Chinese Science Bulletin, Volume 64 , Issue 5-6 : 611-620(2019) https://doi.org/10.1360/N972018-01072

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

More info
  • ReceivedNov 1, 2018
  • AcceptedDec 21, 2018
  • PublishedJan 29, 2019


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.

Funded by





图S1 弹道声子隧穿空心纳米线示意图

本文以上补充材料见网络版csb.scichina.com. 补充材料为作者提供的原始数据, 作者对其学术质量和内容负责.


[1] Li Y, Qian F, Xiang J, et al. Nanowire electronic and optoelectronic devices. Mater Today, 2006, 9: 18-27 CrossRef Google Scholar

[2] Bae K, Kang G, Cho S K, et al. Flexible thin-film black gold membranes with ultrabroadband plasmonic nanofocusing for efficient solar vapour generation. Nat Commun, 2015, 6: 10103 CrossRef ADS Google Scholar

[3] Ma T Y, Dai S, Jaroniec M, et al. Metal–Organic Framework Derived Hybrid Co3 O4-Carbon Porous Nanowire Arrays as Reversible Oxygen Evolution Electrodes. J Am Chem Soc, 2014, 136: 13925-13931 CrossRef Google Scholar

[4] Hochbaum A I, Chen R K, Delgado R D, et al. Enhanced thermoelectric performance of rough silicon nanowires. Science, 2008, 451: 163–167. Google Scholar

[5] Law M, Greene L E, Johnson J C, et al. Nanowire dye-sensitized solar cells. Nat Mater, 2005, 4: 455-459 CrossRef ADS Google Scholar

[6] Xu J, Munari A, Dalton E, et al. Silver nanowire array-polymer composite as thermal interface material. J Appl Phys, 2009, 106: 124310 CrossRef ADS Google Scholar

[7] Zhu Y P, Ma T Y, Jaroniec M, et al. Self-Templating Synthesis of Hollow Co3 O4 Microtube Arrays for Highly Efficient Water Electrolysis. Angew Chem Int Ed, 2017, 56: 1324-1328 CrossRef Google Scholar

[8] Zhang G Q, Yu Q X, Wang W, et al. Nanostructures for thermoelectric applications: Synthesis, growth mechanism, and property studies. Adv Mater, 2010, 22: 1950–1962. Google Scholar

[9] Yang R, Chen G, Dresselhaus M S. Thermal Conductivity Modeling of Core−Shell and Tubular Nanowires. Nano Lett, 2005, 5: 1111-1115 CrossRef ADS Google Scholar

[10] Prasher R. Thermal conductivity of tubular and core/shell nanowires. Appl Phys Lett, 2006, 89: 063121 CrossRef ADS Google Scholar

[11] Huang C, Wang Q, Rao Z. Thermal conductivity prediction of copper hollow nanowire. Int J Thermal Sci, 2015, 94: 90-95 CrossRef Google Scholar

[12] Barceloux D G, Barceloux D. Copper. J Toxicol-Clin Toxicol, 1999, 37: 217-230 CrossRef Google Scholar

[13] Venkatasubramanian R, Siivola E, Colpitts T, et al. Thin-film thermoelectric devices with high room-temperature figures of merit. Nature, 2001, 413: 597-602 CrossRef Google Scholar

[14] Poudel B, Hao Q, Ma Y, et al. High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys. Science, 2008, 320: 634-638 CrossRef ADS Google Scholar

[15] Lanzara A, Bogdanov P V, Zhou X J, et al. Evidence for ubiquitous strong electron–phonon coupling in high-temperature superconductors. Nature, 2001, 412: 510-514 CrossRef Google Scholar

[16] Zheng P, Gall D. The anisotropic size effect of the electrical resistivity of metal thin films: Tungsten. J Appl Phys, 2017, 122: 135301 CrossRef ADS Google Scholar

[17] Geim A K. Graphene: Status and prospects. Science, 2009, 324: 1530-1534 CrossRef ADS arXiv Google Scholar

[18] Sondheimer E H. The mean free path of electrons in metals. Adv Phys, 1952, 1: 1-42 CrossRef Google Scholar

