Heat capacity and vibrational spectra of monolayer films adsorbed in nanotubes

Carbon or boron nitride nanotubes can adsorb condensed-phase monolayer films on their inner surfaces. Examples include inert gas or hydrogen films, which form at low temperatures in nanotubes with radius $>~5\hspace{0.5em}\mathrm{\AA }.$ We study the phonon modes and thermodynamic properties of such films. Azimuthal quantization yields quasi-one-dimensional behavior at low temperature, manifested by a heat capacity linear in T, with quasi-two-dimensional behavior at higher temperature; the crossover between these regimes has a universal form, depending only on the ratio of the film radius to the thermal phonon wavelength. The film radius and mean sound speed can be extracted from the temperature dependence of the heat capacity.