Evidence of 1D Behavior of ${\mathrm{H}\mathrm{e}}^4$ Confined within Carbon-Nanotube Bundles

We present the first low-temperature thermodynamic investigation of the controlled physisorption of ${\mathrm{H}\mathrm{e}}^4$ gas in carbon single-wall nanotube (SWNT) samples. The vibrational specific heat measured between 100 mK and 6 K demonstrates an extreme sensitivity to outgassing conditions. For bundles with a few number of nanotubes the extra contribution to the specific heat, $C_{\mathrm{a}\mathrm{d}\mathrm{s}}$, originating from adsorbed ${\mathrm{H}\mathrm{e}}^4$ at very low density displays 1D behavior, typical for He atoms localized within linear channels as grooves and interstitials, for the first time evidenced. For larger bundles, $C_{\mathrm{a}\mathrm{d}\mathrm{s}}$ recovers the 2D behavior akin to the case of ${\mathrm{H}\mathrm{e}}^4$ films on planar substrates (grafoil).

Figure 1

Vibrational specific heat $C_{\mathrm{v}\mathrm{i}\mathrm{b}}=C_p-C_N$ of the AD sample (per g of sample): pristine state (without He)—III; intermediate adsorption—II; maximum adsorption in our experimental conditions (see text)—I.

Figure 2

Specific heat of ${\mathrm{H}\mathrm{e}}^4$ adsorbate (after subtraction of the corresponding pristine values; $C_{\mathrm{a}\mathrm{d}\mathrm{s}}$ per g of sample), for LV and AD sample. Data (○) and (●) are for maximum adsorption for the LV sample (3 at. % of C atoms) and the AD sample (1.5 at. % ), respectively. Data (■) correspond to the AD sample at intermediate adsorption.

Figure 3

Specific heat of the ${\mathrm{H}\mathrm{e}}^4$ adsorbate at intermediate adsorption: (□) state A of the LV sample and (■) state II of the AD sample. Data (■) below 1 K are fitted by an Einstein specific heat, with ${\Theta }_E=3.8\mathrm{K}$, and data (□) by a quadratic variation below 1.5 K. The same data are plotted in a linear plot in the inset. The plateau values recalculated per atom of He correspond to $1{\mathrm{k}}_B$ for LV and $0.4{\mathrm{k}}_B$ for AD sample. The dashed line is the residual term which was removed in the case of the AD sample [14].