Condensation of Helium in Nanotube Bundles

Abstract

Helium atoms are strongly attracted to the interstitial channels within a bundle of carbon nanotubes. The strong corrugation of the axial potential within a channel can produce a lattice gas system where the weak mutual attraction between atoms in neighboring channels of a bundle induces condensation into a remarkably anisotropic phase with very low binding energy. We estimate the binding energy and critical temperature for 4 He in this novel quasi-onedimensional condensed state. At low temperatures, the specific heat of the adsorbate phase (fewer than 2% of the total number of atoms) greatly exceeds that of the host material.Low temperature research on Helium was initially stimulated by the challenge of determining the condensation temperature of bulk He [1]. In recent decades, two-dimensional He films, in which the superfluid transition differs qualitatively from that of the bulk [2], have been particularly intriguing. While once of only academic interest [3][4][5][6], Helium in one-dimensional or quasi-one-dimensional systems has received increased attention recently since the realization that such systems can be created in the laboratory. He atoms are very strongly bound within the hexagonal lattice of narrow interstitial channels between tubes within the triangular lattice of a bundle of carbon nanotubes [7][8][9][10]. Within this very narrow channel, the transverse degrees of freedom are frozen out even at relatively high temperatures of ∼50 K. The binding energy per atom, 340 K, is the highest known for He, almost twice that calculated for He within individual nanotubes [11] and 2.4 times higher than that on the basal plane of graphite [12,13]. It exceeds the ground state binding energy of bulk liquid 4 He by nearly fifty times [14].Here we describe how the strong axial confinement of the He wavefunctions within a single channel can produce a direct experimental realization of a lattice gas model, wherein the weak coupling between atoms in neighboring channels induces a finitetemperature transition into a remarkably anisotropic and extremely weakly bound condensed state. First we present a localized model wherein the Helium resides in periodic array of relatively deep potential wells; this "bumpy channel" approximation is supported by single-particle Helium band structure calculations. For comparison, we also describe a delocalized model which assumes translational invariance within each channel (a "smooth channel" approximation). The large difference between the models in 1

Lattice-gas Monte Carlo study of adsorption in pores

“…Nevertheless, the behavior in the exact solution is here found to be very similar to that of MFT, in that the coverage rises very rapidly near a threshold value of µ. We note, however, that if there exists a transverse coupling between sites in neighboring pores such a genuine transition does occur (at a relatively high T -usually much higher than might be expected from the strength of the the interpore interaction) [3,4,5,6,7,8].…”

“…The difference is that we here evaluate the system's properties with the Monte Carlo (MC) simulation technique. MC simulations of the lattice gas models have been employed in studying a variety of adsorption and diffusion problems [1,2,8,9,10]. Our method is discussed in Section II along with a test of its sensitivity to the assumption of periodic boundary conditions.…”

Review on carbon nanotubes and carbon nanotube bundles for gas/ion separation and water purification studied by molecular dynamics simulation

“…The interstitial channels are accessible and the most attractive sites among all charge neutral surfaces to adsorb 4 He, H 2 , and Ne (Cole et al 2000;Kahng et al 2011;Stan et al 2000b;Weber et al 2000).…”

Enhanced cohesion of matter on a cylindrical surface

“…The opposite limit, R approaching zero, is here called "lineland", a 1d limit. Matter in lineland has been explored for many years as an abstract problem [7] and has recently received particular attention in connection with the possible realization of 1d phases within interstitial channels or external surface grooves on nanotube bundles [2,8,9,10,11,12,13,14,15,16]. A logical question addressed in this paper is whether the properties of matter in "cylinderland" evolves smoothly (or even monotonically) between these limits as the value of R is varied.…”