Carbon nanotube thermal transport: measuring ballistic heat

Carbon nanotubes exhibit remarkable thermal conductivity, with individual tubes conducting thousands of watts per meter-kelvin along their axis at room temperature. This performance rivals that of diamond but requires specialized measurement techniques due to the limitations of conventional bulk thermal instruments. These techniques include suspended microdevices, electrothermal transients, and optothermal methods. The findings reveal a quasiballistic transport regime where traditional Fourier diffusion models are insufficient for micrometer-scale lengths. This article explores the physics of thermal transport in carbon nanotubes, the measurement methods used, and the implications for practical materials.

The exceptional thermal properties of carbon nanotubes are attributed to their stiff bonds, light atoms, and crystalline order, similar to diamond. However, nanotubes enhance these properties with their one-dimensional geometry, which channels phonons along a single axis, and their defect-poor lattice, allowing phonons to travel long distances without scattering. First-principles calculations confirm that the intrinsic thermal conduction of sp² carbon is extremely high, with real-world samples limited by defects, isotopes, and contacts. Measurements show that individual multiwalled and single-walled nanotubes can achieve axial conductivities of around 103 W m⁻¹K⁻¹ under optimal conditions.

To measure such properties, researchers developed the suspended microdevice platform, which consists of two silicon-nitride membrane islands connected by a nanotube. This setup allows for precise thermal conductance measurements by powering one island and reading temperatures on both. The platform has also been used for other nanostructures, such as silicon nanowires and graphene ribbons. Challenges in measurement include contact resistance and background conductance, which are addressed through systematic protocols and background subtraction.

In a clean nanotube, phonons can travel end-to-end without scattering if the tube is shorter than the phonon mean free path, resulting in ballistic transport. This phenomenon means that conductance, rather than conductivity, is the relevant measure, and the effective conductivity increases with sample length. Experiments have shown that nanotube conductance continues to rise with length, defying predictions from diffusive theory. Similar quasiballistic corrections have been observed in silicon at larger scales.

The effective axial conductivity of a model nanotube can be plotted against its length, illustrating the transition from ballistic to diffusive transport. This model uses a standard series picture where ballistic and diffusive resistances add together. Real nanotubes, however, have a spectrum of mean free paths and are affected by chirality, defects, and contacts, which influence the transport curve.

While individual nanotube conductivities are high, practical applications face challenges due to tube-tube junctions and matrix-tube boundary resistances in bundles and composites. These interfaces significantly reduce the overall thermal conductivity. Engineering efforts focus on improving junctions through alignment, densification, and hybrid architectures. Measurement techniques evolve alongside these developments, moving from single objects to films and arrays, with methods tailored to specific structures and directions.

For individual tubes near room temperature, reported conductivities reach around 103 W m⁻¹K⁻¹, with values dependent on tube type, quality, and measurement conditions. However, in composites, the network's performance is more influenced by junctions than the tubes themselves. Understanding the effective conductivity over various lengths is crucial, as it is a property of the measured geometry rather than an inherent characteristic of carbon nanotubes.