Dynamics of one-dimensional and two-dimensional helium adsorbed on carbon nanotubes

We present inelastic neutron scattering measurements of the dynamics of helium adsorbed on carbon nanotube bundles. The goal is to determine the vibrational properties of the 1D and 2D quantum solids that are stabilized on the nanotube bundle surfaces at different fillings of He. The mean square vibrational amplitude in the 1D solid is large with a Lindemann ratio of γ1D = (〈u〉)/a1 = 0.25 comparable to bulk solid He. The γ2D is significantly smaller. The frequency density of states of the 2D solid, g(ω), has a gap at ω 0.75meV consistent with a commensurate lattice. The 1D solid has no gap or a gap smeared by disorder. The 1D and 2D g(ω) are well described by dispersion curves having no gap and a gap, respectively, with some vibration along additional dimensions indicated. Copyright c © EPLA, 2009 Introduction. – The fabrication of nanotubes has opened the possibility of creating one-dimensional quantum systems [1,2]. Single-walled carbon nanotubes (SWNT) are nearly 1D structures of carbon atoms, tubes of 1 to 2 nm in diameter and 10000 nm in length. The nanotubes self assemble into bundles or ropes of typically 50 nanotubes. The nanotubes in the bundles have a triangular lattice cross-section as shown in fig. 1. One-dimensional He is predicted to form inside (I) the nanotubes, if the tubes are open, in the interstitial channels (IC) between the nanotubes in the bundles, or along the groove (G) sites between two tubes on the surface of the nanotube bundle [1–4]. Figure 1 shows the structures of He atoms absorbed on nanotube bundles observed by Pearce et al. [5]. At the lowest fillings the He forms a line or 1D solid in the G sites between two nanotubes as shown on the LHS of fig. 1. At somewhat higher fillings of He, 55 cm of He at STP per g of nanotubes (cm/g), the He forms three lines along the grooves, which is also a 1D solid (the middle frame of fig. 1). The average lattice spacing of the 1D solid (a)E-mail: [email protected] Fig. 1: The structures of He adsorbed on a carbon nanotube bundle surface at three helium coverages showing: 1D lines (LHS), three-line phase (also 1D) (middle) and a 2D monolayer (4wt%) (RHS) (from ref. [5]). is a1 = 3.40± 0.02 Å. Recent Monte Carlo calculations [4] confirm this spacing. No occupation of the I or IC sites was found. At monolayer completion (220 cm/g), the He forms a 2D monolayer over the bundle surface in a 2D triangular lattice with spacing a2 = 3.63± 0.03 Å. The a2 spacing actually decreased somewhat with filling suggesting a compression of the lattice with filling, from a2 = 3.68 Å at 150 cm /g to a2 = 3.57 Å at 220 cm /g. At monolayer coverage, the He makes up 4At.Wt% of the sample.