Heat conduction in non-metallic materials is due to the propagation of atomic vibrations called phonons. The characteristic dimensions of macroscale structures are understood not to interfere with phonon propagation because phonon wavelengths are on the nanometre scale. On the other hand, the dimensions of a nanostructure are small enough to confine or exclude specific phonon wavelengths. By approximating phonons as lattice waves, elastodynamic theory is helpful in predicting the allowed phonon modes, or frequency harmonics, in the nanostructure.

A recent study published in the journal Nanotechnology shows that the geometry of a nanostructure, i.e. nanotube wall thickness and diameter, both modifies and precludes the existence of certain phonon frequencies altogether. At low temperatures, thin-walled nanotubes are shown to support lower frequency long-wavelength flexural and longitudinal phonon modes when compared with their solid nanowire counterparts having the same outer diameter. When thermally populated, these phonon modes have a greater contribution to the internal energy, specific heat and thermal conductance of the structure. For example, at temperatures between 0.2 and 150 K, thinner-walled nanotubes exhibit a greater thermal conductance when compared with their solid cross-section counterpart. At 20 K the thermal conductance of an Angstrom thick nanotube is shown to have a 300% greater thermal conductance compared with a nanowire with a comparable outer diameter.

At temperatures above 150 K, the sum contribution of the total number of thermally activated phonon modes in the thick-walled nanotubes as well as the solid nanowires far exceeds the enhancement in thermal conductance from the fewer number of lower-frequency long-wavelength phonon modes in the thin-walled nanotube. In this way, the enhancement in thermal conductance of nanotubes versus nanowires is shown to be temperature dependent. The thin-walled nanotubes show enhanced thermal conductance at lower temperatures, while the thick-walled nanotubes and nanowires show higher thermal conductance at elevated temperatures.

More information is available in the journal Nanotechnology.