Thermal conductivity and specific heat of hollow nanowires: Theoretical modeling and size effect analysis

Abstract

Metallic nanowires are widely used in energy conversion and storage, especially in the thermal management area, because of their high specific surface area, rich active sites, and high thermal conductivity. Metallic nanowires, such as copper or silver nanowires, are extensively applied to prepare the next-generation thermal interface materials with excellent thermal conductivity, light weight, high strength and ductility. Metallic hollow nanowires, which hold the typical one-dimension hollow nanostructures, have high axial thermal conductivity to prepare advanced thermal interface materials applied in thermal management and waste heat recovery of high-power microelectronic devices. Thermal conductivity is one of the most important indicators to assess the thermal performance of thermal interface materials. Over the past decades, many studies in both theory and experiment have been carried out to evaluate the thermal conductivity of solid nanowires. Molecular dynamics (MD) simulation has been applied to calculate the thermal conductivity of single nanowires, single core-shell nanowires and super-lattice nanowires. Meanwhile, advanced measuring techniques, including 3ω method, Raman spectroscopy and T-type method, have been invented and developed to measure the thermal conductivity of single nanowires. However, investigations on the thermal conductivity of metallic hollow nanowires are limited. Considering the difficulty in the fabrication and thermal conductivity measurement of single hollow metallic nanowires, creating a theoretical thermal conductivity model is urgently required. This work developed the electrical thermal conductivity model, phonon thermal conductivity model and phonon specific heat model of metallic nanowires to study the size effect on the mean free path, group velocity and specific heat capacity of the material. This study also proposed the effective thermal conductivity model of metallic hollow nanowire. These models have been used to study the effect of the both length and thickness of the metallic hollow nanowire on the effective thermal conductivity as well as the influence of the wall thickness on the electronic and phonon thermal conductivity. Finally, the mechanism of size effect on the thermal conductivity was discussed, and a reasonable interpretation based on the developed model was also proposed. Results show that an exact thermal conductivity model, validated by the experimental data from open-reported literature, was established with a correlation coefficient high than 90%. The size effect on the thermal conductivity of both hollow copper nanowire and solid copper nanowire was observed with the increased length and thickness. The thermal conductivity of solid copper nanowire was about 1.2 times higher than that of the hollow copper nanowire with the same length of 800 nm. In detail, the electronic thermal conductivity of solid copper nanowire was nearly 18.7% higher than that of hollow copper nanowire, while their phonon thermal conductivities almost remained unchanged. The size effect on the specific heat of hollow copper nanowire was also observed. The thermal conductivity of the hollow copper nanowire was 1.6 times higher than that of bulk copper and 1.2 times higher than that of a solid copper nanowire with the similar thickness.