Quantum states and specific heat of low-density He gas adsorbed within   the carbon nanotube interstitial channels: Band structure effects and   potential dependence
  We calculate the energy-band structure of a He atom trapped within the interstitial channel between close-packed nanotubes within a bundle and its influence on the specific heat of the adsorbed gas. A robust prediction of our calculations is that the contribution of the low-density adsorbed gas to the specific heat of the nanotube material shows pronounced nonmonotonic variations with temperature. These variations are shown to be closely related to the band gaps in the adsorbate density of states. 
A. Siber and H. Buljan