[19] Shapira Y, Deutscher G. Heat capacity and thermal conductivity of granular A1-Ge. Phys Rev B, 1984, 30: 166-171 CrossRef ADS Google Scholar

[20] Sur I, Casian A, Balandin A. Electronic thermal conductivity and thermoelectric figure of merit of n-type PbT e/Pb 1x Eu xTe quantum wells. Phys Rev B, 2004, 69: 035306 CrossRef ADS Google Scholar

[21] Huang Q, Lilley C M, Bode M, et al. Surface and size effects on the electrical properties of Cu nanowires. J Appl Phys, 2008, 104: 023709 CrossRef ADS Google Scholar

[22] Huang W Q, Chen K Q, Shuai Z, et al. Lattice thermal conductivity in a hollow silicon nanowire. Int J Mod Phys B, 2005, 19: 1017-1027 CrossRef ADS Google Scholar

[23] Jiang Q, Shi H X, Zhao M. Melting thermodynamics of organic nanocrystals. J Chem Phys, 1999, 111: 2176-2180 CrossRef ADS Google Scholar

[24] Shafai G, Ortigoza M A, Rahman T S. Vibrations of Au13 and FeAu12 nanoparticles and the limits of the Debye temperature concept. J Phys-Condens Matter, 2012, 24: 104026 CrossRef ADS Google Scholar

[25] Hua Y C, Cao B Y. Cross-plane heat conduction in nanoporous silicon thin films by phonon Boltzmann transport equation and Monte Carlo simulations. Appl Thermal Eng, 2017, 111: 1401-1408 CrossRef Google Scholar

[26] Akguc G B, Gong J. Reply to "Comment on 'Wave-scattering formalism for thermal conductance in thin wires with surface disorder' ". Phys Rev B, 2010, 81: 117402 CrossRef ADS Google Scholar

[27] Mingo N, Yang L, Li D, et al. Predicting the thermal conductivity of Si and Ge nanowires. Nano Lett, 2003, 3: 1713-1716 CrossRef ADS Google Scholar

[28] Balandin A, Wang K L. Significant decrease of the lattice thermal conductivity due to phonon confinement in a free-standing semiconductor quantum well. Phys Rev B, 1998, 58: 1544-1549 CrossRef ADS Google Scholar

[29] Kittel C. Introduction to solid state physics. Am J Phys, 2005, 21: 547–548. Google Scholar

[30] Dames C, Poudel B, Wang W Z, et al. Low-dimensional phonon specific heat of titanium dioxide nanotubes. Appl Phys Lett, 2005, 87: 031901 CrossRef ADS Google Scholar

[31] Prasher R. Ultralow thermal conductivity of a packed bed of crystalline nanoparticles: A theoretical study. Phys Rev B, 2006, 4: 165413. Google Scholar

[32] Prasher R S, Phelan P E. Microscopic and macroscopic thermal contact resistances of pressed mechanical contacts. J Appl Phys, 2006, 100: 063538 CrossRef ADS Google Scholar

[33] Jeng M S, Yang R, Song D, et al. Modeling the thermal conductivity and phonon transport in nanoparticle composites using Monte Carlo simulation. J Heat Transfer, 2008, 130: 042410 CrossRef Google Scholar

[34] Zeller R C, Pohl R O. Thermal conductivity and specific heat of noncrystalline solids. Phys Rev B, 1971, 4: 2029-2041 CrossRef ADS Google Scholar

[35] Liang L H, Li B. Size-dependent thermal conductivity of nanoscale semiconducting systems. Phys Rev B, 2006, 73: 153303 CrossRef ADS Google Scholar

[36] Ashcroft N W, Mermin N D. Solid State Physics. New York: Holt Rinehart and Winston, 1976. Google Scholar

[37] Völklein F, Reith H, Cornelius T W, et al. The experimental investigation of thermal conductivity and the Wiedemann–Franz law for single metallic nanowires. Nanotechnology, 2009, 20: 325706 CrossRef ADS Google Scholar

