Thermal Conductivity at the Nanoscale: A Molecular Dynamics Study

Abstract

With the growing use of nanotechnology and nanodevices in many fields of engineering and science, a need for understanding the thermal properties of such devices has increased. The ability for nanomaterials to conduct heat is highly dependent on the purity of the material, internal boundaries due to material changes and the structure of the material itself. Experimentally measuring the heat transport at the nanoscale is extremely difficult and can only be done as a macro output from the device. Computational methods such as various Monte Carlo (MC) and molecular dynamics (MD) techniques for studying the contribution of atomic vibrations associated with heat transport properties are very useful. The Green–Kubo method in conjunction with Fourier’s law for calculating the thermal conductivity, κ, has been used in this study and has shown promise as one approach well adapted for understanding nanosystems. Investigations were made of the thermal conductivity using noble gases, modeled with Lennard-Jones (LJ) interactions, in solid face-centered cubic (FCC) structures. MC and MD simulations were done to study homogeneous monatomic and binary materials as well as slabs of these materials possessing internal boundaries. Additionally, MD simulations were done on silicon carbide nanowires, nanotubes, and nanofilaments using a potential containing two-body and three-body terms. The results of the MC and MD simulations were matched against available experimental and other simulations and showed that both methods can accurately simulate real materials in a fraction of the time and effort. The results of the study show that in compositionally disordered materials the selection of atomic components by their mass, hard-core atomic diameter, well depth, and relative concentration can change the κ by as much as an order of magnitude. It was found that a 60% increase in mass produces a 25% decrease in κ. A 50% increase in interatomic strength produces a 25% increase in κ, while as little as a 10% change in the hard core radius can almost totally suppress a materials ability to conduct heat. Additionally, for two LJ materials sharing an interface, the atomic vibrations altering the heat energy depend on the type of internal boundary in the material. Mass increases across the interfacial boundary enhance excitation of the very low frequency (ballistic) vibrational modes, while the opposite effect is seen as increases in hard core radius and interatomic strength enhance excitation of higher frequency vibrational modes. Additionally, it was found that this effect was diminished for higher temperatures around half the Debye temperatures. In nanodevices and nanomachines, there is an additional factor that degrades heat transport at the boundary. In fact, the interface induces a temperature jump consistent with a thermal resistance created by the boundary. It was found that the temperature jump, which is due to a boundary resistance, was significant in boundaries involving small mass changes, lesser in changes in hard core radii changes and even lesser for interatomic strength changes. The study of SiC nanowires and nanotubes showed that the structural changes produced vastly different κ. The κ in closely packed structures like nanowires and nanofilaments approximated that of the bulk SiC, yet were less sensitive to temperature than the 1/T relationship traditionally found in bulk systems. The more open nanostructures, like nanotubes, had vastly lower κ values and are almost totally insensitive to temperature variation. The results of this study can be used in the design of nano-machines where heat generation and transport is a concern. Additionally, the design of nano-machines which transport heat like nano-refrigerators or nano-heaters may be possible due to a better selection of materials with the understanding of how the materials affect their nanothermal properties at the nano scale.