Bose-Einstein Condensation of Helium and Hydrogen inside Bundles of Carbon Nanotubes

TL;DR

This paper predicts Bose-Einstein condensation of helium and hydrogen molecules inside carbon nanotube bundles due to their quantum states, with observable effects like a singular heat capacity, depending on nanotube radius distribution.

Contribution

It introduces a model for particle states in nanotube bundles showing Bose-Einstein condensation driven by transverse energy minima.

Findings

Bose-Einstein condensation occurs at low temperatures in nanotube channels.

Density of states near the lowest energy varies linearly, enabling condensation.

Condensation transition resembles that of a four-dimensional gas.

Abstract

Helium atoms or hydrogen molecules are believed to be strongly bound within the interstitial channels (between three carbon nanotubes) within a bundle of many nanotubes. The effects on adsorption of a nonuniform distribution of tubes are evaluated. The energy of a single particle state is the sum of a discrete transverse energy Et (that depends on the radii of neighboring tubes) and a quasicontinuous energy Ez of relatively free motion parallel to the axis of the tubes. At low temperature, the particles occupy the lowest energy states, the focus of this study. The transverse energy attains a global minimum value (Et=Emin) for radii near Rmin=9.95 Ang. for H2 and 8.48 Ang.for He-4. The density of states N(E) near the lowest energy is found to vary linearly above this threshold value, i.e. N(E) is proportional to (E-Emin). As a result, there occurs a Bose-Einstein condensation of the molecules into the channel with the lowest transverse energy. The transition is characterized approximately as that of a four dimensional gas, neglecting the interactions between the adsorbed particles. The phenomenon is observable, in principle, from a singular heat capacity. The existence of this transition depends on the sample having a relatively broad distribution of radii values that include some near Rmin.