Bose-Einstein condensation of helium and hydrogen inside bundles of carbon nanotubes

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 = 9.95Å for H 2 and 8.48A for 4 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 − 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 .

Boson Gas in a Periodic Array of Tubes

“…In some other recent theoretical studies 28,29 , the occurrence of BEC of a weakly-interacting quantum gas of Bose particles (parahydrogen or 4 He) adsorbed within the interstitial channels (IC) of a bundle of poly-disperse carbon nanotubes has been predicted. The reported BEC transition and particularly, the dependence of the specific heat on temperature, exhibit features of four dimensions in contrast to the expected one-dimensional behavior that has been, indeed, observed in the experimental report of Lasjaunias et al 30 of the specific heat of adsorbed 4 He in nanotubes.…”

“…A possible mechanism that couple the different IC's is considered in Refs. [28,29], where the authors argue that such a coupling leads to an effective density of states from which a non-vanishing BEC critical temperature is obtained. This effective density of states can be described as an inhomogeneously broadened convolution of the density of the heterogeneous transverse states with the one-dimensional density of states of a free particle that moves along the nanotube axis.…”

Anomalous Low Temperature Specific Heat of3He Inside Nanotube Bundles

“…This system had previously been studied extensively with idealized models of the adsorption geometry, which predict 1D properties of the system. [5,6,7,8,9,10,11,12,13] In the new study, in contrast, it was found that the density of states for single particles ( 4 He or H 2 ) is drastically altered by heterogeneity; some heterogeneity is always present within experimental samples of nanotube bundles [14,15]. We found in I that the density of states N(E) near the very lowest energy has the form:…”

“…In some cases, however, such seemingly straightforward descriptions of the effective dimensionality can be questioned, leading to more careful investigations, with surprises to be found. Such was the case in our recent study (henceforth called I) of particles moving in a system of interstitial channels (ICs) between three adjacent carbon nanotubes [6,7,8].…”

Quantum Fluids in Nanopores

“…The 3 He case is perhaps the most dramatic, because its liquid state does not exist in either 1D or 2D, while the cylindrical liquid 3 He is found to have cohesive energy as high as 1.26 K for R = 0.18 nm.…”