[38] Stojanovic N, Berg J M, Maithripala D H S, et al. Direct measurement of thermal conductivity of aluminum nanowires. Appl Phys Lett, 2009, 95: 091905 CrossRef ADS Google Scholar

[39] Cheng Z, Liu L, Xu S, et al. Temperature dependence of electrical and thermal conduction in single silver nanowire. Sci Rep, 2015, 5: 10718-10730 CrossRef ADS arXiv Google Scholar

[40] 0 Roh J K, Palgaonkar K H, Ham J H, et al. Observation of anisotropy in thermal conductivity of individual single-crystalline bismuth nanowires. ACS Nano, 2011, 5: 3945–3960. Google Scholar

[41] Ou M N, Yang T J, Harutyunyan S R, et al. Electrical and thermal transport in single nickel nanowire. Appl Phys Lett, 2008, 92: 063101 CrossRef ADS Google Scholar

[42] Zarechnaya E Y, Skorodumova N V, Simak S I, et al. Theoretical study of linear monoatomic nanowires, dimer and bulk of Cu, Ag, Au, Ni, Pd and Pt. Comput Mater Sci, 2008, 43: 522-530 CrossRef Google Scholar

[43] Li J, Feng Y, Zhang X, et al. Theoretical and experimental research of thermal conductivity of silver(Ag) nanowires in mesoporous substrate. Int J Heat Mass Transfer, 2018, 121: 547-554 CrossRef Google Scholar

[44] Zhang W, Brongersma S H, Richard O, et al. Influence of the electron mean free path on the resistivity of thin metal films. MicroElectron Eng, 2004, 76: 146-152 CrossRef Google Scholar

[45] Heino P, Ristolainen E. Thermal conduction at the nanoscale in some metals by MD. MicroElectron J, 2003, 34: 773-777 CrossRef Google Scholar

[46] Powell R W, Tye R P, Hickman M J. The thermal conductivity of nickel. Int J Heat Mass Transfer, 1965, 8: 679-688 CrossRef Google Scholar

[47] Rorabacher D B. Electron transfer by copper centers. Chem Rev, 2004, 104: 651-698 CrossRef Google Scholar

[48] Morin F J, Maita J P. Specific Heats of Transition Metal Superconductors. Phys Rev, 1963, 129: 1115-1120 CrossRef ADS Google Scholar

[49] Lin Z Z, Huang C L, Huang Z, et al. Surface/interface influence on specific heat capacity of solid, shell and core-shell nanoparticles. Appl Thermal Eng, 2017, 127: 884-888 CrossRef Google Scholar

  • Figure 1

    (Color online) Schematic diagram of hollow nanowire. (a) Macrographic diagram; (b) Sectional view, r2-r1 is the thickness of hollow nanowire, r2 is the external diameter of hollow nanowire, r1 is the inner diameter of hollow nanowire, h is the thickness of surface atoms

  • Figure 2

    (Color online) ke of hollow copper nanowire, solid platinum nanowire, solid silver nanowire, solid aluminum nanowire and solid nickel nanowire. Structural parameter: r1=25 nm, r2=50 nm for hollow copper nanowire[11]; r2=200 nm for solid platinum nanowire[37]; r2=120 nm for solid aluminum nanowire[38]; r2=50 nm for solid silver nanowire[39]; r2=90 nm for solid nickel nanowire[41]

  • Figure 3

    (Color online) L dependent ke of hollow copper nanowires. (a) ke as a function of L; (b) 1/ke as a function of 1/L

  • Figure 4

    (Color online) kel (a) and kph (b) of hollow and solid nanowires as a function of d

  • Figure 5

    (Color online) lel and lph of hollow and solid nanowires as a function of d

  • Figure 6

    (Color online) Cph and C*ph of hollow and solid nanowires as a function of d

  • Figure 7

    (Color online) lph-b and lph-d of hollow copper nanowire as a function of d, the ratio of ballistic phonon and diffusive phonon on the total number of phonons

Copyright 2020  CHINA SCIENCE PUBLISHING & MEDIA LTD.  中国科技出版传媒股份有限公司  版权所有

京ICP备14028887号-23       京公网安备11010102003388号