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 $({E}_{t}={E}_{\mathit{min}})$ for radii near ${R}_{\mathit{min}}=9.95\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ for ${\mathrm{H}}_{2}$ and $8.48\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ for $^{4}\mathrm{He}$ . 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 $(E\ensuremath{-}{E}_{\mathit{min}})$. 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 ${R}_{\mathit{min}}$ .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 $({E}_{t}={E}_{\mathit{min}})$ for radii near ${R}_{\mathit{min}}=9.95\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ for ${\mathrm{H}}_{2}$ and $8.48\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ for $^{4}\mathrm{He}$. 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 $(E\ensuremath{-}{E}_{\mathit{min}})$. 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 ${R}_{\mathit{min}}$.

arXiv:cond-mat/0310067Physical Review BOct 29, 200418 citations

Giant helium molecules

Benjamin P. Stein

Physics TodayOct 1, 20030 citations

Condensation of helium in interstitial sites of carbon nanotubes bundles

Boris Marcone, Enzo Orlandini, Flavio Toigo +1 more

Helium atoms are believed to be strongly bound within the interstitial channels in bundles of carbon nanotubes. In a recent paper [F. Ancilotto et al., Phys. Rev. B 70, 165422 (2004)] inhomogeneity in the size distribution of nanotube radii was shown to make a system of $^{4}\mathrm{He}$ atoms in such an environment effectively a four-dimensional Bose gas, thus permitting a Bose-Einstein condensation (BEC) of the adsorbed atoms into the minimum energy state. This surprising result was obtained for a model of noninteracting atoms in a continuum distribution of (virtually) infinite interstitial channels. Here we investigate how the singular thermal properties of the ideal system and the occurrence of BEC are affected by a more realistic modeling of a bundle of nanotubes where (i) the number of nanotubes is finite and where (ii) $^{4}\mathrm{He}$ atoms adsorbed within the same interstitial channel interact among themselves. Also in this case we observe an anomalous heat capacity close to the ideal condensation temperature, suggesting the persistence of the condensation transition for interacting $^{4}\mathrm{He}$ atoms, which might be experimentally observed.Helium atoms are believed to be strongly bound within the interstitial channels in bundles of carbon nanotubes. In a recent paper [F. Ancilotto et al., Phys. Rev. B 70, 165422 (2004)] inhomogeneity in the size distribution of nanotube radii was shown to make a system of $^{4}\mathrm{He}$ atoms in such an environment effectively a four-dimensional Bose gas, thus permitting a Bose-Einstein condensation (BEC) of the adsorbed atoms into the minimum energy state. This surprising result was obtained for a model of noninteracting atoms in a continuum distribution of (virtually) infinite interstitial channels. Here we investigate how the singular thermal properties of the ideal system and the occurrence of BEC are affected by a more realistic modeling of a bundle of nanotubes where (i) the number of nanotubes is finite and where (ii) $^{4}\mathrm{He}$ atoms adsorbed within the same interstitial channel interact among themselves. Also in this case we observe an anomalous heat capacity close to the ideal condensation temperature, suggesting the persistence of the condensation transition for interacting $^{4}\mathrm{He}$ atoms, which might be experimentally observed.

Physical Review BAug 21, 200611 citations

Helium 4 Dimer in Two Coaxial Adjacent Nanotubes

J. Brana, Srećko Kilić, Leandra Vranješ Markić

Journal of Low Temperature PhysicsJan 1, 20022 citations

{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}_{\mathit{min}})

for radii near

{R}_{\mathit{min}}=9.95\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}

for

{\mathrm{H}}_{2}

and

8.48\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}

for

^{4}\mathrm{He}

. 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 $(E\ensuremath{-}{E}_{\mathit{min}})$. 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}_{\mathit{min}}

^{4}\mathrm{He}

atoms in such an environment effectively a four-dimensional Bose gas, thus permitting a Bose-Einstein condensation (BEC) of the adsorbed atoms into the minimum energy state. This surprising result was obtained for a model of noninteracting atoms in a continuum distribution of (virtually) infinite interstitial channels. Here we investigate how the singular thermal properties of the ideal system and the occurrence of BEC are affected by a more realistic modeling of a bundle of nanotubes where (i) the number of nanotubes is finite and where (ii)

^{4}\mathrm{He}

atoms adsorbed within the same interstitial channel interact among themselves. Also in this case we observe an anomalous heat capacity close to the ideal condensation temperature, suggesting the persistence of the condensation transition for interacting

^{4}\mathrm{He}

atoms, which might be experimentally observed.