Thermal Properties of Graphene, Carbon Nanotubes and Nanostructured Carbon Materials

TL;DR

The thermal properties of carbon materials are reviewed, focusing on recent results for graphene, carbon nanotubes and nanostructured carbon materials with different degrees of disorder, with special attention given to the unusual size dependence of heat conduction in two-dimensional crystals.

Abstract

Recent years witnessed a rapid growth of interest of scientific and engineering communities to thermal properties of materials. Carbon allotropes and derivatives occupy a unique place in terms of their ability to conduct heat. The room-temperature thermal conductivity of carbon materials span an extraordinary large range - of over five orders of magnitude - from the lowest in amorphous carbons to the highest in graphene and carbon nanotubes. I review thermal and thermoelectric properties of carbon materials focusing on recent results for graphene, carbon nanotubes and nanostructured carbon materials with different degrees of disorder. A special attention is given to the unusual size dependence of heat conduction in two-dimensional crystals and, specifically, in graphene. I also describe prospects of applications of graphene and carbon materials for thermal management of electronics.

Figures (4)

• Figure 1: Thermal properties of carbon allotropes and derivatives. (a) Diagram based on average values reported in literature. The axis is not to scale. (b) Thermal conductivity of bulk carbon allotropes as a function of$T$. The plots are based on commonly accepted recommended values from ref. (29). The curve "Diamond" is for the electrically insulating diamond of type II- $a$; "Polycrystalline Graphite" is for AGOT graphite - a high-purity pitch-bonded graphite; and "Pyrolytic Graphite" is for high-quality graphite analog to HOPG. Note an order of magnitude difference in $K$ of pyrolytic graphite and polycrystalline graphite with disoriented grains. The $K$ value for pyrolytic graphite constitutes the bulk graphite limit of $\sim 2000 \mathrm{~W} / \mathrm{mK}$ at RT. At low $T, K$ is proportional to $T^{\gamma}$, where $\gamma$ varies in a wide range depending on graphite's quality and crystallites size [29-30].
• Figure 2: Thermal conductivity of disordered and nanostructured carbon materials. (a)$K$ of DLC as a function of mass density. Note that ordering of $\mathrm{sp}^{3}$ phase inside grains in NCD results in significant $K$ increase. (b) Scanning electron microscopy images showing the UNCD - Si interface and grain sizes in NCD and MCD. (c) Comparison of $K$ temperature dependence for UNCD and MCD films. (d) Effective thermal conductivity of MCD/Si and UNCD/Si composite substrates indicating that they can outperform Si wafers at elevated $T$ in terms of thermal properties. Figures (a), (c) and (d) are adapted from refs. (41), (42) and (55), respectively.
• Figure 3: Thermal conductivity of quasi-2D carbon materials: intrinsic vs. extrinsic effects. (a) Measured and calculated thermal conductivity of suspended FLG as a function of the number of atomic planes$n$. For $n>4, K$ can drop below the bulk graphite limit due to the onset of the phonon - boundary scattering from the top and bottom interfaces; $K$ recovers for sufficiently thick films. (b) Thermal conductivity of graphene nano-ribbons obtained from MD simulations as a function of $n$ showing a similar trend. (c) Measured $K$ of encased FLG as a function of the thickness $H$. The transport is dominated by the phonon - boundary scattering and disorder resulting in characteristic $K$ scaling with $H$. (d) Thermal conductivity of encased ultra-thin DLC films as a function of the thickness $H$, indicating a similar trend to the encased FLG. Figures (a-d) are adapted from refs. (74), (80), (82) and (42), respectively.
• Figure 4: Thermal properties of low-dimensional carbon materials. (a) Calculated thermal conductivity of CNTs and graphene indicating that the intrinsic$K$ of CNTs is always lower than that of graphene. (b) Experimental thermal conductivity of graphene as a function of temperature reproduced from ref. (92). Experimental data points from other works are indicated by empty rectangular boxes - red (from refs. (16, 17, 74)), green (ref. (93)), and blue (ref. (76)). The experimental uncertainty of these data points should be comparable to those indicated for ref. (92). The filled red and brown boxes are theoretical data points from refs. (62) and ref. (69), respectively. These two points are for different graphene flake sizes $-3 \mu \mathrm{~m}$ and 5 $\mu \mathrm{m}$, respectively. Setting $L=3 \mu \mathrm{~m}$ in ref. (62) would give $K \sim 2500 \mathrm{~W} / \mathrm{mK}$ as in ref. (69). Figures (a) and (b) are adapted from refs. (69) and (92), respectively.