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We consider the adsorption properties of superfluid $^4$He films on carbonnanotubes. One major factor in the adsorption is the surface tension forcearising from the very small diameter of the nanotubes. Calculations show thatsurface tension keeps the film thickness on the tubes very thin even when thehelium vapor is increased to the saturated pressure. The weakened Van der Waalsforce due to the cylindrical geometry also contributes to this. Both of theseeffects act to lower the predicted velocity of third sound propagation alongthe tubes. It does not appear that superfluidity will be possible onsingle-walled nanotubes of diameter about one nm, since the film thickness isless than 3 atomic layers even at saturation. Superfluidity is possible onlarger-diameter nanotube bundles and multi-walled nanotubes, however. We haveobserved third sound signals on nanotube bundles of average diameter 5 nm whichare sprayed onto a Plexiglass surface, forming a network of tubes.

Adsorption properties and third sound propagation in superfluid $^4$He films on carbon nanotubes