Single-walled carbon nanotubes (SWCNTs) of 4 angstrom diameter — the narrowest tubes predicted by theory to remain energetically stable, with a diameter matching the C20 dodecahedron — were first observed in 2000, but only as the innermost shells of multiwalled tubes and, in parallel work, inside the channels of AlPO4-5 zeolite crystals. Every existing route to this diameter is therefore intrinsically confining, and even the superconducting behavior reported for 4 angstrom tubes was measured on zeolite-embedded samples. The unresolved problem is to produce isolated, free-standing 4 angstrom SWCNTs outside any confining environment, to establish whether such tubes are in fact stable without the protection of a template or surrounding shells, and to measure their intrinsic properties directly. A secondary question raised in the same source is whether cage-structured C20 fullerene, the cap unit of the (3,3) tube, can be produced by arc-discharge methods in bulk form.

Background

A single-walled carbon nanotube (SWCNT) is a graphene sheet rolled into a cylinder one atom thick; a multiwalled carbon nanotube (MWCNT) is a set of such cylinders nested inside one another. The rolling direction is labeled by integer chiral indices (n,m)(n,m), which fix the diameter through d=(a/π)n2+nm+m2d=(a/\pi)\sqrt{n^2+nm+m^2} with a≈0.246a\approx 0.246 nm the graphene lattice constant. The armchair tube (3,3) — the family with n=mn=m, whose rim hexagons present an armchair pattern — has d≈0.41d\approx 0.41 nm, and the nearby chiral tubes (4,2), (4,3) and (5,1) lie between about 0.41 and 0.48 nm; conventional SWCNTs have diameters of roughly 1 nm or more. Total-energy arguments (Sawada and Hamada, 1992, 'Energetics of carbon nano-tubes') indicated that about 4 angstrom is the narrowest diameter for which a carbon nanotube remains energetically stable, and ab initio calculations (Blase, Benedict, Shirley and Louie, 1994) predicted that at such extreme curvature the sigma-star and pi-star antibonding states (the two conduction-state families of flat, sp2-bonded graphite) rehybridize so strongly that all of the smallest tubes become metallic, independent of helicity — unlike larger tubes, which are metallic or semiconducting depending on diameter and helicity. The diameter of a 4 angstrom tube coincides with that of the C20 dodecahedron, the smallest possible fullerene cage (twelve pentagons and no hexagons); half of a C20 dodecahedron is exactly the hemispherical cap of an armchair (3,3) tube.

Qin, Zhao, Hirahara, Miyamoto, Ando and Iijima (2000) reported the discovery of 4 angstrom nanotubes — the smallest possible, always metallic — produced by arc discharge (vaporization of graphite electrodes, here in a hydrogen atmosphere) and observed as the innermost shell of an 18-shell MWCNT, with the cap modeled as half of a C20 dodecahedron. In the same issue of Nature, Wang, Tang, Li and Chen (2000) reported uniformly sized 0.4 nm SWCNT arrays grown by pyrolysis of tripropylamine molecules inside the roughly 0.73 nm one-dimensional channels of AlPO4-5 (also called AFI), a microporous aluminophosphate zeolite used as a growth template. In both realizations the ultrathin tube is confined — by surrounding carbon shells or by the zeolite framework — and the confinement is physically consequential: charge transfer and van der Waals interaction with the walls perturb the electronic and vibrational structure. The intrinsic properties of the 4 angstrom tubes have in fact only ever been measured on confined samples; most prominently, Tang, Zhang, Wang, Zhang, Wen, Li, Wang, Chan and Sheng (2001) observed superconducting behavior (anisotropic Meissner effect, i.e. anisotropic expulsion of magnetic flux, a superconducting gap, fluctuation supercurrent, and mean-field transition temperature near 15 K) in 4 angstrom tubes embedded in the zeolite matrix. The source therefore raised the question of whether isolated, free-standing 4 angstrom SWCNTs — unconfined single-walled tubes — could be produced, so that their intrinsic properties could be studied directly, and, as a secondary suggestion, whether cage-structured C20 fullerene itself could be produced by the arc-discharge method.

Problem Statement

Produce isolated, free-standing single-walled carbon nanotubes of approximately 4 angstrom (0.4 nm) diameter — the narrowest diameter predicted by theory to remain energetically stable, corresponding to the (3,3), (4,2) or (5,1) tubes — outside any confining environment, that is, neither grown inside the channels of a zeolite template nor enclosed within the shells of a multiwalled or larger host nanotube, and establish their stability in the free state. Establish a reproducible synthesis or stabilization route for such tubes, confirm that they are single-walled with a diameter of approximately 0.4 nm and an assigned chirality, and measure the intrinsic properties (such as metallicity or transport) of an unconfined 4 angstrom tube directly — thereby testing, among other things, the predicted helicity-independent metallicity and the reported superconducting behavior free of tube-framework and tube-shell interactions. A secondary and explicitly lower-priority part of the same question, as raised in the source: determine whether cage-structured C20 fullerene — the dodecahedral cap of the (3,3) tube — can be produced by the arc-discharge method in bulk, isolable form, beyond the gas-phase, laser-plasma and ion-beam realizations already reported.

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