of nanotubes onto themselves under ultrasonic irradiation to form coils with a narrow distribution of radii (300-400 nm). A simple continuum elastic model is used to discuss the thermodynamic stability of the rings. Their formation involves a balance between tube-tube van der Waals adhesion and the strain energy resulting from the coiling-induced curvature. Our findings suggest that ring formation is a kinetically controlled process where bubble cavitation, generated by ultrasonic irradiation, provides the energy necessary to activate ring formation. The electrical conductance of the rings is measured as a function of temperature and in the presence of a perpendicular magnetic field. While the rings consist of bundles of many metallic and semiconducting SWNTs, they exhibit metallic behavior at low temperatures, and quantum interference effects are clearly observed. Self-organization and the formation of molecular superstruc- tures is a subject of strong current interest. 1,2 This field is driven in part by a desire to understand the formation of biological structures such as proteins, cell membranes, etc., and in part by technological needs. As the push to increased miniaturization of structures and devices continues, conventional fabrication techniques are hard pressed to keep up, and self-assembly and self-organization techniques are sought to replace them. 2,3 One of the most studied processes of self-organization is the coiling and ring formation by bio-polymers such as DNA and pro- teins. 4,5 These processes are complex, involving a number of different types of interactions. Here we discuss a case of self- organization that involves coiling and ring formation by carbon nanotubes, materials known for their high flexural rigidity. 6,7 Unlike the coils of bio-polymers that are usually stabilized through hydrogen bonding and ionic interactions, the coils of nanotubes are stabilized solely by van der Waals forces. 8 Carbon nanotubes (NTs) are a new class of materials that consist of one or several graphene sheets rolled up into a seamless tube, forming single-wall (SWNTs) or multiwall (MWNTs) nanotubes, respectively. 9-11 NT’s very high tensile strength is comparable to that of diamond, 6,7 and depending on their atomic structure, NTs behave electrically as metals or as semiconductors. 12-14 The synthesis of carbon nanotubes is itself a self-organization process, where carbon atoms self-assemble, with or without the help of catalysts, to form the tubes. 15-17 An important characteristic of carbon nanotubes is the strong van der Waals attraction between tubes, and between nanotubes and the substrate on which they are deposited. These van der Waals forces have important implications for the geometry and detailed configuration of the tubes. In the case of SWNTs, the van der Waals attraction between the NTs leads to a second level of self-organization; the nanotubes bunch together to form ropes, in which the NTs are closely packed in a triangular lattice. 16 Within a rope, the tube-tube interactions are strong enough to induce radial deformation of the tubes. 18 Similarly, van der Waals interactions with the substrate have been found to lead to both axial and radial deformations of adsorbed tubes and, most importantly, to stabilize highly strained nanotube * Author to whom correspondence should be addressed. E-mail: avouris@us.ibm.com. © Copyright 1999 by the American Chemical Society VOLUME 103, NUMBER 36, SEPTEMBER 9, 1999 10.1021/jp991513z CCC: $18.00 © 1999 American Chemical Society Published on Web 08/19/1999