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 E-t (that depends on the radii of neighboring tubes) and a quasicontinuous energy E-z 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 (E-t=E-min) for radii near R-min=9.95 Angstrom for H-2 and 8.48 Angstrom 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-E-min). 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 R-min.

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

ANCILOTTO, FRANCESCO;
2004

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 E-t (that depends on the radii of neighboring tubes) and a quasicontinuous energy E-z 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 (E-t=E-min) for radii near R-min=9.95 Angstrom for H-2 and 8.48 Angstrom 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-E-min). 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 R-min.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/1357931
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