Thermal conductivity of carbon-based nanomaterials: Deep understanding of the structural effects

The thermal conductivity of carbon-based nanomaterials (e.g. carbon nanotubes, graphene, graphene aerogels, and carbon fibers) is a physical property of great scientific and engineering importance. Thermal conductivity tailoring via structure engineering is widely conducted to meet the requirement of different applications. Traditionally, the thermal conductivity~temperature relation is used to analyze the structural effect but this relation is extremely affected by effect of temperature-dependence of specific heat. In this paper, detailed review and discussions are provided on the thermal reffusivity theory to analyze the structural effects on thermal conductivity. For the first time, the thermal reffusivity-temperature trend in fact uncovers very strong structural degrading with reduced temperature for various carbon-based nanomaterials. The residual thermal reffusivity at the 0 K limit can be used to directly calculate the structure thermal domain (STD) size, a size like that determined by x-ray diffraction, but reflects phonon scattering. For amorphous carbon materials or nanomaterials that could not induce sufficient x-ray scattering, the STD size probably provides the only available physical domain size for structure analysis. Different from many isotropic and anisotropic materials, carbon-based materials (e.g. graphite, graphene, and graphene paper) have Van der Waals bonds in the c-axis direction and covalent bonds in the a-axis direction. This results in two different kinds of phonons whose specific heat, phonon velocity, and mean free path are completely different. A physical model is proposed to introduce the anisotropic specific heat and temperature concept, and to interpret the extremely long phonon mean free path despite the very low thermal conductivity in the c-axis direction. This model also can be applied to other similar anisotropic materials that feature Van der Waals and covalent bonds in different directions.